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Experimental investigation of a strain softening approach to predicting failure of notched composite… Kongshavn, Ingrid A. 1996

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Experimental Investigation of a Strain Softening Approach to Predicting Failure of Notched Composite Laminates by Ingrid A . Kongshavn B . A . S c , Mechanical Engineering, University o f Waterloo, 1993 A THESIS SUBMITTED IN P A R T I A L F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R OF APPLIED  SCIENCE  in T H E F A C U L T Y OF G R A D U A T E STUDIES Department o f Metals and Materials Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH C O L U M B I A M a y 1996 © I. A. Kongshavn,  1996  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or  by  his or  her  representatives.  It  is  understood  that  copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  r A E T A L S *t*b r 4 A T £ £ . l f l L S  The University of British Columbia | Vancouver, Canada Date  DE-6 (2/88)  B^V^EG^I  ^  Abstract  This work describes an experimental investigation o f a strain softening approach to the prediction o f fracture in notched composite laminates.  This approach has been found to more  accurately predict fracture o f large notched coupons or structures than traditional approaches. Strain softening accounts for the effect o f damage i n front o f the notch tip, by the post-peak region o f a strain softening curve. This region is traditionally defined by a stress that decreases with increasing strain. A physical understanding o f the post-peak region o f the curve is required to better examine the predictive capabilities o f strain softening.  For this to be achieved, a detailed physical  understanding o f the damage i n the process zone is required. reinforced laminate material systems were examined.  In this study, two carbon fibre  A n overheight compact tension ( O C T )  specimen was developed to grow damage in a stable manner. The displacements in front o f the notch tip indicated the progression o f damage across the specimen width throughout the test. A detailed physical description o f the damage, which consisted o f a crack and process zone were obtained.  The sequence o f damage growth in the process zone was determined.  Tensile  specimens cut from the process zones indicated a preliminary shape o f the strain softening curves for the two material systems.  Finally, the experimental results were used to calibrate a  preliminary F E M strain softening analysis o f the O C T specimens. The preliminary F E M results suggest that a strain softening material response is necessary to capture the progressive damage growth across the specimen width.  ii  Sommaire  Ce travail presente une etude experimental de la theorie de l'adoucissement afin de predire la rupture de composites stratifies contenant une entaille.  E n comparaison avec les methodes  conventionelles, cette theorie permet une meilleure prediction de la rupture d'echantillons ou de structures de grande taille contenant une entaille.. L a partie de la courbe d'adoucissement apres le maximum permet de tenir compte des effets de l'endommagement devant le bout de l'entaille. Cette partie de la courbe est caracterisee par une diminution de la contrainte lorsque la deformation augmente. A f i n de mieux evaluer les possibilites de prediction de l a theorie de l'adoucissement, i l est necessaire de comprendre les phenomenes physiques associes a la partie de la courbe apres son maximum.  A i n s i , i l est necessaire de caracteriser la nature des dommages dans la zone  d'endommagement confinee. carbone ont ete etudies.  Dans ce travail, deux types de stratifes renforces de fibres de  U n echantillon C T surdimensione en hauteur a ete developpe et  rendommagement s'est propage de facon stable. Les deplacements mesures devant le bout de l'entaille  indiquent  revolution  de  rendommagement  sur  la  largeur  de  l'echantillon.  L'endommagement obtenu est caracterise par une fissure et une zone d'endommagement confinee.  L'evolution sequentielle de l'endommagement dans la zone d'endommagement  confinee a ete determinee. Des echantillons decoupes dans l a zone d'endommagement confinee ont ete testes en tension et ont permis d'obtenir la forme preliminaire de la courbe d'adoucissement pour les deux materiaux etudies.  Enfin, les resultats experimentaux ont ete  utilises afin de calibrer des analyses par elements finis des echantillons C T modifies.  iii  Les  resultats preliminaries obtenus par les elements finis semble indiquer q u ' i l est necessaire de considerer l'adoucissement du materiau afin de simuler la progression de l'endomagement dans la largeur de l'echantillon.  iv  Table of Contents  Abstract  ii  Sommaire  iii  Table of Contents  v  List of Tables  viii  List of Figures  ix  Acknowledgements  xiv  1. CHAPTER ONE - INTRODUCTION  1  1.1 Motivation  1  1.1.1 Examples o f Damage in a Composite Laminate  1.2 Linear Elastic Fracture Mechanics  2  2  1.2.1 The Process Zone in Quasi-Brittle Materials  1.3 Micromechanical Models Used to Predict Notched Behaviour 1.3.1 Predicting Fracture Based on a Fitted Parameter 1.3.2 Relating Fracture to a Physical Understanding o f the Damage Evolution  1.4 Macromechanical Models Used to Predict Notched Behaviour 1.4.1 Fictitious Crack Model  4  5 5 6  7 8  1.5 A Strain Softening Approach to Predicting Notched Behaviour 1.5.1 Experimental Investigation o f Strain Softening as a Material Property 1.5.2 Geometry o f a Strain Softening Specimen 1.5.3 Experimental Investigation o f Process Zone Softening  1.6 Statement of Objectives  8 10 10 11  13  2. CHAPTER TWO - OCT TEST DEVELOPED TO STUDY NOTCHED BEHAVIOUR  19  2.1 Introduction  19  2.2 The Overheight Compact Tension (OCT) Specimen  19  2.2.1 Development o f a Specimen Which Exhibits Stable Damage Growth 2.2.2 The Standard C T Stress Intensity Factor v  19 20  2.3 Description of the Experimental Setup  21  2.3.1 Loading Train and Specimen Preparation 2.3.2 Measured Specimen Displacements 2.3.3 Loading Train Deflection  2.4 Summary of OCT Tests Performed  21 21 22  23  2.4.1 Materials Studied 2.4.2 Tests Performed 2.4.3 Post-test Analyses  23 23 24  3. CHAPTER THREE - OCT TESTS AND DATA REDUCTION  27  3.1 Introduction  27  3.2 Cross Head and CMOD Displacements  28  3.2.1 General Shape of the Load vs Cross Head and Load vs C M O D Displacement Curves 3.2.2 Repeatability  28 29  3.3 Indications of Damage Growth  30  3.3.1 Surface Line Displacements 3.3.2 Clip Gauge Displacements  30 35  3.4 Discussion of Results  37  3.5 Summary of Results  38  4. CHAPTER FOUR - PHYSICAL DESCRIPTION OF THE DAMAGE  47  4.1 Introduction  47  4.2 Techniques  47  4.2.1 Deply 4.2.2 Sectioning and Micrograph Analysis 4.2.3 Pulse-Echo Ultrasonic Scan  48 48 49  4.3 Deply Results  49  4.4 Description of Damage in the Laminae  50  4.5 Sequence of Damage Progression Throughout the OCT Test  51  4.5.1 Development of Crack and Process Zone Height and Length 4.5.2 Temporal Sequence of Damage Growth in the Process Zone  52 53  4.6 Discussion  54  4.6.1 Notch-Sensitivity 4.6.2 Strain Softening Curve  54 56  4.7 Summary of Results  57 vi  5. CHAPTER FIVE - PROCESS ZONE TENSILE TESTS  70  5.1 Introduction  70  5.2 Background  70  5.3 Experimental Technique  71  5.4 Derivation of the Damaged Moduli  73  5.5 Experimental Results  73  5.5.1 Damage Observed Prior to Tensile Tests 5.5.2 Measured M o d u l i 5.5.3 Damaged M o d u l i  73 74 75  5.6 Discussion  78  5.7 Summary of Results  80  6. CHAPTER SIX - COMPARISON OF THE EXPERIMENTAL RESULTS WITH A PRELIMINARY FEM ANALYSIS  91  6.1 Introduction  91  6.2 Comparison of the Experimental and FEM Results  91  7. CHAPTER SEVEN - CONCLUSIONS AND FURTHER WORK  96  7.1 Introduction  96  7.2 Conclusions  96  7.3 Further Work  97  References  100  Appendix 1  103  Appendix 2  112  vii  List of Tables  Table 2.1 Overheight compact tension (OCT) specimen dimensions where the letters refer to the schematic in Figure 2.1. A l l dimensions are in mm. 25 Table 2.2 Summary o f instrumentation and post-test analysis o f each O C T specimen.  25  Table 3.1 Position in front o f the notch tip at which the scribe line has zero displacement at a given load. The results are for the scribe line closest to the notch mid-plane for specimens A 3 , B l and B 2 , and refer to the specified figures. 39 Table 5.1 Tensile specimen dimensions.  82  Table 5.2 Measured and derived tensile specimen mechanical properties.  82  viii  List of Figures  Figure 1.1 Primary load-bearing structures in the Boeing 777 made o f fibre reinforced composite laminates. (Courtesy o f The Boeing Company) 14 Figure 1.2 Schematic o f a fibre reinforced laminate.  14  Figure 1.3 Schematic showing some o f the damage mechanisms that occur in fibre reinforced composite laminates. Taken from Anderson (1991). 15 Figure 1.4 Centrally cracked plate subject to a uniform far-field stress.  15  Figure 1.5 Stress distribution around two different sized holes in an infinite isotropic plate. This explains the hole size effect according to Whitney and Nuismer. A greater probability exists around the larger hole for a flaw to initiate failure, as the stress concentration is less localized. Reproduced from Whitney and Nuismer (1974). 16 Figure 1.6 Schematic o f damage observed by Kortschot and Beaumont i n cross-ply graphite reinforced epoxy laminates. The damage was observed i n the 'terminal damage state' (TDS) just prior to failure o f double edge-notched specimens. Reproduced from Kortschot and Beaumont (1990a). 16 Figure 1.7 Representation o f the stress distribution i n the process zone i n Hillerborg's Fictitious Crack Model. The process zone is modeled as a fictitious crack, containing a linear cohesive stress distribution as shown. The preformed crack w i l l grow when the maximum stress at the tip o f the fictitious crack reaches the unnotched tensile failure strength. Reproduced from Afaghi-Khatibi et al. (1995). 17 Figure 1.8 The uniaxial strain softening curve predicted by Matzenmiller et al. (1991), based on a Weibull distribution o f fibre failure. Different degrees o f strain softening are predicted by the parameter, m. 17 Figure 1.9 Different regions o f a typical strain softening curve.  18  Figure 2.1 Schematic o f the overheight compact tension ( O C T ) specimen and experimental setup used to monitor displacements during loading.  26  Figure 3.1 Load vs cross head displacement o f specimens A l , A 2 , and A 3 . The cross head displacement is not a true measure o f the displacement at the specimen loading pins due to loading train deflection as discussed in Chapter 2. 40 Figure 3.2 Load vs C M O D and clip gauge displacement o f specimen A 4 .  40  Figure 3.3 Load vs C M O D displacement o f specimens B I and B 2 .  41  IX  Figure 3.4 Load vs cross head and clip gauge displacement o f specimen A 3 . The numbers on the curve indicate where the photos were taken throughout the test. The cross head displacement is not a true measure o f the displacement at the specimen loading pins due to loading train deflection as discussed in Chapter 2. 42 Figure 3.5 Displacement o f line #4 as a function o f position in front o f the notch tip for selected photos o f specimen A 3 . 42 Figure 3.6 Load vs C M O D and clip gauge displacement o f specimen B l . The numbers on the curve indicate where the photos were taken throughout the test. 43 Figure 3.7 Displacement o f line #1 as a function o f position in front o f the notch tip for selected photos of specimen B 1 . 43 Figure 3.8 Load vs C M O D displacement o f specimen B 2 . The numbers on the curve indicate where the photos were taken throughout the test. 44 Figure 3.9 Displacement o f line #1 as a function o f position in front o f the notch tip for selected photos o f specimen B 2 . 44 Figure 3.10 Displacement o f line #3 as a function o f position i n front o f the notch tip for selected photos o f specimen B 1 .  45  Figure 3.11 R-Curve o f specimens A 3 , B l and B 2 , based on the line analysis estimation o f the crack length. G is calculated for the peak loads corresponding to the crack lengths of photos: 1) specimen A 3 : 10, 12, 13, 14 in Figure 3.4, 2) specimen B l : a8, a l 5 , a l 9 , b3 in Figure 3.6, and 3) specimen B 2 : 9, 11, 12, 16 in Figure 3.8. 46 I C  Figure 4.1 Deply schematic o f specimen A l . The fibre direction i n each layer is drawn in the top left or right corner o f each ply. Positive angles are taken counter-clockwise to the 0° fibre direction to be consistent with the standard orientation used to specify lay-up fibre direction. 59 Figure 4.2 Example of a micrograph schematic, showing matrix cracking, fibre failure in the 0° plies and surface delamination. This shows the orientation to which all the micrographs have been redrawn for comparison purposes. The scales i n the x and y direction are not the same. This example is taken at 18 m m in front o f the notch tip in specimen A 3 . 60 Figure 4.3 Typical cross-section o f specimen A 3 , taken at 20.25 m m in front o f the notch tip. This shows delamination o f the surface ply. The layup is[-45/90/45/0/-45/90/45/0] 61 s  Figure 4.4 Typical cross-section o f specimen B l , taken at 10.00 m m i n front o f the notch tip. The layup is [F0/-45/90/45/0/45/90/-45/F0] , F0 = [0/90] weave. 61 T  Figure 4.5 Pulse-echo ultrasonic ( P E U ) scan o f specimen A 3 . Darker regions correspond to a cleaner reflected signal, and most likely represent delamination grown between loads A to E (positions A ' - E ' on the P E U scan). 62 x  Figure 4.6 Reconstructed profile o f the damage in specimen A 3 , with the load vs cross head displacement curve from the O C T test presented in Chapter 3.  63  Figure 4.7 Cross-section at position A ' in Figure 4.6, taken at 1.85 m m in front o f the notch tip in specimen A 3 . The layup is [-45/90/45/0/-45/90/45/0] . 63 s  Figure 4.8 Cross-section at position B ' in Figure 4.6, taken at 4.45 m m in front o f the notch tip in specimen A 3 . The layup is [-45/90/45/0/-45/90/45/0] . 64 s  Figure 4.9 Cross-section at position C in Figure 4.6, taken at 11.45 m m in front o f the notch tip in specimen A 3 . The layup is [-45/90/45/0/-45/90/45/0] . 64 s  Figure 4.10 Typical cross-section between positions C and D ' in Figure 4.6. This micrograph is taken at 18.00 m m in front o f the notch tip in specimen A 3 . The layup is [-45/90/45/0/-45/90/45/0] . 65 s  Figure 4.11 Reconstructed profile o f the damage in specimen B I , with the load vs C M O D displacement curve from the O C T test presented i n Chapter 3.  65  Figure 4.12 Cross-section at position IT in Figure 4.11, taken at 1.00 m m in front o f the notch tip in specimen B I . The layup is [F0/-45/90/45/0/45/90/-45/F0] , F 0 = [0/90] weave. 66 T  Figure 4.13 Cross-section at position V i n Figure 4.11, taken at 2.00 m m i n front o f the notch tip in specimen B I . The layup is [F0/-45/90/45/0/45/90/-45/F0] , F 0 = [0/90] weave. 66 x  Figure 4.14 Cross-section at position W in Figure 4.11, taken at 5.65 m m i n front o f the notch tip in specimen B I . The layup is [F0/-45/90/45/0/45/90/-45/F0] , F 0 = [0/90] weave. 67 T  Figure 4.15 Typical cross-section between positions X ' and Y ' in Figure 4.11. This micrograph is taken at 12.00 m m in front o f the notch tip in specimen B I . The layup is [F0/-45/90/45/0/45/90/-45/F0] , F0 = [0/90] weave. 67 T  Figure 4.16 Cross-section in the process zone o f specimen A 3 , taken at 28.00 m m i n front o f the notch tip. This micrograph shows damage in all but the centre 0° plies. The layup is [-45/90/45/0/-45/90/45/0] . 68 s  Figure 4.17 Cross-section in the process zone o f specimen B I , taken at 35.50 m m i n front o f the notch tip . This micrograph shows damage in all but the centre 0° ply and surface 0°/90° weave plies. The layup is [F0/-45/90/45/0/45/90/-45/F0] , F0 = [0/90] weave. 68 T  Figure 4.18 Diagram o f the failure stress vs the notch length for increasing degrees o f notchsensitivity.  69  Figure 5.1 Diagram o f a strain softening curve back-calculated from process zone tensile specimens.  83  xi  Figure 5.2 Schematic o f tensile specimens cut from the process zones o f O C T specimens A 4 and B2. 83 Figure 5.3 Jig to align end tabs parallel to tensile specimens while gluing, and the experimental setup to measure the specimen displacement during loading. 84 Figure 5.4 Simplification o f the tensile specimen used to determine the damaged modulus, E , using E q . (5.3). 84 D  Figure 5.5 Schematic and micrographs o f tensile specimen A 4 T 1 . These show the face closest to the notch tip. Layup is [-45/90/45/0/-45/90/45/0] . 85 s  Figure 5.6 Schematic and micrographs o f tensile specimen A 4 T 1 before tensile test. This shows the face farthest from the notch tip, and is similar i n damage to the face closest to the notch tip o f A 4 T 2 . Layup is [-45/90/45/0/-45/90/45/0] . 85 s  Figure 5.7 Schematic and micrographs o f tensile specimen A 4 T 3 . This shows the face farthest from the notch tip. Layup is [-45/90/45/0/-45/90/45/0] . 86 s  Figure 5.8 Schematic and micrograph o f tensile specimen B2T1 before tensile test. This shows the face closest to the notch tip. Layiip is [F0/-45/90/45/0/45/90/-45/F0] where FO = [0/90] weave. 87 T  Figure 5.9 Schematic and micrograph o f tensile specimen B 2 T 2 . These show the face closest to the notch tip. Layup is [F0/-45/90/45/0/45/90/-45/F0] where FO = [0/90] weave. 88 T  Figure 5.10 Measured stress vs strain curves o f A 4 tensile specimens.  88  Figure 5.11 Measured stress vs strain curves o f B 2 tensile specimens.  89  Figure 5.12 Plots o f failure stress and strain o f A 4 tensile specimens, derived using the damaged moduli. The most likely combination o f effective load-bearing plies is indicated for each specimen. 89 Figure 5.13 Plots o f failure stress and strain o f B 2 tensile specimens, derived using the damaged moduli. The most likely combination o f effective load-bearing plies is indicated for each specimen. 90 Figure 5.14 Preliminary strain softening curve o f systems A and B (shown by the solid lines), based on the damaged moduli o f specimens A 4 and B 2 . The arrows outline the possible range o f the unloading portion o f the curve. 90 Figure 6.1 Load vs C M O D displacement curve for O C T specimen A 4 predicted by Engels (1996) using several different F E M constitutive model responses. These curves can be compared to the experimental load vs C M O D displacement curve. The optimized strain softening curve is included in the figure. The F E M results are reproduced from Engels (1996). 94 xii  Figure 6.2 Load vs clip gauge displacement o f O C T specimen A 3 , predicted by a F E M strain softening analysis and the experimental results. Points A ' to C and A to C are used to compare the predicted and experimentally estimated crack lengths at the given load, respectively. The optimized strain softening material response is included in the figure. The F E M results are reproduced from Engels (1996). 95  xiii  Acknowledgements  First and foremost, I would like to acknowledge Dr. Anoush Poursartip for the boundless energy he puts into his teaching and direction.  