Applied Science, Faculty of
Materials Engineering, Department of
DSpace
UBCV
Nesbitt, Scott Jonathan
Master of Applied Science - MASc
University of British Columbia
The market demand for reduced operating costs and carbon emissions, together with competition and regulatory changes are primary drivers for improving vehicle efficiency. One method of improving efficiency is lightweighting, where composite materials can play a role due to their high specific stiffness and strength. Aircraft manufacturers have made use of these properties for many years, but they have the benefit of longer design programs (4-8 years) and production run lifetimes (20-30 years) to make extensive prototype testing feasible and economical. Automotive manufacturers do not have such long timescales or price-inelastic customers and must largely rely on computer simulation to design fit-for-purpose components in compressed timelines. Unfortunately, accurate structural simulation of composite materials is a challenge, owing to various path dependent failure modes and the influence of manufacturing processes on the material properties throughout the part, among other complexities. Consequently, new composite product design still relies heavily on physical testing. The aim of this thesis is to assist with improving modelling capabilities by providing insight into how damage develops in composite materials of interest to the automotive industry, through instrumented testing and damage characterization. These tests range from quasi-static deflection to high-velocity transverse impact. The materials investigated are non-crimp fabric (NCF) and 2D braid carbon fibre reinforced epoxy because they show promise for economical, high-rate manufacturing. It is found that the 2D braid does not show a delamination test rate sensitivity, owing to the stiffness mismatch being constrained within a single layer that can arrest cracks with its intra-ply fibres. The result is more localized fragmentation in the 2D braid material. Conversely, NCF materials delaminate substantially more under high-velocity impact conditions due to large shear stresses early on, combined with large stiffness mismatches between plies and the lack of crack arresting features. Damage resistance and permanent dent depth decrease substantially under high-velocity impact in both materials; making the damage easier to create and less detectable with surface-only inspection methods. A numerical model of an impacted NCF panel is also developed and compared to the experimental results, showing good agreement with the structural response (force-displacement), but under-prediction of delamination area.
The Effect of Impactor Mass and Velocity on the Structural Response and Damage Modes of Non-Crimp and 2D Braided CFRP Panels by Scott Jonathan Nesbitt BSc., The University of Calgary, 2013 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Materials Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) December 2020 © Scott Jonathan Nesbitt, 2020 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled: The Effect of Impactor Mass and Velocity on the Structural Response and Damage Modes of Non-Crimp and 2D Braided CFRP Panels submitted by Scott Jonathan Nesbitt in partial fulfillment of the requirements for the degree of Master of Applied Science in The Faculty of Graduate and Postdoctoral Studies Examining Committee: Anoush Poursartip, Materials Engineering Supervisor Reza Vaziri, Civil Engineering Supervisory Committee Member Chadwick Sinclair, Materials Engineering Additional Examiner Daan Maijer, Materials Engineering Additional Examiner iii Abstract The market demand for reduced operating costs and carbon emissions, together with competition and regulatory changes are primary drivers for improving vehicle efficiency. One method of improving efficiency is lightweighting, where composite materials can play a role due to their high specific stiffness and strength. Aircraft manufacturers have made use of these properties for many years, but they have the benefit of longer design programs (4-8 years) and production run lifetimes (20-30 years) to make extensive prototype testing feasible and economical. Automotive manufacturers do not have such long timescales or price-inelastic customers and must largely rely on computer simulation to design fit-for-purpose components in compressed timelines. Unfortunately, accurate structural simulation of composite materials is a challenge, owing to various path dependent failure modes and the influence of manufacturing processes on the material properties throughout the part, among other complexities. Consequently, new composite product design still relies heavily on physical testing. The aim of this thesis is to assist with improving modelling capabilities by providing insight into how damage develops in composite materials of interest to the automotive industry, through instrumented testing and damage characterization. These tests range from quasi-static deflection to high-velocity transverse impact. The materials investigated are non-crimp fabric (NCF) and 2D braid carbon fibre reinforced epoxy because they show promise for economical, high-rate manufacturing. It is found that the 2D braid does not show a delamination test rate sensitivity, owing to the stiffness mismatch being constrained within a single layer that can arrest cracks with its intra-ply fibres. The result is more localized fragmentation in the 2D braid material. Conversely, NCF iv materials delaminate substantially more under high-velocity impact conditions due to large shear stresses early on, combined with large stiffness mismatches between plies and the lack of crack arresting features. Damage resistance and permanent dent depth decrease substantially under high-velocity impact in both materials; making the damage easier to create and less detectable with surface-only inspection methods. A numerical model of an impacted NCF panel is also developed and compared to the experimental results, showing good agreement with the structural response (force-displacement), but under-prediction of delamination area. v Lay Summary The heavier the vehicle, the less efficient it will be. This is particularly true for aircraft because the energy needed to counter gravity ultimately comes from their engines – unlike automobiles, which rest on the ground. Therefore, composite materials have become commonplace on modern aircraft because their weight reduction benefits are substantial and worth the extra expense of designing and manufacturing them. For automobiles though, while weight reduction with composites is beneficial, it is not as economical due to the complexity of developing & manufacturing composite parts, combined with short model sales periods in which to recoup the added cost. This thesis is focused on better understanding how certain types of composite materials – that may be economical for automotive use – respond when impacted by objects. This will improve our ability to predict their behaviour and ideally reduce development complexity so that safer, lighter vehicles can be designed with composites. vi Preface This thesis entitled “The Effect of Impactor Mass and Velocity on the Structural Response and Damage Modes of Non-Crimp and 2D Braided Carbon Fibre Reinforced Fabric Panels” presents the work carried out by Scott Nesbitt under the supervision of Professors Anoush Poursartip and Reza Vaziri at The University of British Columbia. This thesis was written in its entirety by Scott Nesbitt under the supervision of Professors Anoush Poursartip and Reza Vaziri. Materials for this research were provided by the Ford Motor Company. The experimental work carried out using the gas gun at The University of British Columbia was conducted by Scott Nesbitt and assisted by a senior technician, Mr. Roger Bennett. The experimental work carried out using the gas gun at The German Aerospace Centre (DLR) was conducted by Scott Nesbitt and assisted by Ms. Dorothea Schlie, Dr. Matthias Waimer and Mr. Stefan-Andreas Ritt. The experimental work carried out using the drop tower at DLR was conducted by Scott Nesbitt and assisted by Mr. Thomas Feser and Dr. Matthias Waimer. X-Ray computed tomography scans and preliminary post-processing of images at DLR were carried out by Mr. Raouf Jemmali. X-Ray computed tomography scans and preliminary post-processing of images at The University of British Columbia’s Okanagan Campus were carried out by Mr. Armin Rashidi. All final post-processing of X-ray computed tomography images was done by Scott Nesbitt. The density measurement experiments were carried out by Scott Nesbitt with the assistance of Mr. Cheng Chen. The three and four-point bend material characterization tests were managed by Scott Nesbitt with sample preparation and testing carried out by UBC CRN co-op students Ms. Carolina Trujillo Sanchez and Mr. Ryan Li. The Iosipescu shear test samples were vii prepared by Mr. David Zimmermann and the tests were carried out by Scott Nesbitt. Data from unidirectional material characterization tests that was necessary for setting certain damage initiation strain values (IFIBC, IMATT & IMATC) and normal failure stress of tiebreak contacts (NFLS) was provided by the project sponsor, Ford Motor Company. The tensile, over-height compact tension, compact compression, double-cantilever beam, and end-notch flexure tests were managed and carried out by Ms. Sahar Abouali with the assistance of co-op students. All waterjet cutting for material characterization samples was carried out by the machine shop in the Department of Materials Engineering at The University of British Columbia. All numerical analysis in this work was carried out by Scott Nesbitt with instruction and advice from Dr. Johannes Reiner and Professor Reza Vaziri. Some of the results of the experimental work were presented by Professor Reza Vaziri at the 4th International Aerospace Structural Impact Dynamics Conference in Madrid, Spain (2019) in a presentation entitled “Characterization of the Structural Response and Energy Absorption Characteristics of Braided and Non‐Crimp Fabric CFRP Panels Subjected to Transverse Impact Loadings at Variable Strain Rates”, the presentation was created by Scott Nesbitt under the supervision of Professors Anoush Poursartip and Reza Vaziri. Additionally, some of the experimental and numerical work was presented in a conference paper and presentation at the 11th Canadian-International Conference on Composites in Kelowna, Canada in a paper and presentation entitled “Structural Response and Damage Characterisation of Non-Crimp Fabric CFRP Panels under Impact Loading” (Nesbitt et al. 2019). The paper and presentation were written and prepared by Scott Nesbitt under the supervision of Professors Anoush Poursartip and Reza Vaziri with the additional review, editing and approval of Dr. Matthias Waimer and Dr. Nathalie Toso-Pentecôte. A paper regarding the numerical work was also published in the viii SAMPE (Society for the Advancement of Material and Process Engineering) 2020 conference proceedings (Nesbitt et al. 2020), which was presented digitally due to the COVID-19 pandemic. This paper was written by Scott Nesbitt under the supervision of Professors Anoush Poursartip and Reza Vaziri with review, editing and approval of Dr. Johannes Reiner and Ms. Sahar Abouali. ix Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ......................................................................................................................... ix List of Tables .............................................................................................................................. xiv List of Figures ............................................................................................................................. xvi List of Symbols ....................................................................................................................... xxviii List of Abbreviations .................................................................................................................xxx Glossary .................................................................................................................................... xxxi Acknowledgements ................................................................................................................ xxxiii Dedication ............................................................................................................................... xxxvi Chapter 1: Introduction ............................................................................................................... 1 1.1 Motivation for the use of Composites in the Automotive Industry ............................ 1 1.2 Challenges to the Use of Composites in the Automotive Industry ............................. 5 1.3 Appeal of Resin Transfer Moulding with Textile Preforms to the Automotive Industry ................................................................................................................................. 11 1.4 Overview of Non-Crimp Fabric and 2D Braid Reinforced Panels Investigated in this Thesis .................................................................................................................................. 12 1.5 Motivation for the Investigation of Impact Damage ................................................ 16 1.6 Research Objectives & Thesis Outline ..................................................................... 18 Chapter 2: Literature Review .................................................................................................... 22 2.1 Impact Dynamics ...................................................................................................... 22 x Stress Waves ......................................................................................................... 22 Stress Wave Speeds .............................................................................................. 27 Impact Regimes – An Explanation of the Physics of Impact Events and their Governing Characteristics ................................................................................................. 31 2.2 Structural response .................................................................................................... 36 2.3 Damage ..................................................................................................................... 38 Matrix Response ................................................................................................... 40 Effect of HVI and LVI Impact .............................................................................. 42 Delamination, Free-Edge Effects & the Effect of Stiffness Mismatch Between Plies ............................................................................................................................... 44 Damage in NCF Materials .................................................................................... 48 Damage in 2D Braided Materials ......................................................................... 50 2.4 Numerical Modelling ................................................................................................ 54 UBC Composites Damage Model 2 (CODAM2) ................................................. 56 Chapter 3: Experimental Methodology ..................................................................................... 57 3.1 Material Characterization ......................................................................................... 57 General Material Characterization Tests .............................................................. 58 Intralaminar Mechanical Tests .............................................................................. 60 Interlaminar Mechanical Tests .............................................................................. 61 3.2 Transverse Loading Experiments ............................................................................. 62 Sample Geometry.................................................................................................. 63 Support Fixture ..................................................................................................... 64 Impactor/Indenter .................................................................................................. 65 xi Quasi-static Transverse Loading........................................................................... 66 Low-Velocity/High Mass Transverse Impact ....................................................... 67 Low-Velocity/Intermediate Mass Transverse Impact ........................................... 71 High-Velocity/Low Mass Transverse Impact ....................................................... 75 3.3 Damage Characterization .......................................................................................... 78 Permanent Dent Depth .......................................................................................... 78 Ultrasonic Scans.................................................................................................... 79 Tap Testing ........................................................................................................... 80 Computed Tomography ........................................................................................ 81 Chapter 4: Experimental Results and Interpretation ................................................................. 83 4.1 Material Characterization ......................................................................................... 83 General Material Characterization Tests .............................................................. 83 Intralaminar Mechanical Tests .............................................................................. 88 Interlaminar Mechanical Tests .............................................................................. 92 4.2 Transverse Loading Experiments ............................................................................. 93 Calculation of Wave Speeds and Regime Governing Impact Durations .............. 93 Quasi-static Transverse Loading........................................................................... 99 Transverse Impact Experiments .......................................................................... 107 4.3 Damage Characterization ........................................................................................ 121 Effect of Energy and Velocity on the Depth of Permanent Indentations ........... 121 Effect of Energy and Velocity on Damage Resistance ....................................... 122 Ultrasonic Inspection and the Effect of Energy and Velocity on Damage (Delamination) Area ....................................................................................................... 124 xii X-Ray Computed Tomography........................................................................... 129 4.4 Summary of Results ................................................................................................ 135 Chapter 5: Numerical Modelling and Comparison to Experiments ........................................ 138 5.1 Introduction ............................................................................................................. 138 5.2 Particulars of the Numerical Model ........................................................................ 138 Composite Material ............................................................................................. 140 Rate of Loading (Quasi-static) & Initial Conditions (Impact) ............................ 147 5.3 Results of the Numerical Model ............................................................................. 147 Quasi-static Indentation Comparison .................................................................. 147 Quasi-static Deflection Comparison ................................................................... 148 Impact Test Comparison ..................................................................................... 150 Chapter 6: Discussion ............................................................................................................. 156 6.1 Relationship Between Damage Area, Permanent Dent Depth and Velocity Regime .. ................................................................................................................................ 156 Low-Velocity Impact – Both Materials .............................................................. 157 2D braid High-Velocity Impact .......................................................................... 159 NCF High-Velocity Impact................................................................................. 160 6.2 Importance of the Results for Informing Visual Inspection ................................... 161 6.3 Damage Resistance ................................................................................................. 162 6.4 Modelling Considerations ....................................................................................... 163 Chapter 7: Conclusions & Future Work ................................................................................. 165 7.1 Conclusions ............................................................................................................. 165 7.2 Future Work ............................................................................................................ 169 xiii References ...................................................................................................................................171 Appendices ..................................................................................................................................181 xiv List of Tables Table 2-1 Distinguishing characteristics of different impact regimes and the approximate conditions under which they occur ............................................................................................... 33 Table 3-1 Intralaminar material characterization experiments ..................................................... 60 Table 3-2 Interlaminar material characterization experiments ..................................................... 62 Table 3-3 Parameters of test apparatus used for transverse loading experiments ........................ 63 Table 4-1 Density measurement results from NCF and 2D braid samples................................... 84 Table 4-2 Layerwise results from de-ply examination of NCF material ...................................... 85 Table 4-3 Layerwise results from de-ply examination of 2D braid material ................................ 86 Table 4-4 Analysis of dissected 2D braid sample to determine approximate tex (linear density) 87 Table 4-5 Intralaminar mechanical test results ............................................................................. 88 Table 4-6 Interlaminar mechanical test results ............................................................................. 92 Table 4-7 Estimates of cut-off time between high-velocity and low-velocity impact .................. 98 Table 4-8 Quasi-static indentation test parameters for the NCF material; equivalent impact energy is derived from integration of the force-displacement curve during loading .................... 99 Table 4-9 Quasi-static indentation test parameters for the 2D braid material; equivalent impact energy is derived from integration of the force-displacement curve during loading .................... 99 Table 4-10 Quasi-static deflection test parameters for the NCF material; equivalent impact energy is derived from integration of the force-displacement curve during loading .................. 100 Table 4-11 Quasi-static deflection test parameters for the 2D Braid material; equivalent impact energy is derived from integration of the force-displacement curve during loading .................. 100 Table 4-12 List of transverse impact tests and key parameters for the NCF material ................ 107 Table 4-13 List of transverse impact tests and key parameters for the 2D Braid material ......... 108 xv Table 4-14 Primary results for the NCF material to impact conditions ...................................... 109 Table 4-15 Primary results for the Braided material to impact conditions ................................. 109 Table 4-16 Selected impact tests to be used for direct comparison ............................................ 112 Table 4-17 Layer & Interface designations for NCF material .................................................... 130 Table 4-18 Layer & Interface designations for 2D braid material .............................................. 133 Table 5-1 Summary of MAT219 material card parameters used for modelling NCF lamina .... 145 Table 5-2 Model parameters for tiebreak contacts used to model interlaminar damage ............ 147 xvi List of Figures Figure 1-1 Megatonnes of carbon dioxide equivalent greenhouse gases for Canada by sector from 1990-2018; the transport sector has consistently been a major source of greenhouse gases . 1 Figure 1-2 Composite materials are shown to be of similar stiffness to metals, but lighter than aluminum alloys, and significantly lighter than steels .................................................................... 3 Figure 1-3 Locations and manufacturing processes utilized for CFRP components in the BMW 7 series vehicle show the heavy reliance on press consolidation processes such as resin transfer moulding ......................................................................................................................................... 5 Figure 1-4 The building block approach used in the certification of aeronautical composite structures involves tests at numerous levels including coupons, structural elements, subcomponents and components which can make the design and certification process time consuming and expensive ............................................................................................................... 7 Figure 1-5 Typical appearance of an NCF sample cut to a 100 mm x 100 mm impact sample size....................................................................................................................................................... 13 Figure 1-6 Typical appearance of a 2D braid sample cut to a 100 mm x 100 mm impact sample size ................................................................................................................................................ 13 Figure 1-7 Non-Crimp Fabric cross-section during manufacturing (angles shown do not match those of the material in this thesis) ............................................................................................... 14 Figure 1-8 Triaxial braid preform architecture ............................................................................. 14 Figure 1-9 (a) weft-, and (b) warp-knit patterns ........................................................................... 15 Figure 1-10 Schematic of an impact event resulting in stress waves that cause various failure modes resulting in interlaminar and intralaminar damage. The interaction of the stress waves xvii with this damage determines the structural response. Subsequent application of structural loads can then be used to determine the residual strength ..................................................................... 18 Figure 2-1 Types of waves in elastic solids .................................................................................. 24 Figure 2-2 Phase velocity of flexural waves as a function of the wave frequency ....................... 28 Figure 2-3 Quasi-static deflection of a panel showing the first mode of vibration with the half wavelength being equal to the width of the cutout ....................................................................... 29 Figure 2-4 The elongation and contraction of chemical bonds between atoms; (a) undisturbed, (b) elongated, (c) compressed ............................................................................................................. 32 Figure 2-5 Graphical Representation of Plate Response in Different Impact Regimes ............... 33 Figure 2-6 (a) Simply edge supported quasi-static deflection test, (b) Fully supported quasi-static indentation test .............................................................................................................................. 35 Figure 2-7 Effect of impact regime of the force displacement response (initial stiffness increase during high-velocity impact case) ................................................................................................. 36 Figure 2-8 Typical types of damage seen in transversely impacted FRP laminates; (a) micrograph showing cracks extending through the full thickness of layers (both as transverse matrix cracks and fibre fractures) and becoming delaminations (b) schematic diagram for low-velocity impact indicating compressive indentation damage on the front face and tensile damage on the back-face due to flexure of the panel ............................................................................................................ 39 Figure 2-9 Damage in laminated composites due to (a) flexural stresses (typical of compliant laminates under low-velocity conditions), and (b) contact stresses (typical of rigid laminates under low-velocity conditions or all laminates under high-velocity conditions) ......................... 40 xviii Figure 2-10 Strain rate effect on uniaxial compression of unidirectional IM7-8552 CFRP loaded transversely to the fibre direction; the compressive modulus, yield strength and ultimate strength are all higher under dynamic conditions ....................................................................................... 41 Figure 2-11 C-scans showing the effect of beam length on the development of damage in 16 ply (0°,±45°) composite: (a) high velocity impact loading; (b) low velocity impact loading; the reduction of damage in (b) with increasing beam length is due to the additional material available for elastic storage of impact energy, but under high-velocity impact (a) this extra material does not affect the damage area as the response is controlled by transient flexural waves and not the boundary ....................................................................................................................................... 43 Figure 2-12 Free edge effects in (a) [0/60/-60]S laminate produce (b) tensile and compressive interlaminar normal stress couples near free-edges that can result in (c) tensile interlaminar normal stress at the edge, producing a peeling effect that leads to delamination, and (d) interlaminar shear stress that leads to delamination ..................................................................... 47 Figure 2-13 Impact damage in NCF laminate subjected to low-velocity impact showing localization of damage to the backface of the laminate ................................................................ 49 Figure 2-14 Effect of impact energy on measured damage area using C-scanning (divide by 4.34 for J/mm); damage area is similar between LVI (heavy mass) and HVI (light mass) for the ~3.2J/mm case, but at higher energy levels the HVI impacts show larger damage area .............. 51 Figure 2-15 Effect of impact energy on measured (permanent) dent depth using profilometry (divide by 4.34 for J/mm); permanent dent depth for LVI (Heavy) is substantially more than for HVI (Light) ................................................................................................................................... 51 Figure 2-16 optical micrograph of 2D biaxial braid CFRP subjected to low-velocity impact between 7.4 and 8.0 J/mm showing substantial matrix and fibre fracture .................................... 52 xix Figure 2-17 Visible impact damage in triaxially braided CFRP panel subjected to sub-perforation impact (a) front side (b) back side (c) close-up of fibre fracture on back side; the authors found that the damage was highly localized to the impact site and no substantial delamination was experienced ................................................................................................................................... 54 Figure 3-1 NCF sample with x and y directions marked for reference ........................................ 58 Figure 3-2 2D braid sample with x and y directions marked for reference .................................. 58 Figure 3-3 Geometry of the overheight compact tension specimen developed by Kongshavn and Poursartip (1999) .......................................................................................................................... 61 Figure 3-4 (a) front view of transverse loading specimen fixture; (b) side view of transverse loading specimen fixture ............................................................................................................... 64 Figure 3-5 (a) Steel hemispherical impactor used for all tests except high-velocity/low mass; (b) Titanium hemispherical impactor used for all tests except high-velocity/low mass .................... 66 Figure 3-6 (a) Quasi-static indentation of a 2D braid sample showing the 12.7 mm spherical impactor, steel and carbide support plates and clip gauge; (b) Quasi-static deflection of a sample showing the 12.7 mm spherical impactor, aluminum fixture with clamps, and clip gauge.......... 67 Figure 3-7 Drop tower assembly mounted on crosshead of 4-post universal test machine with high speed cameras positioned to record displacement ................................................................ 68 Figure 3-8 Close-up view of drop test mass suspended above impact sample. The force transducer is visible (attached to green wire from left) between the impactor tip and the bulk of the drop mass above ...................................................................................................................... 68 Figure 3-9 Close-up view of drop tower impactor with in-line force sensor and steel tip with speckle pattern for DIC displacement measurements ................................................................... 70 xx Figure 3-10 Backface of transverse impact coupon prior to test with hand applied white speckle pattern ........................................................................................................................................... 71 Figure 3-11 Overview of the UBC CRN gas gun apparatus with the pressure reservoir in foreground ..................................................................................................................................... 73 Figure 3-12 Close-up of the impact region of the UBC CRN gas gun showing the ELVS instrumentation, ELVS barrel adapter and sample support fixture with sample loaded .............. 73 Figure 3-13 Instrumented gas gun projectile showing the impactor tip (left), ELVS obscuring shoulder (center, black), and the guiding surface with integral force transducer (right) .............. 73 Figure 3-14 3D CAD model cross-section view of ELVS Barrell adapter region of gas gun showing how the laser beam is intersected by the shoulder of the projectile shaft in order to provide displacement measurements ............................................................................................ 73 Figure 3-15 free-flying gas gun looking from behind the muzzle towards the sample ................ 76 Figure 3-16 location of high-speed camera for high-velocity experiments .................................. 76 Figure 3-17 DLR gas gun sabot's (aluminum cup with EPS projectile holder) ............................ 77 Figure 3-18 Frame capture from Photron APX camera used for 2D DIC analysis of the projectile displacement ................................................................................................................................. 77 Figure 3-19 Image of a Faro Arm tactile coordinate measurement device used for dent depth measurements during low-velocity/high mass and high-velocity/low mass experiments ............ 79 Figure 3-20 Digital dial gauge with truss structure used for dent depth measurements during low-velocity/intermediate mass experiments ....................................................................................... 79 Figure 3-21 Olympus Omniscan MX2 ultrasonic inspection system with displacement encoder 80 Figure 3-22 GE v|tome|x L450 scanner at the German Aerospace Center’s Institute of Structures and Design .................................................................................................................................... 82 xxi Figure 3-23 xradia MicroXCT-400 scanner at The University of British Columbia Okanagan Campus ......................................................................................................................................... 82 Figure 4-1 Close-up view of 2D braid sample showing the unit cell size of ~18 mm x ~5 mm .. 84 Figure 4-2 Individual plies (a) # 1, (b) #2 & (c) #3 of the 2D braid composite sample ............... 86 Figure 4-3 2D braid composite sample dissected into (L) -60°, (C) 0° & (R) +60° constituent tows ............................................................................................................................................... 87 Figure 4-4 Example CT scan image used for measuring actual ply angles in the NCF material. Three lines each are drawn parallel to the 0° (horizontal), +° and -° plies; by averaging the relative angle of the ±° degree plies from the 0° ply across ~100 images from different sample and positions in sample, the true orientation of the angle plies was found to be ±57° ................. 88 Figure 4-5 Ultrasonic c-scan of NCF OCT sample loaded in the x-direction; substantial delaminations are visible, making direct estimation of the laminate fracture energy by the compliance method impossible ..................................................................................................... 91 Figure 4-6 Ultrasonic c-scan of 2D braid OCT sample loaded in the x-direction; substantial delaminations are visible, making direct estimation of the laminate fracture energy by the compliance method impossible ..................................................................................................... 91 Figure 4-7 Ultrasonic c-scan of NCF OCT sample loaded in the y-direction; self-similar crack growth can be seen, making laminate fracture energy calculation with the compliance method possible ......................................................................................................................................... 91 Figure 4-8 Ultrasonic c-scan of 2D braid OCT sample loaded in the y-direction; self-similar crack growth can be seen, making laminate fracture energy calculation with the compliance method possible ............................................................................................................................ 91 xxii Figure 4-9 Experimental results of OCT tests; damage saturation strains in the numerical model are calibrated through virtual OCT tests to give similar numerical Force-POD curves ............... 92 Figure 4-10 (a) Contour plot of out of plane displacement for the first mode of vibration (ω=2.9932 rad/ms) of a 2.56mm thick NCF panel modelled with 11 lamina through the thickness; (b) Contour plot of out of plane displacement for the first mode of vibration (ω=1.3638 rad/ms) of a 2.56mm thick NCF panel modelled with 1 laminate through the thickness ........................................................................................................................................ 97 Figure 4-11 Quasi-static indentation force vs displacement response showing similar response between NCF and 2D braid materials; non-linear response is representative of increasing contact area of hemispherical indenter as indentation progresses ........................................................... 101 Figure 4-12 Quasi-static indentation force against quasi-static indentation displacement to the power 3/2; the slope represents the contact stiffness .................................................................. 102 Figure 4-13 Force-displacement curves for NCF (red) and 2D Braid (blue) quasi-static deflection tests (solid lines) all the way to complete perforation. The large sudden load drops are characteristic of delaminations and the curve approach an asymptotic force level that represents the frictional force against the sides of the impactor after complete perforation. The dashed lines are the area under the curves and represent total energy; this was subsequently used to target specific energy levels for impact testing ..................................................................................... 