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In-situ measurements of delamination crack tip behaviour in composite laminates inside a scanning electron… Paris, Isabelle 1998

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IN-SITU MEASUREMENTS OF DELAMFNATION CRACK TIP BEHAVIOUR IN COMPOSITE LAMINATES INSIDE A SCANNING ELECTRON MICROSCOPE by ISABELLE PARIS B. Ing., Ecole Poly technique de Montreal, 1992 A THESIS SUBMITTED EST PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Metals and Materials Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1998 ©Isabelle Paris, 1998 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 / f e f e / s And Material* ^ 3 i n e e r i ^ The University of British Columbia Vancouver, Canada Date 4prll 2o /33S DE-6 (2/88) Abstract Delamination is an important failure mode for composite laminates. As it affects the mechanical response of the structure and is difficult to detect from the surface, this type of damage is of great concern, particularly in the aerospace industry. The topic of delamination growth has received much attention, with Linear Elastic Fracture Mechanics (LEFM) being the most common approach to predict the behaviour of a crack from the global applied conditions. However, local perturbations such as resin rich regions, fibre bridging and friction have been noticed by many investigators. Thus global applied loads are often not transposed directly into equivalent local crack tip conditions. Moreover, there is currently considerable controversy about the exact nature of mixed-mode fracture behaviour. Therefore, the objective of this thesis is to measure the load and displacement applied to a specimen and, at the same time, the crack tip behaviour, in order to establish a quantitative relation between them. An experimental loading jig designed to fit inside a scanning electron microscope (SEM) has been developed. Mode I, mode TJ and mixed-mode loadings can be applied. The applied loads and displacements are measured and the images obtained from the SEM are stored. After the test, the crack opening and shear displacements are calculated from the applied loads and displacements using LEFM, and are compared with those measured from the images. Mode I and mode II tests have been conducted that show good agreement between LEFM predictions and measurements. For a brittle material, the behaviour remains linear elastic up to failure. The comparison of the crack faces displacements with the ones obtained from a finite element analysis are also excellent. The effect of the increase in fracture toughness with mode I crack growth on the local crack tip behaviour has been studied. As the crack grows, the magnitude of the measured crack opening displacement profiles is reduced. The assumption that fibre bridging keeps the crack closed is thus confirmed experimentally and quantitatively. As reported by other investigators, 45° microcracks are created ahead of the crack tip under mode II loading. When the load is increased, the ligaments created by the microcracks bend and finally the microcracks coalesce, while more microcracks are created ahead. The growth of this damage zone has been measured and modeled using an analogy with the plastic zone in metals. The stress-displacement curve of the damaged material has also been deduced from the experimental results using a Dugdale approach. One of the most interesting findings of the mode TJ tests is the presence of significant crack opening displacements even though the loading is supposed to induce pure shear. The amount of opening varies with the surface roughness of the crack. This can explain the large scatter observed by many investigators in G//c data, as the tests are not really pure mode U tests, but in fact mixed-mode tests with various proportions of mode I. The determination of the widely used mode II material toughness is therefore questioned. -ii i-Sommaire Le delaminage est un des principaux modes de rupture des lamines de composite. Etant donne qu'il affecte le comportement mecanique de la structure et qu'il est difficile a detecter en surface, ce type d'endommagement est preoccupant, particulierement pour l'industrie aerospatiale. La propagation du delaminage est le sujet de nombreuses etudes et la mecanique de la rupture lineaire elastique (MRLE) est la theorie la plus couramment utilisee pour predire le comportement d'une fissure a partir des charges globales appliquees. Cependant, de nombreux chercheurs ont observe des perturbations locales telles que des zones riches en resine, du pontage de fibres et de la friction. En consequence, les charges globales appliquees ne se transmettent pas directement en charges locales equivalentes en bout de fissure. De plus, la nature du comportement a la rupture en mode mixte est une source de controverse. Ainsi, l'objectif de ce travail consiste a mesurer les charges et les deplacements appliques a un echantillon et, simultanement, le comportement en bout de fissure afin d'etablir une relation quantitative entre les deux. Un appareil de chargement a ete concu pour etre installe a l'interieur d'un microscope electronique a balayage (MEB). Des charges en mode I, mode II et mode mixte peuvent etre appliquees. Les charges et les deplacements appliques sont mesures et les images obtenues du MEB sont enregistrees. Apres le test, les deplacements d'ouverture et de cisaillement de la fissure sont calcules d'apres les charges et les deplacements appliques en utilisant la MRLE et sont compares avec ceux mesures sur les images. Des essais en mode I et mode II ont ete effectues et correspondent aux predictions de la MRLE. Pour un materiau fragile, le comportement demeure lineaire et elastique jusqu'a la rupture. Les -iv-displacements des faces de la fissure sont similaires a ceux obtenus d'apres une analyse par elements finis. L'augmentation de la tenacite lors de la propagation en mode I a ete reliee au comportement local en bout de fissure. L'amplitude des deplacements d'ouverture de la fissure mesures diminue lorsque la fissure se propage. Ceci confirme experimentalement et quantitativement l'hypothese que le pontage de fibres maintient la fissure fermee. Comme souligne par d'autres chercheurs, des microfissures a 4 5 ° sont creees en bout de fissure sous un chargement en mode n. Lorsque la charge augmente, les ligaments crees par les microfissures plient et les microfissures se rejoignent alors que d'autres microfissures se forment a l'avant. La propagation de cette zone d'endommagement a ete mesuree et modelisee en utilisant une analogie avec la zone plastique dans les metaux. L'approche de Dugdale a ete utilisee pour deduire la courbe contrainte-deformation du materiau endommage a partir des resultats experimentaux. Un des points les plus interessants des tests en mode II est la presence d'importants deplacements d'ouverture de la fissure alors que ce mode de chargement devrait induire du cisaillement pur. La quantite d'ouverture varie selon la rugosite de la fissure. Ceci peut expliquer la grande variation de G//c rapportee par de nombreux chercheurs puisque les tests ne sont pas reellement du mode II pur, mais un mode mixte avec diverses proportions de mode I. La facon de determiner la tenacite en mode II des materiaux, une propriete largement utilisee, est done remise en question. Table of Contents Abstract ii Sommaire iv Table of Contents vi List of Tables x List of Figures xi Nomenclature xx Acknowledgments xxiii Dedication xxiv Chapter 1 Introduction 1 1.1 Delaminations in composite laminates 2 1.2 Global approach 4 1.3 Local approach 7 1.4 Summary 9 1.5 Figures 11 Chapter 2 Literature Review 14 2.1 Delamination fracture toughness 14 2.1.1 Effects of resin 15 2.1.1.1 Micromechanisms of mode I delamination 15 2.1.1.2 Micromechanisms of mode II delamination 17 2.1.2 Effect of starter film and precrack 18 2.1.3 Effect of fibre bridging 19 2.1.4 Effect of friction 23 2.1.5 Mixed-mode failure criterion 23 2.2 Direct observation of crack tip behaviour 25 2.2.1 In-situ crack growth observation 25 2.2.2 Measurements in the crack tip area 26 2.3 Literature review summary 28 2.4 Tables 30 2.5 Figures 31 -vi-Chapter 3 Experimental Method 39 3.1 Specimen preparation 39 3.2 Mechanical testing 41 3.2.1 Superposition principle 41 3.2.2 Calculation of the strain energy release rate 42 3.3 Crack tip faces displacements 45 3.4 Data acquisition and test control 46 3.5 Image acquisition 47 3.6 Image analysis 48 3.7 Summary : 50 3.8 Figures 52 Chapter 4 Mode I Results 65 4.1 Verification of global/local agreement in a brittle material 65 4.1.1 Test description 65 4.1.2 Results 66 4.1.2.1 Square root profile: shape and magnitude 67 4.1.2.2 Effect of insert 67 4.1.2.3 Effect of decreasing and increasing loads 68 4.1.2.4 Behaviour at failure 69 4.1.3 Comparison between global and local behaviour 69 4.1.4 Comparison with FEM model 70 4.2 Behaviour of a tougher material 71 4.2.1 Test description 72 4.2.2 Results 72 4.3 Mode I resistance curve 73 4.3.1 Test description 75 4.3.2 Results 76 4.3.3 Behaviour close to failure 77 4.3.4 Specimens with smaller increase in toughness with crack growth 78 4.4 Summary 78 4.5 Tables 80 -vii-4.6 Figures 81 Chapter 5 Mode II Results 103 5.1 Tests description 103 5.1.1 Test from the insert and short crack growth 103 5.1.2 Test from the insert '. 