H i s inspiration as an engineer and researcher, and  kindness as a supervisor are to be greatly admired. I would also like to thank Dr. Reza Vaziri, M r . K . Williams and M r . H . Engels whose knowledge and perpetual optimism o f the modeler have helped wrestle meaning from experimental chaos. Thanks to M r . Roger Bennett and M r . Serge Milaire whose technical assistance I could not have done without.  M u c h inspiration and direction was provided by Dr. Larry Ilcewicz and Dr.  Bernhard Dopker o f the Boeing Company. I also wish to thank all the members o f the Composites Group for their daily support and friendship, and for giving the lab a wonderful environment. I would like to acknowledge the Boeing Company, who provided the material for the project. A n d lastly, my heartfelt gratitude goes out to all my friends and family who turned my mountains into molehills and provided rest stops along the way.  xiv  Chapter One Introduction  1.1  Motivation  Composite materials such as carbon fibre reinforced plastics (CFRJP) offer great advantages for aerospace applications due to their high modulus and strength combined with their light weight. For a given weight, the strength and modulus o f a C F R P can be 10 times that o f a metal. The strength o f the final structure is important in design and typically these materials have a reasonably good strength. However, design potential is frequently sacrificed by an inability to effectively model and predict their structural strength. Structural failure frequently initiates at regions o f high stress, such as at holes, notches or cracks. For simplicity, these discontinuities w i l l be referred to interchangeably i n this chapter.  Holes  may be created by unexpected impact loadings such as collisions with flying debris and tools dropped during repair, which are a frequent hazard. Alternatively, holes may be introduced by design, such as at joints or fasteners. Notched failure is preceded by the onset o f damage, which alters the stress concentration at the notch tip. Traditional means o f modeling fracture in notched specimens do not properly account for the effect o f this damage on the notch tip. The fracture strength o f large coupons or structures is underestimated i f this damage is ignored. A critical design driver o f the aerospace industry is to build damage tolerant aircrafts, with the focus o f current research being to develop predictive tools best suited for composite structural failure.  1  1.1.1  Examples of Damage in a Composite Laminate  One o f the most promising applications o f C F R P ' s in commercial transport aircraft is as the skin of primary load-bearing structures. For example, Figure 1.1 shows the primary structures in the Boeing 777 made of C F R P .  The skin is made o f a carbon fibre reinforced laminate.  The  laminate is made o f individual laminae stacked at different orientations to give specific load bearing abilities as shown in Figure 1.2. The laminae consist o f layers o f long continuous fibres embedded in a matrix. A lamina is a specially orthotropic material when loaded in the fibre direction. If a balanced, symmetric laminate is loaded in a principle material direction, it is also a specially orthotropic material. Damage, shown in Figure 1.3, may grow within a lamina in the form o f fibre pull-out, fibre bridging, fibre/matrix debonding, fibre failure, and matrix cracking (Figure 1.3a). Damage may also propagate as separation o f the individual laminae, called delamination (Figure 1.3b) (i.e. Anderson, 1991). Due to the interaction o f the many layers, damage frequently progresses as a complex combination o f the individual damage mechanisms.  While these mechanisms may  increase the fracture resistance of a laminate by dissipating the concentration o f stresses at the notch tip, they complicate the failure analysis.  Several approaches have been developed to  model damage evolution in notched laminate coupons, with the focus o f current research i n the aircraft industry being to extend these to predicting damage in large composite structures.  1.2 Linear Elastic Fracture  Mechanics  Linear Elastic Fracture Mechanics ( L E F M ) was one o f the first approaches used to predict fracture in notched composite laminates.  A classical stress concentration factor does not take  into account the hole size when predicting fracture strength.  2  In contrast, L E F M attempts to  account for the 'hole size effect', i n which the tensile fracture strength o f notched or centre-holed coupons decreases with increasing hole size (Whitney and Nuismer, 1974). Figure 1.4 shows a plate containing a preformed crack subjected to a load. L E F M predicts that the crack w i l l grow i f the energy release rate, G, is greater than the resistance to crack growth, R, such that:  da where F is the work performed by the external forces, U is the elastic energy stored i n the plate, and da is the increment o f crack extension, and  R-f  (1.2)  da  where dW is the energy required for crack formation. It can be shown that prior to crack extension, G is the same whether the crack is grown under load or displacement control (Broek, 1986). If the plate is under load control, a fixed load is applied and the resultant displacement is dictated by the compliance o f the system.  In  displacement control, a fixed displacement is applied, giving a resultant load. A rising R-curve occurs when the resistance to crack propagation increases with increasing crack length. The R-curve is considered not to be a material property but depends, for example, upon the specimen geometry and loading (Broek, 1986). A stress based L E F M approach predicts failure based on the stress intensity at the tip o f the preformed crack. The elastic solution for the stress field at the tip o f a crack in a body, subject to a load perpendicular to the flanks o f the crack (Mode I loading) is:  C7u ., =  (i-3)  V2  3  where K is the M o d e I stress intensity factor, r is the radial distance from the crack tip, and fy(Q) }  expresses the influence o f the 0 direction on the stress magnitude.  Solutions exist for the stress  intensity factor for many geometries, and for finite-sized specimens, the effects o f the edges are accounted for by a finite width correction factor, Y. For the plate shown i n Figure 1.4, containing a centre crack o f length 2a, subject to a nominal stress, a, the M o d e I stress intensity factor is: K,=Yrsyfiza  (1.4)  For a given crack length, fracture occurs when a reaches a critical value, rjy and Kj is referred to as the fracture toughness o f the material, K . L E F M therefore predicts that the fracture strength I C  of the plate in Figure 1.4 is inversely proportional to the crack length, such that:  CT/«-7=  .  (1.5)  For a specially orthotropic material, Sih et al. (1965) found that K, is related to G by: 7  22  t  2<?i2 + 6 6  (1.6)  a  +  2a, where a =l/E,, n  a =l/E , 22  2  a =-v /E 12  12  h  and a =l/G 66  12  for plane stress. E  h  E, v , 2  ]2  G  12  are the  elastic constants o f the material.  1.2.1  The Process Zone in Quasi-Brittle Materials  When a notched specimen is loaded, E q . (1.3) predicts a stress singularity at the notch tip. In a metal, however, once the stress reaches the yield stress, the material yields and forms a plastic zone.  Analogous to the plastic zone in metals, the material at the notch tip in a quasi-brittle  material forms a process zone, once the stress is high enough to initiate damage. The material in the plastic zone may strain harden, or conversely, the material i n the process zone may strain soften.  4  The process zone consists o f a region o f discontinuous damage. In a fibre reinforced composite laminate, for example, the damage may be a combination o f matrix cracking, fibre pull-out, fibre failure, fibre splitting or delamination. The large safety factors required in design o f composite laminate structures are overconservative, as traditional predictive techniques do not properly account for the effect o f the process zone on the stresses at the notch tip (Ilcewicz, 1995). Fracture mechanics predicts the notched strength to be inversely proportional to the notch size based only on elastic properties and geometry. Several alternate approaches have been developed which attempt to account for the effect o f the process zone v i a a characteristic dimension or a physical description o f the local failure mechanisms.  1.3 Micromechanical  1.3.1  Models Used to Predict Notched  Behaviour  Predicting Fracture Based on a Fitted Parameter  A n initial attempt to account for the influence o f the process zone on the hole size effect was made by Whitney and Nuismer (1974), in their point stress and average stress criteria. They proposed a failure criteria based on the stress or average stress at a characteristic distance in front of a hole.  When the stress reaches the unnotched tensile stress, failure w i l l occur.  They  proposed that at the edge o f a larger hole there is a higher probability that a flaw w i l l initiate failure, as the stress singularity is less concentrated than at a smaller hole, as shown in Figure 1.5.  This would explain the hole size effect.  Such a theory would be highly useful i f the  characteristic distances were material properties. shown otherwise (Pipes et al., 1980).  5  However, experimental evidence has since  Another technique which uses a fitted parameter to account for the hole size effect was proposed by M a r and L i n (Mar and L i n , 1977). They generalized the inverse square root dependence o f notch strength on the crack size predicted by L E F M , to: (1.7)  a , = H (2r)-  m  c  where oy is the fracture strength, r is the crack size, H is a fitted parameter called the composite c  fracture toughness, and the exponent, m, can be calculated from the elastic constants o f the fibre and matrix. In a study o f graphite epoxy laminates, Lagace (1986a) concluded that the M a r - L i n criterion generally provided a better prediction o f notched composite fracture strength than the point stress criterion. The point stress, average stress, and M a r - L i n criteria are still in use today. Rather than a physical description o f the damage, they rely on a fitted parameter to account for the effects o f the local failure mechanisms.  1.3.2  Relating Fracture to a Physical Understanding of the Damage Evolution  Kortschot and Beaumont (1990a, 1990b, 1991c, 199Id) attempted to relate the notch size effect to a physical understanding o f damage evolution at the notch tip.  They developed a damage  criterion based on the state o f subcritical damage just prior to failure, called the 'terminal damage state' (TDS). Using radiography, they examined the T D S i n double-edge notched ( D E N ) crossply graphite reinforced epoxy specimens.  The T D S was incorporated into a finite element  method ( F E M ) model to determine the notch tip stress distribution.  They found that the  remaining load-bearing plies in the T D S were the 0° plies, and a simple failure criterion based on the critical stress o f the 0° ply was used to predict notched strength. In their model, the influence o f layup and notch size on fracture strength was accounted for by their effect on the T D S . Three types o f damage were identified, as shown in Figure 1.6, which 6  consisted o f splits in the 0° plies (matrix splitting), transverse ply cracks in the 90° plies and triangular delamination zones at the 0 7 9 0 ° interface. They found that the greater amount o f fibre splitting in the T D S of a [ 9 0 ° , / 0 ] s laminate than in a [ 9 0 7 0 ° ] o  2  strength.  2  2 S  laminate, doubled its fracture  Increasing the delamination height in the T D S increased the fracture  strength  regardless o f layup, notch length or specimen width, due to its reduction o f the notch tip stress concentration. Webb and Kortschot (1991) tried to identify a T D S in D E N quasi-isotropic carbon fibre reinforced epoxy laminates. However, they were unable to due to the complexity o f the diffuse zone o f cracking and local delaminations surrounding the notch immediately preceding failure. The micromechanical models represent the hole size effect in terms o f mechanisms which operate at the scale o f individual plies. understanding o f the damage.  They are useful in generating a good physical  However, they cannot be directly extended to the more complex  damage mechanisms found in the complex layups o f a composite structure.  1.4 Macromechanical  Models Used to Predict Notched  Behaviour  Rather than examining the hole size effect based on the scale o f the individual plies, the size effect can also be accounted for by its influence on the scale o f the structure. In L E F M , elastic finite width correction factors have been analytically derived for a given geometry. These factors are used to predict fracture o f a structure from tests on small notched coupons. Bazant's empirical size effect law offers a means o f predicting fracture o f large structures in materials to which L E F M cannot be directly applied. This law, frequently used for quasi-brittle geomaterials, was also shown to apply to graphite fibre reinforced composite laminates (Bazant et al., 1995). It can be used to scale the nominal strength o f geometrically similar structures o f different sizes, based on a characteristic dimension, D , on the scale o f the laminate. For example,  7  D may be taken to be the specimen width.  This approach, although simple to use, requires  empirical calibration and does not contribute to a physical understanding o f the origins o f the size effect.  1.4.1 Fictitious C r a c k M o d e l A n F E M based approach to model the stress transfer capability o f the process zone i n quasibrittle materials was initiated about 10 years ago, by Hillerborg et al. (1976). The model is called the Fictitious Crack Model ( F C M ) . Aronsson and Backlund (1986) later extended the model to fibre reinforced plastics, and called it the Damage Zone M o d e l ( D Z M ) . In the F C M or D Z M , the fracture process zone ahead o f a preformed crack is represented as a fictitious macroscopic crack, which transfers a stress distribution that varies with the crack opening displacement, as shown in Figure 1.7. The energy under the stress-displacement curve is equal to the energy absorbed per unit o f newly-formed crack area. The preformed crack w i l l grow when the maximum stress at the tip o f the fictitious crack reaches the unnotched tensile strength o f the material. One draw-back to using this approach is that it is difficult to calibrate the stress-crack opening displacement curve. Either a linear shape is typically assumed, or a data fitting technique is used to calibrate the curve from the far-field load and crack mouth opening displacement. (Hillerborg, 1991; M i l l e r et al., 1991).  1.5 A Strain Softening Approach to Predicting Notched  Behaviour  In the last decade, a promising F E M based approach has surfaced to more accurately predict failure i n notched composite laminates. This approach accounts for the effect o f the process zone on the notch tip by incorporating a strain softening material response.  8  Continuum Damage Mechanics ( C D M ) can be used to describe a strain softening material response i n fibre reinforced composite laminates.  A state variable is defined which represents  the state o f damage in an element of material. The deterioration o f mechanical properties due to damage is accounted for by an effective stress, based on an equivalent undamaged  area.  Matzenmiller et al. (1991) recently developed an anisotropic damage model for fibre reinforced composites. The model, here referred to as the M L T model, uses a damage variable based on a Weibull distribution to define the shape o f a strain softening curve. The shape o f the C D M strain softening curve is based on a Weibull distribution o f fibre failure, and is shown i n Figure 1.8. A s can be seen i n the figure, the post-peak region is defined by a decreasing stress with increasing strain. For this reason, the curve is referred to as a strain softening curve, as opposed to strain hardening. Considerable controversy exists as to the fundamental validity o f strain softening as a material response. Such a response assumes that the behaviour o f the physically damaged material can be represented as a homogeneous continuum. A s well, a strain softening material response violates Drucker's stability postulate (Drucker, 1951). This postulate states that when an external agency applies additional surface and body forces to a volume o f material (Chen and Han, 1988): •  "The work done by the external agency on the changes in displacements it produces must be positive, and  •  the new work performed by the external agency on the changes in displacements it produces must be non-negative."  According to this postulate, the post-peak region o f the strain softening curve is unstable because the work done for an increment o f strain, 5s, is negative (da is less than zero). To allay concerns o f violating basic principles, a load-displacement curve w i l l be substituted for the strain softening stress-strain curve in this discussion. Stress and strain are parameters which  9  apply to a body that is a homogeneous continuum. However, once there is appreciable damage in the process zone, by definition there are voids and empty spaces. In other words, the material is no longer a homogeneous continuum. Therefore, defining the post-peak section o f the curve by the load-displacement response  avoids any implication o f violating basic principles.  However, to be consistent with current terminology, we w i l l refer to the load-displacement curve as the strain softening curve. Strain softening is a laminate property, and is particular to a given material system and loading. In a composite laminate, the material system represents the specific fibre and matrix used, placement (tow vs tape) and layup o f the laminate. In a typical strain softening curve shown in Figure 1.9, the response is initially linear elastic between points A and B , whereupon it behaves nonlinearly due to damage initiation between points B and C . In a notched specimen, for example, damaged material i n the process zone is subject to high local displacements, and at failure unloads to surrounding, less damaged material. This unloading is represented on the curve between points C and D .  1.5.1  Experimental Investigation df Strain Softening as a Material Property  Materials which are considered to strain soften include rocks, concrete, soil, polymers and fibre reinforced plastics, (Read and Hegemier, 1984; Hasan et al., 1993). Read and Hegemier (1984) experimentally investigated the physical basis o f strain softening in rocks, soil and concrete. They concluded that it is not a material property.  