103 Figure 4-14 Force-displacement curves for the interrupted NCF quasi-static deflection tests overlaid on the continuous QSD-N1 test (red); The black curve is created from merging the interrupted tests and it shows good repeatability with the continuous test ................................. 104 xxiii Figure 4-15 Force-displacement curves for the interrupted 2D braid quasi-static deflection tests overlaid on the continuous QSD-B1 test (blue); The black curve is created from merging the interrupted tests and it shows good repeatability with the continuous test ................................. 104 Figure 4-16 Quasi-static deflection force vs isolated global plate displacement; the slope represents the stiffness of the plate to transverse loading ........................................................... 106 Figure 4-17 Force-displacement curves for NCF (red) and 2D Braid (blue) quasi-static deflection tests (solid lines) and quasi-static indentation tests (dashed lines); the region between the solid and dashed lines is the region in which the force-displacement response of impact tests are expected to fall ............................................................................................................................ 106 Figure 4-18 The impact duration for each test coloured by normalized impact energy value and subdivided by material and impact class; all tests above the red box/line are low-velocity impact and all below are high-velocity impact ....................................................................................... 111 Figure 4-19 The thickness normalized impact energies of each test coloured by normalized impact energy value and subdivided by material and impact class ............................................ 112 Figure 4-20 Force vs displacement plots of NCF low energy impacts showing close correlation to quasi-static deflection test results during loading and minimal energy absorbed as evidenced by minimal enclosed area of the curves ........................................................................................... 114 Figure 4-21 Force vs displacement plots of NCF mid energy impacts showing close correlation to quasi-static deflection test results during loading and moderate energy absorption; evidence of delaminations can be seen in the large drops of force near the maximum displacement ........... 114 Figure 4-22 Force vs displacement plots of NCF high energy impacts showing close correlation to quasi-static deflection test results during loading and substantial energy absorption; the xxiv substantial effect of delaminations is visible through the extensive displacement without additional load ............................................................................................................................. 114 Figure 4-23 Force vs displacement plots of 2D braid low energy impacts showing close correlation to quasi-static deflection test results during loading and minimal energy absorbed as evidenced by minimal enclosed area of the curves ..................................................................... 115 Figure 4-24 Force vs displacement plots of 2D braid mid energy impacts showing close correlation to quasi-static deflection test results during loading and moderate energy absorption; evidence of delaminations can be seen in the large drops of force near the maximum displacement ............................................................................................................................... 115 Figure 4-25 Force vs displacement plots of 2D braid high energy impacts showing close correlation to quasi-static deflection test results during loading and substantial energy absorption; the substantial effect of delaminations is visible through the extensive displacement without additional load ............................................................................................................................. 115 Figure 4-26 Digital image correlation contour plot of out of plane displacement for test (a) N1 when max deformation was 1.0 mm (b) B3 when max deformation was 1.0 mm (c) N13 when max deformation was 0.9 mm (d) B14 when max deformation was 1.1 mm; the smooth gradual change in contour colour for (a) and (b) indicates global bending of the panel, whereas the sharp localized change in contour colour for (c) and (d) indicates local shear or “punch-out” deformation of the panel near the impact site ............................................................................. 118 Figure 4-27 DIC out-of-plane displacement measurements along a cross-section through the center of impact for (a) NCF low-velocity (b) NCF high-velocity (c) 2D braid low-velocity, and (d) 2D braid high-velocity impact tests at various time steps between the time of impact and time of maximum displacement; the global bending shape is clearly seen even at the earliest timesteps xxv of the LVI impacts followed by localized deformation after back-face fibre fracture. Conversely, highly localized shear deformation is seen at the earliest HVI timesteps indicating that the panel is not able to bend fast enough; global bending of the panel is seen at later timesteps of the HVI impacts. ....................................................................................................................................... 121 Figure 4-28 Permanent dent depth vs normalized impact energy; there is a clear difference in the results based on the impact regime ............................................................................................. 122 Figure 4-29 Percent of impact energy absorbed by the sample vs normalized impact energy; the reduction in damage resistance for both the NCF and 2D braid materials is evident from the significant difference in the percentage of impact energy absorbed at low impact energies. This indicates that both materials will incur more impact damage for a high velocity impact compared to an impact of the same energy at low velocity (if the impact is low energy) .......................... 124 Figure 4-30 Ultrasonic c-scans of projected damage area in NCF laminates with varying energy levels and loading scenarios; damage area increases with increasing energy, but is substantially increased under high-velocity impact conditions ....................................................................... 125 Figure 4-31 Meso level delamination of complete 0° tow in sample N6 (high energy drop test) as viewed from (a) 0° direction, and (b) 90° direction .................................................................... 127 Figure 4-32 Ultrasonic c-scans of projected damage area in 2D braid laminates with varying energy levels and loading scenarios; there is only a modest increase in damage area with increasing energy, and no difference in the case of high-velocity impact .................................. 128 Figure 4-33 CT scans of NCF laminates with varying energy levels and loading regimes........ 132 Figure 4-34 CT scans of 2D braided laminates with varying energy levels and loading regimes..................................................................................................................................................... 134 xxvi Figure 5-1 Overview of entire LS-DYNA® Model domain; Impactor is the brown sphere; the black circular regions are nodal constrains to mimic the effect of the specimen clamps ........... 140 Figure 5-2 Cross-section view of the LS-DYNA® model domain; the square window shape of the rigid support can be clearly seen below the composite sample .................................................. 140 Figure 5-3 Close-up cross-section view near the impact site; the 11 layers of composite can be clearly seen and in the lowermost layer a strip of material 10 mm wide is present to allow for the possibility of complete tow separation to due matrix splitting. .................................................. 140 Figure 5-4 Close-up cross-section view near the edge showing the rigid support (green) that the sample sits on. An automatic surface-to-surface contact is used between the sample and the support. The colours indicate portions of the model that are specified as separate parts; they do not indicate the material model applied to the part ..................................................................... 140 Figure 5-5 Logic flowchart of automated procedure for "back-calculating" lamina elastic constants from laminate elastic constants by an iterative optimization routine on a non-linear cost function fed by classical laminate plate functions. For any given lamina elastic constants, there is a unique solution for laminate elastic constants according to classical laminate plate theory, but the reverse is not true and must be arrived at through iterative optimization ............................. 144 Figure 5-6 Schematic of the bi-linear traction-separation law used for tiebreak option 9; the area under the curve is the energy release rate and represents the energy absorbed per unit area of delamination created ................................................................................................................... 146 Figure 5-7 Comparison of NCF quasi-static indentation experimental force-displacement vs numerical..................................................................................................................................... 148 Figure 5-8 Comparison of NCF quasi-static deflection experimental force-displacement vs numerical (complete perforation) ............................................................................................... 149 xxvii Figure 5-9 Comparison of NCF quasi-static deflection experimental force-displacement vs numerical (interrupted perforation)............................................................................................. 150 Figure 5-10 Comparison of numerical force-displacement plot for impact N5 to the experimental impact and quasi-static test results; loading curve is well predicted but peak force is too high and peak displacement too low (response is too stiff) ....................................................................... 151 Figure 5-11 Comparison of numerical force-displacement plot for impact N10 to the experimental impact and quasi-static test results; loading curve is well predicted but peak force is too high ....................................................................................................................................... 151 Figure 5-12 Temporal effect of impact duration on early state impact load .............................. 152 Figure 5-13 Comparison of Numerical and Experimental Delamination Areas......................... 153 Figure 5-14 Numerical predictions for the regions of fibre and matrix damage ........................ 154 Figure 6-1 Projected damage area from ultrasonic scanning vs permanent dent depth; there is a clear increase in damage area and reduction in permanent dent depth in the case of NCF high-velocity/low mass, and almost no change in 2D braid high-velocity/low mass ......................... 157 xxviii List of Symbols Symbol Description Units 𝒄𝒄𝑳𝑳 Longitudinal wave speed mm/ms 𝒄𝒄𝑺𝑺 Shear wave speed mm/ms 𝑫𝑫𝒊𝒊𝒊𝒊 i,j component of the bending stiffness matrix for the laminate N mm 𝑬𝑬𝒇𝒇𝒇𝒇,,𝒙𝒙 Flexural modulus in x direction GPa 𝑬𝑬𝒇𝒇𝒇𝒇,𝒚𝒚 Flexural modulus in y direction GPa 𝑭𝑭𝑫𝑫𝒚𝒚𝑫𝑫𝑫𝑫𝑫𝑫𝑫𝑫 Dynamic impact force correction factor - 𝑭𝑭𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒊𝒄𝒄𝒊𝒊 Impact force (at the tip of the impactor) N 𝑭𝑭𝒇𝒇𝑫𝑫𝒊𝒊𝒍𝒍 𝒄𝒄𝒄𝒄𝒇𝒇𝒇𝒇 Impact force measured by the load cell N 𝑮𝑮𝑰𝑰𝒄𝒄 Mode I interlaminar fracture toughness kJ/m2 𝑮𝑮𝑰𝑰𝑰𝑰𝒄𝒄 Mode II interlaminar fracture toughness kJ/m2 𝑮𝑮𝒄𝒄,𝒙𝒙𝑻𝑻 Intralaminar tensile fracture toughness in x direction kJ/m2 𝑮𝑮𝒄𝒄,𝒚𝒚𝑻𝑻 Intralaminar tensile fracture toughness in y direction kJ/m2 𝑮𝑮𝒙𝒙𝒚𝒚 Intralaminar shear modulus GPa 𝒌𝒌𝒄𝒄 Contact stiffness N/mm 𝒌𝒌𝒊𝒊 Plate stiffness transverse to load N/mm 𝒊𝒊𝒃𝒃 Mass behind the force transducer G 𝒊𝒊𝒉𝒉 Mass ahead of the force transducer G 𝑺𝑺𝒙𝒙𝒚𝒚 Intralaminar shear strength MPa 𝑺𝑺𝒙𝒙𝒙𝒙 Interlaminar shear strength in xz direction MPa xxix 𝑺𝑺𝒚𝒚𝒙𝒙 Interlaminar shear strength in yz direction MPa 𝑻𝑻𝒊𝒊 Time for 1st mode flexural wave to reach boundary ms 𝒗𝒗𝒊𝒊 Phase velocity of a flexural wave mm/ms 𝑤𝑤 Displacement in the z direction mm 𝜸𝜸 Wave number mm-1 𝜹𝜹 Impactor displacement mm 𝜹𝜹𝒊𝒊 Indentation displacement mm 𝜺𝜺𝑰𝑰,𝒙𝒙 Tensile initiation strain in x direction - 𝜺𝜺𝑰𝑰,𝒚𝒚 Tensile initiation strain in y direction - 𝝀𝝀 Wavelength mm 𝝂𝝂𝒙𝒙𝒚𝒚 Poisson ratio xy (major) - 𝝂𝝂𝒚𝒚𝒙𝒙 Poisson ratio yx (minor) - 𝝆𝝆 Density kg/m3 𝝆𝝆𝟎𝟎 Density per unit area kg/m2 𝝎𝝎 Angular frequency of sinusoidally oscillating wave s-1 xxx List of Abbreviations BVID Barely Visible Impact Damage CFRP Carbon Fibre Reinforced Polymer CFL Courant-Friedrichs-Lewy condition for time step stability CODAM2 [UBC] Composites Damage Model 2 CT [X-Ray] Computed Tomography DLR Deutsches Zentrum für Luft- und Raumfahrt (German Aerospace Center) ELVS Enhanced Laser Velocity System FE Finite Element (numerical modelling or simulation method) HVI High-Velocity Impact LVI Low-Velocity Impact NCF Non-Crimp fabric OCT Overheight Compact Tension POD Pin-Opening-Displacement RTM Resin Transfer Moulding xxxi Glossary Angular frequency The frequency of a wave with a sinusoidally varying amplitude expressed in radians per unit time Blanket (NCF) A unit of fibre reinforcement composed of more than one lamellae that has been stitched together so it can be handled as a single unit during layup CODAM2 UBC Composites Damage Model 2; a material model capable of representing transversely isotropic materials in both the linear elastic state and the post-peak damaged state using a strain based failure criterion Damage resistance The ability of a structure to withstand an impact and not permanently absorb the kinetic energy of the impactor Lightweighting The reduction of (vehicle) mass through improvements in structural design and/or substitution of the materials within a structure Phase Velocity The velocity at which the phase of any single frequency component of a wave travels Preform A pre-assembled collection of fibre reinforcement layers that has been constructed with roughly the final geometry of the part; the intent being to reduce the time required to lay the material into the mould Sabot A carrier sleeve used to transmit thrust to a smaller projectile placed within. It is designed to fit the caliber of a gun so that gas is trapped behind itself and propels it forward, ultimately releasing the projectile for free flight when the pair arrive at the end of the gun barrel xxxii Schedule (laminate) The order, thickness and orientation of layers within a composite laminate Tex The same as linear density ([M]/[L]); the mass of fibre reinforcement material per linear distance Tool With regards to composite materials, “tool” is generally meant to refer to the surface and structure of the mould onto which the composite material is placed onto in order to form it to the final or semi-final shape of the component being manufactured Warp The longitudinal yarn in a woven reinforcement architecture Weft The transverse yarn in a woven reinforcement architecture xxxiii Acknowledgements There are many people who have contributed greatly to the experiments, simulations and discussions that have made this work possible, and also many people who have made my graduate student experience at UBC so enjoyable. Firstly, I would like to thank my supervisor and co-supervisor, Professors Anoush Poursartip and Reza Vaziri. Their support has been wide ranging from assistance with funding applications, course teaching, regular meetings to discuss experimental plans and results, as well as their ongoing collaboration with the German Aerospace Centre that enabled my research stay abroad. I am happy to have had their support the whole way through. I would also like to thank Emeritus Professor Göran Fernlund for his teaching on fracture mechanics, which has been so important in this work. Thank you to Suzana Topic, our energetic group manager and baker extraordinaire who’s love of baking treats has been enjoyed by all over many group coffee breaks. Thank you to all of the technical staff at UBC who have helped me so much in setting up and running experiments; especially Mr. Roger Bennett for his assistance in experiments, but also for his insight on various hiking opportunities throughout BC and for our extended conversations on motorcycles. My gratitude extends to all the members of the materials engineering machine shop; Mr. Ross Mcleod, Mr. David Torok and Mr. Carl Ng for your assistance with modifying the gas gun apparatus and cutting of test coupons. Thanks also to Mr. Wonsang Kim for his help with the load frames, instrumentation and rapid repair of a variety of electronic equipment. I owe substantial thanks to many, many people at the DLR Institute for Structures and Design in Stuttgart, Germany. Their hospitality in hosting and assisting me with carrying out xxxiv experiments is greatly appreciated. Vielen dank Dr. Heinz Voggenreiter, Dr. Nathalie Toso-Pentecôte, Dr. Matthias Waimer, Herr Thomas Feser, Herr Stefan-Andreas Ritt, Frau Dorothea Schlie, Herr Raouf Jemmali, Herr Tobias Behling, Dr. Ashley Chadwick, Herr Simon Bauer, Frau Saskia Ottinger und das Team in der Maschinenwerkstatt. At UBC I would first like to acknowledge the many visiting professors and students that we had the fortune of hosting here at UBC including Professor Martine Dubé, Professor Marco Petrolo, Alexandre Looten, Raymond Deribains, Vincent Gill, Yuta Kumagai, Yuta Naito, David Zimmerman and Oliver Herb. A great amount of thanks to all of my CRN colleagues who contributed to my experience and occasionally assisted in this work through various discussions; particularly our professional staff, including Dr. Navid Zobeiry, Dr. Casey Keulen and Dr. Christophe Mobuchon. Our post-doctoral research fellows Dr. Janna Fabris, Dr. Sina Amini Niaki, Dr. Bryan Louis, and particularly Dr. Johannes Reiner who played a substantial role in guiding me through the numerical modelling of this work. Our co-op students who assisted with this work including Carolina Trujillo Sanchez, Ryan Li and Jake Quigley. I would particularly like to thank my fellow graduate students with who whom I spent the most time with; thank you to Sahar Abouali, Cheng Chen, Duncan Pawson, Hubert Courteau-Godmaire, Caitlin Duffner, Shayan Fahimi, Gavin Tao, Sherry Kiafar, Nima Bakshi, Nasser Arbabi, Erfan Forghani, Mohammad Mohseni, Margarita Galper, John Park and Dr. Andrew Stewart. I would additionally like to thank Dr. Elvis Cepuš for training me on the Enhanced Laser Velocity System, and a large thanks to Mr. Armin Rashidi at the Okanagan campus of the University of British Columbia for his extensive help with CT scanning of samples. xxxv I would like to acknowledge my sources of funding, without which this project would not have taken place. In particular, the NSERC CRD grant ‘Development of a Computational Tool for Advanced Analysis of Light Weight Composites Structures’ and our corporate partner in this project, Ford Motor Company. The NSERC Canada Graduate Scholarship-Master’s Program scholarship, the UBC Affiliated Fellowship and the Cy and Emerald Keyes Fellowship in Materials Engineering. The NSERC Michael Smith Foreign Study Supplement and the UBC Go Global Self-Directed Research Abroad Award provided the financial support my research stay at DLR. Lastly, and certainly not least I would like to thank my parents – Roy and Marilyn Nesbitt – who have been supporting my pursuit of science and engineering for as long as I can remember; and to my brother Jason, his fiancé Sophie, and Bene the dog for all our get-togethers since I moved to Vancouver. xxxvi Dedication To my parents, for fostering my interests in engineering; and to Jeff “The Gluru” Sharp, for introducing me to composite materials.1 Chapter 1: Introduction 1.1 Motivation for the use of Composites in the Automotive Industry Air pollution has become a significant societal concern following the thermo-industrial revolution beginning in the 1800’s (Steffen et al. 2011; Abram et al. 2016). Since the inception of the locomotive, the automobile and the airplane, the use of fossil-fuel based energy for mobility purposes has become ubiquitous. The transportation sector now accounts for approximately 29% of the United States’ greenhouse gas emissions (“Fast Facts on Transportation Greenhouse Gas Emissions” 2019) and 25% of Canada’s greenhouse gas emissions (“Canadian Environmental Sustainability Indicators: Greenhouse Gas Emission” 2020). As shown in Figure 1-1 below, the transport sector has consistently been one of Canada’s largest greenhouse gas emitting sectors after the oil and gas sector. Figure 1-1 Megatonnes of carbon dioxide equivalent greenhouse gases for Canada by sector from 1990-2018; the transport sector has consistently been a major source of greenhouse gases (“Canadian Environmental Sustainability Indicators: Greenhouse Gas Emission” 2020); Reproduced for non-commercial use, © 2020 Her Majesty the Queen in Right of Canada, represented by the Minister of Environment and Climate Change 2 To combat the growth of greenhouse gas concentration in the atmosphere, global regulatory bodies are applying more stringent emissions regulations. This is pushing vehicle manufacturers to further increase the efficiency of their products. Regulations and standards such as the Corporate Average Fuel Economy (CAFE) standards implemented by the US National Highway Traffic Safety Administration (US Department of Transportation 2014) – which have been adopted by Environment Canada – and EU Regulation 2019/631 (European Union 2019) have become the driving force that is pushing automotive vehicle manufacturers to increase efficiency and reduce greenhouse gas emissions. Such drastic reductions in emissions may well necessitate a large movement away from fossil fuel consuming engines; but the use of “lightweighting” to reduce the overall transport costs of the vehicles will be an important component regardless of energy source. Indeed, a recent survey conducted by Penton Market Research has indicated that “a majority of the [automotive industry] respondents (63%) are focused on lightweighting and the use of lightweight structural materials…” in order to meet the emission reduction targets (CompositesWorld 2016). Electric vehicles in particular stand to benefit from lightweighting as a lighter vehicle requires less energy to operate, and therefore a smaller battery can be utilized to obtain a similar range, or the same battery for a longer range; thus making electric vehicles more attractive to the market (Brooker, Ward, and Wang 2013). Such lightweight structural materials are chosen in large part based on either their specific strength (strength divided by density) or specific stiffness (stiffness divided by density) depending on the constraints of the application. Material property charts such as Figure 1-2 below from Ashby (2011) are used to visualize these values for different materials. In this figure (which is plotted on a log-log scale) it is apparent that carbon fibre reinforced polymer (CFRP) composites have the potential for both high specific strength (the highest of any other materials 3 shown in this chart) and high specific stiffness (eclipsed only by technical ceramics with lower specific strength and lower toughness). It is the high ranking in both of these metrics that make CFRP composites so promising for lightweighting of vehicles. By comparison, the specific strength and stiffness of metals are nearly an order of magnitude lower than CFRP composites as shown in the figure, at least when this figure is taken at face value. In practice, the stiffness and strength of composites are lower than shown in this figure because the strength and stiffness shown are only for loading in the fibre direction of a unidirectional composite; thus the exact amount of advantage that composites have is typically less than shown here, and highly coupled to the component design, loading variability, and processing parameters. Figure 1-2 Composite materials are shown to be of similar stiffness to metals, but lighter than aluminum alloys, and significantly lighter than steels; republished with permission of Elsevier Science & Technology Journals, from “Materials Selection in Mechanical Design”, M. F. Ashby, 4th Edition, © 2011; permission conveyed through Copyright Clearance Center, Inc. 4 In addition to providing a high material efficiency coefficient, CFRP composites also allow the laminate to be tailored towards the loading requirements. By orienting the fibre direction(s) of the plies that make up a composite laminate, the structure can be refined to provide reinforcement only in the directions that require it. In this way, composite parts with well-defined, consistent load paths can be designed having not only a high material efficiency coefficient, but a high structural efficiency coefficient as well. For these reasons above, the automotive industry has great interest in the use of CFRP composite materials. Composites have been used in low-rate, non-structural production vehicles, such as Corvette body panels (Brosius 2019) and select structural applications such as hand crafted race cars & composite leaf springs for some time (Wood 2020). In fact, Henry Ford used a form of composites with soya and hemp fibres held together with plastics in the 1940’s (Sköck-Hartmann and Gries 2011). However, only recently has the industry begun to embrace the benefits of CFRP composites in a substantial way throughout the structural components of high-rate production models. BMW in particular has produced a number of cars with substantial CFRP content including the i3 (CompositesWorld 2013), i8 (CompositesWorld 2013) and 7 Series (Gardiner 2016) vehicles. The use of CFRP composites for the entire structure of the passenger section and all body panels of the i3 and i8 (Compositeslab n.d.) as well as numerous components – shown in Figure 1-3 – of the BMW 7 series provide validation that CFRP composites can benefit lightweighting programs. 5 This figure has been removed from the published version because of copyright restrictions The figure contained a stylized image of the BMW 7 series body-in-white with colour coding of structural components by the type of carbon fibre material/process used to make the sections See figure 1from: Gardiner, Ginger. 2016. “Is the BMW 7 Series the Future of Autocomposites?” CompositesWorld. 2016. https://www.compositesworld.com/articles/is-the-bmw-7-series-the-future-of-autocomposites. Figure 1-3 Locations and manufacturing processes utilized for CFRP components in the BMW 7 series vehicle show the heavy reliance on press consolidation processes such as resin transfer moulding (Gardiner 2016) 1.2 Challenges to the Use of Composites in the Automotive Industry First off, it must be recognized that both repair and recycling of composite structures present their own challenges to the adoption of composite structures in the automotive industry. While these areas of importance will not be addressed in this thesis, it is worth pointing out that the inability of composite materials to absorb energy plastically – and instead absorbing energy through fracture – means that composite parts (whether structural or not) cannot simply be bent back into shape or faired out with putty to restore their shape. The damage incurred has irreversibly degraded their stiffness and strength. Due to the time and skilled labour required to repair composite parts, replacement of components is generally the preferred option. Cars like BMW’s i3 are designed with specific cut-away sections in the structure so that even sections of the chassis can be replaced with standardized parts when damaged (Vossier 2014). While these innovative design ideas make replacement easier and potentially more cost effective than repair, it highlights the issue of recyclability even further as the replaced components must be recycled in addition to whole of the vehicle at the end of its life, along with manufacturing scrap during part production. 6 Composite parts cannot typically be recycled to their original state for several reasons: Firstly, the matrix and fibre reinforcement materials are two distinct phases that are intermingled at micron level scales and thus cannot be easily separated, and recycling multi-material parts is a major challenge for the recycling industry (Pickering 2006). Secondly, many of the materials used for composite parts are created through irreversible chemical processes (Chawla 2019). For example, thermoset polymers used as a matrix material form irreversible chemical cross-links during their cure reaction, and carbon fibres are formed by irreversibly oxidizing and carbonizing a polymer precursor. Counterexamples include thermoplastic polymers and glass fibres that can be reprocessed through heating; but again, separation of the matrix and fibre phases is the primary challenge. Completing the product lifecycle by addressing repair and recyclability remains a top priority for automotive manufacturer’s as they incorporate composite materials in high-production volume applications. As mentioned previously, Figure 1-2 must be viewed with a critical eye because the strength of composite materials is highly variable. The strength values for composite materials in Figure 1-2 is specifically the tensile failure strength. Due to the multiple phases of materials present, their failure modes, the complex interaction of failure modes, and processing effects among other factors, the strength and stiffness of composite parts can be quite variable. Furthermore, there is no single definition of what constitutes failure of a composite, and so strength is also a subjective value (Tuttle 2013). This makes structural design with composite materials challenging and potentially time (and cost) consuming. The complexity of designing with composite materials is handled in the aeronautical industry through the use of a structured design program that makes use of the building block approach shown in Figure 1-4 (Composite Materials Handbook-17, Volume 3 2012) 7 Figure 1-4 The building block approach used in the certification of aeronautical composite structures involves tests at numerous levels including coupons, structural elements, subcomponents and components which can make the design and certification process time consuming and expensive; republished with permission of SAE International, from Composite Materials Handbook, Volume 3, © 2012; permission conveyed through Copyright Clearance Center, Inc. The building block approach works by gathering test data in different quantities inversely proportional to the complexity of the sample. A large quantity of coupon level tests are used to validate analytical methods at a basic level, which are then used to design larger elements that are selectively validated by test and so on. This process is continued up the building block with progressively fewer tests at each level until the full-size structure is developed using analytical methods that have been substantiated by testing at varying levels of complexity. The goal is to design a composite structure that meets all functional and structural requirements in a way that does not depend on analysis alone, but that doesn’t require test programs for every geometry, load case and failure mode as that would be prohibitively expensive (Composite Materials Handbook-17, Volume 3 2012). The result of the building block approach is a very methodical process for designing, analyzing and checking the suitability of structural designs. In this way, once the aircraft design is completed and the first article manufactured, there should be a minimal number of unforeseen challenges encountered despite the complexity of the design. 8 Despite being a more efficient method for designing and substantiating a structure, it is still very expensive and time consuming to implement. Within the aeronautical industry, the time and cost of designing and manufacturing composites structures with this building block approach is still (generally speaking) economically feasible. The primary reasons for this are: • Recurring vs non-recurring costs for aircraft operators – For aircraft, the energy needs of overcoming gravity and moving quickly through the atmosphere must both come from engine thrust. This thrust is generally produced through the combustion of fossil fuels, which is both a recurring cost for the operator and an environmental pollutant. Large commercial aircraft are generally in the air as often as logistics will allow; typically 30-50% of the time for short haul aircraft, and as much as ~65% of the time for long haul aircraft (Morris 2017). This high duty cycle means that the recurring cost of fuel over the life of the aircraft is significant relative to the purchase cost of the airplane itself. A simple analysis of a mid-sized aircraft (Boeing 787) burning ~1280 gallons/hour of jet fuel (Mayerowitz 2013), a duty cycle of 50% (Morris 2017) and an average jet fuel cost of 1.83 USD/gallon (“Diesel and Jet Fuel Prices” n.d.) reveals that over a 30 year lifespan (Ali and Cogdell 2016), an aircraft such as the Boeing 787 may require ~308 million USD worth of fuel to operate (in 2020 dollars). Given a list price of 264.6 million USD and considering the reality that the final purchase price is never as high as the list price (Ausick 2016), it is clear that the cost of fuel over the life of the aircraft can be much greater than its initial purchase price. Assuming a purchase price of 75% of the list price, the cost of fuel over the lifetime is approximately 1.55 times the purchase price. By comparison, the Bureau of Labor Statistics reported that in 2019 the average American consumer spent 2094 USD on fuel and motor oil for transportation 9 (“Consumer Expenditures - 2019” 2020). Assuming 2000 USD for fuel and assuming a vehicle lifetime of 15 years, the average American consumer will spend 30000 USD on fuel over the lifetime of the vehicle. The Kelly Blue Book reports that as of October, 2020, the average transaction price for a light vehicle in the United States was 38723 USD (“Average New-Vehicle Prices …” 2020), a ratio of 0.77. While the cost of fuel for a light vehicle is not insignificant compared to the purchase price, a ratio of 0.77 for light vehicles vs 1.55 for a mid-sized aircraft shows that efficiency will be more highly valued by the aircraft operator. Therefore, aircraft operators are inclined to pay a higher non-recurring cost to purchase a more fuel-efficient airplane that will be more economical over the life of the aircraft, thus lowering their total cost over time. Aircraft manufacturers can use this demand for improved technology to justify the cost of a complex design process, physical testing, certification and advanced manufacturing processes. • Extended cost amortization for non-recurring development cost – Typical new aircraft development cycles last approximately 4 to 8 years (Spitz et al. 2001), which allows for development programs of great complexity to be undertaken. Once serial production begins, the manufacturer’s typically have an extensive amount of time available to produce and sell that model of aircraft before development of the next generation of a similar model. The duration of aircraft model production runs varies greatly, but production runs in the range of 20-30 years are not uncommon. Aircraft such as the Boeing 777 for example, were introduced in 1995 and are still in production today (“Boeing 777 Historical Snapshot” n.d.). The long duration of aircraft production runs 10 allows for the large non-recurring costs of product development to be recouped over a very long period of amortization. By contrast, the automotive industry exists in a very different market largely driven by consumerism and a convergence of automotive design with consumer electronics design (Morely 2019). The automotive industry is even a key topic of the annual Consumer Electronics Show, which serves to highlight automotive customer emphasis on rapid development of novel technologies (“Consumer Electronics Show - Tech Topics” 2020). In this market, the integration of new technologies must be continually pursued to maintain product relevancy and they must be integrated quickly into new vehicle models due to tight constraints on non-recurring development costs. Recurring manufacturing costs must also be kept low with production rates kept high to quickly recoup the return on investment. A recent industry survey found that 71% of automotive product development timelines were less than 2 years in duration (Morely 2019). The lifespan of that product offering is then likely to only be in production for 4-6 years (“Automotive Product Development Cycles and the Need for Balance with the Regulatory Environment” 2017). Beyond the 4-6 year time frame, consumers tend to view the product offering as outdated and inferior to more modern designs with the latest technology. This time crunch imposed by the dynamics of the automotive market has three effects: 1. Design processes must be efficient and reliable (need to produce a quality vehicle design in under 2 years) 2. Production rates must be high so that a sufficient volume of cars can be manufactured and sold in 4-6 years to recoup development costs 11 3. Recurring costs of manufacturing must be low to achieve a return on the development cost and tooling investment; but vehicle pricing must remain competitive with other similar offerings to achieve market share In such a constrained industry there are insufficient resources (employees and time) available within the economic constraints to undertake composite part development projects using the same step-by-step building block approach. In addition, the manufacturing processes often used by aircraft manufacturers are not suited for high rate production. These processes do not scale to produce components fast enough for automotive companies to recoup their development costs in 4-6 years. They are also generally labour intensive, making recurring costs of manufacturing too high. For these reasons, automotive companies must pursue more efficient design programs that make use of efficient manufacturing processes and materials. 1.3 Appeal of Resin Transfer Moulding with Textile Preforms to the Automotive Industry To achieve high-rate production with low recurring manufacturing costs, the material must be deposited onto the tool, processed and removed as quickly as possible. For this reason, the automotive industry is very interested in textile preforms and processes such as resin transfer moulding (RTM). During resin transfer moulding, a textile preform is closed in a mould and subsequently infused with resin and then cured. Processes like this with textile preforms allow for higher material deposition rates through the use of thick preforms, improved ease of material handling through the self-reinforcing properties of textiles, and generally good drapability (Bibo and Hogg 1996). Additionally there is the potential for rapid cycle times depending on the matrix chemistry chosen (Rao et al. 2018), high fibre volume fractions with low void content, and good surface 12 finish on both sides (“Resin Transfer” 2019). Overall, textile reinforced composites with potentially high-rate processes like RTM can allow manufacturers to reduce manufacturing costs for a nominal tradeoff with regards to in-plane mechanical properties, while potentially improving out-of-plane properties due to their architecture (Ogin and Potluri 2016). 1.4 Overview of Non-Crimp Fabric and 2D Braid Reinforced Panels Investigated in this Thesis It is perhaps fitting that Henry Ford’s company – which experimented with composite materials as early as the 1940’s (Sköck-Hartmann and Gries 2011) – would be the automotive company to sponsor the project that has led to this thesis. The Ford Motor Company provided two types of CFRP panels manufactured with textile preforms that are of interest for future automotive applications. Both panels utilize carbon fibre textile preforms in a thermosetting epoxy matrix infused into the preform through resin transfer moulding (RTM). Exact details on the type of carbon fibre and epoxy were not provided by the sponsor for reasons of confidentiality. One textile preform is a warp-knitted, multiaxial non-crimp fabric (NCF) with a nominal layup schedule of [02/60/-60]2S. The other is a two-dimensional braided fabric composed of layers of triaxial 2D braid laminated together with a layup schedule of [0/±60]3. Pictures of both material systems are shown in Figure 1-5 and Figure 1-6 below. 