104 5.1.3 Long precrack test 104 5.2 Crack tip behaviour 104 5.2.1 CSD profiles 106 5.2.2 CSD at failure 107 5.2.3 COD profiles 108 5.2.4 Relation between mode I and mode II 108 5.3 Crack advance 111 5.3.1 Microcrack behaviour 111 5.3.2 Coalescence and damage zone measurements 111 5.3.3 Damage zone size modelling 113 5.4 Delamination resistance curves 116 5.5 Summary 120 5.6 Tables 723 5.7 Figures 124 Chapter 6. Conclusions and Further Work 145 6.1 Conclusions 145 6.2 Further work 7 4 7 References 150 Appendix A. Specimen Preparation 154 A. 1 Bonding of the loading and clamping tabs 7 5 4 A.2 Polishing 7 5 4 A.3 Gold grid deposition 7 5 5 A.4 Figures 7 5 7 Appendix B. Derivation of COD and CSD Orthotropic Equations 159 Appendix C. Load Cells and Displacement Sensors Calibrations 162 C.1 Load cells 7 6 2 -viii-C.2 Displacement sensors 162 C. 3 Figures 163 Appendix D. Material Properties 165 D. 1 Determination of the elastic properties 165 D.2 Determination of shear strength 166 D.3 Determination of fibre volume fraction 167 DA Tables 168 D. 5 Figures 170 E. Additional Results 171 E. 1 Additional mode I results 171 E . l . l Load-displacement curves 171 E.1.2 Singularity zone size in the brittle mode I test 171 E.1.3 Results of preliminary mode I resistance curve tests 172 E. 1.3.1 Tests description 172 E. 1.3.2 Results ...172 E.1.3.3 Summary 174 E.2 Additional mode II results 174 E.2.1 Load-displacement curves 174 E.3 Tables 176 E. 4 Figures 178 F. Montages of Crack Tip Images 196 -ix-List of Tables Table 2.1 Literature review summary 30 Table 4.1 Material properties of AS4/3501-6 and IM7/8551-7 unidirectional laminate 80 Table 4.2 Characteristics of specimens B1, T4 and R l 80 Table 4.3 G,L (J/m2) for the five crack lengths and the three levels of G / G (J/m2) 80 Table 5.1 Characteristics of specimens B8, B l 1 and B13 : 123 Table D.l Flexural and shear modulus obtained experimentally for AS4/3501 and IM7/8551 168 Table D.2 Elastic properties for AS4/3501 -6 and IM7/8551 -7 provided by the manufacturer (Hercules) 168 Table D.3 Apparent Interlaminar Damage and Shear Strength for AS4/3501-6 169 Table D.4 Fibre volume fractions measured by matrix digestion and image analysis 169 Table E. 1 Characteristics of specimens B3 and B5 176 Table E.2 G,L (J/m2) for the three crack lengths of B3 176 Table E.3 GIL (J/m2) for the five crack lengths of B5 177 -x-List of Figures Figure 1.1 Damage types in composite laminates 11 Figure 1.2 Range of scales of interest in the study of composite structural failure 11 Figure 1.3 The three modes of loading 12 Figure 1.4 (a) Double cantilever beam (DCB) and (b) end-notched cantilever beam (ENCB) specimens 12 Figure 1.5 Illustration of the equivalence between the bridge crack and the superposition of an unbridged crack and a crack loaded by pressure at the crack tip faces 13 Figure 2.1 Variation of Mode I and Mode II delamination fracture toughness with the neat resin toughness, for a variety of composites, from (Bradley, 1989) 31 Figure 2.2 Damage zone size difference in a brittle and ductile resin composite (Bradley and Cohen, 1985) 31 Figure 2.3 Mode II in-situ delamination of AS4/3502; Formation (a and b) and coalescence (c and d) of microcracks (Corleto et al., 1987) 32 Figure 2.4 Principal normal stresses ahead of a crack tip in the resin-rich region between plies created by the mode II loading (a), coalescence of microcracks and rotation of hackles due to shear loading (b) (Ffibbs and Bradley, 1987) 32 Figure 2.5 Finite element stress contour plots at the crack tip in an orthotropic, elastic split laminate (Corleto et al., 1987) 33 Figure 2.6 Fibre bridging 33 Figure 2.7 Intermingling of plies during cure in a unidirectional composite (Johnson and Mangalgiri, 1987) 34 Figure 2.8 Formation of fibre bridging by initiation of a defect in the plastic zone in the ply above the original delamination (Johnson and Mangalgiri, 1987) 34 Figure 2.9 Example of a R-curve for a AS4/3501 specimen (Ferguson, 1992) 35 Figure 2.10 Delaminated specimen with damage zone, stress-displacement damage response and delamination R-curve (Suo et al., 1992) 35 Figure 2.11 Mixed-mode test configurations (Crews and Reeder, 1988) 36 Figure 2.12 Mixed mode delamination criterion for AS4/3501-6 (O'Brien, 1997), from (Reeder, 1994) 36 Figure 2.13 Plot of COD Vs r for an applied G, of 34.9 J/m2 (Ferguson, 1992) 37 Figure 2.14 Crack opening displacement measured in fully bridged glass-lead composite. The solid line shows displacement calculated using the measured applied stress intensity factors at initiation (.£=0.4) and propagation (A=0.9) (Bannister et al., 1992) 37 -xi-Figure 2.15 Crack opening displacements as a function of the distance from the crack tip. The solid line shows the square root dependence (Davidson, 1993) 38 Figure 2.16 Crack opening displacements in zinc sulfide containing 10% and 20% of diamond particles (Farquhar, 1994). The applied K is not known 38 Figure 3.1 Photograph of the complete experimental system 52 Figure 3.2 Schematic of the experimental system 52 Figure 3.3 Configuration of the specimens used for (a) mode I and (b) mode II and mixed mode 53 Figure 3.4 Photograph of the loading jig 53 Figure 3.5 Superposition of mode I and mode II on a DCB specimen 54 Figure 3.6 Results from a strain gauged specimen loaded under mode n. The lines show the compressive and tensile bending strains while the markers show the axial strains.. 54 Figure 3.7 Relationship between specimen compliance and crack length for determination of machine compliance Co 55 Figure 3.8 Photograph of the load cells and displacement sensors 55 Figure 3.9 Schematic of the loading arms maximum displacements 56 Figure 3.10 Algorithm for the Labview control and data acquisition program 57 Figure 3.11 Example of a video image overlaid with data 58 Figure 3.12 Algorithm showing the usual sequence of processing and analysis steps in the Labview image analysis program 59 Figure 3.13 Example of a montage of slow scan images 60 Figure 3.14 Measurement of the COD and CSD by the difference in distance between the centroid co-ordinates from the loaded to unloaded image 61 Figure 3.15 Image analysis technique: (a) original image, (b) tresholded image, (c) processed image, (d) image with centroids 62 Figure 3.16 Printout of the screen showing the image analysis software during the thresholding of the image 63 Figure 3.17 Printout of the screen showing the image analysis software during the calibration of the image 63 Figure 3.18 Printout of the screen showing the image analysis software during the measurements of the COD 64 Figure 4.1 Description of specimen B l loading path for the tests presented in Figure 4.3 to Figure 4.20. The horizontal steps show where the loading was held constant to perform slow.scans in the SEM 81 Figure 4.2 Montage of the SEM crack tip images for specimen B l (crack a2), for GIG = 72 J/m2 81 -xii-Figure 4.3 Plot of COD vs. r (distance from the crack tip) for GIG = 30 J/m2 on specimen B l (ai). Solid line shows COD profile calculated from G/L = GIG- Dashed line shows COD profile calculated from Gu that gives the best fit 82 Figure 4.4 Plot of COD vs. r (distance from the crack tip) for GIG = 72 J/m2 on specimen B l (ai). Solid line shows COD profile calculated from G/L = GIG 82 Figure 4.5 Plot of COD vs. r (distance from the crack tip) for G / G = 69 J/m2 on specimen B l (ai). Solid line shows COD profile calculated from G/L = GIG 83 Figure 4.6 Plot of COD vs. r (distance from the crack tip) for GIG = 92 J/m2 on specimen B l (a2). Solid line shows COD profile calculated from G/L = GIG 83 Figure 4.7 Plot of COD vs. r (distance from the crack tip) for GIG = 41 J/m2 on specimen B l (a2). Solid line shows COD profile calculated from G/L = GIG 84 Figure 4.8 Plot of COD vs. r (distance from the crack tip) for GIG = 35 J/m2 on specimen B l (a2). Solid line shows COD profile calculated from G/L = GIG 84 Figure 4.9 Plot of COD vs. r (distance from the crack tip) for GIG = 74 J/m2 on specimen B l (a2). Solid line shows COD profile calculated from G/L = GIG 85 Figure 4.10 Plot of COD vs. r (distance from the crack tip) for GIG = 38 J/m2 on specimen B l (a3). Solid line shows COD profile calculated from G/L = GIG 85 Figure 4.11 Plot of COD vs. r (distance from the crack tip) for GIG = 81 J/m2 on specimen B l (a3). Solid line shows COD profile calculated from Gu - GIG 86 Figure 4.12 Plot of COD vs. r (distance from the crack tip) for G / G = 41 J/m2 on specimen B l (a3). Solid line shows COD profile calculated from G/L = GIG 86 Figure 4.13 Plot of COD1 vs. r for GIG = 69 J/m2 on specimen B l (ai) showing the square root dependence over the first 500 microns 87 Figure 4.14 Pictures showing the interlocking of the Teflon insert fibre bundle and the composite matrix, for the 2 insert fibre bundles closest to the crack tip 88 Figure 4.15 Plot of COD vs. r (distance from the crack tip) for GIG values of 74, 109 and 126 J/m2 on specimen B l (a2). Solid lines show COD profile calculated from GIL = GIG 89 Figure 4.16 Plot of COD versus applied 8/ at r = 430 pm for specimen B1 (a2) 89 Figure 4.17 Plot of G/L vs. GIG for specimen B l , showing that G / L = G / G for all cases but one. The exception occurs for the first loading from the insert and might be explained by the insert sticking effect 90 Figure 4.18 Finite element mesh of the mode I DCB specimen, showing the upper half of the specimen, which is symmetric, and 2 successive enlargement of the crack tip area 91 Figure 4.19 Comparison between COD profile obtained experimentally on specimen B l (a3) and by finite element method, for applied load and applied displacement conditions... 