They showed, for example, that the strain  softening curves o f concrete columns in compression were a function o f specimen geometry. The load bearing area was reduced i n columns which had a large length to diameter ratio, due to slabbing o f the concrete walls. Scaling the force-displacement curve by the unfractured crosssectional area, yielded a strain hardening behaviour. They also noted that the assumption o f a homogeneous continuum inherent in the definition o f a material property was invalidated by  10  inhomogeneous deformation.  They concluded that a continuum mechanics representation o f  these materials is only justifiable i f the scale o f the inhomogeneities is significantly smaller than the material element being considered, which is not the case in these materials. A n extensive discussion o f using strain softening to predict the behaviour o f structures can be found in a book by Bazant and Cedolin (1991).  1.5.2  Geometry of a Strain Softening Specimen  Materials which strain soften w i l l appear brittle in specimens such as a dog-bone, due to limited opportunity for local load redistribution during failure. A special geometry is required to allow the gradual development o f the damage zone. The most common specimens used are a centrenotched or edge-notched tensile specimen, subject to a uniform far-field load (Ilcewicz, 1995). A s the far-field stress increases, locally high displacements occur in the damaged region. The most damaged sections o f the specimen w i l l have progressed to the largest displacements in the post-peak section o f the strain softening curve. In contrast, the undamaged surrounding elastic medium w i l l be on the elastic loading section o f the curve.  1.5.3  Experimental Investigation of Process Zone Softening  A s the load redistribution in the process zone cannot be measured directly, the strain softening curve must be indirectly determined.  Despite the fundamental questionability o f examining  strains instead o f displacements, many researchers have measured notch tip strains to investigate the influence o f the process zone. Evidence o f large strains in the process zone have been noted by Daniel (1978) i n the 1970's. However, relating these strains to a strain softening model has only begun in the last decade.  11  Geers et al. (1995) monitored the 'Active' strain localization ahead o f the notch in a compact tension short glass fibre-reinforced polypropylene specimen, using a retro-reflective  grid  illuminated by halogen light. They defined the 'fictive strains' to be the measured displacements over the crack region. The maximum value o f the notch tip fictive strain aligned with the load line was found to be 10%, while the maximum tensile test strain for the material was 3%. They found that during loading, matrix deformation created an elastically deformed zone prior to the peak load.  After the peak load, the elastically deformed zone unloaded and fibre-matrix  debonding and some fibre pull-out occurred. Other experimental techniques used to monitor displacements developed by Shah and Ouyang (1993) for cement-based  in the process zone  materials.  were  Laser holographic  interferometry was used to map the surface displacements i n a centre-notched plate subject to tension. The effect o f the process zone was found by comparing the measured strain field to that predicted by L E F M .  Behind the notch tip, the size o f the process zone was found to increase  with increasing load, while the size in front o f the notch tip remained constant. It was suggested that the wake zone may thus more significantly affect concrete toughness. Instead o f measuring the strain, Basham et al. (1993) proposed a means o f back-calculating the stress in the process zone. B y measuring the applied load, crack mouth opening displacement ( C M O D ) , and the displacement directly ahead o f the notch in a semicircular specimen, the local stress as a function o f the displacement in the process zone can be back-calculated. However, several assumptions are inherent in their use o f the J integral to back out the stress, such as selfsimilar crack growth. A more detailed investigation o f the displacements in the process zone, coupled with the damage progression, is needed to get a clear physical understanding o f the post-peak region o f the strain  12  softening curve.  Only once this physical understanding exists, can a powerful numerical  technique such as the F E M based strain softening model provide a reliable tool for predicting notched structural failure.  1.6 Statement of  Objectives  The objectives o f this work are to: 1. Develop a specimen which can be used to investigate a strain softening approach to predicting notched behaviour. 2. Generate a variety o f experimental data with which to calibrate an F E M analysis o f the specimen that uses a strain softening curve. 3. Develop a physical understanding o f the damage evolution in the specimen, that can be used to examine the physical basis o f strain softening.  13  Figure 1.1 Primary load-bearing structures in the Boeing 777 made of fibre reinforced composite laminates. (Courtesy of The Boeing Company)  14  Figure 1.3 Schematic showing some of the damage mechanisms that occur in fibre reinforced composite laminates. Taken from Anderson (1991).  2a  a Figure 1.4 Centrally cracked plate subject to a uniform far-field stress.  15  Figure 1.5 Stress distribution around two different sized holes in an infinite isotropic plate. This explains the hole size effect according to Whitney and Nuismer. A greater probability exists around the larger hole for a flaw to initiate failure, as the stress concentration is less localized. Reproduced from Whitney and Nuismer (1974).  transverse ply cracks  delamination |J split  — 90 ply 0 ply - 0 ply — 90 ply r  Figure 1.6 Schematic of damage observed by Kortschot and Beaumont in cross-ply graphite reinforced epoxy laminates. The damage was observed in the 'terminal damage state' (TDS) just prior to failure, of double edge-notched specimens. Reproduced from Kortschot and Beaumont (1990a).  16  °"coh  A  fictitious crack  Figure 1.7 Representation of the stress distribution in the process zone in Hillerborg's Fictitious Crack Model. The process zone is modeled as a fictitious crack, containing a linear cohesive stress distribution as shown. The preformed crack will grow when the maximum stress at the tip of the fictitious crack reaches the unnotched tensile failure strength. Reproduced from Afaghi-Khatibi et al. (1995).  6/x  t  a = stress  A  X =strength t  s = strain X IE = nominal failure strain m = fitted parameter  1 +  t  e / ( x / E ) t  Figure 1.8 The uniaxial strain softening curve predicted by Matzenmiller et al. (1991), based on a Weibull distribution of fibre failure. Different degrees of strain softening are predicted by the parameter, m.  17  C  ro  AB: elastic b e h a v i o u r BC: d a m a g e initiation CD: d a m a g e d material s h e d s load to surrounding l e s s d a m a g e d material  B/  w _i D  A*  Displacement  Figure 1.9 Different regions of a typical strain softening curve.  18  Chapter Two OCT Test Developed to Study Notched Behaviour  2.1  Introduction  This chapter presents the development o f an overheight compact tension ( O C T ) test to study notched behaviour. The specimen geometry and loading method is described, with the experimental setup devised to monitor the surface displacements ahead o f the notch tip during loading. A description is given o f the two material systems tested, with a summary o f the tests and post-test analysis done on each specimen.  2.2 The Overheight  2.2.1  Compact Tension (OCT)  Specimen  Development of a Specimen Which Exhibits Stable Damage Growth  To examine notch tip behaviour, a specimen geometry was required which would grow damage in a stable manner, in a small specimen size that would conserve material. A compact tension (CT) type specimen geometry was chosen, in which a load is applied perpendicular to the flanks of a preformed edge notch. Under displacement control, the load drops during crack extension, and the strain energy release rate, G, may drop below the crack growth resistance, R, o f the material. According to fracture mechanics, a propagating crack is arrested i f G is less than R, and the specimen is said to exhibit stable crack growth.  Initial increments o f unstable crack  extension are followed by crack arrest, leaving the remainder o f the specimen intact for post-test examination.  19  To make efficient use o f material, an investigation was done o f the smallest specimen size which would allow a reasonable amount o f stable crack growth. In the standard C T geometry typically used for testing metals, the specimen height is roughly equal to the width. A sizeable process zone size was expected i n the material systems studied (Ilcewicz, L . , 1995).  A s the exact  dimensions were not known prior to testing, it was necessary to leave sufficient material available for the process zone to develop without the influence o f the boundaries. mind, the first C T geometry tested had a width roughly twice the height.  With this i n  Upon loading, a  through-the-thickness crack grew several millimeters before deviating at an angle o f 45°, tearing off one o f the loading arms which were essentially acting as cantilever beams.  The specimen  height was then increased to twice that o f the specimen width. A successful test was completed with a reasonable amount o f damage grown i n front o f the notch tip, apparently without the influence o f the boundaries.  2.2.2 The Standard C T Stress Intensity Factor For analysis purposes, the stress intensity factor o f a standard C T specimen can be used to model the behaviour o f the overheight C T specimen. The following equation is accurate to within 0.5% for a standard C T geometry, for 0.2 < a/W < 1 is: (Broek, 1986)  K, =  a  Y=-  2+— WJ  P  * Y  BW  3  0.886 + 4.641 — 1-13.32 —  W  \w)  1 -  +14.72 —  \W )  /  \4  -5.6 —  \W  (2.1)  <0 —  WJ  where P is the load, B is the specimen thickness, W is the specimen width, and a is the preformed notch length. B, Wand a correspond to those dimensions shown in Figure 2.1c.  20  2.3 Description  of the Experimental  Setup  The final specimen geometry and experimental setup is shown in Figure 2.1. 2.3.1  Loading Train and Specimen Preparation  The specimen was loaded statically i n an Instron testing machine under displacement control at a rate o f 0.02 inch/minute, using a 20 000 lb load cell. A l l tests were performed at ambient temperature and humidity. A s thin laminates are prone to twisting, two narrow steel stiffener bars were suspended flush on the sides o f the specimen to minimize out-of-plane bending (referred to as 'guide' in Figure 2.1a). Teflon tape was placed under the stiffener bars as well as the loading bars to minimize friction. The specimen was first prepared by cutting out the shape on a band saw. This gave a blunt notch tip. A starter notch and fatigue crack were not made as required by a standard C T test, so that the notch would be a more realistic representation o f a through-the-thickness discontinuity found in a real structure. A s well, the stress concentration would be less localized, increasing the damaged area.  2.3.2  Measured Specimen Displacements  Small modifications were then made to the specimen to measure the following displacements: 1. The displacement near the loading pins was recorded in later tests, by a 50% Instron gauge placed across the notch opening, referred to as a crack mouth opening displacement ( C M O D ) gauge.  2. The displacement at 1 cm in front o f the notch tip was measured by a clip gauge.  21  3. The displacement in front o f the notch, at fixed distances above and below it, were measured by lines inscribed across the width o f the specimen surface. The displacements were measured using a photographic, image analysis technique. Lines were inscribed with a razor blade at successive heights on the front specimen surface, and colored with white correction fluid. This technique broke a few surface fibres, but when examined under a microscope after testing, did not appear to interfere with the damage grown during the test. Photographs were taken throughout the test with a camera using a 105 m m macrolens. Enlarged 8x10 inch photographs were then digitally scanned at an optical resolution o f 100 pixels/inch, and imported into an image analysis program to measure the displacement o f the lines i n front of the notch tip.  2.3.3 Loading Train Deflection The cross head displacement o f an Instron Universal testing machine can be calculated from the set cross head speed i f the time interval is known. In these experiments, the time interval was given by the clock of the microcomputer used for data acquisition o f the load and gauge displacements. A n investigation was done o f the stiffness o f the Instron loading train to determine i f the pin hole displacement could be accurately calculated from the cross head deflection. The composite specimen was replaced by a very stiff steel plate, and the displacement o f the plate measured by a clip gauge placed on the specimen surface. The cross head displacement was measured with a mechanical dial gauge. A t a load o f 5000 N , the plate elongation was negligible (0.005 mm), while the cross head deflected 0.35 mm, as measured by the dial gauge and consistent with the set cross head speed. Therefore, it is clear that the applied deflection o f the cross head is not equivalent to the specimen displacement at the loading pins. The calculated cross head  22  displacement therefore should only be used as a qualitative indication o f the loading pin displacement. The C M O D gauge presents the only accurate measure o f the displacement near the loading pins. In the test with the steel plate, the load vs cross head displacement curve was nonlinear, so no attempt has been made to back-calculate the true loading pin displacement for those tests where C M O D gauge results are not available.  2.4 Summary of OCT Tests  2.4.1  Performed  Materials Studied  Two material systems have been studied, both fabricated at The Boeing Company. System A is a thin laminate, which can be easily modelled i n an F E M analysis. System B is a sandwich panel with an outer weave layer, which, although more difficult to model, is o f interest as it represents a material system similar to that presently proposed for the fuselage skin o f commercial aircrafts. The layup and components o f each system are: 1. System A : • quasi-isotropic layup: [-45/90/45/0/-45/90/45/0]  s  • T 3 0 0 H carbon fibre/F593 epoxy, plate thickness = 3.35 m m 2.  System B : • quasi-isotropic layup: [F0/-45/90/45/0/45/90/-45/F0] where FO = [0/90] weave fabric T  A S 4 tow placed carbon fibre/8552 epoxy sandwhich panel, face thickness = 1.6 mm, core thickness =12.7 m m 2.4.2  Tests Performed  A total o f four O C T specimens o f system A (specimens A 1 - A 4 ) were tested, and two o f system B (specimens B l and B2). Table 2.1 lists the dimensions o f each specimen according to Figure 2.1.  23  2.4.3 Post-test Analyses Several post-test analyses were done to qualitatively and quantitatively examine the damage grown during the test. Chapter 3 presents the damage progression throughout the test as indicated by the load vs cross head or C M O D displacements, and the load vs clip and surface line displacements. A qualitative examination o f the damage is discussed in Chapter 4, as observed by post-test sectioning and deply. A quantitative investigation o f the damage is given in Chapter 5, by a series o f tensile tests o f specimens cut from the damaged area. Table 2.2 summarizes the instrumentation used and post-test analyses done on each specimen.  24  Table 2.1 Overheight compact tension (OCT) specimen dimensions where the letters refer to the schematic in Figure 2.1. All dimensions are in mm. Specimen ID System A Al A2 A3 A4 System B BI B2  a  W  a/W  H  B  b  c  d  e  f  28.3  87  .32  200  3.35  12.12  19.05  7.8  N/A  29.1  87.85  .33  200  3.35  12.15  19.05  7.8  25.26  85.86  .29  200  3.35  12.7  19.05  7.8  N/A N/A N/A  17.63  79.8  .22  207  3.35  22.24  19.05  9.5  28.72  2.5*  17.51  78.77  .22  202.3  1.66*  22.74  27.98  15.9  33.7  2.5  24.45  84.69  .29  204.8  1.66*  15.01  27.98  15.9  36.33  2.5  20 5  s  * thickness of each face sheet. Core thickness is 12.7 mm. ' 9 lines are inscribed above and 9 lines below notch mid-plane 20 lines are inscribed above and 20 lines below notch mid-plane  Table 2.2 Summary of instrumentation and post-test analysis of each OCT specimen. Specimen ID  CMOD gauge  clip gauge  line analysis*  detailed sectioning  deply*  tensile test"  System A Al A2 A3 A4  N N N Y  Y Y Y Y  N N Y N  N N Y N  Y Y N N  N N N Y  System B BI B2  Y Y  Y N  Y N  Y N  N N  N Y  * presented in Chapter 3 f  presented in Chapter 4  * presented in Chapter 4 ** presented in Chapter 5  25  T  f  s  (b) close-up of lines inscribed on specimen surface (a) OCT specimen in loading assembly prior to testing units: mm . ,d  applied displacement, 8  f • • • r-7*T Cl ^—i.—+  L CMOD gauge, slits  -  ; . . i>< K . . If. , * I £4.2) *l /  w  J  notch mid-plane (n.m-p.)  B  .clip gauge holes on back surface  lines inscribed on front surface a distance, f, apart  ? applied displacement, S (c) schematic showing locations at which displacements are measured and specimen dimensions Figure 2.1 Schematic of the overheight compact tension (OCT) specimen and experimental setup used to monitor displacements during loading.  26  Chapter Three OCT Tests and Data Reduction  3.1  Introduction  This chapter discusses the evidence o f damage progression throughout the O C T tests as indicated by the load vs cross head or load vs C M O D displacements, and the surface displacements i n front o f the notch tip. The displacement o f lines inscribed on the specimen surface suggest the progression o f damage across the specimen width throughout the test. A clip gauge provides a continuous measurement o f a local displacement at a fixed location in front o f the notch tip, close to the notch mid-plane. The clip gauge displacements support the results o f the line analysis. Finally, the difference in the surface displacements o f systems A and B is discussed. The following terms are defined: a notch represents a preformed  through-the-thickness  discontinuity in the specimen prior to testing, a crack represents through-the-thickness  fibre  failure, matrix cracking and some delamination which grows in front o f the notch due to loading, and the process zone represents a zone in front o f the crack, in which damage is visible in only some o f the plies. This damage is observed in the post-test sectioning presented i n detail in Chapter 4, but must be mentioned in conjunction with some the results o f this chapter.  The  length o f the crack refers to its dimension i n the same direction as the specimen width, W, i n Figure 2.1c. It includes the preformed notch length (dimension a in Figure 2.1c) and the distance the crack has grown in front o f the notch tip during loading.  