13 Non-crimp fabrics are a class of warp knitted textile preform (Bibo and Hogg 1996) composed of layers of unidirectional tows that are subsequently knitted together into a singular “blanket” of material that is convenient for material handling while offering the capability for high material deposition rates. A cross-sectional figure of a non-crimp fabric during manufacturing is shown in Figure 1-7 below (Linke et al. 2012). Each layer of tows in the blanket can be oriented at different angles, restricted only by the limitations of the machinery that is forming the textile. This allows for customized laminate schedules in a similar fashion to conventional unidirectional composites that are laid down layer-by-layer. A key advantage of non-crimp fabrics over other textile preforms is that – as the name implies – the tows can remain in an aligned orientation, with no undulations (crimp) along their length to interface with tows having different angular orientations (such as in woven or braided fabrics). This allows for improved stiffness and tensile strength of each lamina (Ogin and Potluri 2016). Figure 1-5 Typical appearance of an NCF sample cut to a 100 mm x 100 mm impact sample size Figure 1-6 Typical appearance of a 2D braid sample cut to a 100 mm x 100 mm impact sample size 14 Figure 1-7 Non-Crimp Fabric cross-section during manufacturing (angles shown do not match those of the material in this thesis); Republished with permission of Elsevier Science & Technology Journals, from Automating textile preforming technology for mass production of fibre-reinforced polymer (FRP) composites in The Global Textile and Clothing Industry, Linke et. al., © 2012; permission conveyed through Copyright Clearance Center, Inc. 2D braid fabrics are a class of textile preform where tows are interlaced on an arbitrary (not necessarily orthogonal) bias, or braid angle. These two tow directions separated by the nominal ±θ braid angle are the only directions within biaxially braided fabrics; while a third tow (typically an “axial” direction tow at an angle halfway between the other two tows) is added to produce triaxially braided fabrics as shown in Figure 1-8 below. Braided preforms are better able to resist damage during twisting, shearing and impact when compared to woven preforms, and show reduced notch sensitivity and increased compression after impact strength compared to conventional UD laminate systems (Ogin and Potluri 2016). Figure 1-8 Triaxial braid preform architecture; Republished with permission of Elsevier Science & Technology Journals, from Mechanical performance of 2-D braided carbon/epoxy composites in Composites Science and Technology, Falzon, P., Herszberg, I., Volume 58, Issue 2, © 1998; permission conveyed through Copyright Clearance Center, Inc. 15 Other textile preform architectures that were not considered in this thesis include woven, nonwoven and conventional knit architectures. The conventional knit architecture offers excellent drapability as its primary feature, but it suffers from low in-plane modulus and strength owing to the inherent looped nature of the tows resulting in substantial deviation of the tows from a structurally efficient straight path (Ogin and Potluri 2016) as shown in Figure 1-9 below (Ramakrishna 1997). Nonwovens – having irregularly oriented tows – also suffer from the same limitation. Woven fabrics are the most similar to the braided material in that they are intended to produce a substantially stiff textile without severe amounts of crimp (compared to conventional knit), but as mentioned above they are inferior to 2D braided preforms in twisting, shearing and impact load cases (Ogin and Potluri 2016). Additionally, they lack the structural efficiency of the straight tows in non-crimp fabrics, and are typically not manufactured into thick preforms suitable for higher material deposition rates. Figure 1-9 (a) weft-, and (b) warp-knit patterns; Republished with permission of Elsevier Science & Technology Journals, from Characterization and modeling of the tensile properties of plain weft-knit fabric-reinforced composites in Composites Science and Technology, Ramakrishna, volume 57, © 1997; permission conveyed through Copyright Clearance Center, Inc. Three dimensional preforms – so named because some or all of the tows in the preform span multiple layers within the preform – have advantages in that they often have higher areal 16 density (which results in increased material deposition rates), higher through-thickness mechanical properties (stiffness and strength) and improved damage resistance to impact when compared to two dimensional preforms (Saboktakin 2019). This is particularly true for both impact and compression after impact scenarios. During impact, through thickness structural reinforcement can increase interlaminar fracture toughness (Dransfield, Baillie, and Mai 1994). In compression after impact scenarios, the through-thickness structural reinforcement can act to support the laminate transversely and delay the onset of lamina buckling (Ogin and Potluri 2016; Dransfield, Baillie, and Mai 1994). The primary impediment to widespread usage of three dimensional preforms is that they are expensive to produce (“3-D Woven Reinforcements Update” 2011). Three dimensional preforms are therefore promising technologically, but not particularly economical in the automotive industry due to the need to keep recurring manufacturing costs low. 1.5 Motivation for the Investigation of Impact Damage As identified above, the building-block approach – while being a robust method of development for composite structures – cannot be applied to the automotive industry in the same way as the aeronautical industry. Due to economic constraints, the automotive industry must rely more heavily on numerical analysis and computer-aided engineering to develop structurally adequate composite parts with a minimum of prototype testing. Automotive companies have so far had many decades of experience in improving numerical models for metallic structures to provide the high level of fidelity required to support this dependence on virtual testing. The level of fidelity is so high in fact that automotive manufacturers such as Volvo only carry out full scale physical crash testing of vehicles at the time of final certification (Jergeus 2018). Advanced auto manufacturers have no need to carry out these tests on metallic prototype models because their 17 numerical tools reliably give them results that are sufficiently accurate to real-life. This has a significant benefit in saving development time and cost. Unfortunately, the same cannot be said for vehicles with composite structures. The current state of the art for composite materials numerical analysis is not yet as complete as it is for metals. Again, the complex cascade of numerous interacting and path dependent failure modes makes predicting strength (both undamaged, and residual after impact) a challenge. The concern about numerical model validity is particularly relevant for impact scenarios which have a stress state that is a complex mix of tensile, shear and compressive stress waves that emanate from the impact site at different velocities. As is shown in Figure 1-10 below, the tensile stresses tend to contribute towards fibre dominated failure modes while the shear and compressive stresses tend to contribute towards matrix dominated failure modes. Depending on the duration of the impact, the importance of one or the other may take more prominence and affect the structural response and final damage state. Additionally, strain rate sensitivity of the polymer matrix may also affect the response. Ultimately though, some mixture of interlaminar and intralaminar damage will result; which, when subjected to structural loads may or may not have enough residual strength to maintain load-bearing capability. In any case, the numerous interacting phenomena that occur makes impact testing an excellent proxy test to represent any number of complex loading conditions; and it is for this reason that impact testing of these materials is of importance. 18 Figure 1-10 Schematic of an impact event resulting in stress waves that cause various failure modes resulting in interlaminar and intralaminar damage. The interaction of the stress waves with this damage determines the structural response. Subsequent application of structural loads can then be used to determine the residual strength 1.6 Research Objectives & Thesis Outline The primary purpose of this thesis and the work behind it is to experimentally investigate the structural response and resulting damage state of non-crimp fabric and 2D braid fabric CFRP panels to sub-perforation transverse impact under a variety of strain rates. Improving our understanding of the structural response and damage mechanisms occurring in these materials during impact is of benefit to engineers in many industries as the improved understanding can lead to a more informed choice of material for a part, and an enhanced understanding of the implications of impact on its structural integrity. The components of the experimental work first begin with characterizing the material for the purpose of numerical modelling through experimental tests including tensile, 3 and 4 point bend, shear, overheight compact tension, double cantilever beam and end-notch flexure tests. Transverse loading is then investigated quasi-statically to investigate both the local indentation response when fully supported, and the global bending response when allowed to deflect. The 19 impact response is subsequently investigated using a low and high-speed gas gun and a drop tower. All test equipment is instrumented to gather high fidelity data that is useful for understanding the structural response and validating numerical models. Extensive damage characterization is also carried out with ultrasonic scanning, computed tomography scanning, and dent depth measurement. The secondary purpose of this thesis is to undertake limited numerical analysis of the experimental impacts in order to preliminarily investigate the efficacy of the UBC Composites Damage Model 2 – known as CODAM2 – (Williams et al. 2003; Forghani et al. 2019). This comparison of structural response and damage state is carried out for the NCF material only. At this point, the numerical analysis of the braided material was not attempted owing largely to CODAM2’s origins being for unidirectional composites only. It was felt that the applying CODAM2 to a material having a complex intertwined tow structure, without any currently available methods for representing this in some form would not substantially benefit the main purpose of this thesis. Instead, the focus of numerical validation on NCF panels (that are highly similar in architecture to conventional unidirectional material panels) provides a validation case with material closer to that of the model’s original intent. The thesis is organized in the following sections: • Chapter 2: Literature review – A review of the literature provides an overview of impact dynamics, stress wave propagation and structural response, which is of key importance to understanding how the impact event affects the material throughout the panel and leads to different failure modes. The various forms of damage are then reviewed with a focus on the types of impact damage characterized by other researchers for NCF and 2D braid 20 CFRP panels. Finally, an overview of the numerical modelling of composites damage is given and the UBC Composites Damage Model 2 (CODAM2) model is introduced. • Chapter 3: Experimental Methodology – An overview of the elements of the experimental work undertaken for this thesis is provided, including: o Mechanical property characterization of the NCF and 2D braid panel materials o Transverse loading experiments including quasi-static, low-velocity impact and high-velocity impact o Damage characterization including dent depth measurement, ultrasonic scanning and x-ray computed tomography scanning • Chapter 4: Experimental Results and Interpretation – The results of the experimental work are provided and augmented with the use of additional analysis and cross-comparison of the results. The structure of this chapter largely follows chapter 3. • Chapter 5: Numerical Modelling and Comparison – Utilizing the material characterization results from chapter 4, a numerical model of the transverse loading of the panels is created. This model utilizes a lamina level approach and therefore lamina level properties are first back calculated from the laminate level properties described in chapter 4. An overview of this back-calculation process is given, and the resulting lamina level properties provided. The model is described including its discretization, intralaminar damage model (CODAM2) and interlaminar damage model. Following this, the results of the model are displayed and compared to that of the experimental tests for comparison. This includes quasi-static test results and impact test results for both the structural response of the panels and the resulting damage state. 21 • Chapter 6: Discussion – A discussion of the experimental results in comparison to both the numerical results and the work of others is given. A primary focus is placed on how different velocity regimes affect the structural response and damage in both materials • Chapter 7: Conclusions & Future Work – A summary of the work undertaken, and its primary conclusions is given. Suggestions are also provided for future work to be undertaken that may build off of this work or answer further questions identified in this thesis. 22 Chapter 2: Literature Review The subject of impact damage of composite plates is an extensive one with a wide breadth of literature on various aspects of the subject including contact theory, wave dynamics, damage initiation, damage progression, damage modes, damage resistance, residual strength and other important topics. The following literature review will cover the topics of primary importance for this thesis. 2.1 Impact Dynamics Static or quasi-static loading of structures generally implies that the atomic interactions within a material remain in a state of static balance, where accelerations are minimal and therefore the inertia of the material itself can be neglected. However, under dynamic loading the inertia of infinitesimal elements of the material must be taken into account, and therefore the propagation of stress waves is important to understanding the physics of the problem (Wang 2007). In the following sections, the types of stress waves that are important for understanding impact loading of composite structures are discussed, and their correlation to different types of impact damage identified. The speed at which the different stress waves travel will be presented, and the importance of these speeds, coupled with the geometry of the structure and the duration of the impact will be identified through a discussion of different impact regimes. Stress Waves According to Wang (2007), when a localized region of a deformable solid is acted upon by an external load, only the surface particles that are directly loaded by the external force are moved away from their initial equilibrium positions. This results in relative motion between these first loaded particles and their neighbours, resulting in an acting and reacting force between them that is interpreted as stress. This stress then causes the neighbouring particles to also move 23 from their equilibrium positions, but later than the externally loaded particles – owing to inertia. The result is that the equilibrium disturbance brought on by the external load gradually propagates from the material nearby the impact site to the material far from the impact site. This phenomenon is known as stress waves. According to Zukas et. al. (1982) in their book on impact dynamics, there exists two distinct types of stress waves: 1. Dilatational (longitudinal) waves o Characterized by the motion of the particles in the same direction as the motion of the wave front o Also known as p(primary)-waves (La Saponara 2018) 2. Distortional (transverse or shear) waves o Characterized by the motion of particles perpendicular to the motion of the wave front o Also known as s(secondary)-waves (La Saponara 2018) Giurgiutiu (2014) expands on this further by including separate definitions for flexural, Rayleigh and Lamb waves as shown in Figure 2-1. These other types of waves have elliptical particle motion; essentially a combination of both longitudinal and transverse particle motion. The flexural waves are responsible for the bending action that appears in beams and plates. Rayleigh waves are only applicable at the free-surface of half-spaces and Lamb waves occur at the surface of plates and spheres, but do not contribute appreciably to the deformation of the plates of interest to this thesis (La Saponara 2018) and will not be discussed further. 24 Figure 2-1 Types of waves in elastic solids (Giurgiutiu 2014); Reprinted from Structural Health Monitoring with Piezoelectric Wafer Active Sensors, Giurgiutiu, V., Elastic Waves, p. 202, © 2014, with permission from Elsevier The following sections will discuss the longitudinal (both through-thickness and in-plane), shear and flexural waves in greater detail. 2.1.1.1 Through-Thickness Dilatational Waves These waves emanate from the impact site as compression waves parallel to the direction of the impactor. Once they reach the backface of the sample, they then reflect to form tensile waves. As a result, these waves can cause damage due to both compressive overload of the material, or tensile overload of the material (Olsson 1993). In compression, if the magnitude of the compressive stress caused by the compressive wave is above the yield or ultimate strength of the material, matrix crushing damage will occur. Once reflected from the back-face, if the tensile stress is larger than the interlaminar tensile strength of the composite, spalling will occur at lamellar interfaces (Olsson 1993). The separation or loss of these layers, particularly at the back-face is problematic because the structural fibres on the back would likely have become the most highly loaded fibres of the sample as the impact progresses further and bending stresses develop (Cantwell and Morton 1989). 25 2.1.1.2 In-Plane Dilatational Waves These waves emanate from the impact site perpendicular to the direction of the impactor as compression waves. According to Olsson (1993), in most cases the impact response of the plate is controlled by flexural deformation, and the strains due to in-plane tensile-compressive waves are small in comparison to flexural strains. It is clear that he is referring to low-velocity impact, where the flexural waves have time to develop. In this case, the only substantial in-plane waves will occur after the flexural waves have developed, and only if the deflection of the panel is significant enough to cause membrane stresses. For engineering purposes, the membrane effect is generally only considered relevant when the transverse displacement exceeds the thickness of the sample (Abrate 2001). Under high-velocity impact though, Davies and Olsson (2004) state that the transverse dilatational waves can cause initial damage due to compressive strains on the order of 3% that are capable of causing compressive damage before any flexural response develops. 2.1.1.3 Transverse Shear (Distortional) Waves These waves are partly responsible for mode II delaminations, which are shown to contribute substantially to delamination in composite materials (Olsson 1993; Bibo and Hogg 1996; Davies and Olsson 2004). Transverse shear waves in many ways seem similar to flexural waves in that they are responsible for out of plane motion, but a major difference is that they are non-dispersive and therefore all transverse shear waves travel at the same speed (L. Wang 2007). 2.1.1.4 Flexural (Elliptical) Waves Flexural waves are responsible for the development of a structure’s bending response. The particle motion is elliptic, meaning it includes both longitudinal and transverse motion of the particles. In the case of transverse impact of an isotropic plate, a special case of the general wave 26 equation based on Kirchoff plate theory (plane sections remain plane) can be found for circular-crested flexural waves. Giurgiutiu (2014) provides the general solution for circular-crested flexural waves as: 𝑤𝑤(𝑟𝑟,𝑡𝑡) = 𝐴𝐴𝐻𝐻0(1)𝛾𝛾𝛾𝛾𝑒𝑒−𝑖𝑖𝑖𝑖𝑡𝑡 Eq. 2-1 Where: 𝑤𝑤 = the out-of plane displacement at radius 𝛾𝛾 and time 𝑡𝑡 𝐴𝐴 = a constant 𝐻𝐻0(1) = Hankel function of the first kind (a linearly independent solution of Bessel’s differential equation) 𝛾𝛾 = wave number (the number of wavelengths between 0 and 2𝜋𝜋 distance) 𝛾𝛾 = radius from the impact point 𝜔𝜔 = angular frequency of the wave (the number of oscillations in a time 2𝜋𝜋 at a point) 𝑡𝑡 = time From Eq. 2-1 it can be seen that there is not one single flexural wave that will define the solution, but multiple superimposing flexural waves of different angular frequencies and wave numbers. It is the lowest order, first mode flexural standing wave that is responsible for the quasi-static bending response of the panel (Olsson 1993). Additionally, flexural waves are dispersive in nature, meaning waves of different wavelengths will travel at different speeds. Short, high frequency waves travel fasts, and long, low frequency waves travel slowest (Giurgiutiu 2014). 27 Stress Wave Speeds As will be discussed further in Section 2.1.3, the relative duration of the impact event and the time required for stress waves to traverse the sample to a supportive boundary make a difference in how the structure responds to an impact. Furthermore, the stress waves discussed above do not all travel through the material at the same rate of speed. The following sections provide a literature background on the speed of the different wave types so that the impacts carried out in this work can be classified into different regimes (low-velocity/high-velocity) 2.1.2.1 Through-Thickness Wave Speed Through-thickness waves are dilatational waves and have a wave speed related to the through-thickness modulus of elasticity according to Eq. 2-2 (Zukas et al. 1982; Giurgiutiu 2014). 𝑐𝑐𝐿𝐿 = �𝐸𝐸𝜌𝜌 Eq. 2-2 Where: 𝐸𝐸 = Modulus of elasticity in the orientation of wave propagation 𝜌𝜌 = Density of the material 2.1.2.2 Transverse Shear Wave Speed Similarly to through-thickness waves, the velocity of shear waves can be calculated according to equation Eq. 2-3 (Zukas et al. 1982; Giurgiutiu 2014): 𝑐𝑐𝑠𝑠 = �𝐺𝐺𝜌𝜌 Eq. 2-3 Where: 𝐺𝐺 = the shear modulus of elasticity 28 2.1.2.3 Flexural Wave Speed Unlike the previously described waves, flexural waves are dispersive in nature. This means that there are numerous modes of deflection superimposed on each-other and that each mode travels at its own speed, thereby dispersing into numerous wave fronts (Olsson 1993). The phase velocity of a flexural wave is proportional to the square root of the wave frequency (Giurgiutiu 2014), and therefore higher frequency waves travel at faster speeds as shown in Figure 2-2. Figure 2-2 Phase velocity of flexural waves as a function of the wave frequency The wave fronts will start out together at the point of impact, but gradually disperse across some distance as time progresses. The phase velocity of any given frequency of flexural wave is given by: 𝑣𝑣𝑝𝑝 = 𝑖𝑖𝛾𝛾 = 𝑖𝑖𝜔𝜔2𝜋𝜋 (Giurgiutiu 2014) Eq. 2-4 Where: 𝜔𝜔 = angular frequency of the wave (the number of oscillations in a time 2𝜋𝜋 at a point) 𝛾𝛾 = wave number (the number of wavelengths between 0 and 2𝜋𝜋 distance) 𝜆𝜆 = wavelength 29 Therefore, if the wavelength and angular frequency (the frequency of the sinusoidal vibration modes in units of radians per unit time) of a desired waveform is known, the velocity at which it propagates can be calculated. The wavelength and angular frequency of most interest in the problem of transverse impact is that of the lowest (1st) mode of vibration of the plate. It is this mode that is responsible for the quasi-static flexural response of the plate, and therefore the speed at which it propagates is important to determining the impact duration below which an impact is considered a high-velocity impact. The inputs to Eq. 2-4 are non-trivial and depend on both the geometry of the plate as well as the stiffness and boundary conditions of the plate. The wavelength for the first mode of vibration can be estimated from the geometry of the problem considering the case of quasi-static deflection. During quasi-static deflection, when the full bending response of the plate is developed, it can be inferred directly from the geometry of the problem that half of the wavelength of the first mode of vibration is approximately equal to the width of the cutout in the impact fixture as shown in Figure 2-3. Figure 2-3 Quasi-static deflection of a panel showing the first mode of vibration with the half wavelength being equal to the width of the cutout The frequency of the first mode of vibration is not as simple to estimate as the orthotropic stiffness of the panel must be taken into account. Aydin et al. (2017) derived the equation of 30 motion shown in Eq. 2-5 for the free transverse vibration of a rectangular orthotropic plate based on the discussion of Ashton and Whitney (1970): 𝐷𝐷11𝜕𝜕4𝑤𝑤𝜕𝜕𝜕𝜕4+ 2(𝐷𝐷12 + 2𝐷𝐷66) 𝜕𝜕4𝑤𝑤𝜕𝜕𝜕𝜕2𝜕𝜕𝜕𝜕2 + 𝐷𝐷22 𝜕𝜕4𝑤𝑤𝜕𝜕𝜕𝜕4 + 𝜌𝜌0 𝜕𝜕2𝑤𝑤𝜕𝜕𝑡𝑡2 = 0 Eq. 2-5 Where: 𝜌𝜌0 = density per unit area 𝐷𝐷𝑖𝑖𝑖𝑖 = component of the bending stiffness matrix for the laminate 𝑤𝑤(𝑥𝑥,𝑦𝑦,𝑡𝑡) = displacement in the z direction And after using separation of variables and applying a simply supported boundary condition, the frequency of the m,n mode of vibration may be calculated per Eq. 2-6 𝜔𝜔𝑚𝑚𝑚𝑚2 = 𝜋𝜋4𝜌𝜌0𝑎𝑎4 [𝐷𝐷11𝑚𝑚4 + 2(𝐷𝐷12 + 2𝐷𝐷66)(𝑚𝑚𝑚𝑚𝑚𝑚)2 + 𝐷𝐷22(𝑚𝑚𝑚𝑚)4] Eq. 2-6 Where: 𝜔𝜔𝑚𝑚𝑚𝑚= angular frequency of the m,n mode of vibration 𝑚𝑚, 𝑚𝑚 = mode indices for the two orthotropic directions 𝑚𝑚 = plate aspect ratio 𝑎𝑎/𝑏𝑏; for a plate with dimensions 𝑎𝑎 and 𝑏𝑏 in the x and y directions The limitations of this method need to be considered in that it does not include the effect of the panel material extending beyond the edge of the cutout (beyond the simply supported boundary condition) and it does not account for the effect of any clamps on the surface of the specimen; nor the ability for the plate to rise up off the simply supported boundary. Modal analysis of any structure is highly sensitive to the overall stiffness of the structure, which 31 depends on the accurate definition of boundary conditions, and therefore some error can be expected in such an estimation. A more accurate estimate of the first mode of vibration may be possible with eigenvalue analysis of a 3D finite element stiffness matrix. With an estimate of the angular frequency of the first mode of vibration and its wavelength, estimates of the phase velocity of the first mode of vibration may then be found with Eq. 2-4. Impact Regimes – An Explanation of the Physics of Impact Events and their Governing Characteristics According to Gordon (1968), the transfer of load is really nothing more than the straining of chemical bonds between atoms, as shown in Figure 2-4. The atoms that make up the object must move in order to strain the chemical bonds and transfer the load. This movement of atoms occurs at some finite speed over some non-trivial period of time, during which the impact may or may not still be occurring. Based on this knowledge it is clear then that the duration of the impact event relative to the amount of time for the atoms to move and deform the structure is a key factor in determining how the structure will respond during the impact. 32 Figure 2-4 The elongation and contraction of chemical bonds between atoms; (a) undisturbed, (b) elongated, (c) compressed (Gordon 1968); Republished with permission of Princeton University Press, from “The New Science of Strong Materials: or why you don’t fall through the floor,” Gordon, J.E., © 1968; permission conveyed through Copyright Clearance Center, Inc. For example, if the impact is of a very short duration, there is insufficient time for the structure to displace and create the load path between the impact site and the support. In such an impact, the inertia of the plate itself becomes important, and it is the rapid acceleration of the atoms close to the impact site that give rise to the force opposing the impactor. Such an impact may be said to be “ballistic” and it is governed by the through-thickness response of the material. Conversely, if an impact occurs over a relatively long duration, the structure can displace, create the load path to the support, and provide the opposing force to the impactor by virtue of the elastic springs of the chemical bonds between atoms that become the load path between the impactor and support. Such an impact is said to be a “low-velocity impact”. Between the two there is a regime where both effects are important; the load path to the support may not yet be fully developed, but the amount of load carrying capacity from the support combined with the inertia of the atoms being accelerated is sufficient to decelerate the impactor and push it back. 33 The fundamental distinction between all types of loading and impact are whether the relevant boundary conditions influence the impact dynamics (Richardson and Wisheart 1996; Delfosse and Poursartip 1997; Olsson 1993, 2000; Davies and Olsson 2004). Table 2-1 is used to illustrate this point. Table 2-1 Distinguishing characteristics of different impact regimes and the approximate conditions under which they occur; figures republished with permission of Elsevier Science & Technology Journals, from “Mass criterion for wave controlled impact response of composite plates,” R. Olsson, Composites Part A: Applied Science and Manufacturing, Volume 32, pp. 879-887, © 2000; permission conveyed through Copyright Clearance Center, Inc. Impact Regime General Impact Duration Response Controlled By Timpact Relative to Through Thickness Wave Travel Time (TTT) Timpact Relative to Flexural Wave Travel Time (TFWB) Figure 2-5 Graphical Representation of Plate Response in Different Impact Regimes Quasi-static Loading >~100ms Boundary Conditions (Global Flexure) Tloading>>TTT Tloading>>TFWB (a) Low Velocity Impact (LVI) ~10’s ms Boundary Conditions (Global Flexure) TImpact>>TTT TImpact> TFWB (b) High Velocity Impact (HVI) ms Flexural Waves (Local + Semi-global Flexure TImpact>TTT TImpact<TFWB (c) Ballistic Impact μs Through-thickness Waves (Local) TImpact<TTT TImpact<<TFWB (d) According to Olsson (1993), the loading is considered quasi-static if the duration of the loading is substantially longer than the time taken for the lowest order flexural waves to reach the boundary conditions of the plate. In this case the structure deforms globally as shown in 34 Figure 2-5a. If the velocity of the impactor is increased slightly to the point where the impact duration is still longer than the time required for the flexural waves to reach the boundary, the response is largely the same, but is now referred to as low-velocity impact (Figure 2-5b). Further increasing the velocity of the impactor to the extent that the impact now occurs in such a short time interval that the lowest (and slowest) mode of flexural waves is not capable of traversing the plate to reach the boundary means that at the site of the impact, the structure is “unaware” of its support, and the full flexural response of the plate does not have time to develop. In this case the response is governed by higher order transient flexural waves as shown in Figure 2-5c and is known as high-velocity impact. Lastly if the impact occurs so fast that there is not sufficient time for the very fast through-thickness waves to reach the back-face of the plate, then the impact is known as a ballistic impact; however, this type of impact is not a focus of this work. Out of all the regimes mentioned above, the quasi-static regime is uniquely useful to study because it can be run in two distinct ways in order to study the structural response at the limits of the low and high end of the velocity range. Figure 2-6a (Kakarala and Roche 1987) shows a quasi-static deflection experiment where only the perimeter of the sample is simply supported, and the interior region of the coupon is free to deflect into the cutout of the fixture. This is the same support configuration used for all other transverse impact experiments studied in this work. By contrast, Figure 2-6b shows an indentation experiment where a sample of the composite plate is indented transversely while being fully supported on a hard, flat surface. In this case there is effectively no global sample displacement that can occur, and all displacement occurs within the region directly adjacent to the indenter. 35 (a) (b) Figure 2-6 (a) Simply edge supported quasi-static deflection test, (b) Fully supported quasi-static indentation test; figures reproduced, with permission from Kakarala, S.N. and Roche, J.L., “Experimental Comparison of Several Impact Test Methods,” Instrumented Impact Testing of Plastics and Composite Materials, ASTM STP 936, S. L. Kessler, G. C. Adams, S. B. Driscoll, and D. R. Ireland, Eds., American Society for Testing and Materials, Philidelphia, © 1987, pp. 144-162, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. The utility of these two variations has been shown previously by Delfosse et al. (1995) whereby the quasi-static deflection and indentation experiments provide the lower and upper bounds respectively of the force-displacement plot of an impact event as shown in Figure 2-7 below. It is seen that the force-displacement curve of the quasi-static deflection experiment has the lowest slope due to the steady nature of quasi-static loading and the ability of the sample to fully develop its bending response so as to be more compliant. In contrast to this is the quasi-static indentation curve that has the highest slope because it is not able to deflect. Its only form of compliance is through local shear and compressive deformation & damage of the material. The high mass (low-velocity) impact is seen to have a small initial peak as the impact initiates, however the load quickly drops due to panel bending and the curve largely follows the quasi-static deflection curve. The low mass (high-velocity) curve however, has a very high initial contact force (nearly 8000 N) due to the inability of the sample to quickly bend away. The load 36 then does drop and largely follows the quasi-static deflection curve, but only after the loading curve has followed the quasi-static indentation curve for a substantial amount. Figure 2-7 Effect of impact regime of the force displacement response (initial stiffness increase during high-velocity impact case); reproduced, with permission from Delfosse, D., Poursartip, A., Coxon, B.R., and Dost, E.F., “Non-Penetrating Impact Behavior of CFRP at Low and Intermediate Velocities,” Composite Materials: Fatigue and Fracture—Fifth Volume, ASTM STP 1230, R. H. Martin, Ed., American Society for Testing and Materials, Philadelphia, © 1995, pp. 333-350, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428. 2.2 Structural response According to (Davies and Olsson 2004; Abrate 1991, 1994, 1998) the structural response of the impacted plate is a complex interaction of: • linear-elastic deformation o in-plane dilatational (including membrane effects) o through-thickness dilatational o out of plane shear distortional o flexural • damage/permanent deformation due to excessive linear-elastic deformation exceeding material strengths: 37 o matrix cracks o fibre cracks o delaminations o matrix deformation • local damage/permanent deformation due to indentation caused by compressive and shear failure The order in which the linear-elastic deformation mechanisms occur relative to each other is important in determining which stresses will reach the material strengths first, and determines when and to what extent these various damages will occur in the impacted structure (Abrate 1991). Inelastic deformation and fracture also occur at finite speeds, and therefore the rate of loading has an impact on the response of the material, resulting in strain rate dependent material properties like stiffness and strength (Wang 2007). The damage that occurs within the impacted structure results in changes to local material stiffness, which in turn affects the structural stiffness, deformation and load paths at later stages in the impact sequence, and therefore this problem is path dependent. For example, as the plate deflects further (more than one thickness of the plate itself) the effect of membrane stiffness due to geometrical non-linearity becomes influential to the dynamics of the impact (Abrate 1991). This has the effect of making the plate stiffness to transverse loading increase if there is enough deflection before substantial damage occurs and will increase in-plane tensile loads of fibres and the matrix, possibly causing tensile fracture. Other effects related to the kinematics of the impactor are also important in determining the structural response. It has been noted by Morita et al. (1997) that for an equivalent impact energy, reducing the mass of the impactor and increasing its velocity has the overall effect of 38 reducing its momentum. Therefore, the reduction in momentum is at least partly responsible for the impactor not being able to accelerate the entire structure in the same way that a high mass/low-velocity impactor would. The result being that with less of the structure deflecting (or the whole structure deflecting less), a greater percentage of the impact energy must create local damage near the impact site instead of being elastically stored and released elsewhere in the structure. This increase in apparent stiffness of the structure with increasing impact velocity has been seen in many studies (García-Rodríguez et al. 2018; Bull, Spearing, and Sinclair 2015; Delfosse et al. 1995). From the above it is clear that the structural response in terms of load-time or load-displacement relations is complex and affected by many factors. As was shown by Delfosse et al. (1995) – see Figure 2-7 – the most readily apparent manifestation of impact regime in the load displacement relation is the slope of the initial loading curve which is initially very steep. This has the effect of causing high interlaminar shear stresses before tensile stress can increase substantially on the backface of the sample, making delamination damage initially more likely compared to in-plane fracture. 2.3 Damage Damage in composite materials is a combination of delamination, matrix cracking and fibre breakage. An example of all three of these in an impacted sample is shown in Figure 2-8a below. Additionally, near the impact site there is localized indentation due to compressive and shear failure of the matrix and fibres brought on by concentrated contact loads (Davies and Olsson 2004). Some of this damage is permanent and will manifest itself visibly as a permanent dent at the impact site. As will be discussed further on in this section, the depth of this permanent dent is highly dependent on the velocity regime of the impact. 39 (a) (b) Figure 2-8 Typical types of damage seen in transversely impacted FRP laminates; (a) micrograph showing cracks extending through the full thickness of layers (both as transverse matrix cracks and fibre fractures) and becoming delaminations (b) schematic diagram for low-velocity impact indicating compressive indentation damage on the front face and tensile damage on the back-face due to flexure of the panel; reproduced with permission (Davies and Olsson © 2004) Excepting the indentation damage, it is the order in which delamination, matrix cracking and fibre breakage occur, and the extent to which they progress that is of most importance for determining the final damage state of the structure (Cantwell and Morton 1985). Cantwell and Morton show this in Figure 2-9 below where the low-velocity impact results in damage occurring primarily on the back of the panel due to tensile overload from flexure (see Figure 2-9a). Conversely if the impact is high-velocity, the lack of back-face loading from flexure means that the high contact stresses initiate damage that starts from the top down (see Figure 2-9b). 