92 - x i n -Figure 4.20 Comparison between COD profile obtained experimentally on specimen B1 (a3) and by finite element method, in the region close to the crack tip 92 Figure 4.21 Description of specimen T4 dimensions and loading path of tests presented in Figure 4.23 to Figure 4.27. The horizontal steps show where the loading was held constant to perform slow scans in the SEM 93 Figure 4.22 Montage of the SEM crack tip images for specimen T4, for GIG = 92 J/m 93 Figure 4.23 Plot of COD vs. r (distance from the crack tip) for GIG = 92 J/m2 on specimen T4. Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit 94 Figure 4.24 Plot of COD vs. r (distance from the crack tip) for GIG = 175 J/m2 on specimen T4. Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit 94 Figure 4.25 Plot of COD vs. r (distance from the crack tip) for GIG = 257 J/m2 on specimen T4. Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit 95 Figure 4.26 Plot of COD vs. r (distance from the crack tip) for G/c = 340 J/m2 on specimen T4. Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit 95 Figure 4.27 Plot of COD2 vs. r for G,G values of 92 and 340 J/m2 on specimen T4 showing the square root dependence over the first 500 microns 96 Figure 4.28 Plot of GIL V S . GIG for specimen T4 showing GIL<GIG in all cases 96 Figure 4.29 SEM images of specimen T4 showing the formation of microcracks in front of the Teflon crack tip 97 Figure 4.30 Comparison of GIL and GIG for elastic and dissipative behaviour 98 Figure 4.31 Montage of the SEM crack tip images for specimen RI (crack c5), for GIG = 277 J/m2 98 Figure 4.32 R-curve measured for high fibre volume specimen RI. It shows a clear increase of GicG as a function of crack growth 99 Figure 4.33 Plot of COD vs. r (distance from the crack tip) for G/c = 79 J/m2 on specimen RI (ci). Solid line shows COD profile calculated from GIL = GIG 99 Figure 4.34 Plot of COD vs. r (distance from the crack tip) for G/c values of 82 and 250 J/m2 on specimen RI (C2). Dashed line shows COD profile calculated from G/L that gives the best fit 100 Figure 4.35 Plot of COD vs. r (distance from the crack tip) for G/c values of 85, 252 and 380 J/m2 on specimen RI (C3). Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit 100 -xiv-Figure 4.36 Plot of COD vs. r (distance from the crack tip) for G/c values of 94, 263 and 400 J/m2 on specimen RI (c4). Dashed line shows COD profile calculated from GIL that gives the best fit 101 Figure 4.37 Plot of COD vs. r (distance from the crack tip) for G/c values of 99, 277 and 426 J/m2 on specimen RI (cs). Dashed line shows COD profile calculated from GIL that gives the best fit 101 Figure4.38 Plot of GIL V S . GIG for specimen RI. Dotted line represents a one-to-one correspondence. Dashed line represents Go. Clear marker are obtained from video images and standard deviation is shown as error bar 102 Figure 5.1 Description of specimen B8 loading path 124 Figure 5.2 Description of specimen B l l loading path -. 124 Figure 5.3 Description of specimen B13 loading path 125 Figure 5.4 SEM crack tip image (B8 a,) for Gu = 225 J/m2 125 Figure 5.5 SEM image showing microcracks: the damage and coalescence zones are delimited by a transition from displacement continuity across the crack plane to displacement discontinuity 125 Figure 5.6 Mechanisms of microcracks creation, rotation and coalescence (in agreement with Russell and Street, 1985; Hibbs and Bradley, 1987; O'Brien et al. 1989) 126 Figure 5.7 Definition of crack tip damage zone parameters 126 Figure 5.8 Plot of CSD vs. x (longitudinal position) for specimen B8 (ai and a2). Lines show CSD profiles based on GuL equal to GUG 127 Figure 5.9 Plot of CSD vs. x (longitudinal position) for specimen B8 a3. Lines show CSD profiles based on GUL equal to GUG 127 Figure 5.10 Plot of CSD vs. x (longitudinal position) for specimen B l l aj. Lines show CSD profiles based on GUL equal to GUG 128 Figure 5.11 Plot of CSD vs. x (longitudinal position) for specimen B13 ai. Lines show CSD profiles based on GUL equal to GUG 128 Figure 5.12 Plot of CSD vs. x (longitudinal position) for specimen B8 Unstable failure occurred at 880 J/m2. Lines show orthotropic LEFM prediction based on Gu values of 770 and 880 J/m2. The value rd+rc for 880 J/m2 has been estimated by linear extrapolation 129 Figure 5.13 Plot of COD vs. r (distance from the crack tip) for specimen B8 (ai and fy) loaded under pure mode JJ. Dashed lines show COD profiles for GIL that best fit the measurements 130 Figure 5.14 Plot of COD vs. r (distance from the crack tip) for specimen B8 a3 loaded under pure mode JJ. Dashed lines show COD profiles for GIL that best fit the measurements 130 -xv-Figure 5.15 Plot of COD vs. r (distance from the crack tip) for specimen B l 1 ai loaded under pure mode n. Dashed lines show COD profiles for Gu that best fit the measurements 131 Figure 5.16 Plot of COD vs. r (distance from the crack tip) for specimen B13 ai loaded under pure mode U. Dashed lines show COD profiles for G/L that best fit the measurements 131 Figure 5.17 Local opening displacement created under global shear loading 132 Figure 5.18 Plot of G/L vs. G//G global for specimen B8, B l l and B13. Hollow markers indicate test from insert. The x markers show values at failure (G/L c evaluated by linear extrapolation) 133 Figure 5.19 Effect of neglecting the mode I opening due to surface waviness on the mixed-mode failure envelope 133 Figure 5.20 Mixed mode failure criterion for AS4/3501 (O'Brien, 1997). The arrows show where the data points would move if some local mode I opening due to surface roughness is taken into account 134 Figure 5.21 Plot of GIL vs. GUG- Dashed lines represent the model 134 Figure 5.22 Surface waviness angles used in the model presented in Figure 5.21 135 Figure 5.23 Microcracks angle for increasing GUG (specimen B8 a3). The solid trendlines extremities correspond to the visible edges of the damage zone, while their inflection point is positioned at the origin of the CSD profile 136 Figure 5.24 Relationships between microcrack angle and crack faces displacements 136 Figure 5.25 Plot of the coalesced zone length rc, damage radius and zone length Lj vs. GUG for specimen B8 a3 137 Figure 5.26 Plot of the coalesced zone length rc and damage radius rd vs. Gu for specimen B l l ^ 137 Figure 5.27 Plot of the coalesced zone length rc and damage radius r^ vs. GUG for specimen B13ai 138 Figure 5.28 Plot of coalesced zone length rc vs. GUG obtained from the shifts in the measured COD profiles from specimens B8, B l l and B13. Hollow markers indicate tests from the insert 138 Figure 5.29 Plot of damage radius vs. G// obtained from the shifts in the measured COD and CSD profiles from specimens B8, B l l and B13. Hollow markers indicate tests from insert 139 Figure 5.30 Estimate of damage zone size 139 Figure 5.31 Plot of rd vs. Gu for specimens B8, B11 and B13. The dashed lines represent the Irwin-Williams model for V values of 67 MPa (deviation from linearity) and 101 MPa (failure). Hollow markers indicate test from insert 140 Figure 5.32 R-curve for specimen B11 ai, B8 a3 and B13 ai 140 -xvi-Figure 5.33 R-curve for specimen B8 a3, B l l ai and B13 ai showing how Gu depends on crack size 141 Figure 5.34 Plot of Gu vs. ^ at the damage zone tail for specimen B l l ai 141 Figure 5.35 Stress-displacement curve characterizing the damaged material in specimen B l l a, 142 Figure 5.36 Plot of Gu vs. at the tail of the damage zone for specimen B8 a3, B l l ai and B13 aj. Specimen B l 1 ai showed almost no coalescence 142 Figure 5.37 Damage zone height, at the tail of the damage zone (B8 a3, B l 1 ai and B13 ai).. 143 Figure 5.38 Damage zone height at the tail of the damage zone, hd, as a function of Gu, for specimen B8 a3 144 Figure 5.39 Damage zone height at the tail of the damage zone, hd, as a function of Gu, for specimen B13 ai 144 Figure A. 1 Photograph of the tab bonding jig 157 Figure A.2 Photograph of the gold deposition jig 158 Figure C l Calibration curve for the left load cell 163 Figure C.2 Calibration curve for the right load cell 163 Figure C.3 Calibration curve for the left displacement sensor 164 Figure C.4 Calibration curve for the right displacement sensor 164 Figure D.l Apparent flexural modulus for AS4/3501 and IM7/8551 as a function of span to depth ratio. The apparent modulus is lower than the actual value because the shear deformation has been neglected, especially at low span-to-depth ratios 170 Figure E. l Load-displacement curve for specimen B l (a0 showing the points where the COD profiles were taken (first loading ramp on Figure 4.1) 178 Figure E.2 Load-displacement curve for specimen B l (ai, a2) showing the points where the COD profiles were taken (second loading ramp on Figure 4.1) 178 Figure E.3 Load-displacement curve for specimen B1 (a2) showing the points where the COD profiles were taken (third loading ramp on Figure 4.1) 179 Figure E.4 Load-displacement curve for specimen B1 (a3) showing the points where the COD profiles were taken (fourth loading ramp on Figure 4.1) 179 Figure E.5 Load-displacement curve for specimen T4 showing the points where the COD profiles were taken (loading ramp on Figure 4.23) 180 Figure E.6 Load-displacement curve for specimen RI showing the points where the COD profiles were taken and were crack growth occurred 181 Figure E.7 Plot of COD 2 /Gi L for specimen B1 ai showing the square