27  3.2 Cross Head and CMOD  Displacements  The far-field load vs cross head displacements o f specimens A l to A 3 are given in Figure 3.1, together with the load vs C M O D displacement o f specimen A 4 in Figure 3.2. Figure 3.3 shows the load vs C M O D displacements o f specimens B l and B 2 . Specimens A l , A 2 and A 3 were tested prior to noting the inaccuracy o f using the Instron cross head deflection, so a C M O D gauge was not used in the tests. The loads are presented as a function o f the calculated cross head deflection. A complete test was done on specimen A 2 , such that the specimen fractured in two pieces. The remaining specimens were loaded until roughly the same point i n the test, just after the first large load drop, so that a reasonable amount o f damage was grown. The developing process zone could then be examined by post-test analysis.  3.2.1  General Shape of the Load vs Cross Head and Load vs C M O D Displacement Curves  For both systems, the general shape o f the load vs cross head displacement or load vs C M O D displacement curve is similar. Initially, the loading increases linearly, followed by a region i n which small load drops occur.  The load-carrying ability o f the specimen increases until the  maximum load is reached, followed by a large load drop. Several more load drops may then occur, with decreasing peak loads prior to each load drop, until complete fracture o f the specimen i f the test is carried to completion (i.e. specimen A 2 ) . The significance o f the load drops as regards to damage progression throughout the test w i l l be discussed in section 3.3.  28  3.2.2 Repeatability  The primary purpose o f the O C T specimen was to grow a reasonable amount o f damage as opposed to performing a valid fracture toughness test.  However, an indication o f the  repeatability o f the O C T test can be found by examining the expected results to the predicted behaviour o f two specimens, using E q . (2.1).  Good repeatability is obtained between the  measured and predicted peak loads in specimens B I and B 2 . E q . (2.1) predicts a 17% higher peak load in specimen B I than specimen B 2 for a given K , due to the different a/W. I C  This is  similar to the measured peak load in specimen B I , which is 12% higher than in specimen B 2 . Specimens A l and A 2 have a 3% difference in their a/W which corresponds to a 2 % difference in their predicted peak load for a given K , using E q . (2.1). However, a 19% difference exists in I C  the experimentally measured peak loads. This variability is acceptable given the purpose o f the O C T specimen and the bluntness o f the notch tip. The approximate fracture toughnesses o f systems A and B can be compared to a value in the literature by substituting the peak loads into E q . (2.1). The fracture toughness o f specimens A l , A 2 , A 3 and A 4 are found to vary by 38%, and range from 33 M P a ( m ) . t o 53 M P a ( m ) . 1/2  1/2  A  similar calculation for system B shows that the estimated fracture toughnesses is similar, to  12 / system A . The fracture toughness are 56.2 MPa(m) B 2 , respectively.  12 / and 56.8 MPa(m)  for specimens B I and  These fracture toughness values seem reasonable given that the  fracture  1/2 toughness o f a carbon fibre laminate is listed in the literature as ranging from 40 to 70 MPa(m) (Ashby, 1992).  29  3.3 Indications of Damage  Growth  3.3.1 Surface Line Displacements  The surface line displacements indicate the progression o f damage across the specimen width throughout the test. The results are presented as the total displacement between a pair o f lines inscribed at the same height above and below the notch mid-plane. The lines presented in this section are the lines closest to the notch mid-plane not affected by surface delamination. The line displacement is plotted as a function o f the position in front o f the notch tip, at increasing loads, or photographs, throughout the test. The line displacements are presented in conjunction with the load vs cross head or load vs C M O D gauge displacements, and the load vs clip gauge displacements. The photograph number corresponding to each load is marked. The line displacements for selected photographs for systems A and B are presented in Figure 3.5, Figure 3.7, and Figure 3.9. The figures i n Appendix 1 show all the displacements that have been measured from photos taken throughout the tests.  3.3.1.1 Repeatability and Accuracy A n investigation was done o f the variability o f repeat measurements o f the line displacements measured by the image analysis technique. The average image resolution o f the line analysis o f specimen A 3 in Figure 3.5 is 0.045 mm/pixel, giving repeat measurements a variability o f +0.045 m m . Improving the image resolution to 0.02 mm/pixel was not found to be beneficial, however, as the scribe line thickness was roughly 0.1 m m , and human error was introduced in repeating a measurement at the same location on the scribe line.  30  The clip gauge displacements confirm the displacements measured by the line analysis.  For  example, the displacement o f line #4 o f specimen A 3 at 10 m m in front o f the notch tip (Figure 3.5) can be compared to the clip gauge displacement (Figure 3.4) at the same load. The damage grown after the largest load drop (between photos 15 to 19), corresponds to an opening o f both the line displacement height and the clip gauge o f roughly 0.3 mm. A s the crack extends during loading, the material on either side o f the open crack rotates slightly about the crack tip. This rotation affects the given positions in front o f the notch tip at which measurements are taken o f each scribe line displacement. A marked specimen indicated that in the worst case, the shift o f a given position in front o f the notch tip due to specimen rotation was 0.5 mm. This rotation was therefore ignored when measuring the scribe line displacements.  3.3.1.2 Indication of Damage Length In order to interpret the line analysis, the sectioning results presented in detail in Chapter 4 w i l l be briefly mentioned.  The results indicate that the point o f zero displacement o f each line in  front o f the notch tip roughly corresponds to the length o f the internal damage.  For example,  stopping the test o f specimen A 3 at photo 19 i n Figure 3.4 followed by deply and sectioning, reveals fibre failure running in each layer across the laminate as a crack perpendicular to the load, roughly 25 m m in length. In front o f this is a zone 7 m m in length, in which there is fibre failure and matrix cracking in the outer layers, while the centre layers are undamaged. Inspection of the displacement o f line #4 at the same point in the test (photo 19 i n Figure 3.5), shows that the line has zero displacement at 30 m m i n front o f the notch tip. displacement indicates the length o f the internal damage.  31  Thus, the point o f zero  The line analyses o f specimens B I and B 2 confirm this hypothesis, and indicate a final crack length o f 38 to 40 mm. Post-test sectioning indicates a crack 35 to 40 m m long, with a process zone between 3.5 to 4 m m in front o f it, respectively. For example, at photo b9 o f specimen B I in Figure 3.7, line #1 has zero displacement at roughly 38 m m in front o f the notch tip. Stopping the test at this point in the test (photo b9 i n Figure 3.6), followed by sectioning, reveals a 35 m m long crack with a 3.5 m m long process zone in front o f it.  Similar results are obtained in  specimen B 2 . Stopping the test and sectioning at photo 21 in Figure 3.8, indicates a crack 40 m m long, with a process zone 4 m m long in front o f it.  Line #1 on specimen B 2 has zero  displacement at roughly 40 m m in front o f the notch tip (Figure 3.9). Table 3.1 lists the approximate position in front o f the notch tip at which the line closest to the notch mid-plane has zero displacement, for specimens A 3 , B I and B 2 .  3.3.1.3 Damage Progression as a Function of the Far-field Load The line analysis describes the general sequence o f damage progression i n both systems throughout the test.  During the initial linear elastic load up, the line analysis indicates that  negligible crack growth occurs, as the position o f zero displacement o f the line corresponds to the tip o f the notch. A small amount o f crack growth then follows, during the small load drops or nonlinear section o f the curve o f 5 to 10 mm. This crack growth does not seem to significantly affect the load carrying ability o f the specimen, as after each drop the load rises to a larger peak value. Once the maximum peak load sustained by the specimen is reached, a large load drop occurs during which the crack extends significantly, between 15 to 30 mm. The test is stopped shortly after, with a few specimens haying several millimeters o f crack extension during the small load drops that occur prior to unloading.  32  3.3.1.3.1 System A  The damage progression i n specimen A 3 follows the above damage  sequence,  and the  displacement o f line #4 i n specimen A 3 (Figure 3.5) indicates that negligible crack growth occurs prior to the first load drop, as line #4 i n photos 10 and 11 has zero displacement at the notch tip. U p to 10 m m o f crack extension occurs prior to the large load drop (photo 14), as the line has zero displacement at roughly 10 m m in front o f the notch tip. Once the load has dropped (photo 15), the slope o f the line increases, and has zero displacement at 25 m m i n front o f the notch tip. Therefore, the largest load drop corresponds to the largest growth increment o f 15 mm, after which the crack grows only another 5 m m during the small load drop between photos 18 and 19.  3.3.1.3.2 System B  3.3.1.3.2.1  Specimen  B1  The line analysis indicates a slightly different sequence o f damage growth i n system B . According to the analysis o f line #1 i n Figure 3.7, once the load rises nonlinearly between photos a8 and b3, the crack extends from 1 to 10 m m i n front o f the notch tip. During the largest load drop, which occurs in two sections (photos b3 to b8), there is a notable difference in the behaviour o f the surface lines o f specimen B I compared to specimen A 3 . In specimen A 3 , during the largest load drop, the intersection o f scribe line #4 with the x axis jumps from 10 to 25 m m in front o f the notch tip, representing approximately 15 m m o f crack extension. In contrast, the largest load drop i n specimen B I occurs in two sections, photos b3 to b4, and b7 to b8 i n Figure 3.6. In the first section o f the load drop, photos b3 to b4, the position at which line #1 has  33  zero displacement remains constant at 10 m m i n front o f the notch tip, yet the slope and shape o f the line changes significantly. In the second stage o f the load drop, photos bl to b8, the position of zero displacement jumps from 12 m m to 38 m m i n front o f the notch tip. However, unlike the first section o f the load drop, the shape o f the line i n the second section remains approximately linear.  Thus it appears that local deformation without crack extension is occuring i n the first  section o f the load drop, while in the second section primarily crack extension occurs.  3.3.1.3.2.2  Specimen  B2  Although the sequence o f crack growth i n specimen B 2 is slightly different than i n specimen B 1 the final crack length is the same.  In both specimens, the largest load drop occurs i n two  sections. However, during the first part o f the load drop significant deformation does not occur in specimen B 2 prior to crack extension as was observed i n specimen B l . Instead, the crack grows 18 m m during the first part o f the load drop, Figure 3.9, and 7 m m during the second section o f the load drop, giving a final crack length o f 40 m m .  3.3.1.4 Displacement of Lines Farther Away from the Notch Mid-plane Lines farther from the notch mid-plane show a similar damage progression to the line closest to the notch mid-plane. In specimen B l , for example, line # 3 (Figure 3.10) is 7.5 m m above and below the notch mid-plane, while line #1 (Figure 3.7) is 2.5 m m above and below it, and both indicate a similar sequence o f crack extension. Prior to the peak load, the crack has extended to roughly 10 m m i n front o f the notch. In the first section o f the large load drop, negligible crack extension is observed, and after the second part o f the load drop, the final crack length measured by both lines is roughly 37 to 38 mm.  34  Thus lines not directly adjacent to the notch mid-plane give a reasonable description o f the damage progression, and the displacements o f line #4 i n specimen A 3 may be assumed to give a reasonable representation o f the damage growth.  3.3.1.5 R-Curve Behaviour The line displacements can be used to estimate the amount o f crack growth at increasing loads throughout the test, so that a crack growth resistance or R-curve, can be drawn.  The critical  mode I strain energy release rate, G , is plotted as a function o f the total amount o f crack 1C  extension in front o f the notch tip, Aa, for specimens A 3 , B I and B 2 i n Figure 3.11 (note that K  IC  is calculated using E q . (2.1), and G  IC  plotted up to the largest load drop.  is calculated from K  JC  using E q . (1.6)).  The results are  Beyond this drop the crack is sufficiently large that edge  effects may influence the R-curve behaviour.  The line analysis is used to estimate the crack  length at the photo corresponding to the load, indicated i n Figure 3.11. In specimen A 3 , G  IC  is calculated for the four peak loads prior to photo 15 in Figure 3.4.  However, a photo was not taken at each peak load, so the crack length was estimated from the photo immediately preceding the peak load. Both systems exhibit a rising R-curve, and thus an increasing resistance to crack growth prior to the peak load. It appears that system B has a higher resistance to crack growth, and may be a tougher system, as G  IC  for specimen B 2 rises to a value 2 to 5 times greater than specimen A 3 .  3.3.2 C l i p Gauge Displacements  The clip gauge displacements confirm the results o f the line analysis. For example, during the large load drop in specimen A 4 , (points A and B in Figure 3.2) the clip gauge displacement  35  increases significantly, opening 0.54 mm, while the C M O D gauge opens less (0.2 mm). The line analysis o f specimen A 3 indicated that the largest load drop corresponded to 15 m m o f crack growth in front o f the notch tip. One would expect the displacement o f the C M O D gauge to be negligible during the load drop as it is a displacement controlled test. However, the low stiffness of the loading train, discussed in Chapter 2, would allow some deflection at the pin holes as the compliance o f the specimen increases during crack growth. During the smaller load drop, the clip gauge displacement approximates that o f the C M O D , as the damage front has passed ahead of the gauge. In light o f the results o f system A , one would expect a relatively larger opening o f the clip gauge (0.45 mm) relative to the C M O D gauge (0.39 mm) during the first part o f the largest load drop in specimen B l , Figure 3.6.  However, as their damage sequence is different, in specimen A 3  (Figure 3.4) significant crack extension occurs during the largest load drop, while in the first section o f the load drop in specimen B l , damage other than crack extension occurs. Thus, in specimen A 3 fibre failure would allow free opening o f the crack flanks within the gauge length, whereas in specimen B l intact fibres restrain opening. When these fibres break and the crack extends, during the second part o f the load drop i n B l , (photos b7 to b8) one would expect a large increase in the clip gauge displacement. However, the line analysis indicates that the clip gauge is now behind the tip o f the damage, due to the 26 m m o f crack extension which occurs. A clip gauge was placed on specimen B 2 , however it popped out during the test, invalidating the results.  36  3.4 Discussion  of Results  The line analysis and clip gauge results provide a consistent explanation o f the damage progression in both systems.  The line analysis indicates the progression o f damage across the  specimen width, with the position o f zero displacement o f the line corresponding to the front o f the crack, as w i l l be confirmed by the post-test sectioning presented in Chapter 4.  For both  systems, the onset o f crack growth occurs once the relationship between the specimen load and C M O D displacement or the load and cross head displacement either becomes nonlinear or small load drops are observed. The largest crack growth increment occurs during the largest load drop, corresponding to approximately 15 m m o f crack growth in system A , and 25 m m in system B . During this drop, a significant opening o f the crack flanks is measured by the line analysis and clip gauge, o f 0.5 to 0.8 mm, for systems A and B respectively. The most significant difference that exists in the line analysis o f systems A and B is that crack extension occurs during the largest load drop in system A , while process zone development, most likely due to matrix cracking and a small amount of fibre failure, may occur prior to crack extension during the largest load drop i n system B . This was observed in the line analysis o f specimen B l . This suggests that system B may have a greater capacity to redistribute load during failure than system A . To continue, an investigation to physically map the nature o f the damage in the laminate is needed, and is presented in Chapter 4. Once a spatial description o f the damage is known, it can be used in conjunction with the line analysis to create a picture o f the sequence o f damage growth throughout the test.  37  3.5 Summary of Results  The following summarizes the results o f this chapter: 1. The inscribed line and clip gauge displacements offer a consistent explanation o f the damage progression throughout the test. 2. Discrete load drops indicate damage growth ahead o f the notch, primarily as crack extension. 3. Large displacements in front o f the notch tip are captured by both the line analysis and clip gauge during specimen unload. The largest load drop corresponds to roughly 15 to 25 m m o f crack extension in systems A and B respectively, with an opening o f 0.5 to 0.8 m m measured by the surface displacements. 4.  System B may have a greater ability to redistribute load during failure than system A . Evidence o f this is given by the line analysis o f specimen B I which shows significant local displacement ahead o f the notch, suggestive o f matrix cracking and only a small amount o f fibre  failure, during specimen  unloading prior to crack extension.  In system A ,  predominantly crack extension occurs during unloading. 