40 Figure 2-9 Damage in laminated composites due to (a) flexural stresses (typical of compliant laminates under low-velocity conditions), and (b) contact stresses (typical of rigid laminates under low-velocity conditions or all laminates under high-velocity conditions); republished with permission of Elsevier Science & Technology Journals, from “Detection of impact damage in CFRP laminates”, W. J. Cantwell and J. Morton, Composite Structures, volume 3, pp. 241-257, © 1985; permission conveyed through Copyright Clearance Center, Inc. In the following sections a number of key factors that influence impact damage are discussed with a particular final focus on the fibre architectures of NCF and 2D braid. Matrix Response While many authors have found no strain rate sensitivity of carbon fibre (Davies and Olsson 2004; Cantwell and Morton 1991; J. Harding 1989), many authors (Koerber, Xavier, and Camanho 2010; Hsiao, Daniel, and Cordes 1999; M V Hosur et al. 2001; Tsai and Sun 2005) have noted a rate sensitivity of epoxy matrices. As just one example; Koerber, Xavier, and Camanho (2010) found that when dynamically loading a unidirectional sample of IM7-8552 CFRP with a split-Hopkinson bar, the transverse compressive modulus increased by 12%, the yield strength (0.02% offset) increased by 83%, and the compressive strength increased by 45% when compared to their own quasi-static tests. Figure 2-10 shows the stress-strain results of 41 Koerber, Xavier, and Camanho, where these differences between quasi-static and dynamic response of the material can be clearly seen. Therefore, not only is there a structural rate sensitivity owing to the regime of the impact and the ability of the structure to globally deform, but there are also rate sensitivities in the response of the polymer matrix itself. Figure 2-10 Strain rate effect on uniaxial compression of unidirectional IM7-8552 CFRP loaded transversely to the fibre direction; the compressive modulus, yield strength and ultimate strength are all higher under dynamic conditions; Republished with permission of Elsevier Science & Technology Journals, from “High strain rate characterisation of unidirectional carbon-epoxy IM7-8552 in transverse compression and in-plane shear using digital image correlation”, Koerber, Xavier, and Camanho in Mechanics of Materials, Vol. 42, © 2010; permission conveyed through Copyright Clearance Center, Inc. With regard to the permanent dent depth, it is conceivable that this rate sensitivity is responsible for at least part of the lower permanent dent depth seen in high-velocity impact tests (discussed below), but there is always some ambiguity over the role of matrix plasticity & microcracking in the manifestation of damage and the general rubble or debris preventing the return of the material to its original position due to friction. Lemaitre (1992) notes that although plasticity may be considered as almost non-existent at the mesoscale (where damage is generally viewed as cracking); at the microscale some plastic strain always occurs in very small damaged volumes. Therefore, it is likely that any permanent deformation seen in impact tests is largely the result of fracture and relative movement of material and not extensive plastic deformation. This is particularly true when the material is below its heat deflection/glass transition temperature, 42 where relative movement of polymer chains (viscous effects) is largely inhibited (White and Lipson 2016). The higher strength seen in Figure 2-10 due to dynamic loading may play a greater role in reducing permanent deformation at higher strain rates. Krätzig and Pölling (1998) note for brittle/quasibrittle materials “nonlinearities are caused by initiation, growing and coalescence of microcracks leading to debonding as an indication of a damage process”, therefore the differentiation between small scale microcracking and larger scale delamination and generation of rubble is really just a matter of degrees and it is not easy to clearly distinguish the two. Effect of HVI and LVI Impact As discussed previously, the regime within which a given impact falls has a particularly significant effect on the final damage state of the composite. Previous studies on the effects of high velocity impact vs low velocity impact have shown an increase in damage size (as quantified by projected ultrasonic damage area) in high-velocity impact over low-velocity impact (Olsson 2000; Cantwell and Morton 1989; Morita et al. 1997). This appears to be primarily related to the ability of the structure to elastically store impact energy elsewhere and return it to impactor upon unloading as shown in the 150 mm case of Figure 2-11. This results in a lower overall level of damage in the material under low-velocity impact conditions for a given energy level and therefore a higher damage resistance. 43 Figure 2-11 C-scans showing the effect of beam length on the development of damage in 16 ply (0°,±45°) composite: (a) high velocity impact loading; (b) low velocity impact loading; the reduction of damage in (b) with increasing beam length is due to the additional material available for elastic storage of impact energy, but under high-velocity impact (a) this extra material does not affect the damage area as the response is controlled by transient flexural waves and not the boundary; reprinted from Composites, Volume 20, W.J. Cantwell and J. Morton, “Comparison of the low and high velocity impact response of CFRP”, pp. 545-551, © 1989, with permission from Elsevier. With regard to braided materials, Sutcliffe et al. (2012) found that for hybrid glass-carbon 2D braided composites tested with two different impactor masses, the delamination area was larger for the lighter impactor with the same energy (i.e. higher impact velocity). They theorized that this is because under high velocity impact conditions, there is more localized deformation below the impact site, and that as the flexural wave travels from the impact site a wider area sees correspondingly larger curvatures and strains on the backface, resulting in larger delamination damage. 44 Delamination, Free-Edge Effects & the Effect of Stiffness Mismatch Between Plies It is widely recognized in the literature that delaminations under transverse impact conditions are primarily caused by interlaminar shear stresses (Davies and Olsson 2004; Olsson 1993; Bibo and Hogg 1996; Abrate 1994; Cantwell and Morton 1991). The delaminations are often initiated and transferred between layers by matrix cracks (see Figure 2-8a). For low-velocity impact (where flexure plays a major role), these cracks are often induced by stresses that arise due to ply stiffness mismatch (Hong and Liu 1989). Hong and Liu found larger delamination areas were correlated with larger changes in orientation angle between adjacent plies, indicating that larger changes in the in-plane orthotropic stiffness parameters results in greater structural demands on the matrix to redistribute and reorient stresses into the fibre direction of each ply. Liu (1988) states that the material properties of a composite are anisotropic and inhomogeneous and that it is both of these factors that give rise to material property mismatching in composite materials. Inhomogeneity refers to the separate matrix and fibre constituent materials that have very different properties, and anisotropy refers to the varying orientation of the fibres in a laminate. This causes non-uniform stress distributions in the laminate when loaded owing to the elastic constraint induced on each other by neighbouring plies. This elastic constraint is transmitted via interlaminar shear stress. When the shear stress becomes sufficiently large, the energy available can overcome the mode II fracture energy release rate and cause initiation of delamination or propagation of delamination. Liu (1988) also posits that delamination area is proportional to the bending stiffness mismatching coefficient, M, between two plies which he calculates based on the difference in the bending stiffness in the primary direction (D11) between adjacent layers divided by the difference in the bending stiffness between two layers oriented at 90° to each other. Liu states that the larger 45 the value of M, the larger the area of delamination in that interface will be due to the larger bending stiffness mismatch. He justifies this based on the observation that unidirectional plates loaded transversely tend to bend concave locally along the fibre direction and convex locally along the transverse direction, thus when loaded transversely the lamina tend to pull apart in some locations (when this effect combines to cause relative displacement apart from each other) and push together in other locations (when this effect combines to cause relative displacement towards each other). Morita et al. (1997) point out that if one considered two layers of a uni-directional laminate at slightly different positions through the thickness of the laminate, they would have mis-matched bending stiffness coefficients owing to their different relative positions from the centroid of the laminate cross-section. However, it is generally understood that unidirectional laminates don’t tend to develop large delaminations owing to alignment and intermingling of fibres between layers. Based on this, Morita et al. (1997) proposed a stacking parameter, 𝛽𝛽, based on the difference of in-plane stiffness of adjacent plies rather than flexural stiffness. Their proposed parameter also considers the mismatch of in-plane stiffness through a 360° sweep by integrating the mismatch across all orientations while also considering distance from the neutral axis of the laminate and overall laminate bending stiffness as a function of orientation. Morita et al. (1997) state (much like Liu) that this parameter represents the amount of “bending stress discontinuity at [the] interlaminar interface and… the larger the parameter 𝛽𝛽, the larger the impact damage area.” Critically, because this parameter is based on the difference in in-plane stiffness across an interface, and it is the elastic constraint caused by the difference in in-plane stiffness between layers that gives rise to interlaminar shear stress, this parameter 46 provides a key insight into the generation of interlaminar shear stress caused by bending, in addition to the direct shear stress. In addition to stiffness mismatches throughout the structure at various interfaces, another complex phenomenon leading to delamination can occur at any free-edge of the laminate, whether the free edge is the edge of a panel, a hole in a panel or a crack in a panel (Miracle and Donaldson 2001). Free edge effects are fundamentally a manifestation of stress equilibrium resulting in a change to interlaminar stresses present near the edge of a lamina. This is because both the intralaminar normal stress perpendicular to the edge, and intralaminar shear stress must be zero at a traction-free edge (neglecting local inertial effects). In the case of transverse impact, intralaminar stress can be considered as coming from either bending stress, or membrane stress if the deflection is significant enough. (Liu and Malvern 1987; Fuoss, Straznicky, and Poon 1994). The result is that the intralaminar stress is redistributed into the through-thickness direction. Miracle and Donaldson (2001) use the example of a [0/60/-60]S laminate shown in Figure 2-12a loaded in the x-direction. They state that due to Poisson ratio mismatching between the 0° and ±60° plies, y-direction stresses are generated in each ply. Additionally, due to extensional-shear coupling, intralaminar shear stresses are also generated in the plies. Since these stresses must all be zero at the traction-free boundary (y=±b), equilibrium requires that the interlaminar normal stresses shown in Figure 2-12 b & c develop. These stresses are tensile between the 0° and 60° plies, and compressive between the 60° and -60° plies. Regarding the intralaminar shear stresses, these become counteracted near the boundary by interlaminar shear stress as shown in Figure 2-12d. 47 (a) (b) (c) (d) Figure 2-12 Free edge effects in (a) [0/60/-60]S laminate produce (b) tensile and compressive interlaminar normal stress couples near free-edges that can result in (c) tensile interlaminar normal stress at the edge, producing a peeling effect that leads to delamination, and (d) interlaminar shear stress that leads to delamination; Republished with permission of ASM International, from “Macromechanics Analysis of Laminate Properties”, Miracle and Donaldson, ASM Handbook, Volume 21: Composites, © 2001; permission conveyed through Copyright Clearance Center, Inc. It is important to note that both the general elastic constraint between plies throughout the laminate, and the free-edge effects arise due to orthotropic stiffness and Poisson ratio mismatching between plies, and therefore these effects do not occur on the macroscale if the different fibre directions are integrated within a single ply, such as in braided materials. 48 Damage in NCF Materials Asp, Varna, and Marklund (2011) note that in NCF composites the damage occurs at different scales in the composite including intralaminar matrix cracks at the micro and meso (tow level) scales, fibre fractures and delaminations. They also note that both the mode I and mode II delamination progression processes are largely the same as what is observed in conventional tape-based composites, but are to some extent affected by the reinforcement architecture of the NCF material. They note that due to the stitching yarn, delamination growth within an NCF blanket (between layers that have been stitched together) is retarded to some extent. Instead, the delamination preferentially occurs in-between separate blankets where the delamination crack does not encounter any z-direction (through thickness) stitching. Pickett (2011) agrees with this assessment that through-thickness stitching leads to a higher fracture toughness of the material within each blanket, but confirms that delamination in these regions is still possible. He further notes that the resin-rich regions between the blankets are particularly prone to delamination, possibly owing to the size of the resin rich region which may be locally thicker due to stitches crossing the surfaces of the blankets. It has also been shown by Edgren, Asp, and Bull (2004) that many of the delamination regions seen in NCF materials are of a rectangular shape that is representative of the stitching geometry rather than the “peanut” shape of impact delaminations often seen in tape-laid composite panels subjected to impact (Davies and Olsson 2004). This suggests that even if the mesoscopic level stitch reinforcement does not inhibit delamination development entirely, they at the very least can redirect delaminations and may contain them within several discrete tow widths. This is substantially similar to how “ripstop” fabrics work by making use of reinforcing filaments at regular intervals. 49 Additionally, García-Rodríguez et al. (2018), carried out quasi-static and low-velocity impact tests on thin NCF laminates (2.2mm thick – similar to the laminates in this work) with ultrasonic inspection and x-ray computed tomography scanning to investigate the damage. The standard ply thickness laminate had a layup of [(45/0)/(-45/90)]2S and were made with Chomarat’s T700 GC carbon bi-axial NCF with HexFlow RTM6 epoxy resin applied using the RTM process. They used a 16mm diameter hemispherical indenter with the standard 100 mm x 150 mm specimen on the rectangular cutout. The CT results indicated that one or several of the load drops observed during quasi-static deflection or low velocity impact corresponded to fibre failure that was localized in the lower half of the laminate (away from the impactor) as shown in Figure 2-13. Figure 2-13 Impact damage in NCF laminate subjected to low-velocity impact showing localization of damage to the backface of the laminate; republished with permission of Elsevier Science & Technology Journals, from “A 3D tomographic investigation to elucidate the low-velocity impact resistance, tolerance and damage sequence of thin non-crimp fabric laminates: effect of ply-thickness”, Garcia-Rodriguez et al., Composites Part A: Applied Science and Manufacturing, Volume 113, PP. 53-65, © 2018 This type of damage initiation on the lower surface and progression towards the upper surfaces has been mentioned in numerous literature and is often associated with compliant laminates under low-velocity impact conditions (Cantwell and Morton 1985; Abrate 1991). This effect is shown schematically in Figure 2-9a where the flexure of the laminate results in matrix and potentially fibre cracks in the lowermost layer. Once this crack propagates up to the first 50 interface it deflects into a delamination and extends outwards from the impact site. The delamination then becomes deflected upwards to follow other matrix cracks and this process continues, resulting in an inverted “pine tree” (Bibo and Hogg 1996) pattern of damage beginning at the back surface. If the laminate is sufficiently rigid or the impact velocity sufficiently high so as to produce “high-velocity impact” conditions, then the damage pattern generally follows Figure 2-9b where local high contact stresses produce matrix and fibre cracking at the impact site which similarly forms interlaminar delaminations once they reach the first interface. This spreads out until it is deflected into lower plies by means of matrix shear cracking, and so on (Cantwell and Morton 1985). Damage in 2D Braided Materials Sutcliffe et al. (2012) studied damage in biaxial 2x2 bias braid with varying ratios of carbon and fiberglass tows (including fully carbon) loaded with a 12.5 mm diameter hemispherical indenter under quasi-static, low-velocity impact and high velocity impact. They found that the damage area was roughly circular in shape around the impact site. The damage area was found to increase roughly linearly with the impact energy, but was found to be substantially larger in the high energy, high-velocity case. 51 Figure 2-14 Effect of impact energy on measured damage area using C-scanning (divide by 4.34 for J/mm); damage area is similar between LVI (heavy mass) and HVI (light mass) for the ~3.2J/mm case, but at higher energy levels the HVI impacts show larger damage area; reproduced under Creative Commons CC-BY license, from “Moderate speed impact damage to 2D-braided glass–carbon composites”, M.P.F. Sutcliffe et al., Composite Structures, volume 94, pp. 1781-1792, © 2012. With regards to permanent dent depth, the dent depth was found to also vary linearly with impact energy, and dents were much smaller in depth for the high-velocity case as compared to the low velocity case for the 100% carbon samples as shown in Figure 2-15. Figure 2-15 Effect of impact energy on measured (permanent) dent depth using profilometry (divide by 4.34 for J/mm); permanent dent depth for LVI (Heavy) is substantially more than for HVI (Light); reproduced under Creative Commons CC-BY license, from “Moderate speed impact damage to 2D-braided glass–carbon composites”, M.P.F. Sutcliffe et al., Composite Structures, volume 94, pp. 1781-1792, © 2012. 52 Optical images of a fully carbon braided sample subjected to a low-velocity impact was an energy level of 7.4 – 8.0 J/mm of thickness are shown in Figure 2-16. Substantial tow fibre fracture can be seen in this region below the impact site. Figure 2-16 optical micrograph of 2D biaxial braid CFRP subjected to low-velocity impact between 7.4 and 8.0 J/mm showing substantial matrix and fibre fracture; reproduced under Creative Commons CC-BY license, from “Moderate speed impact damage to 2D-braided glass–carbon composites”, Sutcliffe et al., Composite Structures, volume 94, pp. 1781-1792, © 2012. In their low-velocity impact experiments Hosur et al. (2009) found that triaxially braided 2D fabrics performed substantially better than the biaxially braided fabrics (such as Sutcliffe et al.) due to the presence of the un-crimped 0° tow. They used 100 mm x 100 mm samples, that were between 2.25 mm and 2.40 mm thick, with a 12.5 mm diameter hemispherical indenter (all parameters substantially the same as this work) and a 6.62 kg crosshead drop tower. The fibre and resin were T-700 and SC-15 epoxy resin. For a 0/±60 laminate similar to that of this work, they found that at 4.3 J/mm of thickness, the sample responded elastically with no damage. At an energy level of 8.6 J/mm of thickness, the average delamination area was 40 mm2 and there was some back-face damage in the form of an axial crack. For an energy level of 12.9 J/mm of thickness, the average delamination area was 219 mm2 and there was backface splitting damage. They commented that the damage was localized to the impact site due to the interlacing nature of the tows. Once a tow had been completely fractured, the load carried by that tow would be transferred to a tow running in the other direction and therefore the damage is not allowed to 53 propagate easily across the width of the laminate as it would do in the case of a conventional tape-laid laminate, but rather the damage spreads through the thickness. This localization of damage results in improved residual mechanical properties. Roberts et al. (2005) carried out impact testing on triaxially braided 0/±60° carbon fibre (Toray T700) panels infused with a toughened epoxy system (Hexcel M36). The panels were composed of 6 layers of triaxial braid, with all the 0° tows aligned between layers and the panels had a thickness of 3.2 mm. They found similarly to Hosur et al. that damage was highly localized to the impact site and no delamination damage was experienced. The damage appeared to be fibre and matrix fracture beginning on the backface of the laminate, opposite where the impactor has struck as shown in Figure 2-17 b & c below. Roberts et al. believe that the reason for the lack of delamination was because the interlaminar stresses within the panel during impact are small due to each ply being quasi-isotropic within itself; however, it is important to note that their material has a 24k 0° tow and 12k ±60° tows, and so is not strictly quasi-isotropic, but all three directions are braided into a single ply, with all plies aligned, so quasi-isotropy may not the most important parameter affecting delamination resistance, but rather the lack of stiffness mismatch between layers. 54 Figure 2-17 Visible impact damage in triaxially braided CFRP panel subjected to sub-perforation impact (a) front side (b) back side (c) close-up of fibre fracture on back side; the authors found that the damage was highly localized to the impact site and no substantial delamination was experienced; Republished with permission from the American Society of Civil Engineers (ASCE), from “Ballistic Impact of Braided Composites with a Soft Projectile”, Roberts et al., Journal of Aerospace Engineering, volume 18, pp. 6, © 2005; permission conveyed through Copyright Clearance Center, Inc. In general the results have shown that transverse impact in braided materials tends to result in highly localized damage with a significant amount of matrix and fibre fracture resulting in improved toughness over conventionally tape-laid counterparts at the expense of a reduced in-plane properties (Bibo and Hogg 1996). 2.4 Numerical Modelling Compared to classical laminate plate theory, finite element (FE) modelling provides the ability to accurately model the response of a structure well beyond first-ply failure by utilizing progressive damage models that allow the nonlinear inelastic response to be modelled all the way to ultimate failure (Reiner and Vaziri 2018). This makes FE models advantageous for impact damage simulations where it is critical to capture progressive damage in order to understand the level and extent of damage for further analysis under in-service loads (damage tolerance). Generally, finite element damage models for composite materials can be classified into two main types: 55 • Continuum damage mechanics (CDM), and • Discrete damage mechanics Continuum damage mechanics models operate on the basis of reducing the stiffness of a homogenous element of material in accordance with the predicted effects of stress or strain on the damage state of the material. Therefore, they do not have to model all geometric features of the microstructure, or the change in mesostructured brought about by fracture. This makes them computationally efficient and suitable for modelling large structures (Forghani et al. 2015). Discrete damage mechanics can improve simulation accuracy by bringing some representation of the discrete composite architecture into the simulation. This has the benefit of improving the accuracy of crack propagation direction at the expense of computational effort and set up time to configure the model with this additional complexity (Reiner and Vaziri 2018). The cohesive zone method is a particular type of discrete method suitable for modelling energy dissipation caused during fracture, and it is particularly useful for modelling delamination because the interfaces where the fracture may occur are already known in advance (Reiner and Vaziri 2018). By incorporating cohesive zones, the ability to model delamination is provided since the nodes of adjacent layers are able to move relative to each other and separate while gradually dissipating the energy associated with fracture. Additionally, two temporal discretization methods are available for finite element analysis: implicit and explicit methods. Implicit methods are unconditionally stable and can be used to model problems over large time scales, but they may not reach convergence if the problem is highly nonlinear. Explicit methods are only conditionally stable and must use small timesteps that meet the requirements of the Courant-Friedrichs-Lewy condition to ensure stability (Courant, Friedrichs, and Lewy 1967). This makes them computationally expensive for 56 long duration problems, but they are often the only solution for highly non-linear problems, since convergence is guaranteed. For high-speed, dynamic problems with short durations and large amounts of damage, the explicit method is most appropriate (Reiner and Vaziri 2018) UBC Composites Damage Model 2 (CODAM2) In this thesis, the CODAM2 intralaminar progressive damage model implemented in LS-DYNA (an explicit solver) is used to run impact damage simulations of the NCF coupon to compare with the experimental results. CODAM2 is the second implementation of the UBC Composites Damage Model. The original implementation of this composites damage model – known as CODAM – was developed by Williams et al. (2003). CODAM is an orthotropic linear elastic model with a strain-based damage progression formulation implemented using continuum damage mechanics. It applies damage by degrading the two in-plane principal direction modulii and the in-plane shear modulus of each element as a function of the orthotropic strains through equivalent strain functions (Williams et al. 2003). More recently, Forghani et al. (2013) implemented the updated CODAM2 model into LS-DYNA as MAT219 ("LS-DYNA Keyword User's Manual - Volume II - Material Models" 2017). CODAM2 provides a non-local regularization scheme to eliminate mesh-sensitivity that can artificially skew the damage propagation and extent based on the orientation of the mesh used. It also utilizes equivalent strain functions (and by their extension, damage functions) that consider the orientation of the layers within a sublaminate to more accurately predict damage and the preferential direction of damage propagation along local lamina principal orthotropic directions (Alireza Forghani et al. 2013). 57 Chapter 3: Experimental Methodology The experiments undertaken for this research can be broadly broken out into: • Material characterization • Transverse loading experiments, and • Damage characterization The material characterization experiments provide physical and mechanical data that is used subsequently in the modelling stage of this research. Transverse loading experiments are the primary experiments of this thesis and are used to induce damage into the coupons for further study. Damage characterization uses methods such as ultrasonic inspection and x-ray computed tomography to study the damage that is present after the transverse loading experiments. The methodology for these segments of research is discussed further below. 3.1 Material Characterization Material characterization is critical for modelling of the impact scenarios as it provides the numerical values to be assigned to the material model that is then subjected to an impact event. Subsequent model validation will then show whether the material properties from this testing – in combination with the assumptions made in the creation of the model itself – provide a reasonable approximation of what occurs in a structure during its actual transverse loading. The samples in this work are impact tested as-is at laboratory conditions (room temperature and humidity) without preconditioning and so the material is also characterized at laboratory conditions. Additionally, the effects of process variability, defects, residual stress, aging and degradation are not included in this study. Material characterization is based on the average response with outliers removed where appropriate. 58 Material characterization tests are broadly broken down into general tests (including laminate density and laminate stack-up characterization), intralaminar mechanical tests, and interlaminar mechanical tests. For the purpose of material characterization nomenclature, the x and y directions of the laminate are used to refer to in-plane directions where the x-direction is parallel to the fibres designated as the 0° direction, and the y-direction is parallel to the designated 90° direction. This is shown in 3-1 & 3-2 below. The z-direction is considered out of plane. Figure 3-1 NCF sample with x and y directions marked for reference Figure 3-2 2D braid sample with x and y directions marked for reference General Material Characterization Tests The samples were provided in a prefabricated condition without detailed information on their composition. For this reason, several general characterization tests were necessary including density measurement, relative ply thickness measurement and ply orientation measurement. Having an accurate understanding of the layup schedule is key to the numerical modelling efforts. X-direction Y-direction X-direction Y-direction 59 3.1.1.1 Physical Inspection Physical inspection of the samples was made to identify sample dimensions such as thickness, as well as the size of mesoscale structural feature such as tow width in the NCF material and unit cell size in the braided material. 3.1.1.2 Density The method used for measuring the density of the composite samples was the ASTM displacement method (ASTM D792-13, 2013). By comparing the apparent mass of the sample in both air and water, the density of the coupon was calculated. A Prescia EP 1255M balance with a displacement method kit was used to automatically calculate the density based on mass measurements of samples both immersed in water and not immersed in water. 3.1.1.3 Ply Thickness Measurement The supplier of the material provided nominal information that the panels consisted of a [0/60/-60] layup, but the exact configuration of the laminate was not given. For this reason, a burn-off technique was used to separate the plies. Samples of approximately 50 mm x 33 mm were cut from both the NCF and 2D braid material, placed in a metal foil tray and heated in a muffle furnace. The thermal profile used to burn off the matrix was aimed at gradually decomposing the matrix material without resulting in a fire. The thermal profile consisted of placing the sample into a furnace at 375°C for one hour followed by heating at 425°C for 20 minutes and 450°C for 20 minutes. The samples were then removed from the furnace and allowed to cool, after which the plies were carefully separated. After separating the plies it was possible to measure the approximate ply thicknesses (smaller than actual ply thickness due to the removal of matrix material during the burn-off) and the mass of the plies for the given sample 60 size (again, less than actual due to loss of material). By comparing the mass and thickness of each layer it was possible to determine the stack-up sequence of the laminate. 3.1.1.4 Ply Orientation Measurement Inconsistencies found during the numerical modelling portion of this work indicated that the orientation of the 60° and -60° plies in the NCF coupons was probably not exactly ±60°. This was inferred from the inability to accurately back-calculate lamina level properties from laminate level properties when using the nominal 60° angle. To more accurately determine ply orientations, CT scan data (discussed in Section 3.3.3) was used to measure the relative angles between the 0° plies and the nominally ±60° plies for a number of NCF coupons. The average measured value of ply angle was then used for subsequent numerical analysis. Intralaminar Mechanical Tests Intralaminar experiments provide data that was used to complete the material model card in numerical simulations. A summary of the parameters and the experiments from which they were derived are shown in Table 3-1 below. Table 3-1 Intralaminar material characterization experiments Parameter Symbol Test Tensile modulus in x direction 𝐸𝐸𝑥𝑥 ASTM D3039 Tensile Test Tensile modulus in y direction 𝐸𝐸𝑦𝑦 Tensile initiation strain in x direction 𝜀𝜀𝐼𝐼,𝑥𝑥 Tensile initiation strain in y direction 𝜀𝜀𝐼𝐼,𝑦𝑦 Poisson ratio xy 𝜈𝜈𝑥𝑥𝑦𝑦 Poisson ratio yx (not independent) 𝜈𝜈𝑦𝑦𝑥𝑥 Flexural modulus in x direction 𝐸𝐸𝑓𝑓𝑓𝑓,,𝑥𝑥 ASTM D7264 4-Point Bend Flexural modulus in y direction 𝐸𝐸𝑓𝑓𝑓𝑓,𝑦𝑦 Intralaminar shear modulus 𝐺𝐺𝑥𝑥𝑦𝑦 ASTM D5379 Iosipescu Shear Test Intralaminar shear strength 𝑆𝑆𝑥𝑥𝑦𝑦 Intralaminar tensile fracture toughness in x direction 𝐺𝐺𝑐𝑐,𝑥𝑥𝑇𝑇 Overheight Compact Tension Intralaminar tensile fracture toughness in y direction 𝐺𝐺𝑐𝑐,𝑦𝑦𝑇𝑇 61 The only test not covered by an ASTM standard is the overheight compact tension test that is used to characterize the intralaminar fracture toughness of the material. This test uses a notched sample (see Figure 3-3) loaded eccentrically in order to cause intralaminar damage in a controlled manner that is used to characterize the progression of damage. Further details on this test geometry and procedure can be found in Kongshavn and Poursartip (1999). Figure 3-3 Geometry of the overheight compact tension specimen developed by Kongshavn and Poursartip (1999) Interlaminar Mechanical Tests Interlaminar experiments provide data that was used to complete the tiebreak contact card (see Section 5.2.1.3) and includes interlaminar shear strength and fracture toughness. A summary of the parameter and the experiments from which they were derived are shown in Table 3-2 below. 62 Table 3-2 Interlaminar material characterization experiments Parameter Symbol Test Interlaminar shear strength in xz direction 𝑆𝑆𝑥𝑥𝑥𝑥 ASTM D2344 Short Beam Shear Interlaminar shear strength in yz direction 𝑆𝑆𝑦𝑦𝑥𝑥 Mode I interlaminar fracture toughness 𝐺𝐺𝐼𝐼𝑐𝑐 ASTM D5528 Double Cantilever Beam Mode II interlaminar fracture toughness 𝐺𝐺𝐼𝐼𝐼𝐼𝑐𝑐 ASTM D7905 End-notched Flexure 3.2 Transverse Loading Experiments The transverse loading tests carried out in this work are primarily based on the ASTM standards “Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event” (ASTM D7136-15, 2015) and “Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer-Matrix Composite to a concentrated Quasi-Static Indentation Force” (ASTM D6264-17, 2017). The tests as conducted were a hybrid of these two tests methods in order to ensure consistency of test conditions (impactor diameter, shape of supporting boundary, etc.) between the quasi-static and impact tests. A summary of the five transverse loading experiments are shown in Table 3-3 below. Further details on each experiment are described in this section individually. 63 Table 3-3 Parameters of test apparatus used for transverse loading experiments Designation Impact Regime Equipment Facility Impactor Mass (g) Velocity Range (m/s) Data Recorded Quasi-static Indentation QS Load Frame UBC N/A 2.1E-5 Load & Displacement Quasi-static Deflection QS Load Frame UBC N/A 2.1E-5 Load & Displacement Low-Velocity/High Mass LVI Drop Tower DLR 2818 1.3-3.0 Load & Displacement Low-Velocity/Intermediate Mass LVI Gas Gun UBC 438 4.0-9.5 Load & Displacement High-Velocity/Low Mass HVI Gas Gun DLR 4.75 39.7-85.3 Displacement Sample Geometry The samples used for all transverse impact experiments (with the exception of quasi-static indentation) are square samples 100 mm x 100 mm in planar dimensions and are shown in Figure 1-5 & 1-6. This is modified slightly from the 150 mm x 100 mm standard sample size specified in “Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event” (“D7136-15" 2015). This modification was necessary to increase the number of samples that could be cut from the limited number of 305 mm x 305 mm panels provided. This allowed for 9 samples to be cut from each panel instead of 6. Since the minimum distance from the impact site to the supported edge remains unchanged (37.5 mm), the effect of this dimensional change on the overall impact dynamics is not substantial because the effect of closest boundary will be the one to discriminate an impact event between low-velocity impact or high-velocity impact as discussed in Section 2.1. 64 The quasi-static indentation samples used were smaller offcuts of material. Since the sample is fully supported during this test and cannot bend, a full size 100 mm x 100 mm sample is not necessary. Support Fixture A drawing of the aluminum fixture used in all experiments – except the quasi-static indentation experiments – is shown in Figure 3-4 below. The size of the cutout in the aluminum is 75 mm x 75 mm and the specimen is fully supported around its perimeter with the exception of a 9.5 mm wide band at the center of two edges to allow for instrumentation to view the backface of the sample. (a) (b) Figure 3-4 (a) front view of transverse loading specimen fixture; (b) side view of transverse loading specimen fixture The ASTM standard for damage resistance using a drop weight (ASTM D7136-15, 2015) provided the basis for this fixture design including the square edged cutout shape and the four perimeter toggle clamps with rubber feet for holding the sample lightly in contact with the fixture prior to the test. The cutout dimensions of 75 mm x 75 mm used here are modified from those of the standard (75 mm x 125 mm) to allow for sample sizes of 100 mm x 100 mm. 65 For the quasi-static indentation tests the sample is supported on a hard, flat surface made from silicon carbide, beneath which sits a rigid steel plate. This configuration provides a stiff elastic foundation that minimizes global deflection of the sample. Impactor/Indenter All impactors/indenters (hereafter referred to as impactors) have a hemispherical tip shape with a diameter of 12.7 mm and are shown in Figure 3-5 below. Figure 3-5a shows the steel impactor used in all experiments except the HVI experiments. This steel tip is threaded onto either a load frame for the quasi-static tests, or the remainder of the mass and load instrumentation for the LVI tests. Figure 3-5b shows the titanium ball bearing used for the HVI experiments. Titanium was chosen for its high hardness (to prevent permanent deformation), stiffness (to minimize elastic deformation and energy absorption) and low density (to minimize mass in order to maximize velocity for a given energy level). The diameter of the impactor was chosen as 12.7 mm for several reasons, including: • The ASTM standard for quasi-static indentation (ASTM D6264-17, 2017) requires a hemispherical tip with a diameter of 13.0 mm [0.50 in]. 0.50 in is equivalent to 12.7 mm. • In order to meet the quarter-plate-mass criterion for high-velocity impact (Olsson 1993, 2000), a titanium sphere with a diameter of 12.7 mm gives an impactor with a mass just below that of a quarter-plate with 75 mm x 75 mm sides (the size of the unsupported region of the plate); thus making it possible to achieve high-velocity impacts. • Steel impactors of this size were already available, and titanium ball bearings of this size were an “off-the-shelf” purchase. 