root dependency zone. 182 Figure E.8 Plot of C O D 2 / G I L for specimen B1 a2 showing the square root dependency zone. 183 Figure E.9 Plot of COD 2 /Gi L for specimen B1 a3 showing the square root dependency zone. 184 -xvii-Figure E.10 R-curve measured for specimen B3 185 Figure E . l 1 R-curve measured for specimen B5 185 Figure E.12 Plot of COD vs. r (distance from the crack tip) for G/c = 83 J/m2 on specimen B3 (ci). Solid line shows COD profile calculated from Gu = GIG- Dashed line shows COD profile calculated from GiL that gives the best fit 186 Figure E.l3 Plot of COD vs. r (distance from the crack tip) for GIG = 74 J/m2 on specimen B3 (c2). Solid line shows COD profile calculated from Gu = GIG 186 Figure E.14 Plot of COD vs. r (distance from the crack tip) for G/c = 81 J/m2 on specimen B3 (c3). Solid line shows COD profile calculated from Gu = GIG- Dashed line shows COD profile calculated from Gu that gives the best fit 187 Figure E.15 Plot of COD vs. r (distance from the crack tip) for GIG = 89 J/m2 on specimen B5 (ci). Solid line shows COD profile calculated from GiL = GIG 187 Figure E.l6 Plot of COD vs. r (distance from the crack tip) for GIG = 72 J/m2 on specimen B5 (c2). Solid line shows COD profile calculated from Gu = GIG 188 Figure E.17 Plot of COD vs. r (distance from the crack tip) for G/c = 83 J/m2 on specimen B5 (C3) . Solid line shows COD profile calculated from GIL = GIG 188 Figure E.18 Plot of COD vs. r (distance from the crack tip) for GIG = 75 J/m2 on specimen B5 (c4). Solid line shows COD profile calculated from GIL = GIG 189 Figure E.19 Plot of COD vs. r (distance from the crack tip) for GIG = 81 J/m2 on specimen B5 (c5). Solid line shows COD profile calculated from GIL = G / G 189 Figure E.20 Plot of COD vs. r (distance from the crack tip) for GIG = 81 J/m2 on specimen B5 (c6). Solid line shows COD profile calculated from GIL = GIG 190 Figure E.21 Plot of GIL vs. GIG for specimen B3 and B5. Dotted line represents a one-to one correspondence 191 Figure E.22 Pictures showing the interlocking of the Teflon insert fibre bundles and the composite matrix, for specimen B3 192 Figure E.23 Load-displacement curve for specimen B8 (ai) showing the points where the COD profiles were taken (loading ramp on Figure 5.1) 193 Figure E.24 Load-displacement curve for specimen B8 (a2) showing the points where the COD profiles were taken (loading ramp on Figure 5.1) 193 Figure E.25 Load-displacement curve for specimen B8 (a3) showing the points where the COD profiles were taken (loading ramp on Figure 5.1) 194 Figure E.26 Load-displacement curve for specimen B11 showing the points where the COD profiles were taken (loading ramp on Figure 5.2) 194 Figure E.27 Load-displacement curve for specimen B13 showing the points where the COD profiles were taken (loading ramp on Figure 5.3) 195 Figure F. l Montage of the SEM crack tip images for specimen B l ai, for GIG=0 J/m 196 Figure F.2 Montage of the SEM crack tip images for specimen B1 ai, for GIG=30 J/m 196 -xviii-2 Figure F.3 Montage of the SEM crack tip images for specimen B l ai, for GIG=72 J/m 196 Figure F.4 Montage of SEM crack tip image for specimen B1 a2, for GIG=0 J/m2 197 Figure F.5 Montage of SEM crack tip image for specimen B l a2, for GIG=35 J/m2 197 Figure F.6 Montage of SEM crack tip image for specimen B1 a2, for GIG=74 J/m2 197 Figure F.7 Montage of SEM crack tip image for specimen R l C5, for GIG=0 J/m2 198 Figure F.8 Montage of SEM crack tip image for specimen R l C5, for GIG=426 J/m2 198 Figure F.9 Montage of SEM crack tip image for specimen B8 a3, for GHG=0 J/m 199 Figure F.10 Montage of SEM crack tip image for specimen B8 a3, for GHG=432 J/m2 199 Figure F. l 1 Montage of SEM crack tip image for specimen B8 a3, for GHG=770 J/m2 199 Figure F. l 2 Montage of SEM crack tip image for specimen B l l aj, for GHG=0 J/m 200 Figure F. l 3 Montage of SEM crack tip image for specimen B l l a,, for GHG=297 J/m2 200 Figure F.14 Montage of SEM crack tip image for specimen B l l ai, for GHG=695 J/m 200 -xix-Nomenclature a Crack length aeff Effective crack length a{ Crack length <2jj Unidirectional composite plane stress elastic constants ao Initial crack length A, Elastic function in Mode I A„ Elastic function in Mode II B Specimen width C Compliance Co Machine compliance COD Crack Opening Displacement CSD Crack Shear Displacement E Laminate flexural modulus Ex Laminate longitudinal elastic modulus E2 Laminate transverse elastic modulus E/ Flexural modulus in fibre direction F Work performed by external load G Strain energy release rate Gc Critical strain energy release rate Go Energy dissipated at crack front G, Strain energy release rate in Mode I G„ Strain energy release rate in Mode II G,C Mode I critical strain energy release rate Guc Mode II critical strain energy release rate GIG Mode I global strain energy release rate GUG Mode II global strain energy release rate GIL Mode I local strain energy release rate GUL Mode II local strain energy release rate - X X -GicG Mode I global critical strain energy release rate GIB Mode I bridging strain energy release rate GlcL Mode I local critical strain energy release rate Gfriction Mode II friction strain energy release rate Gss Steady state bridging zone resistance G\2 Laminate in-plane elastic shear modulus h Half beam thickness hd Damage height at the tail of damage zone h Specimen depth (Appendix D) k Load-displacement slope V ^corr Corrected load-displacement slope kindent Load-displacement slope from indentation test kmeasured Load-displacement slope from three point bending test K, Mode I stress intensity factor K„ Mode II stress intensity factor L Specimen length L Support span (Appendix D) Ld Length of the zone containing microcracks that have not coalesced Dis Maximum bridging zone length P Applied load Pi Applied load in Mode I P„ Applied load in Mode II PL Left arm load PR Right arm load r Distance from crack tip rc Length of zone grown by coalescence rd Damage shift n Distance from the COD profile origin ni Distance from the CSD profile origin u Longitudinal displacement U Elastic energy -xxi-V Transverse displacement Vf Fibre volume fraction w Specimen width W Energy required for crack growth 8 Displacement S0 Ligament maximum opening displacement Si Displacement in mode I (opening) SJ, Displacement in Mode II (shear) 8 Damage zone end opening Sso Ligament maximum shear displacement s, Shear displacement at initial crack tip sL Left arm displacement sR Right arm displacement Ss Shear displacement f compression Axial compression strain P tension Axial tension strain Energy consumed by fibre bridging pull-out V i 2 Laminate Poisson's ration 6 Surface waviness angle G Normal stress ^ 0 Ligament initial stress T Shear stress Maximum stress in damage zone -xxii-Acknowledgments I am very grateful to all the people who have helped me throughout the course of my research. First, I would like to express my deepest gratitude to Dr. Anoush Poursartip and Dr. Reza Vaziri for their guidance and enthusiastic support. I am very thankful for the technical support from Roger Bennett, Serge Milaire, Mary Mager and Ross McLeod, whose efforts and experience were indispensable to the development of the experimental system. I am also grateful to Dr. Goran Fernlund for his valuable assistance and ideas. Many thanks to Dr. Alan Russel of DREP for providing the materials used in this research and to Dr. William McCarvill of Hercules Inc. for all the information on the material properties. I also would like to gratefully acknowledge the interaction from Dr. Walter Bradley at Texas A & M University. Many thanks to Etienne Lecomte, for his precious assistance during the preparation, performing and analysis of mode II tests. Sheilah Neumann, Smita Vakil, Catriana McKie and Walter Lau helped me greatly analyzing images and performing tests to determine the material properties. I will keep fond memories of the members of the Composites Group, who have been very supportive friends and have provided a wonderful learning environment. Finally, I would like to acknowledge the Canadian Natural Sciences and Engineering Research Council (NSERC) and Le Fonds pour la Formation de Chercheurs et l'Aide a la Recherche (FCAR) for their financial support. -xxin-qui m a communique to, foateio«t fioun tc metier ct itupettiewi et am ittceteottt de&Oi ct' aftfinettdne. -xxiv-Chapter 1 Introduction As a result of their high specific properties1, composite materials are of great interest in applications such as aerospace and aeronautics, where component weight is a critical factor. In these applications, significant savings in fuel costs are possible through the use of composite structures. In order to take full advantage of their potential, the performance and safe operating lifetime of composite structures must be estimated with precision. At present, accurate predictive methods are lacking, resulting in a great deal of uncertainty and thus overdesign. The application of fracture mechanics to these materials is especially important as a result of their sensitivity to damage and their tendency to degrade their properties when damaged. As heterogeneous materials, composites are characterized by the presence of several types of inherent flaws. In laminated composites, damage mechanisms are classified as follows (Figure 1.1): fibre breakage, interlaminar matrix cracking and interlaminar matrix delamination. Matrix cracking is the cracking of the resin within a layer, parallel to the fibre direction. Delamination consists of the separation of adjacent layers. It is often difficult to detect as it is not always visible from the surface. The major consequence of delamination is a loss of bending stiffness and compressive properties. In practice, different types of damage can be present simultaneously. However, each damage mechanism must first be modeled in isolation before it can be studied in conjunction with others. 