5. The R-curves suggest that system B may be a tougher system, with greater ability to absorb energy, as G  1C  rises more steeply and is significantly higher than system A up to the largest  load drop.  38  Table 3.1 Position in front of the notch tip at which the scribe line has zero displacement at a given load. The results are for the scribe line closest to the notch mid-plane for specimens A3, B l and B2, and refer to the specified figures. System A : specimen A3 line #4, Figure 3.5  System B: specimen B l line #1, Figure 3.7  System B: specimen B2 line #1, Figure 3.9  Photo #  Position in Front of Notch Tip (mm)  Photo #  Position in Front of Notch Tip (mm)  Photo #  Position in Front of Notch Tip (mm)  10 11  0  4a 8a  0 2  5 8  0 1  17a  5  9  2  18a 3b 4b  9 10 10 12  11 12  6 10 15  12 13 14 15  0 1 4  16 18  10 25 25 25  19  30  7b 8b 9b  38 38  39  15 16 17 18 19 20 21  15 33 33 33 40 40  9000  s p e c i m e n A1  a/W = 0.32 specimen A 2  a/W = 0.33 specimen A 3  a/W = 0.29  0  1  2  3  4  5  C r o s s H e a d Displacement (mm) Figure 3.1 Load vs cross head displacement of specimens A l , A2, and A3. The cross head displacement is not a true measure of the displacement at the specimen loading pins due to loading train deflection as discussed in Chapter 2.  40  41  7000 6000 5000 4000 T3 03 O  3000  Clip Gauge  Cross Head 12  -12  •I 11  710  / 1 3  \  / \ \  1—  0  0.5  11  1718 15  0  14  19  15  1  19  Numbers refer to photo #  i  1  1.5  2.5  D i s p l a c e m e n t (mm)  Figure 3.4 Load vs cross head and clip gauge displacement of specimen A3. The numbers on the curve indicate where the photos were taken throughout the test. The cross head displacement is not a true measure of the displacement at the specimen loading pins due to loading train deflection as discussed in Chapter 2. E E  3  •photo 10 -photo 11 -photo 12 -photo 13 photo 14 -photo 15 -photo 16 -photo 18 -photo 19  (U  c: d) E  0) _o ro  q.  notch  clip gauge Position in Front of Notch Tip (mm)  Photo numbers refer to Figure 3.4. Displacement is measured relative to photo 5. Image resolution is .045 mm/pixel. Line #4 is 20 mm above and 20 mm below the notch mid-plane. ^  Figure 3.5 Displacement of line #4 as a function of position in front of the notch tip for selected photos of specimen A3.  42  Clip Gauge 12000  CMOD Gauge  $3—  TJ 03 O  Numbers refer to photo # a = roll #1, b = roll #2 1  0  0.5  1  1.5  2  2.5  Displacement (mm) Figure 3.6 Load vs C M O D and clip gauge displacement of specimen B I . The numbers on the curve indicate where the photos were taken throughout the test.  -s-photo photo - i — photo - s - photo photo photo - * - photo - ° - photo —•—photo  a4 a8 a17 a18 b3 b4 b7 b8 b9  clip gauge Position in Front of Notch Tip (mm) Photo numbers refer to Figure 3.6. Displacement is measured relative to photo al. Image resolution is .048 mm/pixel. Line #1 is 2.5 mm above and 2.5 mm below the notch| mid-plane.  Figure 3.7 Displacement of line #1 as a function of position in front of the notch tip for selected photos of specimen B I .  43  12000  9 i>Jf 1 1 1  B 9 T ^  15  / TJ CO O  \ \  1 7 ^ \  5 /  J f 21  2000 t 1/ 1  0 0  19  0.5  1  1  1  1.5  Numbers refer 1  20 to nphoto # 2.5  CMOD Displacement (mm) Figure 3.8 L o a d vs C M O D displacement of specimen B2. T h e numbers on the curve indicate where the photos were taken throughout the test.  E E,  .clip gauge ' line #1  CD C  C CD  E  CD  O _ro  CL  </) Q  notch  -•-photo 5 -s- photo 8 photo 9 - x - photo 11 - * - photo 12 -©—photo 15 -•-photo 16 — 1 — photo 17 - « - photo 18 photo 19 - * - photo 20 photo 21  ip gauge Position in Front of Notch Tip (mm)  Photo numbers refer to Figure 3.8. Displacement is measured relative to photo 1. Image resolution is .042 mm/pixel. Line #1 is 2.5 mm above and 2.5 mm below the notch| mid-plane. Figure 3.9 Displacement of line #1 as a function of position in front of the notch tip for selected photos of specimen B2.  44  E  E  co photo a 4  c  photo a 8 c  photo a17  E  photo a18  CD CD O  photo b3  _ro  photo b4  o.  photo b7  w b  photo b8 photo b9  notch ti  Position in Front of Notch Tip (mm)  Photo numbers refer to Figure 3.6. Displacement is measured relative to photo a l . Image resolution is .048 mm/pixel. Line #3 is 7.5 mm above and 7.5 mm below the notch mid-plane.  Figure 3.10 Displacement of line #3 as a function of position in front of the notch tip for selected photos of specimen B l .  45  specimen A 3 specimen B1 specimen B 2  0  2  4  6  8  10  12  14  16  A a (mm) Figure 3.11 R-Curve of specimens A3, B l and B2, based on the line analysis estimation of the crack length. G is calculated for the peak loads corresponding to the crack lengths of photos: 1) specimen A3: 10,12,13,14 in Figure 3.4, 2) specimen B l : a8, al5, al9, b3 in Figure 3.6, and 3) specimen B2: 9,11,12,16 in Figure 3.8. I C  46  Chapter Four  Physical Description of the Damage  4.1 Introduction This chapter presents a physical description o f the damage grown during the O C T test. Fibre failure in each lamina is revealed by post-test deplies, i n which the resin is removed in an oven. Lamina matrix cracking, fibre failure and delamination between laminae are observed from posttest sectioning. A crack, containing damage in all plies, is identified growing in front o f the notch tip, in front o f which is a process zone, in which only some o f the plies contain damage. The final dimensions o f the crack and process zone are reconstructed for systems A and B . The line analysis o f Chapter 3 is used to approximate the load at which the damage was created. The spatial sequence o f damage growth in the process zone indicates the temporal sequence o f damage growth.  This information helps to physically explain the notch-sensitivity o f both  systems, and provides a tool with which to calibrate their respective strain softening curves.  4.2 Techniques Three techniques were used to identify the post-test damage in the O C T specimens. Deply showed the path o f fibre failure in each ply. Cross-sections cut perpendicular to the notch revealed through-the-thickness matrix cracking, fibre failure and delamination, at a given position i n front o f the notch tip. Finally, a pulse-echo ultrasonic ( P E U ) scan mapped delaminated areas, as viewed from one side o f the specimen.  47  4.2.1 Deply One specimen o f system A , specimen A l , was deplied. It was first placed in an oven at 400°C to burn off the resin. After roughly 4 hours, sufficient resin had been removed to allow separation o f the individual layers for inspection. The layers were carefully separated, and placed side by side in the same order as the laminate lay-up sequence, to recreate the fibre failure through-thethickness. A transparency was placed on top o f each ply, and an outline traced o f the visible fibre failure. These outlines are drawn in Figure 4.1.  4.2.2 Sectioning a n d M i c r o g r a p h Analysis One O C T specimen each o f system A and B , specimens A 3 and B l respectively, were sectioned parallel to the height o f the specimen, at increasing distances in front o f the notch tip as shown in Figure 4.2. A slow-speed saw was used with a diamond-finished blade to minimize additional damage. The cross-section surfaces were then polished. The cross-section surfaces were examined under an optical microscope. Photographs were taken, called micrographs. A schematic o f the damage patterns observed i n the microscope has been drawn next to each micrograph for comparison purposes, to the same scale and orientation as that shown in Figure 4.2.  The scales in the x and y direction are not the same.  A s some o f the  micrographs are not the best quality, some detail may be drawn on the schematic which is not clearly seen i n the micrograph. Selected micrographs are included at the end o f the chapter, and the complete set o f micrographs are presented in Appendix 2. A s system B was a sandwich panel, the honeycomb core o f specimen B l was first removed on a band saw before sectioning o f each laminate, labeled the front (F) and back (B) laminate in Figure 4.2. Each laminate has an outer (O) and inner (I) side, where the inner (I) side represents the side that was attached to the honeycomb core before sectioning.  48  4.2.3 Pulse-Echo Ultrasonic Scan A map o f the delaminated areas in specimen A 3 is given by a pulse-echo ultrasonic ( P E U ) scan, Figure 4.5 (performed by Integrated Technologies, Inc. o f Bothell, Washington). Darker regions indicate a cleaner signal reflection, thus large delamination surfaces are more easily picked up than, for example, small isolated pockets o f fibre failure or matrix cracking which scatter the reflected signal. The P E U transducer was placed on the back side o f the specimen, as the surface delamination emanating from the notch tip was smaller on that side.  4.3 Deply Results Post-test deplies confirm that fibre failure has been grown in front o f the notch during the O C T test. For example, the deply o f specimen A l , outlined i n Figure 4.1, reveals the following: 1. Localized fibre failure exists in each ply, and the combination o f these failures through all the plies creates a through-the-thickness crack in the specimen. 2. Large visible separations o f the fibres indicate that matrix splitting, in which the matrix cracks parallel to the load, occurred i n the -45°, 90°, and 0° plies during the O C T test. During loading, the splitting reduced the stress concentration at the notch tip, effectively blunting the notch tip. 3. The direction of fibre failure in the centre 0° plies is at -90°, perpendicular to the far-field load. (Positive angles are taken as counter-clockwise to the loading direction to be consistent with the standard orientation used to specify lay-up fibre direction.) 4. In the surface -45° plies, matrix splitting is observed starting at the notch tip. This splitting is followed by fibre failure at roughly 10 m m in front o f the notch tip. Fibre failure occurs once it becomes energetically more favourable for the fibres to break than more splitting and delamination.  Delamination was observed on the surface plies accompanying the matrix  splitting. 49  5. The angle o f fibre failure and matrix splitting in layers sandwiched between the surface -45°'s and centre 0° layers shifts from -45° to -90° with increasing proximity to the centre 0° plies. For example, as mentioned, the surface -45° plies show matrix splitting at an angle o f -45°.  However, in the -45° plies closer to the centre 0° plies, smaller amounts o f matrix  splitting occur, followed by fibre failure, giving a general direction o f propagation at -75°. A second example is given by the 0° plies. Fibre failure propagates at roughly -75° i n the outer 0° plies and at -90° in the centre 0° plies. The direction o f fibre splitting and fibre failure in each layer, is both a function o f the fibre orientation and constraint imposed by the direction of propagation i n the adjoining plies. 6. Fibre failure extends to roughly 15 m m i n front o f the notch tip in the two centre 0° plies, and to roughly 22 m m i n front o f the notch tip i n the remaining plies. Notch tip shielding from damage mechanisms such as the matrix splitting observed in the centre 0° plies, w i l l retard damage propagation in the centre layers. A s well, damage growth w i l l be influenced by the state o f stress which varies through-the-thickness.  The centre layers approach a state o f plane  strain, making the process zone smaller in the in-plane lamina direction than i n the outer layers. The outer layers approach a state o f plane stress. 7. The angle o f fibre failure and fibre splitting in each layer is symmetrical about the centre 0° plies, as expected from the symmetry o f the laminate lay-up.  4.4 Description of Damage in the Laminae Figure 4.3 and Figure 4.4 represent typical damage observed in specimens A 3 and B I respectively. The following three types o f damage are visible: 1. Matrix cracking is observed i n the off-axis plies. Slightly more matrix cracking is observed in system B than in system A . This is shown i n the close-up o f the micrograph o f Figure 4.4.  50  2. Fibre failure is observed in the 0° plies, and in the [ 0 7 9 0 ° ] weave layers o f system B . 3. Delamination is observed in both systems. In the cross-sections, delamination is shown as a vertical split between two adjoining plies. A map o f the delamination in specimen A 3 is given by the P E U scan shown i n Figure 4.5. A dark triangular region is shown between positions A ' and C , extending up to 10 m m i n front o f the notch tip. Most likely, this dark region corresponds to the surface delamination observed on the back surface o f specimen A 3 at the same location in front o f the notch tip. This delamination is grown during the small load drops prior to the peak load in the O C T test, between loads A and C in the load vs cross head displacement curve given i n the figure. Between positions C and D ' in Figure 4.5, a dark band is observed with a width o f 15 m m in the x direction and a height o f 4 m m i n the y direction. This band most likely represents the crack grown during the largest load drop (loads C and D ) , which contained some delamination o f roughly the same height as the dark band, and extends roughly the same distance in front o f the notch tip. A large triangular area appears between positions D ' and E ' in the P E U scan, which was grown between loads D and E , and corresponds to the development o f the process zone. This area most likely also represents delamination, as the sectioning showed some delamination about the centre 0° plies in the process zone.  4.5 Sequence of Damage Progression Throughout the OCT Test The following results relate the damage created in each specimen to the corresponding approximate load in the O C T test. The sequence o f damage progression throughout the test is recreated.  51  A s defined in the introduction, damage i n the laminate consists o f a crack, emanating from the notch tip, which contains through-the-thickness fibre failure, matrix cracking, and delamination. In front o f the crack is a process zone, with visible damage in only some o f the plies.  4.5.1  Development of Crack and Process Zone Height and Length  Profiles o f the final length and height (x and y directions in Figure 4.2 respectively) o f the crack and process zone are given for specimen A 3 in Figure 4.6 and for specimen B I i n Figure 4.11. Cross-sections at several positions in front o f the notch tip are shown for specimen A 3 i n Figure 4.7 to Figure 4.10, and for specimen B I i n Figure 4.12 to Figure 4.15. The corresponding load vs cross head or C M O D displacement is included in the figure, to show the approximate load at which the damage was created. The points o f zero displacement o f the inscribed lines taken from the line analysis presented in Chapter 3 are used to approximate the length o f the damage at a given load.  This gives the approximate load at which the damage i n the cross-section was  created.  4.5.1.1 Specimen A3 A reconstructed profile o f the crack and process zone in specimen A 3 is shown i n Figure 4.6. Figure 4.7 to Figure 4.9 show cross-sections at positions A ' to C in Figure 4.6, and Figure 4.10 shows a typical cross-section between positions C and D ' in Figure 4.6. The damage in each cross-section was created at loads A to D i n the load vs cross head displacement curve in Figure 4.6. The following observations can be made: 1. The final length o f the crack is 25 mm. During the damage grown between loads A to C and prior to the big load drop, the height o f the crack increases to 5 m m (cross-sections at positions A ' to C ) , at an angle, 6, o f roughly 30° to the notch mid-plane. During the large  52  load drop, loads C to D , the crack height remains roughly constant at an average height o f 5 mm. A typical cross-section between positions C and D ' is shown in Figure 4.10. 2. The final length o f the process zone is 7 mm, and the average height is 5 mm. The process zone is grown between loads D and E , and is shown by the shaded area between positions D ' and E ' i n Figure 4.6. 3. Delamination about the centre 0° plies is observed between positions C and D ' , and in the process zone.  4.5.1.2 Specimen Bl The dimensions o f the crack and process zone in specimen B1 are slightly different to those o f specimen A 3 . Cross-sections are shown at positions U ' to W (Figure 4.12 to Figure 4.14), as well as a typical cross-section between positions X ' and Y ' (Figure 4.15), corresponding to loads U to Y i n the load vs C M O D displacement curve, Figure 4.11. The reconstructed profile o f the damage i n specimen B l is shown i n Figure 4.11, and the following observations can be made: 1. The final length o f the crack is 35 mm. During the initiation o f damage between loads U to X , the crack height grows to 12 m m (cross-sections at positions U ' to X ' ) , at an angle, 0, o f roughly 50°. During the large load drop from X to Y , the average crack height is 12 mm. A typical cross-section between positions X ' and Y ' is shown in Figure 4.15. 2. The process zone is 3.5 m m long, and the average height is 12 mm. 3. Delamination is observed at each stage o f the test, joining matrix cracking and fibre failure typically between the - 4 5 7 9 0 ° and + 4 5 7 9 0 ° plies, to give a staircase-like crack profile.  4.5.2  Temporal Sequence of Damage Growth in the Process Zone  The spatial development o f fibre failure, matrix cracking and delamination in the process zone indicates the temporal sequence o f damage growth. In both systems, it appears that the centre 0°  53  plies, and in system B the [0°/90°] weave layers as well, are the last to fail. For example, Figure 4.16 shows a cross-section o f specimen A 3 in the process zone. Damage is visible in all plies but the centre 0° plies. A cross-section in the process zone o f specimen B I , Figure 4.17, shows damage in all but the centre 0° ply and outer [ 0 7 9 0 ° ] weave layers. (Due to poor resolution in the micrographs, the schematic is more clear.)  4.6 Discussion The deply, sectioning, and P E U scan offer a consistent picture o f the damage grown during the OCT  test.  This damage consists o f a narrow band o f fibre failure, matrix cracking and  delamination, propagating as a crack and process zone in front o f the notch. 4.6.1  Notch-Sensitivity  Damage mechanisms in the process zone affect the notch-sensitivity o f the laminate by redistributing the stress concentration at the notch tip. The degree o f notch-sensitivity may range from being notch-sensitive, in which L E F M predicts a square root dependence o f the notched fracture strength on the crack length, to notch-insensitive, in which the only effect o f the notch is to reduce the net section area. A diagram showing the failure stress as a function o f notch length for increasing degrees o f notch-sensitivity is given in Figure 4.18.  A n example o f how the  damage in the process zone may alter the stresses at the notch tip is given by a [ ± 4 5 ° ] laminate, s  in which damage initiates as matrix splitting, followed by decoupling o f the +45° and -45° layers.  This decoupling dissipates the stress concentration at the notch tip, and makes the  laminate effectively notch-insensitive.  Systems A and B are quasi-isotropic laminates, which  according to a study by Wells and Beaumont (1987), typically show intermediate notchsensitivity.  Thus the sequence and distribution o f damage in the process zone w i l l affect the  fracture strength.  