66 (a) (b) Figure 3-5 (a) Steel hemispherical impactor used for all tests except high-velocity/low mass; (b) Titanium hemispherical impactor used for all tests except high-velocity/low mass Quasi-static Transverse Loading The quasi-static experiments are unique amongst the transverse loading experiments in that two separate boundary conditions are investigated: Fully supported plate (quasi-static indentation) and simply supported perimeter (quasi-static deflection). Both of these experiments are very useful in understanding the bounds of the response of the plate due to their ability to emulate the limiting cases of impact as described in Section 2.1. 3.2.4.1 Equipment Utilized A 100kN Instron 5982 load frame was utilized to provide the compressive load onto the samples while acquiring load and displacement measurements. The quasi-static indentation and quasi-static deflection configurations are shown in Figure 3-6a and Figure 3-6b below. The supporting conditions are as described in Section 3.2.2. 67 (a) (b) Figure 3-6 (a) Quasi-static indentation of a 2D braid sample showing the 12.7 mm spherical impactor, steel and carbide support plates and clip gauge; (b) Quasi-static deflection of a sample showing the 12.7 mm spherical impactor, aluminum fixture with clamps, and clip gauge 3.2.4.2 Measurements For both variations of this experiment the load and displacement of the impactor tip is recorded in intervals of 0.1 seconds during the test. This displacement is measured using a clip gauge that is secured between a fixed support on the base of the machine and the impactor assembly so that movement of the impactor is recorded without being affected by displacements of the load frame itself. Low-Velocity/High Mass Transverse Impact The low-velocity/high mass transverse impact tests are conducted using a drop tower with the heaviest impactor mass of the three transverse impact experiments. The following sections outline the equipment used and the measurements made. 3.2.5.1 Equipment Utilized This drop tower is located at the DLR Institute for Structures and Design in Stuttgart, Germany and is shown in Figure 3-7 and Figure 3-8. It is a guided drop tower composed of four steel rods mounted in a square array within which the cylindrical drop mass traverses. The steel 68 rods are supported by a steel column (painted red in Figure 3-7 and Figure 3-8) which has been bolted on top of the support fixture that holds the sample to be impacted (the same fixture as discussed in Section 3.2). To accommodate 3D DIC measurements of the bottom surface of the coupon, the drop tower assembly is placed on top of the crosshead of a large 4-post universal test machine. The crosshead has a large circular opening in the middle that allows for the coupon to be viewed from below. The impactor was held at a pre-determined height with an electromagnet, which, when de-energized allowed the impactor to travel down the tower and impact the sample. A pair of wires on either side of the impactor – initially slack – were manually held taught after the initial impact in order to catch the impactor prior to it making a second impact. Details of the measurements systems are discussed further below. Figure 3-7 Drop tower assembly mounted on crosshead of 4-post universal test machine with high speed cameras positioned to record displacement Figure 3-8 Close-up view of drop test mass suspended above impact sample. The force transducer is visible (attached to green wire from left) between the impactor tip and the bulk of the drop mass above Drop Tower 2D DIC Camera 3D DIC Cameras 69 3.2.5.2 Measurements The force measurements are made using a Kistler 9021A piezoelectric force sensor with the signal conditioned into a voltage output with a Kistler 5011 charge amplifier. The force transducer is shown in Figure 3-9 below. A custom bolt extends through the center of the washer-like force sensor and secures the impactor tip to the steel mass behind the force sensor, sandwiching the force sensor in the process. This custom bolt is pre-tensioned to ensure that during compression loading, it remains in tension; thereby ensuring that the load-voltage relationship of the sensor remains linear by keeping all components of the assembly in their linear-elastic region. Due to the parallel load paths provided by this bolt and the sensor itself, a custom calibration of voltage to force was necessary. This calibration was made with a Zwick 1475 universal testing machine at DLR between 0 and 10000 N of compression load. During impact, the force sensor only measures the force due to the acceleration of the mass behind it, and therefore the actual impact force on the coupon must be obtained by correcting the measured load according to the following equations (McConnell and Han 1986; Delfosse et al. 1993) 𝐹𝐹𝑖𝑖𝑚𝑚𝑝𝑝𝑖𝑖𝑐𝑐𝑡𝑡 = 𝐹𝐹𝑓𝑓𝑙𝑙𝑖𝑖𝑙𝑙 𝑐𝑐𝑐𝑐𝑓𝑓𝑓𝑓 ∙ 𝐹𝐹𝐷𝐷𝑦𝑦𝑚𝑚𝐷𝐷𝑙𝑙𝑟𝑟 Eq. 3-1 𝐹𝐹𝐷𝐷𝑦𝑦𝑚𝑚𝐷𝐷𝑙𝑙𝑟𝑟 = 1 + 𝑚𝑚ℎ 𝑚𝑚𝑏𝑏⁄ Eq. 3-2 Where: 𝐹𝐹𝑖𝑖𝑚𝑚𝑝𝑝𝑖𝑖𝑐𝑐𝑡𝑡 = the impact force experienced at the contact interface between the impactor and composite sample 𝐹𝐹𝑓𝑓𝑙𝑙𝑖𝑖𝑙𝑙 𝑐𝑐𝑐𝑐𝑓𝑓𝑓𝑓 = the impact force as measured by the load cell 𝐹𝐹𝐷𝐷𝑦𝑦𝑚𝑚𝐷𝐷𝑙𝑙𝑟𝑟 = the dynamic force correction factor 70 𝑚𝑚ℎ = the mass ahead of the force transducer (impact tip) 𝑚𝑚𝑏𝑏 = the mass behind of the force transducer In the case of this drop tower, the mass ahead and behind of the load cell are respectively 77.35g and 2740.70g, resulting in a dynamic correction factor of 1.0282. The force measurements were acquired at 500000 samples per second (10x the acquisition rate of the high-speed cameras for displacement tracking) Figure 3-9 Close-up view of drop tower impactor with in-line force sensor and steel tip with speckle pattern for DIC displacement measurements Displacement of the impactor was measured using 2D digital image correlation (DIC) with images taken from a Photron Fastcam APX camera acquiring images at 50000 frames per second. The Correlated Solutions Vic-2D software was used to track the speckle pattern on the impactor tip over time to provide the displacement vs time record of the impactor. Displacement of the back-face of the sample was also captured by utilizing 3D digital image correlation. To do so, the backface of each sample was hand-marked with a white paint speckle pattern using an Edding brand model 751 paint marker as shown in Figure 3-10. This method was chosen over a more traditional spray paint speckle method due to the tendency for the spray paint to flake off the sample during the impact. In contrast, using the black background of the sample with a discontinuous white paint marker pattern allows for the sample to flex substantially without the failure of the more brittle paint. Two Photron Fastcam SA-Z cameras Force sensor Speckle pattern 71 were used to image the backface of the sample at the same 50000 frames per second rate. The cameras imaged the sample via a front-surface mirror (a piece of glass with the reflective coating on the front side rather than behind the glass to prevent double images due reflection from multiple surfaces) due to constraints in mounting the cameras directly below the samples. Figure 3-10 Backface of transverse impact coupon prior to test with hand applied white speckle pattern The camera and force measurement systems were all triggered manually with a push button switch. Finally, dent depth measurements were made on the coupons after impact with a Faro arm device (as discussed in Section 3.3.1). Low-Velocity/Intermediate Mass Transverse Impact The low-velocity/intermediate mass transverse impact tests are conducted using an instrumented gas gun projectile that travels faster than the drop tower impactor. The following sections outline the equipment used and the measurements made. 3.2.6.1 Equipment Utilized The instrumented gas gun within the UBC Composites Research Network’s lab was utilized for the low-velocity/intermediate mass impact tests. It is a fully contained (projectile is 72 guided at all times), compressed-air powered impact apparatus that is instrumented in order to record impact force and impactor displacement continuously during the test. The device – including its force measurement method – has been extensively described in previous literature (Delfosse et al. 1993, 1995). It is comprised of a large gas reservoir that is charged to the desired pressure, a horizontal barrel within which the projectile travels, and a fast-acting pneumatic relay valve to control the air from the reservoir to the barrel. There is also an adjustable timing mechanism that begins when the gun is triggered. Once the set time is reached, the air supply valve is closed and vent valves open to release gas from the barrel so that only the kinetic energy of the impactor is transmitted to the sample, and there is no additional energy from pressurized gas. Lastly, a recent addition to the gas gun is the Enhanced Laser Velocity System (ELVS) that was previously used in ballistic impact investigations (Starratt 1998; Cepuš 2003; Cepuš and Poursartip 2009). The origins and the method of operation of this device is extensively discussed in Starratt et al. (2000), however, modifications were necessary to fit this device onto the gas gun. These modifications included the manufacture and addition of a barrel extension (adapter) onto the gas gun with a horizontal slit offset from center on both sides for the ELVS beamline to pass through (seen in Figure 3-12), and the design and manufacture of a new impactor shaft for the instrumented impactor (Figure 3-13) having a shoulder feature near the middle of the shaft. This shoulder feature acts as the “free-flying projectile” referenced in Starratt et al. (2000) by fully obscuring the beam prior to the impactor contacting the sample (in order to obtain the minimum, background voltage reading), and then providing the straight rear-edge beyond which the laser is able to pass behind as the projectile continues to move forward and impact the sample. Such a position of the impactor is shown in Figure 3-14, which is a 3D CAD model 73 cross-section through the barrel of the gas gun. The ELVS laser beam can be seen emerging from behind the shoulder feature just as the impactor is making contact with the sample. The location of the force transducer can also be seen in this figure. Details of the measurements systems are discussed further below. Figure 3-11 Overview of the UBC CRN gas gun apparatus with the pressure reservoir in foreground Figure 3-12 Close-up of the impact region of the UBC CRN gas gun showing the ELVS instrumentation, ELVS barrel adapter and sample support fixture with sample loaded Figure 3-13 Instrumented gas gun projectile showing the impactor tip (left), ELVS obscuring shoulder (center, black), and the guiding surface with integral force transducer (right) Figure 3-14 3D CAD model cross-section view of ELVS Barrell adapter region of gas gun showing how the laser beam is intersected by the shoulder of the projectile shaft in order to provide displacement measurements Laser beam Force Transducer 74 3.2.6.2 Measurements The force measurements are made using a PCB Piezoelectrics 208M88 force transducer with the signal conditioned into a voltage output with a PCB Piezoelectrics 484B06 ICP signal conditioner. The location of the force transducer is shown in Figure 3-14. As with the drop tower force transducer, only the force due to the acceleration of the mass behind the transducer is measured, and therefore the actual impact force on the coupon must be obtained by correcting the measured load according to Eq. 3-1 and Eq. 3-2. For this gas gun the mass ahead and behind of the load cell are respectively 213.14g and 223.94g, resulting in a dynamic correction factor of 1.9518. The voltage to force calibration was provided by the manufacturer on a calibration certificate, but this was validated by compressing the sensor in the 100kN Instron universal test machine used in Section 3.2.4. The ELVS systems – as previously described – was calibrated (voltage to position) in-place using a digital micrometer instrument to accurately record the position of the object (a micrometer spindle) blocking the laser beam at several intervals over the ~25mm wide laser beam width. Voltage signals from the force transducer and ELVS systems were recorded with a Tektronix MSO 3034 oscilloscope at a rate of 1000000 samples per second. The trigger for the oscilloscope was provided by the falling edge voltage measurement on the ELVS as the impactor shoulder passed though. Finally, dent depth measurements were made on the coupons after impact with a dial gauge device (as discussed in Section 3.3.1). 75 High-Velocity/Low Mass Transverse Impact The high-velocity/low mass transverse impact tests are conducted using a free-flying projectile having the lightest impactor mass of the three transverse impact experiments. The following sections outline the equipment used and the measurements made. 3.2.7.1 Equipment Utilized For the low mass/high-velocity experiments a free-flying, non-instrumented gas gun is utilized in order to fire the impactor at the samples with similar energy levels to the other experiments, but at much faster velocities (39.7 m/s – 88.7 m/s). This gas gun is located at the DLR Institute for Structures and Design in Stuttgart, Germany and is shown in Figure 3-15 and Figure 3-16. 76 Figure 3-15 free-flying gas gun looking from behind the muzzle towards the sample Figure 3-16 location of high-speed camera for high-velocity experiments As discussed in Section 3.2, a 12.7 mm diameter titanium ball bearing is used as the impactor. This ball bearing is placed into a consumable (one shot per unit) sabot (Figure 3-17) to be fired down the gun barrel. The sabots are comprised of a deep-drawn aluminum cup into which expanded polystyrene (EPS) foam is placed. An appropriately sized burrow is created in the EPS foam into which the ball bearing is placed. When fired, the sabot catcher at the end of the gas gun muzzle stops the sabot (crumpling it in the process) and allows the ball bearing to continue as its own free-flying projectile. The ball bearing passes through two light gates to gauge the impact speed as well as trigger the high-speed cameras to record. After striking the sample, the ball bearing bounces back and falls to the floor where it is retrieved. 2D DIC Camera Sample (back) Light gates Muzzle/ sabot catcher Sample (front) 3D DIC Cameras 77 Figure 3-17 DLR gas gun sabot's (aluminum cup with EPS projectile holder) Figure 3-18 Frame capture from Photron APX camera used for 2D DIC analysis of the projectile displacement 3.2.7.2 Measurements Due to the free-flying nature of the projectile required for this test, there is no measurement of force. Transducers behind the fixture were considered but were ruled to be of no use due to the large inertia of the fixture and the complex system involved in transmission of the stress waves through the sample and fixture to any load cell behind. Like the drop tower experiment, the same three high-speed cameras were utilized. The Photron APX camera was used to capture a back-lit image of the ball bearing striking the sample with a capture rate of 100000 frames per second. Ideally, a higher capture rate would have been used, but this value was arrived at as a compromise between the desire for higher frame rates and the desire for a sufficient field of view. During post-processing, the back edge of the impactor was monitored to determine its position at each frame of the captured video. While it would be technically possible to determine force from double-differentiation of the position-vs-time data, the limited frame rate for an impact with a duration of only 0.3 – 0.5 ms means that there are only 30 – 50 video frames of the impact, and therefore 30-50 displacement data points. This limited number of data points (some of which show no change in projectile Sample Fixture 78 displacement from the neighbouring data point result in extremely noisy and inaccurate force values that cannot be filtered out and still retain reliable data. The Photron Fastcam SA-Z cameras were used to image the backface of the sample at the same 100000 frames per second rate to provide sample displacements. The cameras were placed behind and to the side of the sample to directly image the back of the sample without the need for a mirror as used in the drop tower tests. Finally, dent depth measurements were made on the coupons after impact with a Faro arm device (as discussed in Section 3.3.1). 3.3 Damage Characterization Following the impact events, several studies were made in order to characterize the damage within the coupons. This included the dimensional measurement of the coupons at the impact sites (dent depth measurement), the ultrasonic inspection of the entire coupon with verification of the results through tap testing, and a subset of coupons were inspected with X-ray Computed Tomography (CT) of either the full sample (at low resolution) or more locally of the impact site at higher resolution. Permanent Dent Depth As discussed above, measurements of dent depth were made immediately after the impact events in order to characterize the level of permanent local indentation in the samples. At DLR, a Faro Arm (as seen in Figure 3-19) was available for the low-velocity/high mass and high-velocity/low mass experiments. The Faro arm was used to select three points away from the impact site in order to define a reference plane for the undeformed impact surface. From this reference plane, three measurements were then made at the center of the impact site in order to determine the average depth of the permanent indentation. For the intermediate-velocity/high 79 mass impacts, a digital dial gauge mounted on a truss structure (as shown in Figure 3-20) was used. Similarly, the dial gauge was zeroed out in the region of the sample away from the impact site. The sample was then moved around in a cross pattern below the dial gauge to locate the location of greatest dent depth and a reading was taken. Figure 3-19 Image of a Faro Arm tactile coordinate measurement device used for dent depth measurements during low-velocity/high mass and high-velocity/low mass experiments (Photo credit: CRN; reproduced with permission) Figure 3-20 Digital dial gauge with truss structure used for dent depth measurements during low-velocity/intermediate mass experiments Ultrasonic Scans At both the UBC and DLR facilities, an Olympus Omniscan MX2 ultrasonic system was available for inspection purposes. Both systems were equipped with a “glider” system composed of a 2-axis gantry with positional encoders to allow for spatial raster image scans (c-scans) to be generated. The composite samples were fully submerged in water (ultrasonic coupling agent) and secured to the bottom of the inspection tank with vacuum bag tacky tape to prevent movement. This arrangement is shown below in Figure 3-21. 80 Figure 3-21 Olympus Omniscan MX2 ultrasonic inspection system with displacement encoder The benefit of ultrasonic scanning for damage inspection is that it is very sensitive to all delaminations. Even if the two sides of the delamination remain very close together spatially, there will still be a high impedance to the passage of ultrasonic energy at the composite-fluid boundary of the delamination. This results in a large percentage of energy being reflected early and returned to the ultrasonic transducer, thereby indicating a discontinuity in the material. For this reason ultrasonic inspection provides an excellent projected image of the damage zone, which is useful for determining the outermost boundaries of damage (Abrate 1998). Tap Testing To provide additional assurance on the results of the ultrasonic inspection, tap testing was carried out on samples to identify the extent of the delamination region via another method. The size and shape of the area identified by the tap test was then compared back to the size and shape of the region identified through ultrasonic testing. Tap testing is a simple method of identifying delaminations close to the surface of a composite part. It works by striking the surface of the part gently (so as not to cause further damage) with a light, stiff object (typically a coin, small hammer, or small wrench) and listening to the sound given off. The audible sound can then be interpreted by the inspector as to whether 81 or not a delamination exists below the area that was struck. Areas without delaminations will have a hard, even-pitch sound, whereas areas with delaminations will produce a dull, muffled sound (Elhajjar, Grant, and Ashforth 2019). Computed Tomography Computed tomography scanning of the post-impact samples was carried out at two locations: The DLR Institute of Structures and Design in Stuttgart, Germany; and UBC Okanagan in Kelowna, British Columbia. While ultrasonic examination is very useful for determining the extent of damage in the planar direction, it has limited capabilities for more precise interrogation of the structure. Specifically, it can provide an accurate indication of where in the thickness the first delamination is from the surface; however, this discontinuity returns most of the ultrasonic energy, thereby creating an ultrasonic shadow (Heimbs et al. 2009; Ellison and Kim 2019). This prevents further direct examination of damage below the first discontinuity. X-ray computed tomography uses x-ray radiation to take sequential 2D projection images of the object over a 180° rotation. Computations are then made with the 2D images to create a 3D representation, with a greyscale value being applied to each “voxel” (volume pixel). Like cross-sectioning and microscopy, CT scanning allows for a visualization of all damage within the composite sample while having the added benefit of allowing for numerous cross-sections to be made; all without further affecting the structure due to the cutting and polishing actions. 3.3.4.1 DLR v|tome|x L450 CT System The system for CT scanning at DLR is a GE v|tome|x L450 large format, micro CT scanner, as shown in Figure 3-22. The large format of this scanner allows for a 100 mm x 100 mm field of view (encompassing the entire sample), with a voxel size of 90 μm. This allows for the entire sample to be interrogated for damage, but does not allow for small scale defects to be 82 observed. This was a particular challenge for many of the impact samples, as the energy levels of impact were kept relatively low, and there was often very little meso or macro-level damage. Additional scans with a field of view of 40 mm x 40 mm were also made with this scanner, allowing for a resolution of 25 μm. Figure 3-22 GE v|tome|x L450 scanner at the German Aerospace Center’s Institute of Structures and Design 3.3.4.2 UBC Okanagan xradia MicroXCT-400 CT System Upon completing the analysis of CT data from the GE scanner at DLR; it was determined that there were still likely numerous matrix cracks and delaminations that were not visible, even in the 25 μm images. For this reason, additional scans were made with the UBC Okanagan CT scanner in Kelowna, BC. These scans have a field of view of 25 mm x 25 mm and a voxel size of 15 μm to provide additional resolution for identification of smaller delamination zones. Figure 3-23 xradia MicroXCT-400 scanner at The University of British Columbia Okanagan Campus 83 Chapter 4: Experimental Results and Interpretation The results of the experiments described in the methodology above are provided here along with interpretation of their data. In keeping with the same order as Chapter 3 this chapter begins with the results of the material characterization experiments, followed by the transverse loading experiments. Calculations of wave speed are presented to provide a numerical distinction between the low-velocity and high-velocity impact tests, and the effects of these two impact regimes on the NCF and 2D braid are shown through the damage quantification in the final section. 4.1 Material Characterization General Material Characterization Tests As discussed in Section 3.1.1, general material characterization tests consist of physical inspection (measurement of features), density measurements, ply thickness measurements and ply orientation measurements. 4.1.1.1 Physical Inspection The NCF samples are a warp-knitted multiaxial NCF (Schnabel and Gries 2011) and have an average measured thickness of 2.56 mm and a nominal tow width of 5mm (as measured from stitch to stitch). The braided samples are a two-dimensional braided fabric composed of layers of triaxial 2D braid laminated together with no additional stitching. The average thickness of the samples is 2.28mm. The unit cell of the braided material is shown in Figure 4-1 and is approximately 18mm wide (perpendicular to the 0° tow) and 5mm high (parallel to the 0° tow). 84 Figure 4-1 Close-up view of 2D braid sample showing the unit cell size of ~18 mm x ~5 mm 4.1.1.2 Density Two samples of each material were tested. The NCF samples were approximately 40.5 mm x 33.0 mm x 2.56 mm and the 2D braid samples were approximately 40.5 mm x 38.0 mm x 2.28 mm. The results are shown in Table 4-1. Table 4-1 Density measurement results from NCF and 2D braid samples Parameter Test NCF 2D Braid Unit Min Max # of Samples Nominal Min Max # of Samples Nominal Density ASTM D792 (Test Method A) 1.516 1.53 2 1.523 1.549 1.553 2 1.551 g/cm3 4.1.1.3 Ply Thickness Measurement Photographic images of the separated plies for both NCF and 2D braid material can be found in Appendix A. The results of the examination of the NCF material are shown in Table 4-2 below. ~18 mm ~5 mm 85 Table 4-2 Layerwise results from de-ply examination of NCF material Layer Approximate Orientation (°) Thickness of Layer (mm) Mass of Layer (mg) 1 0 0.48 794 2 +60 0.23 392 3 -60 0.26 402 4 0 0.45 866 5 +60 0.23 407 6 -60 0.25* 443* 7 -60 0.25* 443* 8 +60 0.23 426 9 0 0.48 838 10 -60 0.26 450 11 +60 0.24 406 12 0 0.52 863 0° Orientation Average 0.48 840 ±60° Orientation Average 0.24 421 *Layers cannot be separated; values shown here are total for both divided by two From the average thickness and mass values shown in Table 4-2, it is clear that the 0° layers are twice as thick as the ±60° layers, and therefore the nominal layup schedule of the laminate is [02/+60/-60]2S. It was found that there was diagonally positioned residue across all of the 0° tows from the burnt off stitches at each sub-laminate interface. This indicates that the stitching was done at the [02/60/-60] sub-laminate level. This stitched unit of material is conventionally known as an NCF “blanket” (Pickett 2011); therefore, the stitches do not provide any continuous through thickness reinforcement, other than inside the sub-laminate itself. The 2D braid sample separated into three layers as shown in Figure 4-2. Results from the examination of the 2D braid material are shown in Table 4-3 below. 86 Table 4-3 Layerwise results from de-ply examination of 2D braid material Layer Approximate Orientation (°) Thickness of Layer (mm) Mass of Layer (mg) 1 0/±60 1.42 2151 2 0/±60 1.42 2105 3 0/±60 1.35 2073 Average 1.40 2110 Based on the data in Table 4-3 it is clear that the layup schedule is [0/±60]3; however, visual observations indicated that the linear density (tex) of the 0° tow was different than that of the ±60° tows, therefore the properties of the laminate are not quasi-isotropic. Each layer was further dissected to separate out the different tows (Figure 4-3). With each orientation completely separated, the samples were weighed and all tows from each sample were placed end-to-end and measured for length. This allowed for the calculation of the linear density as shown in Table 4-4. It was found that the approximate linear density of the 0° tows was 3400 mg/m while the linear density of the ±60° tows was 1000 mg/m; a ratio of 3.4 to 1.0. (a) (b) (c) Figure 4-2 Individual plies (a) # 1, (b) #2 & (c) #3 of the 2D braid composite sample 87 Figure 4-3 2D braid composite sample dissected into (L) -60°, (C) 0° & (R) +60° constituent tows Table 4-4 Analysis of dissected 2D braid sample to determine approximate tex (linear density) -60° Layer 0° Layer +60° Layer Sample mass (mg) 1428 2689 1497 Sample combined length (m) 1.480 0.788 1.485 Approximate sample linear density (mg/m) 965 3412 1008 Ratio of 0° layer linear density to average ±60° layer linear density 3.46 4.1.1.4 Ply Orientation Measurement As discussed in Section 3.1.1.4, it was found that the actual ply orientations in the NCF material were not likely exactly ±60°. To improve the accuracy of the numerical models, measurements of the true average orientation angles were made using the CT scan images. An example CT scan image used for measuring true ply angles is shown in Figure 4-4 below. In this figure it can be seen how for each image, 3 lines are drawn in each of the 0° (horizontal), +60° and -60° directions by visually tracing the edges of tows. After averaging the angles of the lines and determining the relative angle between them it was found that on average, the true angle of the ±° plies was actually 57°. This value of 57° was subsequently used for numerical modelling. 88 Figure 4-4 Example CT scan image used for measuring actual ply angles in the NCF material. Three lines each are drawn parallel to the 0° (horizontal), +° and -° plies; by averaging the relative angle of the ±° degree plies from the 0° ply across ~100 images from different sample and positions in sample, the true orientation of the angle plies was found to be ±57° Intralaminar Mechanical Tests The results of intralaminar tests discussed in Section 3.1.2 are shown in Table 4-5 below. Table 4-5 Intralaminar mechanical test results Parameter Test NCF 2D Braid Unit Min Max # of Samples Nominal Min Max # of Samples Nominal Tensile modulus in x direction ASTM D3039 Tensile Test 70.62 72.6 2 71.61 63.84 67.28 3 65.93 GPa Tensile modulus in y direction 32.17 38.78 3 35.95 23.63 27.60 3 26.01 GPa Tensile initiation strain in x direction 0.01283 0.01365 2 0.01324 0.01057 0.01232 3 0.01147 - Tensile initiation strain in y direction 0.00973 0.00993 3 0.00984 0.00679 0.00774 3 0.00711 - Tensile strength in x direction 906 991 2 949 675 829 3 757 MPa Tensile strength in y direction 313 385 3 354 182 188 3 184 MPa 89 Parameter Test NCF 2D Braid Unit Min Max # of Samples Nominal Min Max # of Samples Nominal Poisson ratio xy ASTM D3039 Tensile Test 0.33 0.34 2 0.33 0.32 0.35 3 0.34 - Poisson ratio yx 0.19 0.20 3 0.19 0.15 0.16 3 0.16 - Flexural modulus in x direction ASTM D7264 4-Point Bend 82.07 83.33 3 82.84 54.71 63.84 3 60.3 GPa Flexural modulus in y direction 27.83 27.88 3 27.88 31.68 32.71 3 32.4 GPa Intralaminar shear modulus Gxy ASTM D5379 Iosipescu Shear Test 14.1 15.4 5 14.58 8.74 13.71 10 11.06 GPa Intralaminar shear strength ~150 ~190 5 ~170 ~120 ~180 10 ~150 MPa The results of the OCT tests are not suitable for direct entry into a table because the force-displacement results from these tests are used to directly calibrate the material parameters by adjusting their values in a virtual OCT test that is specific to the mesh size chosen. By adjusting the values in the virtual test so that the experimentally observed force-displacement response is emulated, the correct values of the parameters are determined. This type of model calibration by virtual testing is specifically required where non-stable (non self-similar) damage propagation occurs. This is because energy is dissipated as both intralaminar damage and interlaminar damage. This can be seen as the large areas of delamination highlighted in the circled regions of 4-5 & 4-6 below and is in contrast to the self-similar crack growth highlighted in Figure 4-7 & Figure 4-8. In these figures the data represented by the contour plot colours is the percentage of energy from the transducer that is reflected by the backface of the sample (as opposed to elsewhere in the sample; i.e. damage located between the front and backface). This is determined by the amount of energy returned to the transducer at a time delay consistent with travelling to 90 the backface and returning to the transducer. The colour scheme and thresholding is chosen specifically to segment and highlight damaged regions in red (white regions encircled in red are also damaged). This is done by identifying the average backface return signal percentage of a known good sample and then setting the threshold below which red is used at half of this value. In this way, regions of the material that don’t have a strong signal return from the backface (owing to internal damage or other features) are identified. Other non-circled regions of colour are representative of porosity in the material or geometrical features of the samples. Since this form of damage cannot be expressed as a crack length, it is not possible to calculate the laminate fracture toughness using the compliance method. Instead, saturation strains in the numerical model (a model which is capable of producing similar delaminations) must be calibrated for the specific mesh size chosen so that the numerical load vs. pin-opening-displacement (POD) curve matches closely to that of the experimental load vs. POD curve shown in Figure 4-9. This procedure was described by Abouali, Reiner, and Vaziri (2019) and uses the OCT test method developed by Kongshavn and Poursartip (1999). 91 Figure 4-5 Ultrasonic c-scan of NCF OCT sample loaded in the x-direction; substantial delaminations are visible, making direct estimation of the laminate fracture energy by the compliance method impossible (image credit: Sahar Abouali) Figure 4-6 Ultrasonic c-scan of 2D braid OCT sample loaded in the x-direction; substantial delaminations are visible, making direct estimation of the laminate fracture energy by the compliance method impossible (image credit: Sahar Abouali) Figure 4-7 Ultrasonic c-scan of NCF OCT sample loaded in the y-direction; self-similar crack growth can be seen, making laminate fracture energy calculation with the compliance method possible (image credit: Sahar Abouali) Figure 4-8 Ultrasonic c-scan of 2D braid OCT sample loaded in the y-direction; self-similar crack growth can be seen, making laminate fracture energy calculation with the compliance method possible (image credit: Sahar Abouali) 92 Figure 4-9 Experimental results of OCT tests; damage saturation strains in the numerical model are calibrated through virtual OCT tests to give similar numerical Force-POD curves (data courtesy: Sahar Abouali) Interlaminar Mechanical Tests The results of interlaminar mechanical tests discussed in Section 3.1.3 are shown in Table 4-6 below. Interlaminar shear strength and interlaminar fracture toughness can be conveniently entered directly into the tiebreak contact without further manipulation. Table 4-6 Interlaminar mechanical test results Parameter Test NCF 2D Braid Unit Min Max # of Samples Nominal Min Max # of Samples Nominal Interlaminar shear strength in x direction ASTM D2344 Short Beam Shear 72.7 77.9 10 75.4 45.8 64.1 10 53.3 MPa Interlaminar shear strength in y direction 49.4 55.1 10 51.7 35.8 53.6 10 45.4 MPa Average Interlaminar shear strength N/A N/A 20 63.6 N/A N/A 20 49.4 MPa Mode I interlaminar fracture toughness ASTM D5528 Double Cantilever Beam 0.46 0.54 4 0.49 1.06 1.35 5 1.26 kJ/m2 Mode II interlaminar fracture toughness ASTM D7905 End-notched Flexure 1.53 2.25 4 1.80 1.44 1.77 4 1.59 kJ/m2 93 4.2 Transverse Loading Experiments Calculation of Wave Speeds and Regime Governing Impact Durations As shown in Section 2.1, it is important to have an understanding of the speed of the waves that are prominent during a transverse impact. The duration of the impact event relative to the time required for these waves to reach a boundary is an important metric for determining which impact regime a given experiment falls into, and thereby what the literature tells us we can expect as well as what we can contribute to the literature. 4.2.1.1 Through-Thickness Waves For the NCF and 2D braid materials, the through thickness modulus was not measured experimentally, but can generally be assumed around 10 GPa for carbon fibre-epoxy laminates (Daniel and Ishai 2006). Based on a density of 1.52 g/cm3 for the NCF material (Table 4-1), and using Eq. 2-2, the through-thickness wave velocity is: 𝑐𝑐𝐿𝐿,𝑇𝑇𝑇𝑇 = �� 10𝐸𝐸9 𝑃𝑃𝑎𝑎1.52 𝑔𝑔 𝑐𝑐𝑚𝑚3� �� 1 𝑚𝑚100 𝑐𝑐𝑚𝑚�3 �1000 𝑔𝑔1 𝑘𝑘𝑔𝑔 � = 2565𝑚𝑚𝑠𝑠 Eq. 4-1 Similarly, for the braided material with a density of 1.55 g/cm3 the through-thickness wave velocity is 2540 m/s. Using these velocities in conjunction with the sample thicknesses, it takes ~0.0010 ms and 0.0009 ms for the through-thickness waves to travel from the point of impact to the back-face of the sample for the NCF and 2D braid samples respectively. It will be seen in the results that the minimum impact duration experienced in these experiments is 0.3 ms and therefore the through thickness waves are able to traverse the thickness of the sample 94 approximately 300 times during the impact period. Therefore, none of the impact tests are considered ballistic. 4.2.1.2 Transverse Shear Waves For the NCF and 2D braid materials, the interlaminar shear modulus was not measured experimentally, but can generally be assumed around 5 GPa for carbon fibre-epoxy laminates (Daniel and Ishai 2006). Based on a density of 1.52 g/cm3 for the NCF material (Table 4-1), the Transverse shear wave velocity is: 𝑐𝑐𝑆𝑆 = �� 5𝐸𝐸9 𝑃𝑃𝑎𝑎1.52 𝑔𝑔 𝑐𝑐𝑚𝑚3� �� 1 𝑚𝑚100 𝑐𝑐𝑚𝑚�3 �1000 𝑔𝑔1 𝑘𝑘𝑔𝑔 � = 1814𝑚𝑚𝑠𝑠 Eq. 4-2 When considering the distance between the impact point and the nearest boundary in these experiments being 37.5 mm, it takes ~0.02 ms for the transverse shear waves to travel from the point of impact to the support boundary. This is 15 times shorter than the minimum impact duration in these experiments and therefore there is time for a shear response of the panel to develop during the impact. 4.2.1.3 Flexural Waves Returning to Eq. 2-4 for the phase velocity of a wave with a given wavelength and angular frequency, we are reminded that flexural waves are dispersive in nature and therefore there is no single flexural wave speed. According to Olsson (1993, 2000), it is the phase velocity of the first mode of vibration (responsible for the quasi-static flexural response) that is important for determining whether or not and impact is considered high-velocity. As shown in Figure 2-3, half the wavelength of the first mode of vibration (quasi-static bending mode) is ~75 mm. To facilitate the calculation of the phase velocity we also require the 95 angular frequency of this first mode of vibration. This is a function of the geometry, boundary conditions and elastic properties of the samples and can be found through either analytical approximations (Eq. 2-6) or eigenvalue analysis of the assembled stiffness matrix in a finite element simulation. At first, the analytical approximation of Eq. 2-6 was investigated for the NCF material. Eq. 2-6 is re-shown below for convenience. 