1 modulus- and strength-to-weight ratios -1-Chapter 1 Introduction The prevalent failure mode in composite stuctures used in the aerospace industry is delamination. This complex failure mechanism is one of the principal factors limiting the use of composite structures in this industry. Thus, delamination failure must be better understood and this is the aim of this project. 1.1 Delaminations in composite laminates Delaminations can be created during manufacturing of the part or during service. The manufacturing of composite materials introduces delamination by (Garg, 1988): • contamination of the lay-up by foreign materials preventing adhesion between plies • improper curing of the matrix • resin rich region between layers which provide paths of least resistance • residual thermal stresses due to the cooldown after curing • machining • impact by tools and improper handling Delamination may also be introduced in service by mechanical loads. Local out-of-plane loads create interlaminar stresses which may lead to delamination. They are caused by (Garg, 1988): • impacts (for example, in aircrafts: runway debris, hailstones, bird strikes, ground service vehicle and ballistics) • eccentricities in the load path • discontinuities in the structure Chapter 1 Introduction • mismatch of properties between layers near the free edge of a laminated composite • environmental conditions (moisture gradient through the thickness, thermal stresses due to in service conditions) Typical composite structures have complex geometries and carry complex loadings (see Figure 1.2). As seen in Figure 1.2, the range of scales of interest is very large. Even with current computational ability, it would be prohibitive to have one finite element method (FEM) model of the whole structure with the mesh density necessary to provide the detailed local stress fields needed for fracture mechanics calculations. Instead, the overall problem can be split into a number of sub-problems. Using a building block approach (Martin, 1995), the stress distribution obtained from a global model (see Figure 1.2) is used to determine the areas where failure is likely to occur. The global model also provides the boundary conditions to apply to a more detailed model of the sub-structure. This analysis is further refined at the coupon level, where a crack is included in the model (Murri, Salpekar and O'Brien, 1991). The strain energy release rates for the various mode components are calculated and compared with a mixed-mode failure envelope. If the mixed-mode failure behaviour is known, one can iterate through all the steps and refine the design until it is acceptable. Two related problems exist. First, there is a lack of confidence in the pure mode failure criteria Gic and G//c. Secondly, there is little to inspire confidence in the generality of mixed-mode failure envelopes, nor are there good explanations or understanding of what determines mixed-mode failure criteria. Therefore, the objective of this work is to study quantitatively the local crack tip behaviour and compare the results to those obtained from the global applied conditions, in order to guide and justify the development of failure criteria and failure envelopes. Without a Chapter 1 Introduction sound basis for failure criteria, it is difficult to design generically against delamination. If successful, the current work will support the development of standards, as well as increase confidence in the accuracy and validity of building-block approaches as shown schematically in Figure 1.2. To achieve this objective, a method for studying quantitatively the local crack tip behaviour, while knowing the globally applied conditions, was needed. At the macroscopic scale, the global approach uses the global applied loads and geometry to provide the crack tip stress field. On the other hand, the local approach looks into the fracture process at the scale of ply, interface, fibres, resin region and crack tip profile. 1.2 Global approach Using this approach, global parameters such as applied load or deflection, geometry, crack length and material compliance are used to evaluate the local conditions in the crack tip area, using Linear Elastic Fracture Mechanics (LEFM). In isotropic and homogeneous materials such as metals, LEFM has proven very useful. However, the use of this approach with composite materials is more complex, as the material is both anisotropic and heterogeneous. Nevertheless, in the case of delamination, the crack is well defined and stress, crack length and specimen geometry can be combined in one similitude parameter, such as the stress intensity factor K or the strain energy release rate G, to describe the crack tip stress field. The stress intensity factor relates the far field applied loads to the local stress field. However, in the case of composite materials, the evaluation of the stress intensity factor is rather complicated. A more convenient approach is the energy method (e.g., Broek, 1986). This approach states that Chapter 1 Introduction the crack will grow if there is sufficient energy available to create new surfaces. In a body with crack of length a subjected to a load P, the Griffith criterion for growth is: da da where U is the elastic energy stored in the plate, F is the work performed by the external load and W is the energy required for crack growth. The left hand side is defined as G, the strain energy release rate, while the right hand side represents the material resistance to crack growth (Broek, 1986). For a linear elastic system under a load P, the load application points will undergo a relative displacement S. By calculating the work done by the external force and the elastic energy stored in the plate, the expression for G becomes (Broek, 1986), G=P-d± (..2) IB da where C is the compliance and B is the width of the specimen. Thus the strain energy release rate is known if dC/da is evaluated, either by experiment or by calculation. When the crack driving force just equals the energy necessary to create new surfaces, the crack begins to grow. G is then equal to the critical strain energy release rate, Gc, also referred to as the fracture toughness. As G is the total energy, it can be partitioned into the energies due to different load components: mode I, mode II and mode EH, depending if the crack is submitted to opening, in-plane shear or anti-plane shear loading (Figure 1.3). In practice, the crack can be submitted to any combination Chapter 1 Introduction of these three modes. A combination of mode I and mode JJ loading is very common and we will refer to it as "mixed-mode" loading. For pure modes, the compliance can be calculated for some geometries using simple beam theory. In the case of a specimen such as the Double Cantilever Beam (DCB) (Figure 1.4a), for the mode I case, we have (Williams, 1990): and for the End-Notched Cantilever Beam (ENCB) under mode II loading (Figure 1.4b): where h is the half beam thickness, B is the width and L is the specimen length. Correction factors (Hutchinson and Suo, 1992; Williams, 1989) have been developed to take into account the shear deformation and, if necessary, the effect of large displacements and the stiffening effect of bonded end blocks. The details of the equations used in this work will be presented later. The subscript "G" used in equations (1.3) and (1.4) indicate that the strain energy release rates are calculated from the global values. Thus, with this approach, the global applied loads and geometry are used to determine the behavior of the crack. However, as composite materials are anisotropic and heterogeneous, some local perturbations might alter the behavior of the crack. Local perturbations such as resin-rich regions, fibre bridging, microcracking, crack path wandering, and friction have been noticed by investigators (e.g., Davies and Benzeggah, 1989; Davies, Moulin and Kausch, 1990). Thus, global applied loads are perhaps not transferred directly into equivalent local crack tip conditions. G IIG ~ (1.4) Chapter 1 Introduction In addition, in the general and realistic case of mixed-mode loading, the global applied loads have to be partitioned into the different mode (I, II) components. Depending on the test geometry, the partitioning is done using beam theory analysis or numerical methods such as finite element, finite difference, boundary element or energy calculations. In all cases, the approximations and idealizations necessary to partition the loads and calculate Gi and Gu may lead to inaccuracies (e.g. Hashemi, Kinloch and Williams, 1991; Williams, 1988; Hutchinson and Suo, 1992). Consequently, it is again important to study the local crack tip behaviour. 