54  A greater emphasis is placed in this work on the role o f fibre failure in the O C T specimens than by others studying damage in notched carbon fibre laminates (Kortschot and Beaumont, 1990a; Webb and Kortschot, 1991). In this work, the damage is considered to develop as a localized band o f fibre failure in front of the notch, with relatively little matrix cracking and delamination. In contrast, Webb and Kortschot (1991) have described the development o f a diffuse zone o f matrix cracking and delamination prior to failure in quasi-isotropic double edge-notched ( D E N ) carbon fibre laminates. This different emphasis on fibre failure is due in part to the different investigative techniques used to examine the damage mechanisms.  Webb and Kortschot used the absorption o f a  radiographic dye to reveal the damage prior to failure. However, detailed cross-sectioning was used on the O C T specimens. The sectioning and deply results suggest that the dominant damage mechanism i n the development o f the O C T process zones is fibre failure. The geometry o f the specimen allows a gradual development o f the process zone, from which the sections can be cut to reveal the gradual onset o f fibre failure., It is not clear whether the D E N specimen used elsewhere is large enough to allow this gradual fibre failure without catastrophic failure o f the specimen. The weave i n system B may increase notched strength by resisting surface delamination. Lagace (1986b) noted that surface delamination greatly decreased notched strength in a quasi-isotropic carbon fibre reinforced laminate.  The laminates  failed by  fibre  splitting followed by  delamination o f the outer +45° and -45° plies. However, when the +45° and -45° plies were replaced by a [±45°] fabric, and the centre 0° and 90° plies by a [ 0 7 9 0 ° ] weave, no delamination occurred and the strength was comparatively higher.  55  A greater ability to carry and redistribute load during failure may exist i n system B due to the greater height and staircase pattern observed in the sectioning. Damage in system B initiates as fibre failure and matrix cracking in the off-axis plies at a greater height difference between adjoining plies than in system A . A t a given height, therefore, a greater amount o f undamaged material exists through the thickness to sustain load.  A greater number o f load path  combinations are therefore available in which to redistribute the load, and dissipate the notch tip stress concentration.  4.6.2 Strain Softening Curve The post-peak region o f the strain softening curve accounts for how damage evolution i n the process zone affects the notch-sensitivity o f the material. The physical description o f the damage given in this chapter provides useful information with which to determine the strain softening curve o f the O C T specimens. In the F E M model, the element size must be sufficiently large to include the effects o f strain softening within each element.  The steady-state height and final  length o f the process zone in systems A and B might define the minimum element size needed to model the O C T specimen behaviour. A qualitative description o f the damage in the process zone has been given in this chapter, which can be used to calibrate the F E M mesh and explain differences i n the post-peak shape o f the strain softening curve for each system. These results, in conjunction with the load vs surface displacement curves o f Chapter 3, may be used to calibrate a F E M model o f the O C T specimens. However, the actual shape o f the strain softening curve is unknown. Therefore, a preliminary shape with which to begin modeling the O C T specimens would be useful, as well as any additional knowledge o f the evolution o f damage in the process zones. Chapter 5.  56  This is presented in  4.7 Summary of Results The following lists the results presented in this chapter: 1. The deply, sectioning and P E U scan indicate that damage exists as a narrow band o f fibre failure, surrounded by a small amount o f matrix cracking and delamination. 2. This damage grows as a crack, containing damage in all the plies, in front o f which is a process zone, containing damage in only some of the plies. 3. The final length o f the crack in specimen A 3 is 25 mm, and the average height is 5 mm, while the final crack length in specimen B I is 35 mm, and the height is 12 mm. 4. The final length o f the process zone in specimen B I is half that o f specimen A 3 (3.5 vs 7 m m respectively), while the height i n specimen B I is twice that o f specimen A 3 (12 vs 5 m m respectively). We may assume that as the height has reached a steady-state value, it represents the fully-developed process zone height for different a/W o f the O C T specimens. 5. In the process zone, the spatial sequence o f fibre failure and matrix cracking mirrors the temporal sequence o f damage growth. The sectioning shows that the centre 0° plies in both systems and the [0790°] weave in system B , are the last to fail. 6. The physical description o f the damage provides quantitative information with which to calibrate the strain softening curve for each system.  For example, the final steady-state  height o f the process zone can be used in conjunction with a final length, to determine the minimum dimensions o f the elements needed to include the effects o f strain softening. 7. This physical understanding o f the damage also provides qualitative information with which to generate a physical understanding o f the strain softening curve for each system.  For  example, the larger height and staircase-like profile o f the damage in system B may indicate a  57  greater ability to redistribute load during failure than in system A . This might influence the shape of the strain softening curve o f system B .  58  Front S i d e  Figure 4.1 Deply schematic of specimen A l . The fibre direction in each layer is drawn in the top left or right corner of each ply. Positive angles are taken counter-clockwise to the 0° fibre direction to be consistent with the standard orientation used to specify lay-up fibre direction.  59  Layup: [-45/90/45/0/-45/90/45/0]  s  delamination x = 18.00 mm Top  Back  Top  C H . =4.20 mm units: mm  B - 10 - 9  fibre "failure - 7 - 6 - 5 ,, matrix ^ 3 cracking - 2 - 1 - 0 - -1 - -2 - -3  N.M-P.H  - -4  C H . = crack height P.Z.H. = process zone height N.M-P.: notch mid-plane F = front side of laminate B = back side of laminate Top = top side of laminate 0 = 0° ply  - -5 - -6 - -7 - -8 - -9 L-10 O = outer side  £4  3.35  Figure 4.2 Example of a micrograph schematic, showing matrix cracking, fibre failure in the 0° plies and surface delamination. This shows the orientation to which all the micrographs have been redrawn for comparison purposes. The scales in the x and y direction are not the same. This example is taken at 18 mm in front of the notch tip in specimen A3.  60  3.35 Figure 4.3 Typical cross-section of specimen A3, taken at 20.25 mm in front of the notch tip. This shows delamination of the surface ply. The layup is[-45/90/45/0/-45/90/45/0] . s  x = 10 Front CH. = units: n  Figure 4.4 Typical cross-section of specimen B l , taken at 10.00 mm in front of the notch tip. The layup is [F0/-45/90/45/0/45/90/-45/F0] , F0 = [0/90] weave. T  61  Back  orientation of P E U s c a n T  °P  Fron Back  o  o  3 3  f x  o  -  100 m m notch tip 70006000z 5000"D 4000CO O  _J  3000200010000  0  0.5  1  1.5  2  2.5  C r o s s H e a d Displacement (mm)  Figure 4.5 Pulse-echo ultrasonic (PEU) scan of specimen A3. Darker regions correspond to a cleaner reflected signal, and most likely represent delamination grown between loads A to E (positions A ' - E ' on the PEU scan).  62  7000  to scale: angle, 8  6000 j 5000 ^4000  N. M-P.  5 3000-1  k~1 25 mm  w  7 mm  5 mm  0  0.5  1  1.5  2  2.5  C r o s s Head Displacement (mm)  = 0 2 8  Figure 4.6 Reconstructed profile of the damage in specimen A3, with the load vs cross head displacement curve from the OCT test presented in Chapter 3.  x = 1. CH. = units: i  3.35  Figure 4.7 Cross-section at position A' in Figure 4.6, taken at 1.85 mm in front of the notch tip in specimen A3. The layup is [-45/90/45/0/-45/90/45/0] . s  63  x = 11.45 m m C H . = 6.1 mr units: m m  3.35  Figure 4.9 Cross-section at position C in Figure 4.6, taken at 11.45 mm in front of the notch tip in specimen A3. The layup is [-45/90/45/0/-45/90/45/0] . s  64  Top  x = 18.00 m m  F  B  T o  P B  -10 - 9 " 8  C H . =4.20 m m units: m m  -  7 6  -  5  - 4 - 3  - 2 - 1 - 0  N.M-P.  - -1  - -2  - -3 - -4 - -5  - -6 - -7  - -8 - -9 -10  Figure 4.10 Typical cross-section between positions C and D' in Figure 4.6. This micrograph is taken at 18.00 mm in front of the notch tip in specimen A3. The layup is [-45/90/45/0/-45/90/45/0] . s  to scale:  V  W  12000 -angle, 6  10000 8000 £  o  35 mm — W  6000f  0.5  3.5 mm  = 0 22  1  1.5  2  2.5  C M O D Displacement (mm)  Figure 4.11 Reconstructed profile of the damage in specimen B l , with the load vs CMOD displacement curve from the OCT test presented in Chapter 3.  65  x = 1.0 m m Front S i d e  Top  C H . = 1 mm units: mm  N.M-P  —  O  Top  I  14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2  O  H  - -3 - -4 - -5 - -6 - -7 - -8 - -9 -10 -11 -12 -13 14  1.66  Figure 4.12 Cross-section at position U' in Figure 4.11, taken at 1.00 mm in front of the notch tip in specimen BI. The layup is [FO/-45/90/45/0/45/90/-45/FO] , F0 = [0/90] weave. T  Top  x = 2.0 m m Front S i d e  14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14  O  C H . = 3 mm units: mm  N.M-P—H  O  Top  I  1.66  Figure 4.13 Cross-section at position V in Figure 4.11, taken at 2.00 mm in front of the notch tip in specimen BI. The layup is [F0/-45/90/45/0/45/90/-45/F0] , F0 = [0/90] weave. T  66  1.66  Figure 4.14 Cross-section at position W in Figure 4.11, taken at 5.65 mm in front of the notch tip in specimen B l . The layup is [F0/-45/90/45/0/45/90/-45/F0] , FO = [0/90] weave. T  Figure 4.15 Typical cross-section between positions X' and Y' in Figure 4.11. This micrograph is taken at 12.00 mm in front of the notch tip in specimen B l . The layup is [F0/-45/90/45/0/45/90/-45/F0] , FO = [0/90] weave. T  67  P.Z.H. = units: mr  Figure 4.16 Cross-section in the process zone of specimen A3, taken at 28.00 mm in front of the notch tip. This micrograph shows damage in all but the centre 0° plies. The layup is [-45/90/45/0/-45/90/45/0] . s  Figure 4.17 Cross-section in the process zone of specimen BI, taken at 35.50 mm in front of the notch tip . This micrograph shows damage in all but the centre 0° ply and surface 0790° weave plies. The layup is [F0/-45/90/45/0/45/90/-45/F0] , F0 = [0/90] weave. T  68  r j = failure stress G = yield stress in a metal, or the stress at which damage initiates in a fibre reinforced composite f  y  Figure 4.18 Diagram of the failure stress vs the notch length for increasing degrees of notch-sensitivity.  69  Chapter Five Process Zone Tensile Tests  5.1 Introduction This chapter examines the effect o f damage in tensile specimens which have been cut from the process zone in systems A and B . A simple equation is derived to extract the modulus o f the damaged section o f each tensile specimen from the measured modulus. Laminated Plate Theory is used to reconstruct possible combinations o f the load-bearing plies according to the damaged moduli. The change in load-bearing combinations indicates the sequence o f damage growth in the process zone. Finally, the damaged moduli are used i n conjunction with the measured failure stress to back-calculate several points in the post-peak region o f the strain softening curve. A preliminary shape o f the strain softening curve for systems A and B is presented.  5.2 Background A preliminary strain softening curve is presented in this chapter, which is back-calculated from the response o f tensile specimens o f systems A and B . For reasons discussed in Chapter 1, it is preferable to represent the strain softening curve as the load-displacement response o f a given material system.  However, for ease o f implementation into a Finite Element Method ( F E M )  model, it is numerically convenient to represent the response i n terms o f stress and strain. These material responses are numerically equivalent for a constant element size.  The preliminary  results o f an F E M analysis o f the O C T specimen are discussed in Chapter 6. Tensile specimens cut from the process zone provide a quantitative measure o f the strain softening curve.  In the O C T specimen, the material i n the fully developed process zone is  70  subject to a high stress concentration, and large local displacements result from the damage presented in Chapter 4. A s w i l l be shown in this chapter, the displacements in the process zone translate into strains which exceed the laminate failure strain.  The growth o f the zone is  represented by the post-peak region o f the strain softening curve, shown between points A and C in Figure 5.1. If the material in the process zone is loaded to point B i n Figure 5.1, for example, it w i l l follow the path O A B .  During unloading, i f strain softening is caused by damage, the material w i l l  unload along the path B O . If this material is then removed, and made into a tensile specimen, it w i l l reload along the path O B and w i l l fail at point B . This gives the location o f point B on the strain softening curve, which was previously unknown. This technique provides an experimental back-calculation o f points on the post-peak region o f the strain softening curve, which cannot be directly measured from the O C T specimen. Many tensile specimens cut at different locations in the process zone should thus give the overall shape o f the curve. It should be noted that during unloading from point B , a strain softening material model predicts a different unloading path than does an elastic-plastic model. The elastic-plastic model predicts that material initially at point B unloads along the path B O ' , with the same modulus as the undamaged modulus, E . UD  However, the tensile tests presented in this chapter indicate that the  material would unload along the path B O , with a new damaged modulus E . D  5.3 Experimental Technique A process zone similar to that presented in Chapter 4, was reproduced in one O C T specimen o f each system (specimens A 4 and B 2 ) . The zones were sectioned perpendicular to the notch m i d plane into thin strips roughly 2 m m wide. A diamond-finished blade slow-speed saw was used to minimize additional damage.  Figure 5.2 shows the approximate location o f the tensile  71  specimens, and Table 5.1 lists their dimensions. The specimens are numbered A 4 T 1 to A 4 T 4 , and B2T1 to B 2 T 3 , where a higher number represents increasing distance in front o f the notch tip. The sandwich core o f specimen B 2 was first removed before cutting strips out o f the front and back laminates. The damage before and after the tensile test was recorded i n a schematic, and as the specimens were very delicate, only a few faces were polished and micrographs taken (Figure 5.5 to Figure 5.9). The orientation o f the micrographs is the same as that used for the sectioning results o f Chapter 4 (Figure 4.2). However, the position relative to the notch mid-plane is not included as the micrographs were taken primarily to show the type o f damage in the plies.  A scale is  included to indicate the approximate damage height. The ends o f the specimens were first embedded in hollow cylindrical steel tabs and bonded with an epoxy, as shown in Figure 5.3, before mounting them in the Instron grips. A special j i g was built to align the end tabs parallel to the specimen, as shown in the figure, to minimize eccentric loads during testing. To glue the tabs onto the specimen, each tab was temporarily taped to the specimen, enclosed in the j i g placed upright, and the glue poured into the larger end o f the hollow cylinder. The epoxy was then cured for 16 hours at room temperature.  This procedure  was repeated with the other tab, and the specimen was placed i n an oven at 100° C for three hours to complete the cure cycle. A clip gauge was placed on one side o f the specimen to measure the displacement during loading, as shown in Figure 5.3. In order to ensure that the gauge was within a region o f uniform loading, each arm o f the gauge was placed at least one specimen thickness away from the application o f the load. The tensile specimens were then statically tension loaded in an Instron testing machine until failure.  72  5.4 Derivation of the Damaged Moduli The moduli o f the damaged sections o f the tensile specimens were back-calculated from the measured moduli.  A s shown i n Figure 5.4, the tensile specimen is simplified to contain a  uniform region o f damaged material with modulus E , surrounded by a region o f undamaged D  If the tensile specimen is subject to- an applied stress, a, then by  material with modulus E . UD  compatibility:  where 5  M  is the total displacement measured by the clip gauge, 5  D  is the displacement o f the  damaged region, and 5 ^ is the displacement o f the undamaged region. Substituting Hooke's law, E q . (5.1) becomes:  °"M  <*D D  L  H  E where h  D  +  u(- )  CT  L  h  D  (5.2)  D  "UD  D  is the height o f the damaged section, and L is the clip gauge length, as shown in  Figure 5.4. A s o  M  =o  D  =o , UD  E q . (5.2) is simplified to:  1 " =  "V" /L  "(L-h )/" /L + D  (5.3)  •^UD  The damaged modulus, E , can then be back-calculated using E q . (5.3), where h , is determined D  by visible inspection.  D  The undamaged modulus, E , UD  is the measured undamaged tensile  specimen modulus.  5.5 Experimental Results 5.5.1 Damage Observed Prior to Tensile Tests Slightly more damage is visible with increasing proximity to the notch tip, in the tensile specimens taken from O C T specimen A 4 , given in Figure 5.5 to Figure 5.7. The face farthest 73  from the notch tip o f A 4 T 1 (Figure 5.6) is similar to the damage observed i n A 4 T 2 , for which no micrograph was obtained. The schematics show that: 1. In all specimens, matrix cracking is observed in all the +45°, -45° and 90° plies. 2. None o f the specimens show fibre failure in the centre 0° plies. Fibre failure i n the outer 0° plies is visible in specimens A 4 T 1 (specimen closest to the notch tip) and A 4 T 2 , but not in specimen A 4 T 3 . 3.  Significant delamination about the centre 0° plies is apparent in A 4 T 1 and A 4 T 2 , and only a small amount o f delamination to one side o f the centre 0° plies is evident in A 4 T 3 .  The following damage is visible in the tensile specimens o f specimen B 2 , given in Figure 5.8 and Figure 5.9: 1. Specimen B 2 T 1 (taken from the front laminate) appears to be the most damaged, as it has damage i n all the plies. This damage was observed in the face closest to the notch tip, and the specimen was still able to carry load. 2.  