𝜔𝜔𝑚𝑚𝑚𝑚2 = 𝜋𝜋4𝜌𝜌0𝑎𝑎4 [𝐷𝐷11𝑚𝑚4 + 2(𝐷𝐷12 + 2𝐷𝐷66)(𝑚𝑚𝑚𝑚𝑚𝑚)2 + 𝐷𝐷22(𝑚𝑚𝑚𝑚)4] Eq. 2-6 The values of 𝐷𝐷11, 𝐷𝐷12, 𝐷𝐷22 and 𝐷𝐷66 were calculated using classical laminate plate theory using the lamina level values from Table 5-1 calculated in Section 5.2.1.2. From classical laminate plate theory, the values were calculated as: 𝐷𝐷11 = 121.61 𝑁𝑁𝑚𝑚 𝐷𝐷12 = 15.11 𝑁𝑁𝑚𝑚 𝐷𝐷22 = 41.09 𝑁𝑁𝑚𝑚 𝐷𝐷66 = 14.40 𝑁𝑁𝑚𝑚 After replacing 𝜌𝜌0 with 𝜌𝜌𝑡𝑡 (volumetric density times thickness = areal density), substituting 𝑚𝑚 = 𝑚𝑚 = 1 for the first modes of vibration in both directions, and 𝑚𝑚 = 1 (square plate) and taking the square root of both sides, we have Eq. 4-3 𝜔𝜔11 = � 𝜋𝜋4𝜌𝜌𝑡𝑡𝑎𝑎4 [𝐷𝐷11 + 2(𝐷𝐷12 + 2𝐷𝐷66) + 𝐷𝐷22] Eq. 4-3 Inserting values gives: 96 𝜔𝜔11 =�𝜋𝜋4�1523𝑘𝑘𝑘𝑘𝑚𝑚3�(0.00256 𝑚𝑚)(0.075 𝑚𝑚)4 �121.61 𝑁𝑁𝑚𝑚 + 2�15.11 𝑁𝑁𝑚𝑚 + 2(14.40 𝑁𝑁𝑚𝑚)� + 41.09 𝑁𝑁𝑚𝑚 � =14064 𝑟𝑟𝑖𝑖𝑙𝑙𝑠𝑠 Inserting this angular frequency into Eq. 2-4 gives: 𝑣𝑣𝑝𝑝,11 = 𝑖𝑖𝜔𝜔2𝜋𝜋 = (14064 𝑟𝑟𝑖𝑖𝑙𝑙/𝑠𝑠)(2∙0.075 𝑚𝑚)2𝜋𝜋 = 335.8 𝑚𝑚/𝑠𝑠 Eq. 2-4 Since the distance between the point of impact and the nearest boundary is equal to half the side length of the 75 mm square cutout, the time required for the wave to reach the boundary at these speeds is: 𝑇𝑇𝑝𝑝,1 = 𝑓𝑓𝑣𝑣𝑝𝑝,1,𝑚𝑚𝑚𝑚𝑚𝑚 = �0.075 𝑚𝑚2 �335.8 𝑚𝑚/𝑠𝑠 ∙ 1000 𝑚𝑚𝑠𝑠1 𝑠𝑠 = 0.11 𝑚𝑚𝑠𝑠 Similar calculations for the braided material using its elastic constants from Table 4-5 gives: 𝐷𝐷11 = 147.01 𝑁𝑁𝑚𝑚 𝐷𝐷12 = 23.52 𝑁𝑁𝑚𝑚 𝐷𝐷22 = 58.00 𝑁𝑁𝑚𝑚 𝐷𝐷66 = 6.26 𝑁𝑁𝑚𝑚 𝜔𝜔11= � 𝜋𝜋4�1551 𝑘𝑘𝑔𝑔𝑚𝑚3� (0.00228 𝑚𝑚)(0.075 𝑚𝑚)4 �147.01 𝑁𝑁𝑚𝑚 + 2�23.52𝑁𝑁𝑚𝑚 + 2(6.26𝑁𝑁𝑚𝑚)� + 58.00 𝑁𝑁𝑚𝑚 �= 15531 𝛾𝛾𝑎𝑎𝑟𝑟𝑠𝑠 97 𝑣𝑣𝑝𝑝,11 = 𝑖𝑖𝜔𝜔2𝜋𝜋 = (15531 𝑟𝑟𝑖𝑖𝑙𝑙/𝑠𝑠)(2∙0.075 𝑚𝑚)2𝜋𝜋 = 370.0 𝑚𝑚/𝑠𝑠 Eq. 2-4 𝑇𝑇𝑝𝑝,1 = 𝑙𝑙𝑣𝑣𝑝𝑝,1,𝑚𝑚𝑖𝑖𝑥𝑥 = �0.075 𝑚𝑚2 �370.0 𝑚𝑚/𝑠𝑠 ∙ 1000 𝑚𝑚𝑠𝑠1 𝑠𝑠 = 0.10 𝑚𝑚𝑠𝑠 Therefore, based on the analytical predictions, if the impact duration is shorter than ~ 0.1 ms in either material, it can be considered high-velocity impact. Due to the high sensitivity of the frequency of the first mode of vibration to the boundary conditions of the problem, eigenvalue analysis of the assembled stiffness matrix in a finite element simulation was also undertaken as a check. Additionally, for the NCF material, two separate eigenvalue analyses were undertaken to get a sense of the level of uncertainty. The first simulation was made with a model consisting of 11 laminae through the thickness, each being given orthotropic elastic constants corresponding to a unidirectional layer (see Table 5-1 in Section 5.2.1.2). The second simulation is modelled with a single laminate that was given the elastic properties corresponding to the material characterization tests as shown in Table 4-5. In this case the flexural moduli from 4-point bend tests were used as the in plane tensile moduli. The results of these simulations are shown in Figure 4-10 below. (a) (b) Figure 4-10 (a) Contour plot of out of plane displacement for the first mode of vibration (𝝎𝝎=2.9932 rad/ms) of a 2.56mm thick NCF panel modelled with 11 lamina through the thickness; (b) Contour plot of out of plane displacement for the first mode of vibration (ω=1.3638 rad/ms) of a 2.56mm thick NCF panel modelled with 1 laminate through the thickness 98 The lamina level simulation produced an angular frequency of 2.9932 rad/ms and the laminate level simulation gives 1.3638 rad/ms. Inserting these numbers into Eq. 2-4 gives: 𝑣𝑣𝑝𝑝,11,𝑚𝑚𝑖𝑖𝑥𝑥 = 𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝜔𝜔2𝜋𝜋 = (2993.2 𝑟𝑟𝑖𝑖𝑙𝑙/𝑠𝑠)(2∙0.075 𝑚𝑚)2𝜋𝜋 = 71.46 𝑚𝑚/𝑠𝑠 Eq. 2-4 𝑣𝑣𝑝𝑝,11,𝑚𝑚𝑖𝑖𝑚𝑚 = 𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝜔𝜔2𝜋𝜋 = (1363.8 𝑟𝑟𝑖𝑖𝑙𝑙/𝑚𝑚𝑠𝑠)(2∙0.075 𝑚𝑚)2𝜋𝜋 = 35.56 𝑚𝑚/𝑠𝑠 Eq. 2-4 As before, since the distance between the point of impact and the nearest boundary is equal to half the side length of the 75 mm square cutout, the time required for the wave to reach the boundary at these speeds is: 𝑇𝑇𝑝𝑝,11,𝑚𝑚𝑖𝑖𝑚𝑚 = 𝑓𝑓𝑣𝑣𝑝𝑝,1,𝑚𝑚𝑚𝑚𝑚𝑚 = �0.075 𝑚𝑚2 �71.46 𝑚𝑚/𝑠𝑠 ∙ 1000 𝑚𝑚𝑠𝑠1 𝑠𝑠 = 0.52 𝑚𝑚𝑠𝑠 𝑇𝑇𝑝𝑝,11,𝑚𝑚𝑖𝑖𝑥𝑥 = 𝑓𝑓𝑣𝑣𝑝𝑝,1,𝑚𝑚𝑚𝑚𝑚𝑚 = �0.075 𝑚𝑚2 �35.56 𝑚𝑚/𝑠𝑠 ∙ 1000 𝑚𝑚𝑠𝑠1 𝑠𝑠 = 1.05 𝑚𝑚𝑠𝑠 A similar laminate level only analysis of the 2D braid material resulted in an angular frequency of 1.0793 rad/ms, phase velocity of 25.77 m/s, and time to reach boundary of 1.46 ms. Therefore, based on the finite element analysis, if the duration of an impact is less than approximately 0.52 – 1.05 ms for NCF material or less than ~1.46 ms for the 2D braid material, the flexural response of the impact cannot be influenced by the boundary conditions, and the impact is a high-velocity impact. The results of all cut-off times from the above calculations have been summarized in Table 4-7 below. Table 4-7 Estimates of cut-off time between high-velocity and low-velocity impact NCF 2D Braid Analytical estimate 0.11 ms 0.10 ms Lamina Level Eigenvalue Estimate 0.52 ms N/A Laminate Level Eigenvalue Estimate 1.05 ms 1.46 ms 99 Quasi-static Transverse Loading As per the methodology outlined in Section 3.2.4, both quasi-static indentation and quasi-static deflection tests were carried out in advance of any impact tests in order to characterize the progression of damage that could be expected. Three quasi-static indentation tests were carried out per material as outlined in 4-8 & 4-9. Each of these three tests were effectively repeat tests and post-processing included averaging the curves to produce the single curves shown in Figure 4-11. Table 4-8 Quasi-static indentation test parameters for the NCF material; equivalent impact energy is derived from integration of the force-displacement curve during loading Table 4-9 Quasi-static indentation test parameters for the 2D braid material; equivalent impact energy is derived from integration of the force-displacement curve during loading The quasi-static deflection tests are outlined in 4-10 & Table 4-11 below. Due to limitations in the number of coupons available, only two coupons per material were used for quasi-static deflection tests to allow for more impact testing. The first tests conducted with NCF and 2D braid samples were loaded until the point of complete perforation in order to characterize the complete damage progression under quasi-static conditions. The second coupons were interrupted multiple times in order to characterize the progression of damage under quasi-static conditions. After interrupting the test, the sample was unloaded while continuing to record data. Indentation Test ApparatusThickness (mm)Equivalent Impact Energy (J)Normalized Equivalent Impact Energy [by Sample Thickness] (J/mm)QSI-N1 Load Frame 2.55 5.04 1.98QSI-N2 Load Frame 2.53 4.88 1.92QSI-N3 Load Frame 2.55 5.08 1.99Indentation Test ApparatusThickness (mm)Equivalent Impact Energy (J)Normalized Equivalent Impact Energy [by Sample Thickness] (J/mm)QSI-B1 Load Frame 2.27 5.20 2.29QSI-B2 Load Frame 2.26 6.40 2.83QSI-B3 Load Frame 2.28 6.00 2.64100 After each interrupted test the coupon was inspected visually and with ultrasonic c-scan to determine the extent of damage. Table 4-10 Quasi-static deflection test parameters for the NCF material; equivalent impact energy is derived from integration of the force-displacement curve during loading Table 4-11 Quasi-static deflection test parameters for the 2D Braid material; equivalent impact energy is derived from integration of the force-displacement curve during loading The results of these quasi-static tests are presented in the following sections. 4.2.2.1 Quasi-static Indentation Tests and Contact Stiffness The averaged curves of the NCF and 2D braid quasi-static indentation tests are shown in Figure 4-11 below. Due to the lack of any global structural deformation in these experiments, the rigidity is very high and the load increases sharply with indentation, as expected. Indentation rigidity is mostly the same regardless of material and sample thickness. This is because the Static Deflection Test NumberDeflection TestMaterial Sample NumberApparatus Thickness (mm)Equivalent Impact Energy (J)Normalized Equivalent Impact Energy [by Sample Thickness] (J/mm)3 QSD-N1 4 Load Frame 2.68 25.60 9.5414 QSD-N2 1 Load Frame 2.63 1.82 0.6915 QSD-N3 1 Load Frame 2.63 3.82 1.4516 QSD-N4 1 Load Frame 2.63 5.57 2.1217 QSD-N5 1 Load Frame 2.63 7.19 2.7318 QSD-N6 1 Load Frame 2.63 8.86 3.3719 QSD-N7 1 Load Frame 2.63 10.84 4.1220 QSD-N8 1 Load Frame 2.63 13.80 5.25Static Deflection Test NumberDeflection TestMaterial Sample NumberApparatus Thickness (mm)Equivalent Impact Energy (J)Normalized Equivalent Impact Energy [by Sample Thickness] (J/mm)4 QSD-B1 1 Load Frame 2.35 18.34 7.826 QSD-B2 2 Load Frame 2.36 1.40 0.597 QSD-B3 2 Load Frame 2.36 2.02 0.868 QSD-B4 2 Load Frame 2.36 3.65 1.549 QSD-B5 2 Load Frame 2.36 4.71 2.0010 QSD-B6 2 Load Frame 2.36 5.35 2.2711 QSD-B7 2 Load Frame 2.36 7.16 3.0312 QSD-B8 2 Load Frame 2.36 9.16 3.8813 QSD-B9 2 Load Frame 2.36 10.83 4.59101 indentation response is largely representative of the through thickness compressive and shear moduli, as well as the shear strength and the strain-softening response; both of which are not expected to change substantially based on fibre architecture since they are primarily matrix driven properties. A clearly non-linear response is also visible, which represents the increasing contact force resulting from increased surface area in contact as the hemispherical indenter progresses further into the sample. Figure 4-11 Quasi-static indentation force vs displacement response showing similar response between NCF and 2D braid materials; non-linear response is representative of increasing contact area of hemispherical indenter as indentation progresses The contact stiffness for a hemispherical impactor contacting an isotropic plate, the force and indentation distance are related for a linear elastic material according to: 𝐹𝐹 = 𝑘𝑘𝑐𝑐𝛿𝛿𝑖𝑖3 2� (Goldsmith 2001) Eq. 4-4 Where: 𝐹𝐹 = Force 𝑘𝑘𝑐𝑐 = Contact stiffness 𝛿𝛿𝑖𝑖 = Indentation displacement 102 By plotting the force against the indentation displacement from the extensometer to the power of 3/2, a nearly linear result is achieved as seen in Figure 4-12. The slope of this linear curve is the contact stiffness of Eq. 4-4 for the 12.7 mm diameter impactor in contact with both the NCF and 2D braid samples. It can be inferred from the fact that both the NCF and 2D Braid curves are similar, that the local fibre fracture and matrix cracking progression in the vicinity of the impactor are comparable between the two materials. It is believed that the deviation from linearity seen in Figure 4-12 may be due to the damage occurring under the impactor tip as damage is not accounted for in the contact stiffness formulation of Eq. 4-4. Error may additionally be attributed to the non-isotropic stiffness of the NCF and 2D braid samples. Figure 4-12 Quasi-static indentation force against quasi-static indentation displacement to the power 3/2; the slope represents the contact stiffness 4.2.2.2 Quasi-static Deflection Tests and Plate Stiffness The force vs deflection curves from the two continuous quasi-static deflection tests are shown in Figure 4-13 below. 103 Figure 4-13 Force-displacement curves for NCF (red) and 2D Braid (blue) quasi-static deflection tests (solid lines) all the way to complete perforation. The large sudden load drops are characteristic of delaminations and the curve approach an asymptotic force level that represents the frictional force against the sides of the impactor after complete perforation. The dashed lines are the area under the curves and represent total energy; this was subsequently used to target specific energy levels for impact testing From Figure 4-13 the lower flexural rigidity of the braided sample is evident from its shallower initial slope. This can be attributed mainly to the smaller thickness and therefore second moment of area of the 2D braid samples (thickness of 2.28 mm for the 2D braid vs 2.56 mm for NCF), but also due to the lower elastic moduli of the braided material as shown in Table 4-5. Additionally, by integrating the force-displacement curve from the quasi-static deflection tests, a measure of the impact energy required to achieve a given displacement was found. By doing so, stopping points of interest could be identified on the force-displacement plot, which could then be directly translated into an estimated impact energy required to achieve these stopping points. In this way, it was possible to pre-set the energy levels of interest for the impact experiments without using several impact trials to determine the energy at which damage 104 initiates and the energy at which penetration occurs. This was a very important consideration given the limited amount of material available. 4-14 and 4-15 below show all quasi-static deflection tests for NCF and 2D braid respectively plotted together on the same figure. The thick black lines were formed by merging together all the interrupted tests of the second coupon. It can be seen that these merged tests show good agreement with the initial continuous tests. Figure 4-14 Force-displacement curves for the interrupted NCF quasi-static deflection tests overlaid on the continuous QSD-N1 test (red); The black curve is created from merging the interrupted tests and it shows good repeatability with the continuous test Figure 4-15 Force-displacement curves for the interrupted 2D braid quasi-static deflection tests overlaid on the continuous QSD-B1 test (blue); The black curve is created from merging the interrupted tests and it shows good repeatability with the continuous test 105 To better quantify the difference in plate stiffnesses, the stiffness of the plates to lateral loading is calculated according to Eq. 4-5. 𝐹𝐹 = 𝑘𝑘𝑝𝑝(𝛿𝛿 − 𝛿𝛿𝑖𝑖) Eq. 4-5 Where: 𝑘𝑘𝑝𝑝 = Stiffness of the plate to transverse load 𝛿𝛿 = Total displacement of the impactor during the quasi-static deflection test 𝛿𝛿𝑖𝑖 = Indentation displacement The subtraction of indentation displacement from total displacement is necessary in order to isolate the amount of impactor displacement that is only due to global flexure and shear of the plate. By plotting force versus the isolated global displacement in Figure 4-16, a linear relationship is achieved and the linear regression of the data provides the slope (which corresponds to the plate’s stiffness to transverse loading). It can be seen from this figure that the NCF panel has a stiffness of 947 N/mm. This is 34% higher than the 2D braid panel stiffness of 708 N/mm. Considering that bending stiffness increases with the cube of the height of a beam or panel, one would expect that a panel with the same elastic properties would be 42% higher; therefore, the difference of 8% is likely due to the reduced flexural modulus of the braided material. 106 Figure 4-16 Quasi-static deflection force vs isolated global plate displacement; the slope represents the stiffness of the plate to transverse loading Lastly, when plotted together as shown in Figure 4-17 below, the quasi-static indentation and quasi-static deflection curves outline respectively, the upper and lower boundaries of the expected force-displacement response during impact as outlined in Section 2.1. It is anticipated that the force-displacement response of all impact tests will be found within the region between these solid and dashed curves. Figure 4-17 Force-displacement curves for NCF (red) and 2D Braid (blue) quasi-static deflection tests (solid lines) and quasi-static indentation tests (dashed lines); the region between the solid and dashed lines is the region in which the force-displacement response of impact tests are expected to fall Expected region of NCF impact data Expected region of 2D braid impact data 107 Transverse Impact Experiments A total of 36 instrumented impact tests were carried out. This was largely driven by the quantity of material available for these experiments. These 36 tests were distributed evenly (18-18) between NCF and 2D Braid material, and further sub-divided evenly between each of the three impact apparatus; therefore, there are 6 tests per material, per impact apparatus. The parameters of each of these tests are shown in Table 4-12 for the NCF material, and Table 4-13 for the 2D braid material. Each test can be uniquely identified by the impact test number (left-most column). Tests can also be identified uniquely through the material type and material sample number. Table 4-12 List of transverse impact tests and key parameters for the NCF material Impact TestMaterial Sample Number ApparatusDrop Height (mm)Pressure (kPa)Projectile Mass (g)Thickness (mm)Impact Velocity (m/s)Impact Energy (J)Normalized Impact Energy [by Sample Thickness] (J/mm)N1 17 Drop Tower 134 N/A 2818 2.6 1.56 3.41 1.33N2 19 Drop Tower 287 N/A 2818 2.6 2.31 7.54 2.96N3 22 Drop Tower 287 N/A 2818 2.6 2.32 7.56 2.94N4 23 Drop Tower 385 N/A 2818 2.6 2.70 10.23 3.97N5 18 Drop Tower 449 N/A 2818 2.6 2.93 12.06 4.73N6 21 Drop Tower 474 N/A 2818 2.6 3.01 12.74 4.91N7 5 Instrumented Gas Gun N/A 13.1 437 2.6 5.48 6.57 2.56N8 10 Instrumented Gas Gun N/A 13.1 437 2.6 6.35 8.81 3.45N9 6 Instrumented Gas Gun N/A 13.1 437 2.6 7.06 10.88 4.23N10 7 Instrumented Gas Gun N/A 13.1 437 2.5 7.24 11.46 4.51N11 9 Instrumented Gas Gun N/A 16.5 437 2.5 8.25 14.87 5.95N12 8 Instrumented Gas Gun N/A 16.5 437 2.7 9.10 18.11 6.77N13 11 Free-flying Gas Gun N/A 44.0 4.75 2.6 42.29 4.25 1.66N14 13 Free-flying Gas Gun N/A 51.0 4.75 2.5 56.48 7.58 2.99N15 12 Free-flying Gas Gun N/A 51.0 4.75 2.5 59.24 8.33 3.27N16 16 Free-flying Gas Gun N/A 65.0 4.75 2.6 72.28 12.41 4.85N17 14 Free-flying Gas Gun N/A 66.0 4.75 2.5 77.15 14.14 5.55N18 20 Free-flying Gas Gun N/A 77.0 4.75 2.6 85.28 17.27 6.62108 Table 4-13 List of transverse impact tests and key parameters for the 2D Braid material 4.2.3.1 Structural Response Upon completion of the impact testing with the three different apparatus; instrumentation data was analyzed with the aid of Matlab® software to convert raw instrumentation data into a variety of continuous and discontinuous metrics. The primary details of the impact tests are summarized briefly in Table 4-14 and Table 4-15 below. Impact TestMaterial Sample Number ApparatusDrop Height (mm)Pressure (kPa)Projectile Mass (g)Thickness (mm)Impact Velocity (m/s)Impact Energy (J)Normalized Impact Energy [by Sample Thickness] (J/mm)B1 17 Drop Tower 94 N/A 2818 2.3 1.27 2.27 1.00B2 18 Drop Tower 163 N/A 2818 2.3 1.71 4.12 1.81B3 19 Drop Tower 163 N/A 2818 2.3 1.72 4.17 1.83B4 22 Drop Tower 257 N/A 2818 2.2 2.19 6.73 3.01B5 21 Drop Tower 257 N/A 2818 2.3 2.22 6.92 3.05B6 20 Drop Tower 449 N/A 2818 2.3 2.93 12.06 5.16B7 7 Instrumented Gas Gun N/A 12.4 437 2.3 4.05 3.58 1.55B8 8 Instrumented Gas Gun N/A 12.4 437 2.4 4.33 4.10 1.69B9 9 Instrumented Gas Gun N/A 12.4 437 2.2 5.17 5.85 2.61B10 5 Instrumented Gas Gun N/A 13.1 437 2.3 7.11 11.04 4.84B11 6 Instrumented Gas Gun N/A 13.1 437 2.5 7.22 11.40 4.61B12 10 Instrumented Gas Gun N/A 17.2 437 2.3 9.51 19.76 8.75B13 13 Free-flying Gas Gun N/A 40.0 4.75 2.3 39.70 3.74 1.63B14 14 Free-flying Gas Gun N/A 41.0 4.75 2.3 47.14 5.28 2.31B15 11 Free-flying Gas Gun N/A 46.0 4.75 2.3 49.97 5.93 2.60B16 12 Free-flying Gas Gun N/A 50.0 4.75 2.3 55.74 7.38 3.24B17 16 Free-flying Gas Gun N/A 63.0 4.75 2.3 71.83 12.25 5.37B18 15 Free-flying Gas Gun N/A 64.0 4.75 2.3 72.37 12.44 5.46109 Table 4-14 Primary results for the NCF material to impact conditions Table 4-15 Primary results for the Braided material to impact conditions Impact TestProjectile Mass (g)Impact Duration (ms)Maximum Impact Force (N)Maximum Impactor Displacement (mm)Permanent Dent Depth (mm)% Permanent Dent Depth Compared to Maximum Impactor DisplacementImpact Energy (J)Kinetic Energy of Impactor After Impact (J)Percentage of Impact Energy Absorbed by PlateN1 2818 5.7 2737 2.9 0.06 2% 3.41 2.73 20%N2 2818 5.8 4004 4.0 0.41 10% 7.54 3.57 53%N3 2818 5.7 3968 4.0 0.32 8% 7.56 3.97 47%N4 2818 5.8 4239 4.7 0.46 10% 10.23 4.65 55%N5 2818 6.0 3964 5.1 0.77 15% 12.06 4.60 62%N6 2818 7.1 4248 5.5 0.91 16% 12.74 2.93 77%N7 437 2.1 3366 3.6 0.12 3% 6.57 4.05 38%N8 437 2.2 3554 4.1 0.42 10% 8.81 3.44 61%N9 437 2.5 3570 4.7 0.73 15% 10.88 3.23 70%N10 437 2.4 3594 4.9 0.63 13% 11.46 3.93 66%N11 437 2.8 3573 5.8 1.25 22% 14.87 3.33 78%N12 437 4.0 2987 9.0 2.68 30% 18.11 0.14 99%N13 4.75 0.3 N/A 2.3 0.03 1% 4.25 1.43 66%N14 4.75 0.4 N/A 4.1 0.05 1% 7.58 2.68 65%N15 4.75 0.3 N/A 3.4 0.07 2% 8.33 2.65 68%N16 4.75 0.4 N/A 5.0 0.13 3% 12.41 3.38 73%N17 4.75 0.4 N/A 5.0 0.14 3% 14.14 3.53 75%N18 4.75 0.4 N/A 6.1 0.21 3% 17.27 3.99 77%Impact TestProjectile Mass (g)Impact Duration (ms)Maximum Impact Force (N)Maximum Impactor Displacement (mm)Permanent Dent Depth (mm)% Permanent Dent Depth Compared to Maximum Impactor DisplacementImpact Energy (J)Kinetic Energy of Impactor After Impact (J)Percentage of Impact Energy Absorbed by PlateB1 2818 6.3 2115 2.6 0.02 1% 2.27 2.02 11%B2 2818 6.4 2637 3.4 0.10 3% 4.12 2.80 32%B3 2818 6.4 2745 3.4 0.17 5% 4.17 2.62 37%B4 2818 6.9 3081 4.5 0.38 8% 6.73 3.10 54%B5 2818 7.3 2965 4.5 0.46 10% 6.92 2.53 63%B6 2818 9.4 3263 6.5 1.49 23% 12.06 2.22 82%B7 437 2.5 2100 3.1 0.09 3% 3.58 2.35 34%B8 437 2.5 2190 3.4 0.10 3% 4.10 2.49 39%B9 437 2.5 2503 3.9 0.17 4% 5.85 3.23 45%B10 437 3.8 2243 6.3 1.53 24% 11.04 1.78 84%B11 437 4.2 2498 6.6 1.51 23% 11.40 1.66 85%B12 437 1.9* 2290 19.0* 2.26* 100%* 19.76 0.00 100%B13 4.75 0.4 N/A 2.3 0.06 3% 3.74 1.31 65%B14 4.75 0.4 N/A 3.0 0.05 2% 5.28 1.89 64%B15 4.75 0.4 N/A 3.2 0.06 2% 5.93 1.91 68%B16 4.75 0.4 N/A 3.2 0.08 3% 7.38 2.79 62%B17 4.75 0.4 N/A 6.1 0.37 6% 12.25 3.63 70%B18 4.75 0.5 N/A 6.6 0.21 3% 12.44 3.52 72%*Impactor was lodged in sample without rebound110 Of primary interest is determining whether or not a given impact corresponds to a high-velocity impact or a low-velocity impact. As determined in Section 4.2 according to the eigenvalue analysis, if an NCF impact is shorter than 0.52 – 1.05 ms it is considered a high-velocity impact. Similarly, if a 2D Braid impact is shorter than ~1.46 ms, it is considered a high-velocity impact. The analytical solution predicted a relatively lower cutoff of ~0.1 ms for both materials. The impact durations are plotted as a bar graph in Figure 4-18. It can clearly be seen that all tests carried out with the drop tower (low-velocity/high mass) and instrumented gas gun (low-velocity/intermediate mass) have impact durations longer than the cutoff durations and are therefore low-velocity impacts (response governed by boundaries). All tests carried out with the free-flying gas gun (high-velocity/low mass) have impact durations shorter than the critical duration as predicted by the eigenvalue analysis and are therefore high-velocity impacts. If one were to consider the cutoff duration predicted by the analytical method this would not be the case, however it is believed that this analytical solution may be slightly too conservative in its prediction as described in Section 4.2.1.3. As will be seen later, there are sufficient differences seen between the structural response and damage state to indicate that high-velocity impact was achieved with the free-flying gas gun. 111 Figure 4-18 The impact duration for each test coloured by normalized impact energy value and subdivided by material and impact class; all tests above the red box/line are low-velocity impact and all below are high-velocity impact To better illustrate the spread of impact energies by material and apparatus, the bar chart of Figure 4-19 provides a visual representation of the normalized impact energies. Normalized energies are used to provide an equivalent comparison between the NCF samples (nominal thickness 2.56 mm) and the 2D braid samples (nominal thickness 2.28 mm). This method of normalization is in line with the impact energy specification of the ASTM D7136-15 (2015) standard and has also been used in other studies (Sasikumar et al. 2019). Three rectangular regions have been superimposed on top of this figure that represent the three energy level groupings that will be used for the analysis of damage. By comparing the ultrasonic and x-ray Computed Tomography (CT) within and across these three bands, two materials, and two velocity regimes; conclusions can be drawn with respect to the effects of impactor mass, velocity, energy and fibre architecture on the final damage state within the material. 112 Figure 4-19 The thickness normalized impact energies of each test coloured by normalized impact energy value and subdivided by material and impact class The initial aim of the experiments was to target three different energy levels per material and carry out 2 repeats at each energy level for a total of 6 tests. In practice, it was difficult to achieve accurate reproduction of impact velocity from test to test when using either of the gas guns. In particular, the gas gun used for low-velocity/intermediate mass impacts was greatly affected by stiction at low energy levels and the projectile would either fail to move at a given pressure, or would move faster than desired, making it a challenge to achieve low energy impacts (under 5J). When making comparisons between materials for a given structural response of damage state, the following groupings are made based on where each impact in Figure 4-19 falls relative to the three energy groupings. Table 4-16 Selected impact tests to be used for direct comparison NCF 2D Braid Low Energy N1, N7*, N13 B1, B2, B3, B7, B8, B13 Mid Energy N2, N3, N8, N14, N15 B4, B5, B9, B15, B16 High Energy N5, N6, N10, N16, N17 B6, B10, B11, B17, B18 *It is noted that this impact’s energy is at the lower range of mid energy High energy level group Mid energy level group Low energy level group 113 Based on these six groupings the following force-displacement plots are produced. In each figure the curves from the impact tests are contrasted with their quasi-static deflection and quasi-static indentation equivalents to gauge whether the response is representative of low-velocity impact or high-velocity impact. As noted in the methodology section, there is no force data for the free-flying gas gun experiments, and therefore tests N13-N18 and B13-B18 are not represented here. Independent force vs displacement figures for each impact test can be found in Appendix B. 114 NCF Low Energy Figure 4-20 Force vs displacement plots of NCF low energy impacts showing close correlation to quasi-static deflection test results during loading and minimal energy absorbed as evidenced by minimal enclosed area of the curves NCF Mid Energy Figure 4-21 Force vs displacement plots of NCF mid energy impacts showing close correlation to quasi-static deflection test results during loading and moderate energy absorption; evidence of delaminations can be seen in the large drops of force near the maximum displacement NCF High Energy Figure 4-22 Force vs displacement plots of NCF high energy impacts showing close correlation to quasi-static deflection test results during loading and substantial energy absorption; the substantial effect of delaminations is visible through the extensive displacement without additional load 115 2D Braid Low Energy Figure 4-23 Force vs displacement plots of 2D braid low energy impacts showing close correlation to quasi-static deflection test results during loading and minimal energy absorbed as evidenced by minimal enclosed area of the curves 2D Braid Mid Energy Figure 4-24 Force vs displacement plots of 2D braid mid energy impacts showing close correlation to quasi-static deflection test results during loading and moderate energy absorption; evidence of delaminations can be seen in the large drops of force near the maximum displacement High Energy Figure 4-25 Force vs displacement plots of 2D braid high energy impacts showing close correlation to quasi-static deflection test results during loading and substantial energy absorption; the substantial effect of delaminations is visible through the extensive displacement without additional load 116 From these graphs it can clearly be seen that during loading, the initial force response is very steep and follows the quasi-static indentation curve briefly. This is similar to what was seen by Delfosse et al. (1995) – see Figure 2-7. After the brief spike, the force-displacement plot of the impacts begins to leave the quasi-static indentation curve almost immediately. The loading response then generally follows the same slope as the quasi-static deflection curve, but at a slightly elevated load indicating the dynamic nature of the impact. Undulations in the force data can be attributed to the recurrent passing of longitudinal stress waves back and forth over the transducer inside of the impactor at the natural frequency of the impactor (Delfosse et al. 1993). As discussed in the methodology section, certain filtering operations were applied to the force signals to remove these frequencies from the force response to more accurately capture the force at the site of the impact. It can be seen in both Figure 4-20 and Figure 4-23 (the low energy impacts), that there are no substantial load drops and the hysteresis loop is relatively small (unloading curve is substantially similar to the loading curve) and therefore it is not expected that there is much damage, although local matrix cracking can be expected to occur at the impact site. Due to the high frequencies and low amplitudes associated with the local matrix cracks it is not expected that they would be visible in the force-displacement response. As impact energy is increased further, particularly to the high energy impact levels, there is a stiffness reduction due to damage being imparted on the sample. This is visible as a reduction in slope of the force-displacement plot, but also as a large area inside the hysteresis loop. The force-displacement curves of these low-velocity impacts during damage at high energy do largely follow the damage progression curves of the quasi-static deflection samples. 117 4.2.3.2 Deformation Characterization As shown in Figure 4-18, the drop tower experiments are low velocity impacts and the low mass gas gun tests are high velocity impacts. This is based on the duration of the impacts relative to the time required for the first order flexural wave to reach the boundaries of the sample. Based on this, it is expected that the drop tower experiments should show a deformation pattern consistent with fully developed bending, while the low mass gas gun tests should show deformation patterns that are initially characterized by localized deformation around the impact site. To confirm these expectations and the resulting implications they have for interpreting the damage modes involved over the course of an impact, the 3D digital image correlation (DIC) results are found to be useful. Contour plots of out-of-plane displacement taken at frames where the maximum displacement was approximately 1.0 mm are shown below in Figure 4-26. These figures are for select low-velocity and high-velocity tests with both the NCF and 2D Braid materials. It can be seen in these contour plots that regardless of the type of material, the low-velocity impact tests show very evenly spaced out contours of displacement, and at the perimeters of the data area, a displacement of ~0.4 mm is observed. This indicates that the plate as a whole is deflecting as a result of global bending. By contrast, the high-velocity impact tests show very sharp, concentrated contours of displacement that are consistent with localized deformation, and the perimeter of the data area show almost no movement. This is consistent with the first mode flexural wave having not yet travelled out to the perimeter regions of the panel. 118 NCF 2D Braid LVI (a) (b) HVI (c) (d) Figure 4-26 Digital image correlation contour plot of out of plane displacement for test (a) N1 when max deformation was 1.0 mm (b) B3 when max deformation was 1.0 mm (c) N13 when max deformation was 0.9 mm (d) B14 when max deformation was 1.1 mm; the smooth gradual change in contour colour for (a) and (b) indicates global bending of the panel, whereas the sharp localized change in contour colour for (c) and (d) indicates local shear or “punch-out” deformation of the panel near the impact site To provide a more precise view of these deformation patterns, cross-sections were made through the impact center, parallel to the y-axis of the coupons (as defined in Figure 3-1 and 3-2) and the out-of-plane displacements were extracted along these cross-sections. These out-of-plane displacements are shown in Figure 4-27 below. The global bending deformation of the panels 75 mm 75 mm 75 mm 119 subject to LVI (Figure 4-27 a & c) are clearly apparent, as the entire panel shows changes in out-of-plane displacement across the width of the data area early on in the impact sequence. Later on in the LVI impact sequence (particularly for test B3; Figure 4-27c), there are signs of localized deformation occurring; but this is due to fibre fracture on the back-face and subsequent localized deformation. By contrast, the panels subject to HVI (Figure 4-27 b & d) show substantial local shear deformation in the vicinity of the impact site early on while the global bending response only begins to develop at later timesteps. (a) 120 (b) (c) 121 (d) Figure 4-27 DIC out-of-plane displacement measurements along a cross-section through the center of impact for (a) NCF low-velocity (b) NCF high-velocity (c) 2D braid low-velocity, and (d) 2D braid high-velocity impact tests at various time steps between the time of impact and time of maximum displacement; the global bending shape is clearly seen even at the earliest timesteps of the LVI impacts followed by localized deformation after back-face fibre fracture. Conversely, highly localized shear deformation is seen at the earliest HVI timesteps indicating that the panel is not able to bend fast enough; global bending of the panel is seen at later timesteps of the HVI impacts. 4.3 Damage Characterization The following section will examine the observed damage such as permanent dents, delamination or damage areas and fibre/matrix cracks and how the energy and velocity regime of an impact relates to them. Effect of Energy and Velocity on the Depth of Permanent Indentations As outlined in chapter 3, ASTM standard D7136-15 (2015) specifies that the depth of the dent created by the impactor is measured immediately after the impact event, and this was done for tests reported here. These results are plotted against the normalized impact energy in Figure 4-28 below. 122 Figure 4-28 Permanent dent depth vs normalized impact energy; there is a clear difference in the results based on the impact regime It can be seen from this figure that there is a substantial difference in the depth of the permanent indentation created by the impactor depending the impact regime that was observed. For a given energy level the order of size of the permanent dent depth is: Depth (HVI) << Depth (LVI) < Depth (Quasi-static) Moreover, with quasi-static and low-velocity impact, the growth in dent depth appears to follow an exponential growth with impact energy, whereas the high-velocity impact growth can best be described as linear. We can therefore say that as impact energy is increased, the depth of the permanent indentation is dependent on the impact regime Effect of Energy and Velocity on Damage Resistance It was shown in the literature review that for a given impact energy, imparted damage on the coupon is generally more severe if the impact satisfies the high-velocity impact condition (Olsson 2000; Cantwell and Morton 1989; Morita et al. 1997). To test this observation Figure 4-29 shows a plot of the percent of energy absorbed as damage in an impact versus the 123 normalized impact energy. It can be seen in this figure that indeed at lower impact energies there is a clear distinction in the percentage of the impact energy absorbed between quasi-static/low-velocity impact and high-velocity impact. This indicates a clear reduction of damage resistance under high velocity impact for both materials. It is seen that at low energy levels (1-3 J/mm) there is still a substantial amount of the overall impact energy that is absorbed permanently by the sample under high-velocity impact conditions (60-70%), whereas impacts for the same normalized energy range in the quasi-static or low-velocity regimes absorb anywhere between 10-50% of their total impact energy. This can in part be attributed to the fact that during low-velocity impacts, a larger amount of the sample is able to be engaged in elastic bending (without damage) as there is sufficient time for the flexural stress waves to propagate throughout the structure. In fact, this is most likely the only major factor contributing towards this outcome as the results seem to be nearly identical between the two materials, and therefore the mismatch in bending stiffnesses between plies of the NCF material and the effect of intertwined tows via the braiding process do not appear to be significant contributing factors with regards to damage resistance. 124 Figure 4-29 Percent of impact energy absorbed by the sample vs normalized impact energy; the reduction in damage resistance for both the NCF and 2D braid materials is evident from the significant difference in the percentage of impact energy absorbed at low impact energies. This indicates that both materials will incur more impact damage for a high velocity impact compared to an impact of the same energy at low velocity (if the impact is low energy) Ultrasonic Inspection and the Effect of Energy and Velocity on Damage (Delamination) Area Figure 4-30 and Figure 4-32 below show the c-scan results of ultrasonic inspection on the selected quasi-static and impact samples of interest in NCF and 2D braided samples respectively. The complete set of ultrasonic images from all impact tests can be found in Appendix C along with images showing the highlighted region identified as damage for the purposes of quantifying damage size. The data represented by the contour plot colours is the percentage of energy from the transducer that is reflected by the backface of the sample (as opposed to elsewhere in the sample; i.e. damage located between the front and backface). This is determined by the amount of energy returned to the transducer at a time delay consistent with travelling to the backface and returning to the transducer. Red indicates a high percentage of energy reflected at the backface while blue and white indicates a low percentage of energy reflected by the backface. 125 Delaminations and other damage within the material show as blue and white, whereas delaminations at the back surface of the NCF material (see Figure 4-31) appear as very red regions owing to the stronger reflection off the delaminated interface that is near the backface. Impact Energy Range Quasi-static Deflection Low-Velocity/ High Mass Low-Velocity/ Intermediate Mass High-Velocity/ Low Mass Low Energy (a – QSD-N3) (b - Impact N1) (c - Impact N7) (d - Impact N13) Mid Energy (e – QSD-N5) (f - Impact N3) (g - Impact N8) (h - Impact N15) High Energy (i – QSD-N8) (j - Impact N5) (k - Impact N10) (l - Impact N17) Figure 4-30 Ultrasonic c-scans of projected damage area in NCF laminates with varying energy levels and loading scenarios; damage area increases with increasing energy, but is substantially increased under high-velocity impact conditions From these scans of the NCF material above, it is clear there is a substantial dependence of the overall size of the damage area on both impact energy and impact regime. Low energy impacts (Figure 4-30 a, b, c & d) result in only localized indentation damage that does not spread from the impact site. This observation matches the force-displacement responses seen in Figure 4-20 and Figure 4-23 where the response remained largely elastic and the hysteresis curve area 100 mm 126 fairly small. As energy is increased into the mid energy range (Figure 4-30 e, f, g & h) the results become more interesting. Firstly, it can be seen in the Quasi-static and low-velocity impacts (e, f & g) that the delamination area becomes slightly larger and elongated. This can be seen in the samples themselves as longitudinal splitting cracks on the back-face (Figure 4-31) and delamination can be heard through the use of a tap test. More interestingly, in the high-velocity impact (h) the delamination area is substantially larger and more equiaxed (extending out to the side beyond the rectangular delamination region) when compared to the slower impacts. A similar result is seen in the high energy impacts (Figure 4-30 i, j, k & l), where the rectangular delamination region for low velocity impacts becomes larger in width and length, and the delamination region for high-velocity impact becomes substantially larger in size. This indicates that high-velocity impact tends to produce larger delamination regions as has been noted by others (Olsson 2000; Cantwell and Morton 1989; Morita et al. 1997). The rectangular regions of delamination seen in Figure 4-30 e, f, g, h, i, j and k are a prominent example of damage influenced by the mesoscopic structure. An example of their visible appearance is shown in Figure 4-31 below where the tow has completely separated all the way to an edge of the sample. This is caused by matrix splits (likely cause by tensile fracture) which first occur along the edges of the fibre tows (and also coincide with the stitching yarns). These splits isolate the tows from others around them, leaving only the matrix bond strength to the layer beneath keeping them attached. As the delaminations in the sample progress, the reduced attachment area (cause by the splits) makes the tows susceptible to rapid delamination along their entire surface area since less energy is required to propagate this delamination compared to other regions that are not isolated by matrix splits. 