1.3 Local approach As a first attempt, qualitative observations of the microstructural aspects of delamination can provide some understanding about the mechanisms involved. Such work includes observations of fractographic surfaces resulting from delamination and in-situ microscopic observation of crack growth. However, these techniques lack quantitative results. Another approach is to measure some local quantities such as the displacements in the crack tip area, from which the strains can be calculated. Furthermore, the stress intensity factor or the strain energy release rate can be related to the local displacement field, more specifically to the crack tip face displacements. A delaminated specimen subjected to a combined opening and shear mode loading is shown in Figure 1.2. The inset depicts the displacements of the crack tip faces. A grid applied on the specimen edge prior to loading would deform as shown. The applied opening mode forces the crack faces to move apart: this results in the crack opening displacement (COD) profile. The applied shear mode creates a sliding of a crack face with respect to the other; the resulting shift in the vertical lines of the grid is called the crack shear Chapter 1 Introduction displacement (CSD) profile. The COD and CSD are functions of r, the distance behind the crack tip. The crack tip displacement field equations for rectilinearly isotropic materials, such as unidirectional composites, were derived by Sih et al. (1965). These equations relate the displacements to the stress intensity factor. The same authors also provided a relationship between the strain energy release rate and the stress intensity factor in rectilinearly isotropic materials. Thus the displacements can be related to the local strain energy release rate. The displacements of the crack face behind the crack tip are of the form: where A/ and An are functions of the elastic properties of the laminate and will be developed later. These equations are only valid close to the crack tip. The COD and CSD profiles are measured just behind the crack tip and therefore Gu and Gm are the actual, local strain energy release rates. They are evaluated using equations (1.5) and (1.6), and can then be compared with the one obtained from global measured values. As the G evaluated in both cases is the same physical parameter, the two approaches should be equivalent, unless some local crack tip mechanisms have an effect. One mechanism which is likely to have such an effect is fibre bridging under mode I loading: as the crack grows, some fibres cross over the crack surfaces, resulting in a measured increase in GIG at failure. One possible explanation is that the fibre bridges restrain the crack from opening and therefore, Gu is smaller than GIG- Using the superposition principle for the displacements, (1.5) (1.6) Chapter 1 Introduction the bridged crack is equivalent to the unbridged crack minus the crack loaded by distributed pressure on the crack tip faces corresponding to the stresses in the fibre bridges (Figure 1.5). Therefore, CODbridged c r a c k = CODunbridged c r a c k — CODjibre jorces (1.7) The COD budged crack is the one actually measured and is related to GIL via equation (1.5). If the fibre bridges are removed, the crack would open up while the load would remain the same. Thus, using equation (1.5), the COD"unbridged crack is related to the GIG calculated from the applied load Pi and displacement 8W. Since Sw is unknown, we will have to use an equation involving only Pi to calculate G/c- Finally, we define G/B as the strain energy release rate associated with the fibre bridge forces; GIB is related to the CODfare forces using equation (1.5). Therefore: Consequently, measuring the local COD profile and the global load permits us to obtain GIL and GIG and therefore the fibre bridging behaviour and its effect on the increase in toughness. 1.4 Summary The main goal of the present research is to perform simultaneous quantitative measurements of the applied conditions (load, displacement) and the crack tip face displacements, in order to compare the local and global behaviour and provide a better understanding of delamination behaviour. The thesis is organized as follow: Chapter 1 Introduction 1) A review of the research found in the literature on delamination crack behaviour is first presented in Chapter 2. Based on the literature review, our objectives to study delamination crack tip behaviour are formulated. 2) Then, the in-situ scanning electron microscope experimental method is described in Chapter 3. 3) Experiments are conducted on a delamination crack under mode I loading. The results are presented and interpreted in Chapter 4. 4) Another series of experiments is conducted under mode U loading. The results are presented and interpreted in Chapter 5. 5) Finally, the main conclusions and the recommendations for further studies are given in Chapter 6. -10-Chapter 1 Introduction 1.5 Figures interface between 2 plies Figure 1.1 Damage types in composite laminates 10n.m 100 n / n 1mm 10 mm 100 mm 1m 10 m < I | I—, 1—, I ! I ! I • 0.001 in. 0.01 in. 0.1 in. 1 in. 1ft. 10 ft. Figure 1.2 Range of scales of interest in the study of composite structural failure Chapter 1 Introduction Figure 1.3 The three modes of loading Figure 1.4 (a) Double cantilever beam (DCB) and (b) end-notched cantilever beam (ENCB) specimens -12-Chapter 1 Introduction P, | Figure 1.5 Illustration of the equivalence between the bridge crack and the superposition of an unbridged crack and a crack loaded by pressure at the crack tip faces. -13-Chapter 2 Literature Review Many studies have been dedicated to obtaining the strain energy release rate of composite materials in mode I, mode II and mixed-mode loading from the global conditions, as it is a useful value to predict the fracture failure of a material. The investigators have then tried to study what factors are affecting the resistance to delamination. Some have tried to understand the micromechanisms by directly observing the crack tip. A few have attempted to make measurements of the local crack tip behavior. Finally, even fewer investigators have used these measurements to verify how well the strain energy release rate calculated from the global conditions corresponds to what is happening at the crack tip. 2.1 Delamination fracture toughness Numerous investigations have been aimed at obtaining the strain energy release rate, based on the global approach described previously. Tests are usually performed on a testing machine applying mode I, mode II or mixed-mode loads. In order to ensure that the delamination crack will propagate along the midplane, a starter film is introduced at the mid-plane of the laminate at manufacturing. From the measured global parameters such as load, displacement and crack length, the strain energy release rate is calculated, and it reaches its critical value when the crack grows. The critical strain energy release rate or fracture toughness is assumed to be a material property. However, several factors can affect the measured value. Thus, the test conditions are important in order to obtain a valid strain energy release rate. Moreover, some of these effects are due to local perturbations. Consequently, the global applied loads may not be entirely transmitted to the crack tip as predicted. -14-Chapter 2 Literature Review 2.1.1 Effects of resin The resin has been found to play a very important role in the delamination behaviour. Several authors have studied the effect of the type of resin on the delamination fracture of composite materials. To do so, the composite fracture toughness is measured for materials containing different types of resins. Bradley and Cohen (1985) found that the composite fracture toughness is sensitive to the resin fracture toughness, the interfacial strength and the thickness of the resin rich region. Bradley (1989) plotted the composite fracture toughness G/ c and G//c as a function of the neat resin fracture toughness, for various materials (Figure 2.1). The results showed that the composite G/ c increases when the neat resin G/ c increases. However, above a certain value, the increase in composite G/ c becomes less significant. It was also found that, although the composite toughness is significantly higher in mode II than in mode I, the composite mode II toughness is not as sensitive to the resin toughness. In order to understand the relationship between the neat resin and the composite fracture toughness, the micromechanisms of delamination growth were studied, using three methods: the observation of post-fracture mode I, mode II and mixed-mode delamination surfaces using a scanning electron microscope (SEM) (Bradley and Cohen, 1985), the real-time observation of delamination growth under pure mode I and mode Et using an SEM (Bradley and Cohen, 1985; Bradley, 1989) and the measurement of the strain field around the delamination crack tip using an SEM (Bradley, 1989). 