Specimen B 2 T 2 (taken from the back laminate) appears to have damage i n all but the centre 0° ply.  5.5.2 Measured Moduli The measured stress vs strain curves o f the tensile specimens for system A and B are presented in Figure 5.10 and Figure 5.11, respectively. The measured moduli are listed in Table 5.2. From the graphs, the following conclusions can be made: 1. The measured moduli o f specimens A 4 T 1 to A 4 T 3 decrease with increasing proximity to the notch tip. This is consistent with the observed damage, where more damage is visible in specimens nearer the notch tip. A s only one damaged specimen was retrieved from each laminate's process zone in specimen B 2 , a similar conclusion cannot be made.  74  However,  B 2 T 1 , which had greater visible damage prior to testing, had a lower measured modulus than B 2 T 2 , as shown in Figure 5.11. 2. In most specimens, the stress increases linearly with the strain until failure. However, small drops in stress are observed which significantly lower the modulus in specimen A 4 T 2 . T w o significant drops i n the measured modulus occur, Figure 5.10, where E  M  drops from 16 G P a  between points A and B to 6 G P a between points B and C . During loading, popping noises were heard and delamination observed during the load drops, indicating damage growth. For analysis, the two different moduli are represented as two separate specimens.  A4T2a  represents the behaviour o f specimen A 4 T 2 between points A and B and A 4 T 2 b the behaviour between points B and C . 3. In specimens A 4 T 1 and A 4 T 2 , the failure strain exceeds the undamaged failure strain. For example, the failure strain o f specimen A 4 T 2 is 2.45% while the undamaged failure strain is 1.1%. Such large strains must be made possible by the damage in the specimen. A measure of this damage is given by the damaged moduli, which are presented in the following section.  5.5.3 Damaged Moduli Various combinations o f the undamaged plies were reconstructed such that the modulus, determined by Laminated Plate Theory ( L P T ) , was similar to the calculated damaged modulus of Eq. (5.3). Coupled with the visible damage prior to and post-testing, this provided a measure of the effective load-bearing plies remaining in each specimen. The damage height, h , was estimated from the visible damage prior to and post-testing. In the D  specimens where the damage height increased during the test, an average o f the initial and final damage height was used for h . D  This yields a higher damaged modulus in E q . (5.3) than using  the initial height only, and therefore may underpredict the damage i n the specimen. However,  75  the average height more accurately represents the effective damage in the specimen, as the visible damage prior to testing may not show all the existing damage. A graph o f the failure stress and strain of each specimen based on the damaged moduli is shown in Figure 5.12 and Figure 5.13 for specimens A 4 and B 2 respectively. The failure stress, oy is the measured specimen failure stress, and the failure strain, Sy, is back-calculated from the damaged moduli, E  D  and oy according to:  (5.4)  5.5.3.1 Specimen A4 A s indicated in Figure 5.12, the following are the most likely combinations o f effective loadbearing plies in each tensile specimen: 1. The specimen farthest from the notch tip, specimen A 4 T 3 , has roughly 2 0° plies (out o f 4) which effectively bear load. This combination would give a laminate with an approximate modulus o f 14 G P a , which is in the range o f the damaged A 4 T 3 modulus o f 13 G P a . This is the only load-bearing combination which is consistent with the damaged modulus and the damage observed prior to testing. (The micrograph showed damage in all +45°, -45° and 90° plies, with only some fibre splitting in the 0° plies, before testing, Figure 5.7.) 2. The damaged modulus o f specimen A 4 T 2 a (10 GPa), suggests that only between 1 and 2 o f the 0° plies are load-bearing. This combination would give a laminate that has a modulus between 7 and 14 G P a respectively. Either o f these load-bearing combinations are consistent with the damage observed prior to testing, i n which damage was visible in all but the centre 0° plies. 3. The damaged moduli of both specimens A 4 T 2 b and A 4 T 1 effectively represent less than one 0° load-bearing ply. The damaged moduli are 6 and 4 G P a respectively, which represent a 76  laminate containing only 85% and 57% o f one 0° ply, respectively. The damaged moduli indicate that slightly more damage exists than that observed prior to testing. A t that time, no fibre failure was observed in either o f the two centre 0° plies in either specimen, Figure 5.5 and Figure 5.6. Thus the damaged moduli indicate that the development o f the process zone in specimen A 4 represents the progressive failure o f the 0° plies. The number o f intact 0° plies predicted by L P T represent an effective load-bearing ability o f the 0° plies i n the specimen.  For example, in  specimen A 4 T 2 b , 85% o f the fibres in one 0° ply cannot be completely intact, as the strain in the fibres would exceed the fibre failure strain by a factor o f roughly 2.5.  The 0° fibres must  therefore contain damage, but the load is redistributed through the undamaged portion o f the fibre by the adjoining layers.  Furthermore, one effective load-bearing 0° ply may actually  represent the load-bearing ability o f several 0° fibres dispersed throughout the specimen.  5.5.3.2 Specimen B2 The following represents the most likely combination o f effective load-bearing plies i n the B 2 tensile specimens, Figure 5.13, prior to testing: 1. The damaged modulus o f B 2 T 2 (37 GPa), indicates that the centre 0° ply is undamaged, and the [ 0 7 9 0 ° ] weave layers and +45° and -45° layers are at least partially intact. This indicates a greater load-bearing ability than that expected based on the visible damage prior to testing. The micrograph shows damage in all but the centre 0° ply, Figure 5.9. However, i f only the centre 0° ply carried load, L P T underpredicts the damaged modulus by 55%. 2. The visible damage prior to testing and the low damage modulus o f specimen B 2 T 1 (5 GPa), indicate that roughly only 30% o f the 0° fibres o f one 0° ply bear load. Prior to testing,  77  damage is visible i n all plies, Figure 5.8, and the damage length did not change during testing. The most likely failure sequence o f system B is failure o f the off-axis plies, followed by the [0790°]  weave layers and finally, the centre  0°  ply. The visible damage in the process zone  sectioning o f specimen B I , presented in Chapter 4 (Figure 4.17), shows that the off-axis layers fail first.  The centre 0 ° ply is the last to fail, as it is the only visibly undamaged ply before  testing in tensile specimen B 2 T 2 .  However, the damaged modulus o f B 2 T 2 indicates that,  although damage may exist in all but the centre 0 ° ply, the damaged plies are still able to carry and redistribute a significant amount o f load.  5.5.3.3 Preliminary  Strain Softening  Curves for Systems A and B  The damaged moduli give a preliminary shape for the strain softening curve for specimens A 4 and B 2 , which is shown in Figure 5.14.  The failure stress and strain are plotted for those  specimens which did not fail prematurely.  Although these curves are derived from only one  notched specimen, they provide a general preliminary shape for the F E M softening curve for systems A and B . They represent the strain softening behaviour o f the steady-state process zone in an O C T specimen.  5.6 Discussion The tensile specimens offer a quantitative means o f explaining the damage evolution in the process zone. Crack growth is dictated by the failure o f the 0 ° plies, as these are the primary load-bearing plies. In specimen A , L P T predicts that the growth o f the process zone primarily represents progressive failure o f the 0 ° plies. This would explain the large drops in the measured moduli o f the tensile specimens with increasing proximity to the notch tip. Although the 0 ° fibres must contain damage to exceed a nominal strain greater than the true fibre failure strain,  78  load redistribution must occur such that the fibres are still able to carry a significant amount o f load. The spread o f damage in the process zone is unique to the O C T specimen, in that failure o f the 0° plies occurs gradually, giving a gradual loss in load-bearing ability. In contrast, a dog-bone style specimen fails instantaneously once the 0° fibres reach the fibre failure strain.  A notched  specimen is thus needed to grow the type o f damage represented by the post-peak region o f the strain softening curve. The tensile specimens provide a preliminary shape o f the strain softening curve to input into an F E M model.  However, several difficulties are apparent when trying to determine the strain  softening curve with this technique. For example: 1.  The technique is labor intensive. M a n y specimens must be tested to obtain an average value for each point on the strain softening curve. Detailed knowledge o f the damage grown prior to and during the test is required.  2. Many sources o f error exist.  For example, the small specimen size increases the risk o f  damage being introduced during specimen preparation.  A s well, surface imperfections and  other stress risers increase the risk o f premature specimen failure. Finally, care must be taken to properly align the specimens with the load to minimize eccentric loading. 3. The failure stress is based on the cross-sectional area, yet as damage progresses during failure, the actual load-bearing area decreases. 4. The properties o f the damaged material must be extracted from the tensile specimens.  The  specimen must be simplified analytically, and the damage height, h , must be known. D  Care must be taken when determining a preliminary shape for the curve from the tensile specimens, as the shape w i l l be affected by the dimensions o f the process zone.  79  The process  zone o f system A is twice the width o f system B , and consequently more specimens, may be retrieved to plot points on the strain softening curve. Unless sufficient specimens o f system B are tested, the shape o f the curve may be underdeveloped, and the contrast in shape between the two systems not noticed. Regardless o f the exact shape o f the post-peak region o f the curve, the tensile specimens suggest that a gradual post-peak loss in stiffness is needed to model failure o f the O C T specimen. F E M analyses o f notched composite laminate failure traditionally model an instantaneous  failure  response. This assumes that once failure initiates in a lamina the stiffness and stress o f the ply drop to zero.  However, the tensile specimens are proof that once damage initiates, a loss in  stiffness only gradually occurs.  5.7 Summary of Results The following results were presented in this chapter: 1. Tensile specimens were cut from the process zones o f an O C T specimen o f system A and B . 2. A simple equation was derived to back-calculate the modulus o f the damaged section o f the tensile specimens from the measured modulus o f each tensile specimen. 3. Large drops in the measured moduli occur with increasing proximity to the notch tip. 4. The large drops in measured moduli are explained by the sequence o f damage growth in the process zone. This sequence was determined using Laminated Plate Theory in accordance with the damaged moduli. In both specimens, the off-axis plies fail first followed by failure o f the 0° plies. In system A , the development o f the process zone represents the progressive failure o f the 0° plies. The number o f intact 0° plies decreases from 2 plies (out o f 4) in the tensile specimen farthest from the notch tip, to less than one in the specimen closest to the  80  notch tip. In system B , the off-axis plies fail first, followed by the [ 0 7 9 0 ° ] plies, and lastly the centre 0° ply. 5. Preliminary shapes for the strain softening curve o f systems A and B were back-calculated from the tensile specimens, based on the damaged moduli. 6. The type o f damage grown in the O C T specimen is different from that grown in a dog-bone style specimen.  Systems A and B are 0° dominated systems, and failure o f the 0° plies  occurs gradually as the load is redistributed. Strains on the order o f 2.5 times the fibre failure strain have been measured. In contrast, a dog-bone style specimen would fail instantaneously once the 0° plies reach the fibre failure strain. 7. The tensile specimens provide physical proof o f why a F E M instantaneous failure material response underpredicts the strength o f a notched laminate. This response assumes that the lamina stiffness and stress drop to zero once failure initiates.  However, the growth o f  damage in the process zone leads to a gradual loss in load-bearing ability. A strain softening material response models this loss in the post-peak section o f the curve.  81  Table 5.1 Tensile specimen dimensions. Specimen Width*  Damage Length Before  Damage Length After  (mm)  Clip Gauge Length (mm)  Testing (mm)  Testing (mm)  1.39  35  -  -  A4T3  1.43  29.2  7.5  22  A4T2  1.24  29.5  15  29.5  A4T1  2.70  40  18.5  18.5  1.65  29.7  -  -  Specimen A4 Undamaged A4T4 Damaged  Specimen B2 Undamaged B2T3 (back laminate) Damaged B2T2 (back laminate)  1.66  30  10.8  28.4  B2T1  1.95  30.2  3.7  3.7  (front laminate)  * Indicates width at the mid-height of the tensile specimen. **Represents L, used in Eq. (5.3) and drawn in Figure 5.4. Note: Specimen thickness for system A is 3.35 mm, and for system B is 1.66 mm for each front and back laminate.  Table 5.2 Measured and derived tensile specimen mechanical properties. Measured Failure Stress (MPa)  Measured Failure Strain (%)  Measured Modulus (GPa)  Calculated Damaged Modulus (GPa)  Damage Height, h \ Used in Eq. (5.3) (mm)  399  1.10  36  -  -  A4T3  132  0.60  19  13  14.8""  T  D  Specimen A4 Undamaged A4T4 Damaged A4T2a  140  1.10  16  10  15  A4T2b  170  2.45  6  6  29.5  A4T1  98  1.18  8  4  18.5  467  1.16  40  -  -  B2T2 (back laminate)  408  1.08  38  37  19.5  B2T1 (front laminate)  125  .62  22  5  3.7  Specimen B2 Undamaged B2T3 (back laminate) Damaged  Y Calculated damaged modulus, E , derived from Eq. (5.3), and drawn in Figure 5.4. D  * Damage height, h , used in Eq. (5.3) and drawn in Figure 5.4. D  **Based on the average of the damage height observed prior to and post testing (listed in Table 5.1).  82  E  U D  E  D  = undamaged modulus = damaged modulus  Strain (%) Figure 5.1 Diagram of a strain softening curve back-calculated from process zone tensile specimens.  Specimen B2  Specimen A4  Back Laminate  Front Laminate  A4T1-3 o o  B2T2-3 \  W o o  CM  O O CM  CM  100  100  O< O  100  units: mm P r o c e s s z o n e positions, m e a s u r e d a s d i s t a n c e s in front of the notch tip: • s p e c i m e n A4: 34.5 to 43.85 m m • s p e c i m e n B2, front laminate: 42.56 to 45.36 m m • s p e c i m e n B2, back laminate: 41.09 to 45.98 m m Figure 5.2 Schematic of tensile specimens cut from the process zones of OCT specimens A4 and B2.  83  applied displacement, 5  cylindrical hollow tab V  epoxy  tensile specimen  2 mm  t  50-65 mm  .damaged material clip gauge  E E oo  J^U  \  ±T4  CO  applied displacement, 5  82 mm  Figure 5.3 Jig to align end tabs parallel to tensile specimens while gluing, and the experimental setup to measure the specimen displacement during loading.  1 -UD  a is the failure s t r e s s •E is the u n d a m a g e d s p e c i m e n m o d u l u s • E is the d a m a g e d s p e c i m e n m o d u l u s • L is the g a u g e length • h is the d a m a g e height f  U  D  D  D  -UD CTf  Figure 5.4 Simplification of the tensile specimen used to determine the damaged modulus, E , using Eq. (5.3). D  84  F a c e closest to notch tip: :  A4T1 x = 34.5 m m  Top  B  P.Z.H. = 3.06 m m units: m m  3.35  before tensile test  after tensile test  Figure 5.5 Schematic and micrographs of tensile specimen A4T1. These show the face closest to the notch tip. Layup is [-45/90/45/0/-45/90/45/0] . s  F a c e farthest from notch tip: A4T1 x = 37.2 m m  Top  B  Top F  20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0  P.Z.H. = 3.60 m m units: m m  3.35  Figure 5.6 Schematic and micrographs of tensile specimen A4T1 before tensile test. This shows the face farthest from the notch tip, and is similar in damage to the face closest to the notch tip of A4T2. Layup is [-45/90/45/0/-45/90/45/0] . s  85  Face farthest from the notch tip: A4T3 x = 41.57 mm P.Z.H. = 4 mm units: mm  Figure 5.7 Schematic and micrographs of tensile specimen A4T3. This shows the face farthest from the notch tip. Layup is [-45/90/45/0/-45/90/45/0] . s  86  F a c e closest to notch tip:  Figure 5.8 Schematic and micrograph of tensile specimen B2T1 before tensile test. This shows the face closest to the notch tip. Layup is [F0/-45/90/45/0/45/90/-45/F0] where FO = [0/90] weave. x  87  Face closest to notch tip: B2T2 Back Laminate x = 41.09  Top  Top  O  O  28' 27 26  25 24  P.Z.H. = 10.76 units: mm  23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0  close up  1.66  1.66 before tensile test  after tensile test  Figure 5.9 Schematic and micrograph of tensile specimen B2T2. These show the face closest to the notch tip. Layup is [F0/-45/90/45/0/45/90/-45/F0] where FO = [0/90] weave. T  400  ^/MTT""  ro CL C/5 W CU  co  A4T2 —  A4T3  f  ^ —  i  0.5  C  A4T1  _i  i  1  1.5 Strain (%)  Figure 5.10 Measured stress vs strain curves of A4 tensile specimens. 88  2.5  Figure 5.12 Plots of failure stress and strain of A 4 tensile specimens, derived using the damaged moduli. The most likely combination of effective load-bearing plies is indicated for each specimen.  89  Figure 5.13 Plots of failure stress and strain of B2 tensile specimens, derived using the damaged moduli. The most likely combination of effective load-bearing plies is indicated for each specimen.  Figure 5.14 Preliminary strain softening curve of systems A and B (shown by the solid lines), based on the damaged moduli of specimens A 4 and B2. The arrows outline the possible range of the unloading portion of the curve.  90  Chapter Six Comparison of the Experimental Results with a Preliminary FEM Analysis  6.1 Introduction The experimental results are compared with an F E M analysis o f the O C T specimen.  The  experimental load vs C M O D displacement o f specimen A 4 is compared to that predicted by an F E M analysis by Engels (1996).  In addition, the experimentally determined crack growth in  front o f the notch tip for specimen A 3 is compared to that predicted by a strain softening material model.  6.2 Comparison of the Experimental and FEM Results The experimental results presented in the previous chapters have been used by Engels (1996) to investigate whether a strain softening material response can predict the damage progression observed in the O C T specimen. Based on the experimental work, an F E M analysis o f the O C T specimen was performed by Engels (1996). He used the A B A Q U S ™ / S t a n d a r d Code, in which he modeled a strain softening material response using an anisotropic piece-wise linear elastoplastic material model. Engels calibrated the strain softening curves for O C T specimens A 3 and A 4 , using the experimental load vs C M O D displacement and load vs clip gauge displacement curves presented in Chapter 3. He assumed a linear post-peak unload i n the strain softening curves, as shown in Figures 6.1 and 6.2.  