127 (a) (b) Figure 4-31 Meso level delamination of complete 0° tow in sample N6 (high energy drop test) as viewed from (a) 0° direction, and (b) 90° direction 128 In comparison to the NCF material, ultrasonic scans of the braided material are shown below in Figure 4-32. Impact Energy Range Quasi-static Deflection Low-Velocity/ High Mass Low-Velocity/ Intermediate Mass High-Velocity/ Low Mass Low Energy (a – QSD-B4) (b - Impact B2) (c - Impact B7) (d - Impact B13) Mid Energy (e – QSD-B7) (f - Impact B4) (g - Impact B9) (h - Impact B16) High Energy (i – QSD-B9) (j - Impact B6) (k - Impact B10) (j - Impact B18) Figure 4-32 Ultrasonic c-scans of projected damage area in 2D braid laminates with varying energy levels and loading scenarios; there is only a modest increase in damage area with increasing energy, and no difference in the case of high-velocity impact The fact that as the impact energy is increased, the overall damage area in the braided material does not change significantly should be noted; particularly the absence of any meso-level damage such as the delaminated tows as seen in the NCF material. This type of damage is impossible to develop in a 2D braided material due to the intertwining of the tows, which prevents any one individual tow from delaminating for any substantial distance. Of even greater importance is the absence of any change in damage area with the transition of the impact regime 100 mm 129 into high-velocity. By looking at these ultrasonic images, it would be impossible for a technician to distinguish the velocity of impact by c-scan alone. Additional information such as the depth of any permanent dent and a general knowledge about the approximate impact energy would be necessary to have a comprehensive understanding of what type and level of severity of impact occurred here. This independence of damage area (delamination area) from both energy and velocity indicates that the lack of any stiffness mismatch between layers of the 2D braid is a substantial benefit for limiting the size of damage. By avoiding the stiffness mismatch that is often present in conventionally tape laid laminates or NCF laminates, there is insufficient interlaminar shear stress from the direct shear loads alone to develop any substantial driving force for delamination to progress far away from the impact site. X-Ray Computed Tomography In the following section, x-ray CT images of the damaged samples are shown for both materials, at varying energy levels and impact velocities. All images below are taken at cross-sections which intersect the impact site. Additional images taken at cross-sections that are 2.5 mm, 5.0 mm, 7.5 mm and 10.0 mm away from the impact site can be found in Appendix D to allow for viewing the damage that has occurred at different distances from the impact site. Depending on the sample, the images may have been made with 15 μm, 25 μm or 90 μm resolution and will be identified as such. It is important to recognize that the CT scanners used do have limitations in resolving very small features such as delaminations where both delaminated faces may remain close together. Other challenges include the relatively limited contrast between the air within a crack and the composite material itself. These limitations have been noted by others (Sutcliffe et al. 2012) and should be considered when viewing the images. 130 To aid in the annotation of these images, the following abbreviations have been made: • ff = fibre fracture • dl = delamination • dl-I# = delamination in interface # • mc – matrix cracking Additionally, Table 4-17 provides a schematic view of the laminate for the NCF material with layers, angles, interfaces and blankets all labelled. It should be noted that interfaces 3 and 9 are the only interfaces having a change in orientation without the presence of stitching across the interface. Table 4-17 Layer & Interface designations for NCF material Impact Side Blanket 1 2 3 4 Back Side Layer 1* 2 3 4* 5 6 7 8 9* 10 11 12* Angle 0 60 -60 0 60 -60 -60 60 0 -60 60 0 Interface 1 2 3† 4 5 6†** 7 8 9† 10 11 *Contains 2 layers of 0° fibres (interface cannot be distinguished between them – omitted for simplicity) **Adjacent layers have the same angle and therefore cannot delaminate † This interface is a blanket interface and has no stitches crossing its boundaries Figure 4-33 shows the CT scanning images for the NCF material. Beginning with the low energy collisions we can see that in general there is very little (if any) observable impact damage. Some damage can be seen on the backface of the impact N7 coupon (b), but this impact was closer to the mid energy level range (see Figure 4-19) and therefore may not be entirely representative of the equivalent to impact N1 (a) or N13 (c) that are grouped with it. N1 (a) and N7 (b), do show a small amount of visible permanent indentation depth. At the mid energy level, damage can now be clearly seen in all samples. The low-velocity impacts N3 (d) and N8 (e) have clearly identifiable dents and substantial interlaminar and intralaminar cracks visible close to the impact site. They also show delaminations at many 131 interfaces near the impact site, but most of those delaminations do not extend far away radially from the impact site. The exception to this is in the 3rd, 9th and 11th interfaces for the N8 sample. The delaminations in the 3rd and 9th interfaces (which are interfaces between NCF blankets that have a fibre orientation change) do show that the delamination region extends further away from the impact site than just the immediate vicinity. In the case of the 11th interface for impact N8, it is clear that the delaminations extend substantially far away from the impact site. This is caused by the tows on the back side only being held on by a single matrix interface to the adjacent layer. The substantial matrix splits that occur are able to produce delamination along a large section of the coupon resulting in the tows on the back side being almost completely removed from the sample. Impact N15 (f) under high-velocity conditions looks almost unchanged from impact N13 (its low energy equivalent) with the exception of almost imperceptibly small (but long) delaminations running at what appears to be the 3rd, 9th and 11th interfaces. Lastly at high energy levels there is substantial damage in all samples. The quasi-static sample (g) in particular shows fracture extending from the back surface all the way to the midplane of the laminate accompanied by numerous delaminations and shear cracks. The Low-Velocity/High mass impact N5 (h) looks almost identical to the quasi-static case. Impact N10 (i) shows that the 11th interface has delaminated substantially similar to impact N8 with wide reaching delaminations in the 9th interface as well. There is considerable fragmentation in the sample, particularly in what appears to be layers 10 and 11. The high-velocity impact N17 shows fracture on the backface accompanied with extensive, but fine fractures throughout the impact zone. Delamination regions can also be seen to extend far away from the impact site at varying depths, but their thickness is very small. Any permanent dent depth is also almost imperceptibly small. 132 Energy Range Quasi-static Deflection Low-Velocity/ High Mass Low-Velocity/ Intermediate Mass High-Velocity/ Low Mass Low Energy N/A (a - Impact N1) (25μm) (b - Impact N7) (25μm) (c - Impact N13) (25μm) Mid Energy N/A (d - Impact N3) (25μm) (e - Impact N8) (25μm) (f - Impact N15) (25μm) High Energy (g – QSD-N8) (15μm) (h - Impact N5) (25μm) (i) - Impact N10) (15μm) (j - Impact N17) (15μm) Figure 4-33 CT scans of NCF laminates with varying energy levels and loading regimes dl dl-I3 dl dl-I1 dl-I9 ff/mc dl-I9 dl- dl ff/mc dl-I3 dl-I9 ff/mc dl-I9 dl-I3 dl-I1 dl-I9 dl-I3 dl-I9 dl-I9 dl-I3 dl-I9 ff/mc dl ff/mc 133 In the braided coupons shown in Figure 4-34, the following designations in Table 4-18 are used for interfaces. Table 4-18 Layer & Interface designations for 2D braid material Impact Side Layer 1 2 3 Back Side Angle 0/±60 0/±60 0/±60 Interface 1 2 It can be seen that for both low-velocity, low energy impact samples (B2 and B7), there is more damage than their NCF counterparts including fibre fracture on the backface and delaminations. The high-velocity impact sample B13 shows no indication of any amount of damage. At mid-level energies, the level of damage observed appears more substantial than equivalent NCF mid energy low-velocity impacts. Both impacts B4 and B9 show extensive fibre fracture and matrix cracking near the impact site and have delaminations that appear to be at the two interfaces extending radially outwards ~5 – 8 mm from the impact site. The high velocity impact B16 only shows minimal fracture on the back surface with no apparent damage further inside the sample. The high energy level samples show extensive amounts of damage at all velocity levels which can best be described as fragmentation. In the region of the impact site it is near impossible to distinguish between fibre fracture, matrix cracking and delamination, such is the extent of the damage. Moving further away from the impact site there is evidence of the localization of delaminations to the two interfaces, but they do not extend more than 8 – 10 mm from the impact site, even in the case of high-velocity impact. This is somewhat less than the extensive cracks seen in NCF high-velocity impacts such as impacts N15 & N17, where delaminations can be seen extending more than 20 mm (outside of the field of view) away from the impact site. 134 Energy Range Quasi-static Deflection Low-Velocity/ High Mass Low-Velocity/ Intermediate Mass High-Velocity/ Low Mass Low Energy N/A (a - Impact B2) (25μm) (b - Impact B7) (25μm) (c - Impact B13) (25μm) Mid Energy N/A (d - Impact B4) (25μm) (e - Impact B9) (15μm) (f - Impact B16) (90μm) High Energy (g – QSD-B9) (15μm) (h - Impact B6) (25μm) (i - Impact B10) (15μm) (j - Impact B18) (15μm) Figure 4-34 CT scans of 2D braided laminates with varying energy levels and loading regimes dl dl dl ff/mc dl ff/mc ff/mc ff/mc ff/mc dl-I2 dl-I1 dl-I2 dl-I1 dl-I2 dl-I1 dl-I2 dl dl-I1 dl-I2 ff/mc dl-I1 dl-I2 ff/mc dl-I2 dl-I1 dl-I2 dl-I1 ff/mc dl-I2 dl-I1 ff/mc dl-I2 135 Overall, from these CT images it can be seen that there is clearly an increase in permanent dent depth with increasing impact energy, but also a decrease in permanent dent depth under high-velocity impact conditions. Both the NCF and braided material show minimal internal damage at low energy levels, but the braided material does shows slightly more damage relative to NCF. Both materials also show substantial inter and intralaminar damage at the site of the impact at mid and high energy levels, but the level of intralaminar damage rapidly decreases as the distance from the impact site increases. At these distances there may still be interlaminar delaminations, particularly in the NCF high-velocity impact cases. In the NCF material, delaminations far away from the impact site appear to occur mostly in the 3rd and 9th interfaces. These interfaces are the blanket interfaces that contain a fibre orientation change between adjacent layers. The 6th interface is also a blanket interface, but because of the symmetrical layup there is no stiffness mismatch here and the filaments from neighbouring layers remain well connected to each other. The 11th interface is also a common site for delamination, probably due to the ease at which matrix splitting and subsequent complete separation of the tow from layer 11 can occur. The level of fragmentation in braided high energy impacts is substantial and appears to be more than in the NCF material. It is also noted that fibre and matrix fracture can be seen to begin on the backface of the sample and moves its way further forwards to the impact site if the impact energy is sufficient. 4.4 Summary of Results To summarize, it has been shown through both the analysis of impact durations relative to the various wave velocities that all impact tests have fully developed through thickness and shear responses, but not all tests have fully developed flexural responses. In particular, the high-mass drop tower and intermediate mass gas gun have impact durations long enough for the 136 flexural response to fully develop, while the low-mass gas gun occurs over a short enough time-span that the sample cannot bend away. This result was additionally confirmed through analysis of 3D DIC data, which clearly shows the difference in displacement fields of the samples. Somewhat counterintuitively, the HVI tests that have more localized displacement during the impact event itself exhibited the smallest permanent dent depth when measured immediately after the impact test. The LVI tests showed considerably larger permanent dent depths for the same normalized impact energy and the quasi-static tests showed slightly more than the LVI tests, suggesting an inverse relationship between impact velocity and permanent dent depth for a given energy level. Even though permanent dent depth was less in the HVI tests, they do show a reduction in damage resistance as evidenced by the large percent of impact energy absorbed at low impact energy levels (Figure 4-29). Ultrasonic inspection shows that the NCF material produces large, equiaxed delamination regions when impacted under high-velocity conditions, but under low-velocity conditions it is more susceptible to matrix splitting and delamination on the backface that is localized to mesoscale geometry features (tow width/stitch spacing). The braided material does not show much difference in damage regions size as velocity increases, and even increases in energy do not substantially enlarge the damage area, suggesting the fibre architecture does a good job of interrupting crack paths or preventing stresses that would cause the development of cracks. X-Ray CT inspection of the NCF material shows that delamination appears to be most preferential in the 3rd, 9th and 11th interfaces. The preference for delamination in the 3rd and 9th interfaces is likely due to the change in fibre orientation (60°) coupled with the lack of any through-thickness stitching in these interfaces. The 11th interface is susceptible to delamination because of its change in fibre orientation (60°) and the effect of matrix splits on the back-face 137 creating large zones having only the matrix of the interface beneath them to maintain connection with the rest of the structure. In both the NCF and 2D braid material, evidence of tensile cracks beginning on the backface of LVI coupons is evidence of the importance of back-face strain in the progression of damage, while HVI coupons show more general fragmentation without clear evidence of initiation from back-face fracture. This general fragmentation may be indicative of large compressive and shear strains that can develop quickly (as discussed) taking precedence over the slower to develop back-face tensile strains caused by flexure. In general, the 2D braid material appears to localize the damage much better than the NCF material, with cracks not extending much further than ~10 mm radially from the impact site. 138 Chapter 5: Numerical Modelling and Comparison to Experiments 5.1 Introduction To better understand the progression of damage within the impacted samples and also to evaluate the efficacy of the UBC CODAM2 model under both low and high velocity impact loading, numerical simulations of the NCF material under impact loading using LS-DYNA® are performed and results shown in this chapter. Modelling was restricted to the NCF material primarily because the experimental aspect is considered the primary focus of this research. There are certainly many further numerical studies that could be made by utilizing the experimental data generated here. Additionally, focus was kept on modelling the NCF material because of the inherent challenges in accounting for a braided fibre architecture with a material model that has been developed for conventional tape-laid laminates consisting of a flat fibre architecture. 5.2 Particulars of the Numerical Model The geometry and mesh of the model is shown in Figure 5-1 through Figure 5-4. The composite sample of size 100 mm x 100 mm x 2.56 mm is supported on a fixture with a 75 mm x 75 mm square cutout. A 12.7 mm diameter hemispherical impactor composed of a layer of solid elements is initially 0.1 mm above the surface of the composite and is given an initial downwards velocity. Both the support fixture and the impactor are modelled as rigid bodies. The support fixture is constrained against displacement in all three translational degrees of freedom (solid elements do not require rotational constraints) while the impactor is constrained in the two degrees of freedom corresponding to the plane of the sample while being allowed to translate perpendicularly to the sample. The density of the impactor material is adjusted to achieve the same impactor mass as the actual experiments. 139 Surface based contacts are used between the composite and fixture as well as the composite and impactor. On the top surface of the composite, four groups of nodes have been selected to have their out-of-plane degree of freedom fixed to emulate the effect of the fixture clamps. Since the fixture clamps during the experiment are made of rubber and are only adjusted to lightly press on the sample in order to keep it in contact with the fixture prior to impact, no preload is considered, and in-plane movement is allowed. The composite is modelled at the lamina level with 11 layers of solid elements used to discretize the laminate. The mesh is one element thick in each layer and the elements are 1 mm x 1 mm in size in-plane. This consistent element size was selected to allow for the saturation strains of the CODAM2 model to be the same in all elements of the model – thereby allowing the same material to be applied to all elements having the same fibre orientation – (see Section 4.1.2), make the fracture energy identical to the fracture energy density for convenience and clarity (owing to the fracture energy density being the fracture energy divided by the 1 mm characteristic length), and provide mesh independency as validated by the good match in elastic force-displacement results compared to the experimental tests. Between each lamina, a surface-based tiebreak constraint is used with option 9 selected (this is the same implementation as MAT138 cohesive elements). This ensures that all lamina act together as a single laminate at the beginning of the simulation but are free to form delamination zones as the impact progresses. The layer on the backface of the impact sample also contains a separate 10 mm wide strip that has been isolated for its own independent delamination through the use of tiebreak constraints. This modelling choice was made based on observations of actual tow delaminations in experimental trials. 140 The material properties of the model are applied as defined in Sections 5.2.1.2 and 5.2.1.3. These material properties are based on experimental testing conducted at laboratory conditions (room temperature and ambient humidity) without sample conditioning. The effects of residual stress, process variability, aging and degradation are not considered. Figure 5-1 Overview of entire LS-DYNA® Model domain; Impactor is the brown sphere; the black circular regions are nodal constrains to mimic the effect of the specimen clamps Figure 5-2 Cross-section view of the LS-DYNA® model domain; the square window shape of the rigid support can be clearly seen below the composite sample Figure 5-3 Close-up cross-section view near the impact site; the 11 layers of composite can be clearly seen and in the lowermost layer a strip of material 10 mm wide is present to allow for the possibility of complete tow separation to due matrix splitting. Figure 5-4 Close-up cross-section view near the edge showing the rigid support (green) that the sample sits on. An automatic surface-to-surface contact is used between the sample and the support. The colours indicate portions of the model that are specified as separate parts; they do not indicate the material model applied to the part Composite Material 5.2.1.1 Through-thickness spatial discretization CODAM2 was conceived as a sub-laminate based model whereby material parameters for the sub-laminate building blocks are applied to each sub-laminate, which are then stacked on top of each other to create the full laminate. To simplify things further, the material properties for the sub-laminate model can be identically applied to a laminate model having a single element Impactor Nodal constraints (x4) Sample 10 mm wide delamination strip Support 141 through the thickness of the plate. There are consequences to such a decision including complications around the failure of integration points near the point of impact and what that means with regards to failure of the through-thickness element as a whole; but the greatest consequence is with regards to delamination. If a decision is made to model the full thickness of the panel with a single element, it is then implicitly assumed that delamination must not be a failure mode that occurs in the actual specimens. As has been shown in the experimental results, this is not true; delamination is a substantial damage mode during impact in these coupons. Therefore, the modelling of the impacted plates with a laminate-based approach is not appropriate. Indeed Lu and Liu (1992) state that “in order to consider the continuity of interlaminar stresses across the interface, the composite laminates have to be modeled by individual layers.” For this reason, the model used here is discretized through-thickness at the lamina level in order to achieve the most accurate results. Other options often considered for larger problems where the computational cost of lamina-level modelling may be prohibitive include modelling the structure with sub-laminates, or some other modification that may be computationally less expensive (two elements with a single delamination plane for example – referred to here as a merged sub-laminate). These methods allow for the delamination failure mode to be taken into account in some measure, however, the orthotropic material properties must be applied with the same orientation in all elements and therefore there is no stiffness mismatch which exists between the modelled units. This greatly simplifies the model and reduces computational time; however, with any cross-ply or angle ply laminate it is known that the stiffness mismatch in conjunction with the requirement for stress equilibrium can give rise to substantial interlaminar stresses (tensile and shear) that superimpose themselves on the interlaminar shear stresses from bending or direct punch shear. Therefore, the 142 sub-laminate and merged sub-laminate models may under-predict interlaminar stresses, thereby delaying the initiation of any delamination that is predicted and resulting in a higher than expected peak load during impact. A lamina level approach is the most accurate in that the orthotropic material parameters are applied to each layer with their varying orientation. The true stiffness mismatch between layers is then accurately included in the model and its effect on delamination is captured (Abrate 1998). 5.2.1.2 Intralaminar Modelling For the simulations carried out in this study, the built-in CODAM2 model within LS-DYNA® (MAT219) was utilized. This model allows for the inclusion of orthotropic elastic and damage properties. Due to the importance of local through-thickness deformation involved in transverse impact, the use of regular (thin) shell elements was precluded due to their lack of degrees of freedom in the through-thickness direction. In order to accurately capture through-thickness deformations and stress state, the use of thick-shells or solid elements was required (Dogan et al. 2012); for this simulation solid elements were chosen. The elastic material properties for a lamina were calculated from the experimental tests made on the NCF laminate found in Table 4-5. This was accomplished utilizing the MATLAB® “fmincon” constrained non-linear multivariate optimization routine which uses an interior-point algorithm and linear constraints to find local minima of a non-linear multivariate function (MathWorks 2020). The non-linear function being solved is Eq. 5-1 below. This function is a cost function that provides a single scalar measure of how accurately the trial material properties match the optimum material properties. This function is a quartic function with some quadratic terms. The choice of setting terms to be quadratic or quartic was made based on an informed 143 interpretation of which terms would most affect the accuracy of the structural response of a plate under transverse loading (the load case of interest). Therefore, an error in flexural modulus was deemed worse than tensile modulus, and so the flexural modulus error terms are raised to a higher power. It was also found during virtual tests of the overheight compact tension test (for saturation strain calibration), that the result was highly sensitive to the value of intralaminar shear modulus, so this term was also made quartic. In effect, an error in the quartic terms is more highly penalized, and so the solver is driven to minimize the error in those terms more than the quadratic terms. 𝑓𝑓𝑐𝑐𝑙𝑙𝑠𝑠𝑡𝑡 = �𝐸𝐸𝑥𝑥 − 𝐸𝐸𝑥𝑥,𝑙𝑙𝑝𝑝𝑡𝑡�2 + �𝐸𝐸𝑓𝑓𝑓𝑓,𝑥𝑥 − 𝐸𝐸𝑓𝑓𝑓𝑓,𝑥𝑥,𝑙𝑙𝑝𝑝𝑡𝑡�4 + �𝐸𝐸𝑦𝑦 − 𝐸𝐸𝑦𝑦,𝑙𝑙𝑝𝑝𝑡𝑡�2 + �𝐸𝐸𝑓𝑓𝑓𝑓,𝑦𝑦 − 𝐸𝐸𝑓𝑓𝑓𝑓,𝑦𝑦,𝑙𝑙𝑝𝑝𝑡𝑡�4+ �𝐺𝐺𝑥𝑥𝑦𝑦 − 𝐺𝐺𝑥𝑥𝑦𝑦,𝑙𝑙𝑝𝑝𝑡𝑡�4 + �𝜈𝜈𝑥𝑥𝑦𝑦 − 𝜈𝜈𝑥𝑥𝑦𝑦,𝑙𝑙𝑝𝑝𝑡𝑡�2 Eq. 5-1 where, 𝑓𝑓𝑐𝑐𝑙𝑙𝑠𝑠𝑡𝑡 is a singular scalar measure of how well the trial values match the optimum values, “𝑜𝑜𝑜𝑜𝑡𝑡” variables are the optimal values (i.e. the values found in the material characterization tests; Table 4-5). All other variables are the trial values being tested by the optimizer. The six trial values of Eq. 5-1 are themselves computed according to classical laminate plate theory equations from the trial lamina values. The classical laminate plate equations relate orthotropic ply properties to orthotropic laminate properties based on ply thickness, orientation, and stacking sequence (Daniel and Ishai 2006). By providing initial values of the lamina elastic properties along with constraints on their minimum and maximum values, the fmincon procedure would calculate the laminate properties through classical laminate plate equations, calculate the cost function, and iterate until finding an “optimal” solution. This procedure is shown in Figure 5-5 below. 144 Figure 5-5 Logic flowchart of automated procedure for "back-calculating" lamina elastic constants from laminate elastic constants by an iterative optimization routine on a non-linear cost function fed by classical laminate plate functions. For any given lamina elastic constants, there is a unique solution for laminate elastic constants according to classical laminate plate theory, but the reverse is not true and must be arrived at through iterative optimization Damage parameters were found using a combination of material characterization tests and virtual tests for calibration. The initiation strain for tensile failure in the fibre direction (IFIBT) was estimated as the average strain at failure for the laminate tensile coupons tested along the x-direction (or 0° direction of the 0/60/-60 laminate) since this failure mode is dominated by tensile failure of the 0° fibres. Other initiation strains were estimated from unidirectional test data supplied by the project sponsor, Ford Motor Company, because these parameters were not possible to estimate from laminate level tests, and unidirectional samples were not supplied by the project sponsor to facilitate our own independent testing. 145 The saturation strain values for the model were then calculated to give fracture energies consistent with the fibre fracture energy and matrix fracture energy density as calibrated by Abouali, Reiner, and Vaziri (2019). In their work they found a fibre fracture energy of 86 kJ/m2 and a matrix fracture energy density of 3.5 N/mm2 calibrated by modeling characterization tests such as the over-height compact tension (OCT) test and adjusting saturation strains until the force-POD curve reasonably matched the experimental results (see Abouali, Reiner, and Vaziri, 2019 for an example). Element erosion at a strain value of 1 was also included to prevent simulation termination due to negative volumes associated with severely distorted elements caused by large element stiffness reduction. Table 5-1 Summary of MAT219 material card parameters used for modelling NCF lamina Parameter LS-DYNA® Variable Name Value Unit Density RO 0.0015230 g/mm Young’s Modulus in fibre direction EA 116000 MPa Young’s Modulus in transverse direction (in-plane) EB 14000 MPa In-plane Poisson’s ratio (minor) PRBA 0.03 - Out-of plane Poisson’s ratio PRCB 0.50 - In-plane shear modulus GAB 3000 MPa Matrix damage initiation strain in tension IMATT 0.0043 - Fibre damage initiation strain in tension IFIBT 0.0138 - Matrix damage initiation strain in Compression IMATC 0.0150 - Fibre damage initiation strain in Compression IFIBC 0.0160 - Matrix damage saturation strain in tension SMATT 0.1167 - Fibre damage saturation strain in tension SFIBT 0.1074 - Matrix damage saturation strain in compression SMATC 0.0333 - Fibre damage saturation strain in compression SFIBC 0.0927 - Element erosion parameter ERODE 2 Flag Element erosion strain ERPAR2 1.0000 - 5.2.1.3 Interlaminar Modelling The effect of delamination is included in the model through the use of automatic, one-way, surface-to-surface tiebreak contacts between laminae. These tiebreak contacts are penalty-based techniques for modelling the transfer of load between adjacent surfaces (via nodes) in both 146 tension and compression, while allowing for failure criteria to modify the load transfer as damage progresses. For this model, tiebreak option 9 was chosen. LS-DYNA® has implemented this tiebreak option to be identical to the MAT138 mixed-mode cohesive element. In this model (shown simplified in Figure 5-6) as the traction moves the surfaces relative to each other, the displacement of the nodes is governed by the contact stiffness of both in-plane (shear) and out of plane (normal/CN) until the strength/critical displacement is reached. Since this is a mixed-mode model, the strength/critical displacement is actually a complex function developed by Benzeggagh and Kenane (LSTC 2017) that considers both in-plane and out of plane tractions. The stiffness of the coupling between nodes is then degraded in such a way that the energy dissipated during failure of the interface is equal to the energy release rate as determined by the energy release rates for mode I and mode II combined according to the mode-mixity. Figure 5-6 Schematic of the bi-linear traction-separation law used for tiebreak option 9; the area under the curve is the energy release rate and represents the energy absorbed per unit area of delamination created The parameter values used in the tiebreak contacts are shown in Table 5-2 below. Most important are the normal and shear failure stress criteria “NFLS” and “SFLS” and the mode I and mode II energy release rates “ERATEN” and “ERATES”, respectively. SFLS, ERATEN and ERATES were found through short-beam shear, double cantilever beam and end-notch flexure tests respectively, as previously described in Section 3.1.3. 147 Table 5-2 Model parameters for tiebreak contacts used to model interlaminar damage There are ten interfaces in total where tiebreak contacts were inserted. They are identified as interfaces 1-5 and 7-11 in Table 4-17. Rate of Loading (Quasi-static) & Initial Conditions (Impact) For impact scenarios, the initial conditions were set so that the impactor had the same impact velocity as shown in Table 4-12 and Table 4-13. In the case of quasi-static tests, the simulations were run with a constant impactor velocity and were allowed to run over a total period of 100 ms (10 times longer than the low-velocity/high mass tests) so as to ensure that the modelled response of the plates was as close as practically possible to quasi-static. 5.3 Results of the Numerical Model Quasi-static Indentation Comparison With a slightly modified model having a fully supported coupon as in the experimental test, the through-thickness response of this numerical model can be validated. This response is particularly important for the high-velocity impact simulations as this local response is critical to predicting the correct peak forces early on. The results are shown in Figure 5-7. Parameter LS-DYNA® Variable Name Value Unit Static coefficient of friction FS 0.2 - Dynamic coefficient of friction FD 0.2 - Viscous damping coefficient VDC 10 % Flag for setting which algorithm to use OPTION 9 Flag Normal (Mode I) strength NFLS 60.0 MPa Shear (Mode II) strength SFLS 63.6 MPa Exponent of the mixed mode criteria (negative specifies Benzeggagh-Kenane law) PARAM -2 - Mode I energy release rate ERATEN 0.49 kJ/m2 Mode II energy release rate ERATES 1.80 kJ/m2 Mode I Contact Stiffness CN 100000 MPa/mm 148 Figure 5-7 Comparison of NCF quasi-static indentation experimental force-displacement vs numerical It can be seen that while there is some deviation in the exact values of the models compared to the experimental results, the overall trend and order of magnitude is correct. This should be sufficient for achieving accurate force predictions in the early stages of high-velocity impact simulations. The model with delamination does experience additional undesirable activation of its tiebreak constraints and complete element matrix damage which is not ideal; however, since the impact simulations will experience delamination anyway and the correct overall upward trend and magnitude is correct below 10000 N (all impact loads recorded were below 10000 N), this is not seen as a significant error. Quasi-static Deflection Comparison To examine the capabilities of the numerical model under quasi-static deflection condition, both the complete perforation test and an interrupted test are investigated. Figure 4-18 shows the results during complete perforation. The elastic region of the loading curve follows the experimental results very closely, but then overpredicts the peak load. Interestingly, the post peak response appears to be very similar to the experimental curve, but it is offset by a certain Onset of delaminations Steady delamination growth Increased delamination & element matrix damage growth rate 149 amount. It was not expected that the model would accurately predict all of this post-peak response because it is determined by the erosion of elements, which is controlled by the minimum required timestep of an element – to prevent the simulation duration becoming excessive – or maximum equivalent strain in an element – to guard against largely skewed elements and negative volume errors. The erosion of elements is activated by the minimum timestep falling below 80% of its initial value or the effective strain exceeding a value of 1. Figure 5-8 Comparison of NCF quasi-static deflection experimental force-displacement vs numerical (complete perforation) In the case of the interrupted test shown in Figure 5-9 there is again an over-estimation of peak force, but the maximum displacement is predicted accurately. Some substantial load drop features are accurately predicted, but they occur at loads higher than expected from the experimental data. 150 Figure 5-9 Comparison of NCF quasi-static deflection experimental force-displacement vs numerical (interrupted perforation) Impact Test Comparison Since the low-velocity impact tests have previously been shown to be substantially similar to the quasi-static tests, it was expected that based on the good fit of the quasi-static structural response data, the low-velocity impact structural response would also be accurately predicted. Two such low-velocity impact test datasets are shown in Figure 5-10 and Figure 5-11 below. As expected, the response is similar to the quasi-static results and is fairly accurate, but it does over-predict the peak load and slightly underpredict the peak displacement. Overall, the model appears to be slightly too resistant to damage. It should also be noted that the load returns to zero at a smaller displacement than is observed in the experiments. This is due to the fact that the CODAM2 model is an orthotropic linear elastic model with a strain-based damage progression formulation and does not include any mechanisms to account for permanent dent depth. The fact that it does not return to zero load at zero displacement is only indicative of the fact that some element erosion under the impactor has occurred in order to facilitate the 151 continued computation and is not an indication that the model is accurately predicting a certain permanent dent depth. Figure 5-10 Comparison of numerical force-displacement plot for impact N5 to the experimental impact and quasi-static test results; loading curve is well predicted but peak force is too high and peak displacement too low (response is too stiff) Figure 5-11 Comparison of numerical force-displacement plot for impact N10 to the experimental impact and quasi-static test results; loading curve is well predicted but peak force is too high 152 Since there is no experimental force data available for the high-velocity impact case it is not possible to carry out validation of the numerical model’s structural response prediction, however it is possible to query the force response of the numerical test in order to interrogate what likely occurred during the experimental impact. This result is shown in Figure 5-12 below where the high-velocity impact test N17 has its force-displacement response plotted against the experimental quasi-static indentation and deflection tests as well as the numerical low-velocity tests from Figure 5-10 and Figure 5-11 above. In this figure it can be seen how the high-velocity impact curve follows the quasi-static indentation curve to a much higher force level than the low-velocity impacts. The first peak in this figure (before the impact curve falls away from the quasi-static indentation curve) occurs at a time of 0.0027 ms which corresponds closely to the predicted time for the through thickness stress wave to travel to the backface and return to the impactor (~0.002 ms). After this point the response begins to deviate from the quasi-static indentation curve as expected, but critically, it has reached a very high load early on compared with the low-velocity impacts. Figure 5-12 Temporal effect of impact duration on early state impact load First peak 153 It is also important to compare the predicted delamination areas of the numerical tests with the experimental tests to determine whether the model is able to accurately predict the overall damage size and shape. This comparison for the selected high-energy tests is shown in Figure 5-13 below. Quasi-static Test QSD-N8 Low-Velocity/High Mass – Drop Tower – Test N5 Low-Velocity/Interme-diate Mass – Instrumented Gas Gun– Test N10 High-Velocity/Low Mass – Free Flying Gas Gun – Test N17 Numerical (a) (b) (c) (d) Experimental (e) (f) (g) (h) Figure 5-13 Comparison of Numerical and Experimental Delamination Areas Additionally, the predicted regions of fibre and matrix damage are shown in Figure 5-14 below. 154 Quasi-static Test QSD-N8 Low-Velocity/High Mass – Drop Tower – Test N5 Low-Velocity/Interme-diate Mass – Instrumented Gas Gun– Test N10 High-Velocity/Low Mass – Free Flying Gas Gun – Test N17 Numerical Fibre Damage (a) (b) (c) (d) Numerical Matrix Damage (e) (f) (g) (h) Figure 5-14 Numerical predictions for the regions of fibre and matrix damage It can be seen that the numerical model predicts the size of the delaminations around the impact site in the quasi-static and low-velocity impact quite well, but it does not properly predict the large delamination region associated with the matrix splitting and complete tow delamination on the backface, even though a 10 mm wide tow segment was modelled with the ability to completely split off from the surrounding material. Additionally, while the impact delamination prediction for the high-velocity case is slightly larger than the low-velocity cases, the size of this delamination is nothing like that of the true high-velocity delamination area from the experiments. These disparities in damage size could well explain the tendency for the model’s structural response prediction being too stiff (high peak force and under-prediction of maximum displacement). 155 The prediction of intralaminar matrix damage size in Figure 5-14 does seem reasonable based on comparison to CT imaging results, however the fibre damage is clearly affected by the local damage method used by the built in MAT219 material model. There appears to be very little damage predicted in the ±57° layers and this is likely due to the misalignment of the mesh from the fibre direction in these layers. 