2.1.1.1 Micromechanisms of mode I delamination In mode I, for composites with brittle resins, the composite fracture toughness is higher than the neat-resin fracture toughness (Figure 2.1). This can be explained by the increase in fracture -15-Chapter 2 Literature Review surface due to a more tortuous path and the presence of fibres that may bridge the crack and restrain its opening, or dissipate energy when they break (Bradley and Cohen, 1985). For composites with thicker resin-rich regions, the crack path is less tortuous and there is less fibre bridging, therefore the toughness is lower, closer to the neat resin toughness. Moreover, Corleto et al. (1987) have shown, using linear finite element analysis, that the stresses in front of the crack tip are more distributed in the orthotropic composite than for the isotropic resin. Therefore, a higher load can be applied to the composite specimen before the critical crack tip stress is reached. This is confirmed by in-situ measurement of the strain field around the crack tip: the strain field observed in the composite is longer and narrower than in the neat resin (Bradley, 1989). In a ductile resin, a larger plastic zone is formed in front of the crack tip (Figure 2.2) and the crack tip is more blunted. This is confirmed by the in-situ measurement of strain field in neat resin specimen, where the extent and intensity of the strain field is much higher in more ductile resins (Bradley, 1989). Consequently, the load is redistributed in front of the crack tip and the resistance to delamination is increased. In the composite, the plastic zone size increases with the neat resin fracture toughness, until it reaches the size of the resin rich region between plies and becomes constrained by the fibres (Figure 2.1). Above this point, the composite fracture toughness is less than the neat resin fracture toughness and an increase in the resin fracture toughness has little effect on the composite resistance to delamination. As opposed to brittle resin composites, a ductile resin composite with thicker resin rich region between plies has a higher fracture toughness, since a bigger plastic zone can develop (Bradley and Cohen, 1985). -16-C h a p t e r 2 L i t e r a t u re R e v i e w It has also been noted that the improvement provided by the matrix is fully used only if there is good interfacial adhesion (Bradley, 1989). 2.1.1.2 Micromechanisms of mode II delamination In mode n, for brittle resin composites, a very different micromechanism of fracture was observed: as can be observed in Figure 2.3, a series of sigmoidal shaped microcracks are formed in front of the crack tip with an orientation of approximately 45° to the fibre direction and the crack grows as a result of the coalescence of these microcracks (Hibbs and Bradley, 1987; O'Brien et al., 1989; Bradley, 1989). The microcracks are created on the principal normal stress plane, which for pure shear loading forms a 45° angle with the specimen midplane (Figure 2.4a). As the load is increased, the ligaments formed by microcracks rotate due to the shear loading and coalescence occurs between the microcracks (Figure 2.4b) resulting in the creation of hackles. Since the microcrack creation and coalescence requires more energy than the continuous crack growth observed in mode I, G//c is higher than G/6 (Figure 2.1). This is confirmed by the observation of a much longer damage zone in mode n. The in-situ measurement of strains ahead of a crack tip also show a long and narrow strain field which include shear deformation and microcracking and result in load redistribution and energy dissipation (Bradley, 1989). Furthermore, these results are consistent with the stress field ahead of the crack tip calculated by a linear finite element analysis (Corleto et al., 1987). In mode U, the shear stress ahead of the crack tip decays much more slowly than the normal stress ahead of the crack tip in mode I (see Figure 2.5), resulting in a load redistribution over a longer distance and therefore, in a higher -17-C h a p t e r 2 L i t e r a t u re R e v i e w toughness. A model for the mode TJ fracture toughness based on the resin properties and the failure process has been proposed by Lee (1997). For very ductile resin composites, the sigmoidal shaped microcracks are not observed and the fracture is similar to mode I, with plastic deformation, and G/ c and G//c are comparable (Ffibbs and Bradley, 1987; Russell and Street, 1987; O'Brien et al., 1989) Thus, in mode n, we have two very different processes, the microcracking process for brittle resins and the plastic deformation process for ductile resins. G//c is not as sensitive to neat resin toughness as G/c, probably because the two different processes accomplish the same load redistribution effect (Bradley, 1989). 2.1.2 Effect of starter film and precrack Another factor that has an important effect on the fracture toughness is the insert. It has been shown (Davies et al., 1990) that when the starter film is thicker, the values of G/ c and Gnc obtained from the insert are higher and there is more scatter. This is because the thick film acts like a blunt crack. Moreover, they studied the effect of the presence of a precrack created with mode I loading or mode II loading . Compared to the tests with no precrack, the mode I precrack gave a higher value of G[C while the mode U precrack gave a lower one. The high value with mode I precrack may be explained by fibre bridging the crack and increasing the resistance to crack growth. In the case of the planar, well defined mode II precrack, there is no fibre bridging and the G/6 value is close to the one obtained with the thinnest insert. Therefore, for unidirectional carbon fibre/epoxy specimens, a starter film thickness of the order of 20 microns or less provides an -18-Chapter 2 Literature Review appropriate value of the initiation mode I toughness. O'Brien et Martin (1993) also reported tests with different inserts types and thicknesses. With inserts of 13 microns or less, the toughness value did not change much anymore. Guc values were also obtained (Davies et al., 1990; Prel et al., 1989; Carlsson and Gillespie, Jr., 1989; Russell, 1991) from the insert and for specimens with mode I precrack and mode U precrack. The highest values were obtained with specimens with no precrack, because the crack tip is blunted at the end of the starter film. This effect seems to be more severe than in mode I, as the value obtained for the thinnest starter film (20 microns) is still significantly higher than with the mode I precrack (Davies et al., 1990). The values obtained with mode I precrack were slightly lower than those obtained with a mode JJ precrack (Carlsson and Gillespie, Jr., 1989; Russell, 1991). A cyclic mode U precrack gave the same results as a static mode JJ precrack (O'Brien et al., 1989). These results show the difficulty in creating a valid crack for standard testing. The starter film has to be as thin as possible to minimize the matrix-rich region, and yet a minimum thickness is required to avoid wrinkling of the film during moulding (Davies and Benzeggah, 1989). If a mode I precrack is used, it should be sufficiently long to avoid a matrix-rich pocket, but short enough to reduce the amount of fibre bridging (Davies and Benzeggah, 1989). 2.1.3 Effect of fibre bridging Fibre bridging consists in fibres crossing over the crack faces (Figure 2.6). During the lay-up process, successive layers of fibres preimpregnated with resin are stacked, forming distinct plies. During cure, those plies become more or less intermingled, especially in unidirectional laminates -19-Chapter 2 Literature Review (Figure 2.7). When a crack grows, those fibres going from one layer to the other create a bridge between the two crack surfaces. Moreover, especially in tougher composites (Figure 2.8), if flaws in planes above or below the crack plane are loaded, the crack can change to that plane and a bridge is created (Davies and Benzeggah, 1989). These bridges restrain the opening of the crack and increase the fracture resistance. Thus the critical energy release rate Gc may increase as the crack propagates and more fibre bridging is created (Figure 2.9). In this case, the critical energy release rate is not a unique value. There is an initiation value for Gc, then it increases and eventually reaches a stable plateau value if fibre bridges are broken at the same rate as they are created (Davies and Benzeggah, 1989). If the specimen thickness increases, the initiation value does not change, but the propagation value increases significantly due to the increase in fibre bridging (Russell and Street, 1982; Prel et al., 1989). Thus the crack behaviour beyond the initiation value is not a material property. Since R-curves are specimen dependent, it has become more popular to characterize a material resistance behaviour using bridging laws (Suo et al., 1992; Spearing and Evans, 1992). According to these authors, the determination of the bridging tractions a created by the bridging fibres as a function of the local crack opening 8 can provide a general description of the resistance curve behaviour, applicable to various specimen geometries. It can be determined experimentally or by modelling. In polymer matrix composite materials, it can be used to model the increased resistance with crack growth that occurs under different micromechanisms: fibre bridging, micro-cracking damage, etc. This approach uses the Dugdale model (Dugdale, 1960), which uses an array of continuously distributed non-linear springs to simulate the material in the damage zone (see Figure 2.10). -20-Chapter 2 Literature Review Each point in the damage zone experiences the same relationship between the bridging tractions <7 and the local crack opening 5. It is assumed that the traction law o~(S) is characteristic of a given material and damage type and is independent of geometry. The traction <7 has an initial value <T0 and becomes zero above a maximum separation value S0. Applying the J-integral conservation (Rice, 1968), G = G0 + f*<j{S)dS (2.1) where 5 is the end-opening of the damage zone (Figure 2.10), G is the applied strain energy release rate and Go is the energy dissipated at the crack front. When the end-opening