91  The F E M results showed that of the three different material responses considered in the study, a strain softening response was necessary to model the gradual progression o f damage observed in the O C T specimens. He compared the load vs C M O D displacement behaviour o f specimen A 4 predicted by a plasticity based strain softening response,  an elastic-instantaneous  failure  response, and an elastic-perfectly plastic response. These curves are reproduced in Figure 6.1, as well as the experimental results for the specimen.  The elastic-instantaneous failure response  resulted in severe mesh distortions at the notch tip, raising doubts as to the validity o f the solution. The elastic-perfectly plastic material response did not capture the load drops that occur once failure initiates. However, the strain softening material model predicts drops in load similar to the experimental results.  During the largest experimentally measured load drop (between  points A and B in Figure 6.1), which corresponded to roughly 15 m m o f instantaneous crack growth, the F E M model did not converge to a solution. This numerical instability is analogous to the unstable crack growth observed experimentally. A difference exists between the plasticity based strain softening model used by Engels and a C D M based strain softening model, such as the M L T model (Matzenmiller et al., 1991).  The  F E M strain softening curve used by Engels implies that during unloading the modulus o f increasingly damaged material in the process zone does not change from the modulus.  undamaged  In the M L T model, however, the modulus o f material unloading in the post-peak  section o f the curve decreases. The M L T model corresponds more closely to the tensile test results o f Chapter 5, in which the modulus o f the material i n the process zone decreased with increasing proximity to the notch tip. (i.e. increasing damage) Despite this difference, the strain softening material model used by Engels provides a reasonable description of the damage growth across the specimen width. The crack length at different loads  92  throughout the test was estimated by Engels by plotting the plastic strain i n the elements. Figure 6.2 shows the predicted and experimental load vs clip gauge displacement o f specimen A 3 . A predicted plastic strain greater than 3.15% translates experimentally into the presence o f damage (i.e. the crack). The F E M results predicted that no crack growth occured prior to point A ' in Figure 6.2. This was followed by 12.5 m m o f crack growth just prior to the largest load drop at point B ' . A total o f 30 m m o f crack growth had occured just after the largest load drop, roughly at point C .  This agrees well with the experimental results, which indicated no crack growth  prior to point A , 10 m m o f crack growth at point B and 25 m m o f crack growth (with a process zone 7 m m long) at point C .  93  FEM strain softening curve: 390 —  A  /  "co  \\  / /  \ 4  s (%)  18000 F E M elastic - perfectly plastic 16000 14000 12000 F E M strain softening 10000 T3  ro o  '•A experimental  8000 \  F E M elastic instantaneous failure  6000 4000 2000  'B  0 0  0.5  1  1.5  2  2.5  3.5  C M O D D i s p l a c e m e n t (mm)  Figure 6.1 Load vs CMOD displacement curve for OCT specimen A4 predicted by Engels (1996) using several different F E M constitutive model responses. These curves can be compared to the experimental load vs CMOD displacement curve. The optimized strain softening curve is included in the figure. The F E M results are reproduced from Engels (1996).  94  7000  6000+  5000+  4000+ T3  §  FEM strain softening experimental  3000+  200OH 10004  0.2  0.4  0.6  0.8  1  1.2  1.4  Clip Gauge Displacement (mm)  Figure 6.2 Load vs clip gauge displacement of OCT specimen A3, predicted by a F E M strain softening analysis and the experimental results. Points A' to C and A to C are used to compare the predicted and experimentally estimated crack lengths at the given load, respectively. The optimized strain softening material response is included in the figure. The F E M results are reproduced from Engels (1996).  95  Chapter Seven Conclusions and Further Work  7.1 Introduction Conclusions are drawn from the results presented in Chapters One to Six. Further work is suggested.  7.2 Conclusions The following conclusions can be drawn from the results o f the previous chapters: 1. A specimen and test methodology have successfully been developed which can be used to study notched composite laminate behaviour.  The specimen is an overheight compact  tension ( O C T ) specimen which has the following advantages: •  it exhibits stable damage growth, allowing a post-test investigation o f the damage evolution.  Information can be gathered concerning how the damage develops both  spatially and temporally. • it provides several different types o f results with which to calibrate the strain softening curve o f a given material system. • it does not require a large amount o f material.  2. A comprehensive picture o f the damage evolution in the O C T specimen has been described in two material systems.  A good understanding o f the crack length at increasing loads  96  throughout the test has been given, as well as a picture o f the sequence "of damage evolution in the process zone. 3. The material in the process zone softens. The damage differs from that developed in a dogbone style tensile specimen, in that: • it has a gradual decrease in load-bearing ability.  • the failure strain o f the damaged material can exceed the fibre failure strain by as much as two times. • the dominant sequence o f damage growth consists o f progressive failure o f the 0° plies.  4. A strain softening material response i n an F E M analysis can be used to model failure o f the O C T specimen. Preliminary results indicate that a strain softening curve, calibrated from the experimental load vs displacement results, captures the progressive growth o f damage across the specimen width.  7.3 Further Work The experimental results indicate that despite substantial damage formed in the process zone of the O C T specimen, the damaged material is still able to carry a significant amount o f load. With increasing amounts o f damage, this material has a progressive decrease in load-bearing ability. Physically, therefore, the concept o f a strain softening curve is sound. A clearer understanding o f the predictive capabilities and fundamental validity o f the strain softening curve must now be developed.  97  A useful feature o f the O C T specimen is that it provides detailed information with which to calibrate the strain softening curve o f a given material system.  For example, after assuming a  shape for the curve, the curve can then be calibrated using the far-field load and C M O D displacement o f the specimen. The influence o f modifications to the shape, such as altering the slope o f the tip and tail region o f the curve, can then be examined by comparing the predicted damage growth to that indicated by the line analysis. Once the strain softening curve is found which best predicts failure in the O C T specimen, the curve can then be used to model failure in an F E M analysis o f a large aircraft structure. Detailed knowledge o f the damage growth from sectioning results provide physical evidence with which to make the F E M strain softening analysis physically meaningful.  For example,  using the experimental results presented in this thesis, the following future work is suggested: 1.  A n investigation should be performed to see how a different element size alters the optimized strain softening curve o f an O C T specimen. The appropriate element size is a function o f the damage created in the process zone.  For example, the minimum element size required to  capture the effects o f strain softening may be a function o f the steady-state process zone dimensions. 2. The numerical strain softening curve o f system B should be determined and compared to system A . Different shapes o f the curve should be examined to compare the predicted and experimental surface displacements and damage growth.  Differences in the curves for the  two systems may then be related to the physical understanding o f the differences in the damage pattern.  For example, the stair-case like crack profile and greater steady-state  damage height may translate into a greater ability to redistribute load during failure in system B . This increased load-redistribution would be reflected in the post-peak shape o f the curve.  98  Following this, other tests should be performed to address the useful range o f application o f the strain softening curve. For example, different O C T coupon sizes could be tested to examine the expected capabilities o f the strain softening curve to predict the fracture strength o f small and large coupons and structures. A s well, the usefulness o f the strain softening curve to other types of loading should be examined.  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Composite Materials, v o l . 8, 1974, pp. 253-265.  102  Appendix 1 Additional Surface Line Analyses  The figures in Appendix 1 show additional surface line measurements o f all analysed photos taken during the O C T test o f specimen A 3 and specimens B l and B 2 .  103  Table A l . l Table of the position in front of the notch tip at which scribe line #4 has zero displacement at a given load, for system A, specimen A3. The values refer to Figure A1.2. line #4, specimen A3 Position in Front Photo # of Notch Tip (mm) 9  0  10 11  0 0 1  12  4  13 14 15  10 25  16 18  25 25 30  19 20  23 30 30  21 22  104  Table A1.2 Table of the position in front of the notch tip at which the scribe line has zero displacement at a given load, for system B, specimen Bl. The values refer to Figures A1.4 and A1.5. line #1, specimen Bl Photo # Position in Front of Notch Tip (mm)  line #3, specimen Bl Position in Front Photo # of Notch Tip (mm)  2a 4a  0 0  2a 4a  N/A N/A  6a  2  6a  2  8a 10a  2 2  8a 10a  2 2  12a 14a 16a  5 5 5 10 10  12a  5  14a 16a  5 5  18a 3b 4b  10 10 12 12  18a 3b 4b  5b 6b 7b 8b 9b  10 10 12 12  5b 6b 7b 8b 9b  38 38  105  20 20 37 37  Table A1.3 Table of the position in front of the notch tip at which the scribe line has zero displacement at a given load, for system B, specimen B2. The values refer to Figures A17 and A1.8. line #1, specimen B2 Position in Front Photo # of Notch Tip (mm)  line #2, specimen B2 Photo # Position in Front of Notch Tip (mm)  9  1  9  0 3 4  11 12  6  11  8  10  12  8  15 15 33  15  20  16 17 18  20 35 35 35 40 40  5 8  15 16 17 18 19 20 21  0 1  5 8  33 33  19 20 21  40 40  106  Clip Gauge  Cross Head  Displacement (mm)  Figure A l . l Load vs cross head and clip gauge displacement of specimen A3, showing all the analysed photos of the OCT test.  -®— p h o t o 9 - a - p h o t o 10 p h o t o 11 - * - p h o t o 12 - • - p h o t o 13 - • - p h o t o 14 — • — p h o t o 15 - • - p h o t o 16 p h o t o 18 - * - p h o t o 19 photo 2 0 photo 21 photo 22  notch  clip gauge  Position in Front o f N o t c h T i p ( m m ) Photo numbers refer to Figure A l . l . Displacement is measured relative to photo 5. Image resolution is .045 mm/pixel. Line #4 is 20 mm above and 20 mm below the notch mid-plane.  Figure A.2 All displacements of line #4 as a function of position in front of notch tip analysed for specimen A3.  107  clip gauge 12000  a20  CMOD gauge —  a  1  5  a20  b 3  10000 8000 XJ 03.  _l  6000 4000 2000 Numbers refer to photo #  0.5  1  1.5  2  2.5  Displacement (mm)  Figure A1.3 Load vs CMOD and clip gauge displacement of specimen BI, showing all the valid photos taken during the OCT test.  E  E cu  c c  CD  E  CD O  ro CL  40 notch tidf  T* clip gauge Position in Front of Notch Tip (mm)  - • — photo photo - * - photo - * - photo -°—photo photo - * - photo - • - photo — ^ photo -o-photo photo photo - B - photo £0 -«—photo photo ^f—photo  a2 a4 a6 a8 a10 a12 a14 a16 a18 b3 b4 b5 b6 b7 b8 b9  Photo numbers refer to Figure A 1 . 3 . Displacement is measured relative to photo al. Image resolution is .048 mm/pixel. Line # 1 is 2.5 mm above and 2.5 mm below the notch mid-plane.  Figure A1.4 AH displacements of line #1 as a function of position in front of notch tip analysed for specimen BI.  108  -•-photo a2 - * - photo a4 - * - photo a6 -•-photo a8 photo a10 photo a12 - * - photo a14 - ° - photo a16 —•—photo a18 - ® - photo b3 - a - photo b4 photo b5  E  E co c c 0  E 0 o  m a. <n  b  -B-photo b6  notch  Position in Front of Notch Tip (mm)  photo b7 photo b8 photo b9  Photo numbers refer to Figure A 1.3. Displacement is measured relative to photo a l . Image resolution is .048 mm/pixel. Line #3 is 7.5 mm above and 7.5 mm below the notch mid-plane.  Figure A1.5 A l l displacements of line #3 as a function of position in front of notch tip analysed for specimen B l .  109  12000 g11 1 2 ^ i j j 6  10000  V^O fl  8000 + T3 CO O  /  6000  /  4000  /  2000 0  ^5  15  \  5  19  5  4  22 20  1  1  0.5  1  2 1  Numbers refer to photo # r —  1.5  1  1  2  2.5  1  C M O D Displacement (mm)  Figure A1.6 Load vs CMOD displacement of specimen B2, showing all the valid photos taken during the OCT test, (the clip gauge results are invalid as the gauge popped out during loading) 1.8•photo 5 •photo 8 -photo 9 •photo 1 1 -photo 1 2 -photo 1 5 -photo 1 6 -photo 1 7 -photo 1 8 -photo 1 9 -photo 2 0 -photo 2 1  E  CD  c  c cu E 0 o  m a.  w Q  ip gauge Position in Front of Notch Tip (mm) Photo numbers refer to Figure A 1.6. Displacement is measured relative to photo 1. Image resolution is .042 mm/pixel. Line #1 is 2.5 mm above and 2.5 mm below the notch mid-plane.  Figure A1.7 All displacements of line #1 as a function of position in front of notch tip analysed for specimen B2.  110  -•-photo 5 - o - photo 8 - * - photo 9 - * - p h o t o 11 - * - p h o t o 12 p h o t o 15 - • - p h o t o 16 - ^ - p h o t o 17 - e - p h o t o 18 - * - p h o t o 19 -*  photo 20  - ° - p h o t o 21  notch tipT  clip gauge Position in Front o f N o t c h T i p ( m m )  Photo numbers refer to Figure A 1 . 6 . Displacement is measured relative to photo 1 . Image resolution is . 0 4 2 mm/pixel. Line # 2 is 5 mm above and 5 mm below the notch mid-plane.  Figure A1.8 All displacements of line #2 as a function of position in front of notch tip analysed for specimen B2.  Ill  Appendix 2  Additional Micrographs  These figures show all the micrographs taken o f O C T specimen A 3 and O C T specimen B 1 .  112  A2.1 Micrographs of Specimen A3  Figure A2.1 Reconstructed profile of the damage in specimen A3, with the load vs cross head displacement curve from the OCT test presented in Chapter 3. A2.11 Damage Grown Prior to Load C  x = 1.  CH. = units: r  3.35 Figure A2.2 Cross-section at 1.85 mm in front of the notch tip.  113  Figure A2.3 Cross-section at 4.45 mm in front of the notch tip. A2.12 Damage Grown Between Loads C-D  Figure A2.4 Cross-section at 11.45 mm in front of the notch tip.  114  x = 12.10 mm  C H . = 5 . 5 9 mm units: mm  3.35  Figure A2.5 Cross-section at 12.10 mm in front of the notch tip.  x = 18.00 n  C H . = 4.20 units: mm  Figure A2.6 Cross-section at 18.00 mm in front of the notch tip.  115  Figure A2.7 Cross-section at 20.25 mm in front of the notch tip.  116  A2.13 Damage Grown Between Loads D-E  Figure A2.10 Cross-section at 25.37 mm in front of the notch tip.  117  118  B  x = 32.00 m m P.Z.H. = 1.11 units: mm  B  Top  -10 " 9 - 8  mm  - 7 -  6  - 5  -4 - 3 - 2 - 1 - 0 - -1  N.M-P —  - -2 - -3  - -4 - -5 - -6  - -7  - -8 - -9 --10  3.35  Figure A2.14 Cross-section at 32.00 mm in front of the notch tip.  119  A2.2 Micrographs of Specimen B1 - Front Side Layup: [F0/-45/90/45/0/45/90/-45/F0] , FO = [0/90] weave s  to scale:  0  _  35 m m — W  0  3.5 mm  = 0 22  0.5  1  1.5  2  2.5  C M O D D i s p l a c e m e n t (mm)  Figure A2.15 Reconstructed profile of the damage in specimen B l , with the load vs CMOD displacement curve from the OCT test presented in Chapter 3. A2.21  Damage Grown Prior to Load X  x = 1.00 mrr  Top 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 h-3 -4 -5 -6 -7 -8 -9 10 11 12 13 14  O C H . = 1 mm units: m m  N.M-P  —  H  O  Top  1.66  Figure A2.16 Cross-section at 1.00 mm in front of the notch tip.  120  Figure A2.17 Cross-section at 2.00 mm in front of the notch tip.  1.66  Figure A2.18 Cross-section at 5.65 mm in front of the notch tip.  121  A2.22 Damage Grown Between Loads X-Y  X =  10  CH. = units: r  Figure A2.19 Cross-section at 10.00 mm in front of the notch tip.  122  x = 11.00 mm  Top  0  14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14  C H . = 17.80 m m units: mm  N.M-P-  I  Top  O  »  f  1.66  Figure A2.20 Cross-section at 11.00 mm in front of the notch tip. x = 12.00 mm  O  Top r  C H . = 20.65 m m units: m m  s  N.M-P -  j  -  14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 Q  I  Top  O  - -o -- 1-9 0 -11 -12 -13 L-14  1.66  Figure A2.21  Cross-section at 12.00 mm in front of the notch tip.  123  Figure A2.22 Cross-section at 19.50 mm in front of the notch tip.  Figure A2.23 Cross-section at 20.89 mm in front of the notch tip.  124  Figure A2.24 Cross-section at 34.62 mm in front of the notch tip.  125  A2.23 Damage Grown Between Loads Y-Z  126  A2.3 Micrographs of Specimen B1 - Back Side A2.31 Damage Grown Prior to Load X  127  x = 2.00 CH.  mm  Top  0  = 3 mm  units: mm  N.M-P  U  —  1.66 Figure A2.27 Cross-section at 2.00 mm in front of the notch tip.  x = 5.65 m m T.C.H. = 8 mm  Top  I r  O  units: m m  -  13 12 11 10  -  9 8 o 7 6 5 4 3 2 1 0 -1 -2  -  N.M-P —  Top  O  1 4  -o - -4 - -5 - -6 - -7 - -8 - -9 -10 -11 -12 -13 -14  1.66 Figure A2.28 Cross-section at 5.65 mm in front of the notch tip.  128  A2.32 Damage Grown Between Loads X-Y  129  x = 11.00  mm  C H . = 11.62 units: m m  Top  0  Top  I  V- 14  O mm  f- 13 12 11  h  h  10  -  9 8 7 6 5 4 3 2 1  N.M-P.H  - 0  :i -3 -4 -5 -6 -7 -8  r  9  1—10 |~11  1-12 13 14  1.66  Figure A2.30 Cross-section at 11.00 mm in front of the notch tip. x = 12.00  mm|  Top 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8  O C H . = 3.92 units: m m  mm  N.M-P —  O  Top  I  r H O I—11 9  H 2  -13 -14  1.66  Figure A2.31 Cross-section at 12.00 mm in front of the notch tip.  130  Figure A2.33 Cross-section at 20.89 mm in front of the notch tip.  131  Figure A2.35 Cross-section at 35.50 mm in front of the notch tip.  132  133  A2.33 Damage Grown Between Loads Y-Z  x = 38.22 m m  0  Top  Tip  |  10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9  O P.Z.H. = 11.19 m m units: m m  N.M-P.H  12 13 14 15 16  1.66  Figure A2.37 Cross-section at 38.22 mm in front of the notch tip. x = 39.06 m m  Top  O P.Z.H. = 12.30 m m units: m m  O 10 9 8 7 6  Tip  |  I  n 2  N.M-P  —  li -5 -6 -7 -10 -11 -12 -13 -14 -15 16  1.66  Figure A2.38 Cross-section at 39.06 mm in front of the notch tip.  134  

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