156 Chapter 6: Discussion Through the calculations of wave velocities in Section 4.2 it has been shown that for both the NCF and 2D braid coupons used in this study, the critical impact duration that divides high-velocity impact from low-velocity impact is in the range of 0.52 to 1.46 ms. This criterion is based on the speed of the lowest mode flexural wave and the length of time it takes this wave to reach the nearest boundary. After carrying out the impact tests, it was found that both the instrumented gas gun and drop tower resulted in impact durations longer than this critical duration, while the free-flying gas gun produced impacts that were shorter than this duration. Therefore, it was expected that the structural response and damage to the samples between these two groups would contain key differences. These key differences do appear to manifest themselves in smaller permanent dent depths for all high-velocity impacts regardless of fibre architecture, and in the case of NCF material, much larger delamination areas. The following section will further examine these two results and their interconnectedness. 6.1 Relationship Between Damage Area, Permanent Dent Depth and Velocity Regime By plotting the damage area found in the ultrasonic c-scans against the permanent dent depth from contact measurements, the interconnection between these two methods of damage absorption can be examined. The results are shown in Figure 6-1and they have been overlaid with coloured regions to highlight the general trends. 157 Figure 6-1 Projected damage area from ultrasonic scanning vs permanent dent depth; there is a clear increase in damage area and reduction in permanent dent depth in the case of NCF high-velocity/low mass, and almost no change in 2D braid high-velocity/low mass From this figure, three main responses can be seen and their contributing effects will be discussed below. Low-Velocity Impact – Both Materials For both materials, the relationship between dent depth and damage area is fairly similar. At lower energy levels there is a rapid growth in damage area which can largely be attributed to local indentation (matrix and fibre cracking immediately below the impactor) (Davies and Olsson 2004); but the damage area quickly reaches a plateau region. In this plateau region there is a tendency to produce more localized damage instead of the damage radiating further out from the impact site. This is explained by the fact that for low-velocity impact there is sufficient time for the sample to bend and fully load the fibres and matrix on the backface of the sample. This phenomenon was clearly shown through analysis of the deformation patterns as recorded by the high-speed cameras and analyzed with 3D digital image correlation. As shown in Figure 4-27 a & b, the global bending response of the NCF and 2D braid panels subjected to LVI appears fully developed throughout the duration of the impact, whereas the HVI tests (Figure 4-26 c & d) initially result in only localized shear deformation. This tensile overload of material on the back-NCF – High-Velocity/Low MassNCF – Low-Velocity/High Mass& Quasi-static2D Braid – High-Velocity/Low Mass2D Braid – Low-Velocity/High Mass& Quasi-static158 face in the LVI tests causes fracture of the rearmost layers, just as shown by the micrograph of García-Rodríguez et al. (2018) in Figure 2-13. This results in increased compliance of the panel and leads to further bending and more fracture towards the midplane of the sample as the damage progresses through the sample from back to front as shown in Figure 2-9a and described by Cantwell and Morton (1985) and Abrate (1991). This mode of damage can be readily seen in low-velocity CT scans of the current work such as Figure 4-33 and Figure 4-34 g, h & I. Others who have studied damage in low-velocity impact on braided materials have found the same including Sutcliffe et al. (2012) who provided cross section micrographs showing similar forms of substantial damage involving “significant tow fibre fracture near the impact site.” (Figure 2-16). As was shown by Sutcliffe et al. and Roberts et al. (2005), the damage in braided samples largely manifests itself as matrix and fibre fracture in close proximity to the impact site. CT cross sections such as Figure 4-34 g-j and micrographs by Sutcliffe et al. (2012) – while being slightly lower in energy level (~5 J/mm) compared to the micrographs by Sutcliffe et al. (7.4 – 8.0 J/mm) shown in Figure 2-16 – both indicate substantial matrix and fibre fracture throughout the thickness of the laminate. When compared to the triaxially braided laminate studied by Hosur et al. (2009), the current work appears to indicate more damage than that of Hosur et al. who found that at 4.3 J/mm, their samples responded elastically without damage. The latter were even able to support an impactor energy of 12.9 J/mm whereas the current work showed penetration (impactor displacement of 19.0 mm) at only 8.75 J/mm (sample B12, Figure 4-19). The epoxy resin used by Hosur et al. was Applied Poleramic Inc.’s SC-15 epoxy, which is a toughened vacuum-assisted resin transfer moulding compatible resin (Wang, McAninch, and Scala 2011). It is possible that this difference in performance may be attributable to the extra toughening within the SC-15 system. 159 The higher delamination area of the NCF material compared to the braided material can be in part attributed to the mesoscale delamination/spalling of tows that are directly opposite the impact site on the backface of the sample (Cantwell and Morton 1989). The damage modes involved in this may begin with matrix cracking and splitting between tows on the backface, which then enters the interlaminar region and manifests itself as large scale delamination of tows. Because of the importance of splitting in generating these back-face delaminations, it is limited to a single layer only. This type of delamination can be clearly seen in Figure 4-31. It does largely appear to be limited to only two tows in width, which does match the observation of Edgren, Asp, and Bull (2004) who noted that delaminations in NCF materials are often constrained to the rectangular shape of the stitched NCF areas. 2D braid High-Velocity Impact In this case there is neither a substantial permanent dent, nor a large delamination area. The lack of a permanent dent at high-velocity corroborates the evidence of similar behavior shown by Sutcliffe et al. (2012) in Figure 2-15 where they found a marked decrease in permanent dent depth in 2D braided material when using a light impactor compared to a heavier impactor at the same energy level. The lack of any substantial delamination matches the result of Roberts et al. (2005) and may be attributable to two effects. Firstly, the lack of any macroscale stiffness mismatch between plies on either side of the interfaces implies that flexure of the panels does not generate interlaminar shear stress as discussed by Liu (1988) and Morita et al. (1997). Secondly, the braided architecture within each layer serves to impede any mesoscale matrix cracks as they will inevitably encounter a tow crossing their path as discussed by Hosur et al. (2009). Most of the impact energy then is likely absorbed through the fragmentation of matrix and fibre locally around the impact site as shown in the CT image of Figure 4-34 j. This result is 160 somewhat in contrast to Sutcliffe et al. (2012) who noted that their delamination area in 2D braid material was larger under high velocity impact conditions as shown in Figure 2-14. Since they did not include images of the c-scans used to produce Figure 2-14 it is difficult to examine this discrepancy further. NCF High-Velocity Impact In this case there is no substantial permanent indentation (similar to the braided material), however there is a very large growth in the total delamination area observed with increasing energy. The NCF material does not have the two key benefits of the braided material with regards to stiffness mismatch and architecture. First, there is a difference in fibre angle of up to 60° between plies. This is well beyond the 30° difference in fibre angle that Ma and Liu (2015) state as the critical angle above which delamination becomes the dominant damage mode over fibre bridging. Essentially, this 60° fibre orientation change between plies provides a sufficient orthotropic elastic property mismatch to result in a substantial elastic constraint interaction between adjacent plies and/or Poisson ratio mismatch. This interaction gives rise to large interlaminar shear stress owing to either elastic constraint (Hong and Liu 1989; Liu 1988; Morita et al. 1997) or free-edge effect (Miracle and Donaldson 2001) and is a primary cause of delamination. Furthermore, the lack of intertwining tows also means that a delamination crack can extend through the low-toughness matrix material without ever encountering any of the tougher fibres as would happen to a delamination trying to extend within a ply of the braided material. There are stitches that the delamination either needs to navigate around, fracture, or deform; but these stitches (often polyester) have lower tensile and shear modulus than the epoxy matrix and so do not provide much structural support. Even still there is some evidence in the CT images of Figure 4-33 that show delaminations far away from the impact site appear to 161 preferentially occur in interfaces between NCF blankets where there is no stitch reinforcement. This would corroborate statements from Asp, Varna, and Marklund (2011) and Pickett (2011) who state that the fracture toughness inside an NCF blanket is higher than the interface between blankets. The resin-rich region between blankets noted by Pickett may also be a cause of preferential delamination in these interfaces. 6.2 Importance of the Results for Informing Visual Inspection Visual inspection techniques have a high efficacy for detecting damage when substantial surface indications are present. It is generally reported that a dent depth of at least 0.25 mm to 0.5 mm is highly likely to be detected (Sasikumar et al. 2019) and therefore, the size of permanent dent is an important consideration for those tasked with identifying impact damage. Therefore, the absence of permanent dents above 0.5 mm deep under high-velocity impact conditions at the energies tested (Figure 4-28 or Figure 6-1) is of great concern for those in the field of non-destructive testing, and is known as “barely visible impact damage”. This is particularly concerning for the NCF material as it has been shown that the size of delamination areas increases under high-velocity impact conditions. Without visually detectable damage on the surface, the only method to find this damage is other more complex non-destructive inspection techniques such as ultrasonic scanning and lock-in thermography. All are time consuming and require skilled operators. Delaney, Fung, and Kim (2018) found that for low-velocity impact there was a clear relationship between dent depth and internal damage for hemispherical impactors with a diameter of less than 25.4 mm; but they did importantly note that for larger diameter impactors (e.g. 50.8 to 76.2 mm) there was no such relationship. For these larger impactors it was found that a wide disparity in delamination can exist for a given measured dent depth. Therefore, barely 162 visible impact damage is also of concern for low-velocity impacts if the impactor is sufficiently large enough. 6.3 Damage Resistance Figure 4-29 clearly shows two main trends that are distinguished by whether or not an impact is considered low-velocity or high-velocity impact. For both impact velocity regimes there is a linear correlation between impact energy and the percent of that impact energy that is converted to damage. Importantly though, this trendline appears to pass close to the right of the origin only in the case of low-velocity impact, indicating the intuitive result that at low impact energies there is little damage. At low energies, the panel is capable of almost complete elastic absorption and return of energy to the impactor. This provides a mechanism for the sample to avoid permanent damage. At higher impact velocities though, the slope of this trend is lower and remains high even for relatively low impact energies. In this case, under high-velocity impact conditions there is insufficient time for the energy to be stored elastically (strain energy) in a larger portion of the structure, and therefore the sample acts more like the immovable plate seen in quasi-static indentation trials. This is clearly seen in 3D digital image correlation results (Figure 4-26 & Figure 4-27) where deformation early on in the impact period is highly localized. It can be seen in these figures that much of the perimeter of the data area is experiencing no out of plane deformation at all. This lack of global compliance of the panel causes the contact force to rise rapidly (see quasi-static indentation curves in Figure 4-11). Therefore, damage occurs with relatively small impact energies since this energy must be contained by a smaller amount of material before the shear and flexural stress waves have time to spread through the sample. This is recognized by several other authors as the cause of this behavior including Olsson (1993, 2000), Cantwell and Morton (1989), Morita et al. (1997), García-Rodríguez et al. (2018), Bull, 163 Spearing, and Sinclair (2015), and Delfosse et al. (1995). Therefore, damage resistance is reduced under high-velocity impact conditions as a result of both the inability of the structure to elastically deform over a larger area and the increased contact forces that come as a result of that and are shown in Figure 5-12. 6.4 Modelling Considerations In this work, the numerical modelling was made using a lamina level model where each layer was included as its own part with tiebreak constraints modelled between each layer. This is a computationally expensive method that is time consuming to set up. However, according to Lu and Liu (1992) this level of modelling is a necessity in order to properly consider interlaminar stresses and their effects across the interfaces between layers of fibre with differing orientations. If the model is built up at the sub-laminate, laminate, or any other level where each layer has the same type of elastic anisotropy, then the model will not properly consider how stresses are redistributed between adjacent layers and interlaminar stresses will be underestimated. This has the effect of possibly missing delamination failure modes altogether. In the case of this lamina level model, good agreement was found between the experimental and numerical structural response (force-displacement) even though the projected delamination area from the simulations was less than that observed in the experiments (Figure 5-13). This could be due to the total delamination area of the simulation matching that of the experiments (more numerical interfaces with delamination compared to the experiment; particularly considering that the effect of stitching was not accounted for in the model), or it could be due to an under-estimation of delamination damage energy dissipation coupled with an over-estimation of intralaminar damage energy dissipation. It is not possible to confirm this with the data available. An improvement of the delamination area prediction could be made with the 164 inclusion of non-local damage methods to remove the mesh orientation dependency on intralaminar damage progression as well as coupling the delamination initiation to matrix cracking within the laminate. Additionally, it has been seen that delamination areas in all forms of 2D braided impacts are minimal. No numerical models were evaluated with the braided material properties; however, it should be noted that the ability of the braided architecture to arrest delamination within a ply could be an important consideration for the modelling of impact damage in such materials. The current model was also not capable of properly representing the delamination/spalling of tows off the backface of the coupon and therefore there was a substantial under-estimation of delamination area and delamination energy due to this shortcoming. Lastly, it is noted that since CODAM2 is an orthotropic linear elastic model with a strain-based damage progression formulation, it currently does not possess the ability to model permanent indentation apart from element erosion. Since element erosion in CODAM2 is currently dependent on either in-plane strains or a certain reduction in characteristic length (minimum timestep according to the Courant-Friedrichs-Lewy (CFL) condition) if enabled; there is currently no way of including this effect in terms of its true causes and no way of accounting for the rate-dependency observed (Figure 4-28). 165 Chapter 7: Conclusions & Future Work 7.1 Conclusions The work covered in this thesis has focused primarily on improving our understanding of how a carbon fibre epoxy composite material system with two different fibre architectures of interest to the automotive industry – non-crimp fabric and 2D braided fabric – respond to transverse impact. Transverse impact is an important load case in that it may be a primary load case of interest for automotive applications, but it also provides an excellent proxy case for arbitrarily complex states of stress at varying strain rates and thus provides a challenging numerical model validation case that can be used to test the efficacy of different models. This is important because improving and validating the analytical methods available to composite structure engineers will enable them to rely upon simulation results with a greater degree of certainty. Eventually, this will allow for more efficient design-by-analysis techniques to substitute a larger portion of design substantiation that is currently heavily dependent on costly and time-consuming physical testing – the building-block approach. Through the experimental work in this thesis, quantitative data of the structural response during impact (force-displacement-time) has been generated at test rates ranging from quasi-static to high-velocity impact. Subsequent data – both quantitative (delamination area, permanent dent depth) and qualitative (delamination region shape, damage features in CT scans) – was collected to characterize the resulting damage state. Failure modes induced in the samples include matrix fracture, matrix splitting, fibre fracture, and delamination. The relationship between data gathered and the parameters of the tests (impact velocity and energy) have been analyzed, discussed, compared and contrasted with observations from other literature. Additionally, numerical models have been created with the CODAM2 model in order to 166 preliminarily test its efficacy for predicting impact damage in transverse impact experiments with NCF material. The primary findings from this work are: • Reduced damage resistance under HVI – Damage resistance is reduced under high-velocity impact conditions for both materials. This was evidenced by the larger percentage of energy absorption by the samples during high-velocity impact and is likely due to damage from high shear loads due to high contact forces. This is caused by the inability of the structure to deform in a flexural mode in such a short time and elastically absorb more of the impact energy for eventual return to the projectile. • Reduced permanent dent depth under HVI – The damage from low-velocity impact in both materials is readily visible due to a substantial permanent dent depth remaining after the impact. Conversely for high-velocity impact there was no substantial permanent dent depth for the energies tested. The lack of a substantial permanent dent is an important finding for those who are concerned with the detection of damage. The small permanent dent depth means that this damage can be classified as barely visible impact damage, and the large delamination area means the consequences of this damage on the residual properties of the structure are more substantial than for the more visible low-velocity impact damage. • Localization of damage in 2D braid – The size and shape of the damage zone were not significantly altered between low-velocity impact damage and high velocity impact damage. In all cases the damage was localized and produced mainly matrix and fibre cracks. At higher energy levels substantial fragmentation of the laminate was observed. It is believed that the lack of any stiffness mismatch between plies of the 2D braid material 167 and the intertwining nature of the braided architecture were effective in limiting the overall size of the damage area. • Variation of damage in NCF according to impact conditions and location – o LVI – Increasing impact energy under LVI conditions for the NCF material results in additional fibre and matrix fracture in the vicinity of the impact site along with substantial matrix splitting between the tows on the back side of the coupon. The splitting can lead to substantial delamination of the tows on the backface of the sample, but this region is constrained in overall size due to the mesoscopic effect of the stitching. o HVI – Rather than create mostly substantial fracture and rubble as in the case of the 2D braid, more of the impact energy is absorbed through delamination over a wide area. This is caused by the high contact forces brought about by the lack of time for the panel to deflect elastically and it is assisted by the substantial stiffness mismatch between layers and the lack of any tough material intersecting the interlayer to arrest the delamination. o Intrablanket vs interblanket interfaces – Some evidence was found that delaminations further away from the impact site do tend to be inhibited in layers within NCF blankets. This may be due to the through thickness stitching of the NCF material or potentially other microstructural features due to processing conditions. • Efficacy of CODAM2 - Using a lamina level model it was found that the structural response is fairly accurate to the experiments; but the current model is slightly too resistant to delamination, resulting in higher predicted peak loads. The size of the damage 168 zone was found to be too small when compared to experimental results, but this could be improved with non-local damage methods to eliminate mesh dependency, and the coupling of the delamination initiation to matrix cracking within the laminate. The results summarized above match well with those observed in the literature and thus serve to support and enhance the existing literature regarding transverse impact of CFRP panels; specifically for 2D braid and NCF fibre architectures. This work is unique in that it provides a direct comparison between both 2D braid and NCF CFRP material having the same matrix, fibre and manufacturing conditions, thereby allowing a side-by-side comparison from quasi-static all the way to high-velocity impact conditions. The data collected during this experimental work is of high fidelity and suitable for comparison to numerical simulations for validation of structural response and resulting damage state. It is also novel in the use of 3D DIC to visually characterize the difference in deformation between LVI and HVI impact in CFRP panels; providing an opportunity to accurately observe the levels of local and global deformation in the CFRP panels under different impact regimes. By utilizing the data and observations collected in this work, engineers will have better understanding of what damage modes and extents to expect in NCF and 2D braid CFRP materials. This allows them to make a more informed choice between the two (or others) depending on their application. Numerical models validated with this data can be relied upon with greater confidence that they are predicting the correct result. This in turn improves the efficiency of the design cycle by eliminating at least some of the need for physical prototype testing, thereby lowering the non-recurring cost of design. When combined with efficient high-rate processes such as resin transfer moulding with near-net shape preforms; manufacturing 169 capacity of the composite parts may have a low enough recurring cost to enable cost effective production manufacturing. If these goals are achieved and the use of composite materials for lightweighting automotive vehicles is increased, the efficiency of traditional vehicles can be improved and electric vehicles will become less constrained by range, enabling the further reduction of greenhouse gas emissions to meet targets. 7.2 Future Work Building upon and branching off from this work, the following are areas where additional work and research would add value to the data herein or improve the modelling capabilities of CODAM2: • Investigation of the relation between impact energy and the amount of energy absorbed inelastically – Given the trends plotted in Figure 4-28 and Figure 4-29 further efforts should be put into creating simple energy balance equations and analysis to broadly explain these trends, along the lines of, for example, Delfosse and Poursartip (1997). • Compression after impact – The samples used in this work remain unchanged from their post-impact state (with the exception of one that was cut to examine different CT scan settings). Compression after impact is a common test that is carried out to gauge damage tolerance of a material system/laminate. Together with a custom fixture for 100 mm x 100 mm samples, the samples used in this work may be tested to gather further data on how well these NCF and 2D braid materials fare with regards to damage tolerance. • Fracture toughness of intrablanket vs interblanket interfaces – It has been shown in CT data that at a sufficient distance from the impact site, the internal structure of NCF 170 blankets may provide additional resistance to delamination propagation. This provides some indication that the fracture toughness of layer interfaces between blankets (interblanket interface) may be slightly lower than layer interfaces inside blankets (intrablanket interface). Experimental work to further understand if this is truly the case – and if so, what are the causes (stitches, resin rich regions, etc.) – and to characterize this difference would help to improve model accuracy and potentially tie process simulation into damage modelling. • Generalization of CODAM2 from transversely isotropic to orthotropic – Currently, the MAT219 material model in LS-DYNA® is transversely isotropic and uses the same elastic constants for the in-plane transverse direction as it does for the out of plane direction. Model accuracy (particularly for high-velocity transverse impact) could be improved by making the through thickness material properties independent of in-plane properties, allowing for a more accurate impact force under HVI conditions. Through-thickness modulus could then be calibrated based on the quasi-static indentation force-displacement response for example. 171 References “3-D Woven Reinforcements Update.” 2011. CompositesWorld. 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New York: John Wiley & Sons. 181 Appendices Appendix A — Burn-off examination of NCF material system Figure A-1 De-ply of NCF material layers 1-6 showing ply fibre orientation, thickness and mass 182 Figure A-2 De-ply of NCF material layers 7-12 showing ply fibre orientation, thickness and mass 183 Appendix B— Force vs Displacement Figures from Impact tests B.1 NCF Low-Velocity/High Mass Structural Response Figure B-1 Force vs displacement plot from the drop-tower apparatus; impact N1; impact velocity 1.55 m/s; impact energy 3.41 J Figure B-2 Force vs displacement plot from the drop-tower apparatus; impact N2; impact velocity 2.31 m/s; impact energy 7.54 J 184 Figure B-3 Force vs displacement plot from the drop-tower apparatus; impact N3; impact velocity 2.32 m/s; impact energy 7.56 J Figure B-4 Force vs displacement plot from the drop-tower apparatus; impact N4; impact velocity 2.69 m/s; impact energy 10.23 J Figure B-5 Force vs displacement plot from the drop-tower apparatus; impact N5; impact velocity 2.93 m/s; impact energy 12.06 J 185 Figure B-6 Force vs displacement plot from the drop-tower apparatus; impact N6; impact velocity 3.01 m/s; impact energy 12.74 J B.2 NCF Low-Velocity/Intermediate Mass Structural Response Figure B-7 Force vs displacement plot from the drop-tower apparatus; impact N7; impact velocity 5.48 m/s; impact energy 6.57 J 186 Figure B-8 Force vs displacement plot from the drop-tower apparatus; impact N8; impact velocity 6.35 m/s; impact energy 8.81 J Figure B-9 Force vs displacement plot from the drop-tower apparatus; impact N9; impact velocity 7.06 m/s; impact energy 10.88 J Figure B-10 Force vs displacement plot from the drop-tower apparatus; impact N10; impact velocity 7.24 m/s; impact energy 11.46 J 187 Figure B-11 Force vs displacement plot from the drop-tower apparatus; impact N11; impact velocity 8.25 m/s; impact energy 14.87 J Figure B-12 Force vs displacement plot from the drop-tower apparatus; impact N12; impact velocity 9.10 m/s; impact energy 18.11 J B.3 NCF High-Velocity/Low Mass Structural Response There are no figures for force displacement of the low mass/high-velocity impacts due to the absence of force transducer data B.4 Braided Low-Velocity/High Mass Structural Response Figure B-13 Force vs displacement plot from the drop-tower apparatus; impact B1; impact velocity 1.27 m/s; impact energy 2.27 J 188 Figure B-14 Force vs displacement plot from the drop-tower apparatus; impact B2; impact velocity 1.71m/s; impact energy 4.12 J Figure B-15 Force vs displacement plot from the drop-tower apparatus; impact B3; impact velocity 1.72 m/s; impact energy 4.17 J Figure B-16 Force vs displacement plot from the drop-tower apparatus; impact B4; impact velocity 2.19 m/s; impact energy 6.73 J 189 Figure B-17 Force vs displacement plot from the drop-tower apparatus; impact B5; impact velocity 2.22 m/s; impact energy 6.92 J Figure B-18 Force vs displacement plot from the drop-tower apparatus; impact B6; impact velocity 2.93 m/s; impact energy 12.06 J 190 B.5 Braided Low-Velocity/Intermediate Mass Structural Response Figure B-19 Force vs displacement plot from the drop-tower apparatus; impact B7; impact velocity 4.04 m/s; impact energy 3.58 J Figure B-20 Force vs displacement plot from the drop-tower apparatus; impact B8; impact velocity 4.33 m/s; impact energy 4.10 J 191 Figure B-21 Force vs displacement plot from the drop-tower apparatus; impact B9; impact velocity 5.17 m/s; impact energy 5.85 J Figure B-22 Force vs displacement plot from the drop-tower apparatus; impact B10; impact velocity 7.11 m/s; impact energy 11.04 J Figure B-23 Force vs displacement plot from the drop-tower apparatus; impact B11; impact velocity 7.22 m/s; impact energy 11.40 J 192 Figure B-24 Force vs displacement plot from the drop-tower apparatus; impact B12; impact velocity 9.51 m/s; impact energy 19.76 J B.6 Braided High-Velocity/Low Mass Structural Response There are no figures for force displacement of the low mass/high-velocity impacts due to the absence of force transducer data. 193 Appendix C- Ultrasonic Scans of Impacted Samples C.1 NCF Low-Velocity/High Mass Structural Response Impact Test Ultrasonic C-Scan Image Ultrasonic C-Scan Image with Mask Showing Area Identified as Damaged N1 (a) (b) Figure C-1 Post-test ultrasonic c-scan images of the sample from impact test N1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N2 (a) (b) Figure C-2 Post-test ultrasonic c-scan images of the sample from impact test N2 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N3 (a) (a) Figure C-3 Post-test ultrasonic c-scan images of the sample from impact test N3 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 194 N4 (a) (b) Figure C-4 Post-test ultrasonic c-scan images of the sample from impact test N4 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N5 (a) (b) Figure C-5 Post-test ultrasonic c-scan images of the sample from impact test N5 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N6 (a) (b) Figure C-6 Post-test ultrasonic c-scan images of the sample from impact test N6 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 195 C.2 NCF Low-Velocity/Intermediate Mass Structural Response Impact Test Ultrasonic C-Scan Image Ultrasonic C-Scan Image with Mask Showing Area Identified as Damaged N7 (a) (b) Figure C-7 Post-test ultrasonic c-scan images of the sample from impact test N7 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N8 (a) (b) Figure C-8 Post-test ultrasonic c-scan images of the sample from impact test N8 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N9 (a) (b) Figure C-9 Post-test ultrasonic c-scan images of the sample from impact test N9 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 196 N10 (a) (b) Figure C-10 Post-test ultrasonic c-scan images of the sample from impact test N10 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N11 (a) (b) Figure C-11 Post-test ultrasonic c-scan images of the sample from impact test N11 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N12 (a) (b) Figure C-12 Post-test ultrasonic c-scan images of the sample from impact test N12 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 197 C.3 NCF High-Velocity/Low Mass Structural Response Impact Test Ultrasonic C-Scan Image Ultrasonic C-Scan Image with Mask Showing Area Identified as Damaged N13 (a) (b) Figure C-13 Post-test ultrasonic c-scan images of the sample from impact test N13 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N14 (a) (b) Figure C-14 Post-test ultrasonic c-scan images of the sample from impact test N14 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N15 (a) (b) Figure C-15 Post-test ultrasonic c-scan images of the sample from impact test N15 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 198 N16 (a) (b) Figure C-16 Post-test ultrasonic c-scan images of the sample from impact test N16 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N17 (a) (b) Figure C-17 Post-test ultrasonic c-scan images of the sample from impact test N17 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) N18 (a) (b) Figure C-18 Post-test ultrasonic c-scan images of the sample from impact test N18 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 199 C.4 Braided Low-Velocity/High Mass Structural Response Impact Test Ultrasonic C-Scan Image Ultrasonic C-Scan Image with Mask Showing Area Identified as Damaged B1 (a) (b) Figure C-19 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B2 (a) (b) Figure C-20 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B3 (a) (b) Figure C-21 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 200 B4 (a) (b) Figure C-22 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B5 (a) (b) Figure C-23 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B6 (a) (b) Figure C-24 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 201 C.5 Braided Low-Velocity/Intermediate Mass Structural Response Impact Test Ultrasonic C-Scan Image Ultrasonic C-Scan Image with Mask Showing Area Identified as Damaged B7 (a) (b) Figure C-25 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B8 (a) (b) Figure C-26 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B9 (a) (b) Figure C-27 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 202 B10 (a) (b) Figure C-28 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B11 (a) (b) Figure C-29 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B12 (a) (b) Figure C-30 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 203 C.6 Braided High-Velocity/Low Mass Structural Response Impact Test Ultrasonic C-Scan Image Ultrasonic C-Scan Image with Mask Showing Area Identified as Damaged B13 (a) (b) Figure C-31 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B14 (a) (b) Figure C-32 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B15 (a) (b) Figure C-33 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 204 B16 (a) (b) Figure C-34 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B17 (a) (b) Figure C-35 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) B18 (a) (b) Figure C-36 Post-test ultrasonic c-scan images of the sample from impact test B1 (a) un-segregated (b) segregated to show the region of impact damage (non-darkened region) 205 Appendix D- X-Ray CT Scans of Impacted Samples D.1 NCF Quasi-static CT Scans Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center QSD-N8 (a) (b) (c) (d) (e) Figure D-1 Post-test x-ray computed tomography images of the sample from quasi-static test QSD-N8 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 206 D.2 NCF Low-Velocity/High Mass CT Scans Impact Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center N1 (a) (b) (c) (d) (e) Figure D-2 Post-test x-ray computed tomography images of the sample from impact test N1 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center N3 (a) (b) (c) (d) (e) Figure D-3 Post-test x-ray computed tomography images of the sample from impact test N3 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 207 N5 (a) (b) (c) (d) (e) Figure D-4 Post-test x-ray computed tomography images of the sample from impact test N5 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 208 D.3 NCF Low-Velocity/Intermediate Mass CT Scans Impact Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center N7 (a) (b) (c) (d) (e) Figure D-5 Post-test x-ray computed tomography images of the sample from impact test N7 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center N8 (a) (b) (c) (d) (e) Figure D-6 Post-test x-ray computed tomography images of the sample from impact test N8 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 209 N10 (a) (b) (c) (d) (e) Figure D-7 Post-test x-ray computed tomography images of the sample from impact test N10 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 210 D.4 NCF High-Velocity/Low Mass CT Scans Impact Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center N13 (a) (b) (c) (d) (e) Figure D-8 Post-test x-ray computed tomography images of the sample from impact test N13 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center N15 (a) (b) (c) (d) (e) Figure D-9 Post-test x-ray computed tomography images of the sample from impact test N15 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 211 N17 (a) (b) (c) (d) (e) Figure D-10 Post-test x-ray computed tomography images of the sample from impact test N17 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 212 D.5 2D Braid Quasi-static CT Scans Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center QSD-B9 (a) (b) (c) (d) (e) Figure D-11 Post-test x-ray computed tomography images of the sample from quasi-static test QSD-B9 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 213 D.6 Braided Low-Velocity/High Mass CT Scans Impact Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center B2 (a) (b) (c) (d) (e) Figure D-12 Post-test x-ray computed tomography images of the sample from impact test B2 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center B4 (a) (b) (c) (d) (e) Figure D-13 Post-test x-ray computed tomography images of the sample from impact test B4 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 214 B6 (a) (b) (c) (d) (e) Figure D-14 Post-test x-ray computed tomography images of the sample from impact test B6 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 215 D.7 Braided Low-Velocity/Intermediate Mass CT Scans Impact Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center B7 (a) (b) (c) (d) (e) Figure D-15 Post-test x-ray computed tomography images of the sample from impact test B7 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center B9 (a) (b) (c) (d) (e) Figure D-16 Post-test x-ray computed tomography images of the sample from impact test B9 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 216 B10 (a) (b) (c) (d) (e) Figure D-17 Post-test x-ray computed tomography images of the sample from impact test B10 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 217 D.8 Braided High-Velocity/Low Mass CT Scans Impact Test Center (0 mm) 2.5 mm Off-Center 5.0 mm Off-Center 7.5 mm Off-Center 10.0 mm Off-Center B13 (a) (b) (c) (d) (e) Figure D-18 Post-test x-ray computed tomography images of the sample from impact test B13 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center B16 (a) (b) (c) (d) (e) Figure D-19 Post-test x-ray computed tomography images of the sample from impact test B16 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center 218 B18 (a) (b) (c) (d) (e) Figure D-20 Post-test x-ray computed tomography images of the sample from impact test B18 (a) at the center of the impact (b) 2.5 mm off-center (c) 5.0 mm off-center (d) 7.5 mm off-center (e) 10.0 mm off-center
Thesis/Dissertation
eng
Materials Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
The effect of impactor mass and velocity on the structural response and damage modes of non-crimp and 2D braided CFRP panels
Text