is equal to the critical separation, S = SQ, G reaches a plateau corresponding to the steady-state resistance Gss, which is equal to the sum of G0 and the area under the CJ{S) curve and does not depend on the specimen geometry (see Figure 2.10). At this point, the length of the bridging zone, L, also reaches a maximum, Lss, which depends on both the bridging mechanism and the specimen geometry (see Figure 2.10). Using finite element analysis, Suo et al. (1992) have provided equations for calculating the R-curve for various delamination beams and idealized bridging laws, once the parameters are known. The difficulty is to determine the parameters of the bridging laws, and several experimental and analytical approaches have been taken. One very elegant approach has been suggested (Suo et al., 1992). Differentiating (2.1) yields: -21-Chapter 2 Literature Review Therefore, the bridging law can be measured experimentally by measuring the damage zone end-opening (S) together with the R-curve. Another approach for measuring the bridging law has been adopted (Spearing and Evans, 1992), for a DCB specimen. By modelling a bridging ligament as a short cantilever beam deforming in shear and bending, they have shown that a linear strain softening law is the appropriate approximation of the bridging law: Then they measured the R-curve for several ceramic composites and for carbon fiber-PEEK DCB specimens. The initiation resistance G0 and the steady-state bridging zone length Lss and resistance Gss were obtained from those curves. The maximum end-opening 80 was calculated from beam theory, at a distance L„ from the crack tip, neglecting the effect of the fibre bridging on the beam profile. Then o~0 was calculated using equation (2.4). Finally, the entire R-curve was calculated using an equation for DCB specimens loaded by end-moments (Suo et al., 1992). The results show good agreement with the experimentally measured R-curve, even for various specimen thicknesses and the fibre bridging parameters o~0 and S0 obtained are reasonable. A test designed to measure directly the closure pressure vs. displacement curve has also been designed (Kaute et al., 1993). Ceramic matrix composites specimens were precracked from side to side, with only the fibre bridges holding the faces together and pulled apart. The resulting (2.3) Using (2.1) gives: (2.4) -22-Chapter 2 Literature Review curve shows a steeply rising part followed by a shallow fall, typical of a strain-softening behaviour. They have also modelled the fibre bridging using basic constituents and interface properties and the shape of the closure pressure curve obtained is similar to the experimentally measured one. 2.1.4 Effect of friction Fibre bridging is not observed in mode II loading (Russell and Street, 1985), but another energy dissipating mechanism is present. A mode II load applied by bending may create friction between the crack surfaces of the two delaminated beams. The relative sliding of the two half beams is then restricted and some energy is absorbed in overcoming this friction. For end notched flexure (ENF) geometry, the effect of friction has been evaluated using finite element analysis, and the error induced in the strain energy release rate was 2-5% for a coefficient of friction varying between 0.25 and 0.5 and a thickness to crack length ratio h/a less than 0.05 (Gillespie, Jr. et al., 1986). According to this analysis, the error induced by friction on the strain energy release rate is proportional to the coefficient of friction and to the thickness to crack length ratio. However the real value of the interfacial friction coefficient is unknown. The hysterisis was measured in the loading and unloading curve (Russell and Street, 1985), indicating less than a 2% overestimate of the strain energy release rate. However, this is a global value that would be insensitive to any localized friction near the crack tip. 2.1.5 Mixed-mode failure criterion There has been extensive testing in pure mode I and pure mode U, and values for the fracture toughness G/ c and G//c for different materials are well established. But delamination cracks are -23-Chapter 2 Literature Review often loaded under a combination of mode I and mode U loads. It would be useful to have a simple failure criterion, but unfortunately, this is not what has been observed experimentally (Garg, 1988). Investigators have proposed several different equations in order to fit their test results. Different tests configuration have been used to introduce a mixed-mode loading (Figure 2.11). Cracked lap shear (CLS) and mixed-mode flexure (MMF) rely on an eccentric load path to induce mixed-mode loading. Their inconvenience is that they require a different lay-up of the specimen with different thickness of the two half beams to obtain a different mixed-mode ratio. Other configurations use special test jigs to apply the two loads. In the mixed-mode bending (MMB) test, a lever is used to apply simultaneously mode I and mode II and its position determines the mixed-mode ratio. Finally, mixed-mode can be created by asymmetrically loading a double cantilever beam specimen. From the loads measured at initiation, the mode I and mode II components are partitioned and G/ and Gu are calculated. Depending on the test geometry, the partitioning is done using beam theory analysis or numerical methods such as finite elements, finite difference, boundary elements or energy calculations. In all the cases, the approximations and idealizations necessary to partition the loads and calculate Gj and G// may lead to inaccuracies. Figure 2.12 shows a plot of the sum of the critical mode I and mode II component as a function of the proportion of mode II loading: at the left of the graph are the values for pure mode I and at the right, for pure mode II. As pointed out by O'Brien (1997), the scatter in the toughness values increases significantly with the mode TJ loading, and there is considerable scatter for the the pure mode II toughness. -24-C h a p t e r 2 L i t e r a t u re R e v i e w 2.2 Direct observation of crack tip behaviour Another approach to understanding the delamination process is to observe the micromechanisms. We have already mentioned that some authors used those observations to try to explain the changes in the fracture toughness when some factors were varied. 2.2.1 In-situ crack growth observation Several authors have tried to directly observe the crack tip delamination process by developing a delamination test inside a scanning electron microscope (SEM). However, their approach has been largely qualitative. Transverse ply cracking was observed using a tensile jig inside an SEM (Smith et al., 1985). An attempt to take strain measurements at the crack tip did not succeed because the reference mesh was not fine enough. Another group of investigators (Hibbs and Bradley, 1987) have performed real-time mode I and mode TJ delamination tests inside an SEM and observed the region of the crack tip on a polished edge of the specimen. By studying the individual processes, interfacial debonding, resin deformation, microcracks, they attempted to determine the overall mechanisms of crack advancement. Those qualitative observations can be related to a change of materials or loading modes. The fracture mechanisms of ceramic matrix composites was observed within a SEM using four point bending and double cantilever beam specimens to study the location and orientation of fibre bridges across the crack (Shercliff et al., 1994). In recent years, an increasing number of authors have conducted in-situ SEM studies to observe fracture and fatigue behaviour in metals, ceramics and composites (Davidson, 1993; Sun et al., 1993; Sun et al., 1995; Kohyama and Sato, 1993). -25-Chapter 2 Literature Review 2.2.2 Measurements in the crack tip area Using a photoresist technique to apply a reference grid on the edge of a double torsion epoxy specimen, Mao et al. (1983) took a few COD measurements in order to evaluate KIc. Theocaris (1988; 1990) used the scanning electron microscope (SEM) to measure the distance between two points close to the crack tip under a series of incremental loads. The displacements were then analyzed by a system of linear equations, yielding the displacement and strain field around the crack tip. The resulting strain field is calculated from only one displacement measurement: it is therefore an ideal strain field, which might be very different from the real strain field. Using a labour intensive method, Kortshot (1988) used the movement of silver particles on the surface with respect to a loose fine metallic mesh to calculate the displacements and strains. Also using the SEM, Bradley (1989) measured the strain field around a delamination crack tip in a composite material. A dot map was created by burning small holes in the gold-palladium coating. The specimen was then loaded in an SEM and, from the measurements of the dots displacements, the strains were calculated. The method was used to compare the strain fields in the neat resin and in the composite to understand the micromechanisms involved. Ferguson et al. (1991) compared the results of SEM measurements with those predicted by the global approach from the applied displacement (Figure 2.13). In the SEM, the crack opening and shear displacements profiles were measured. Mode I, mode II and different mixed-mode ratios were applied. The results were compared with the values calculated from the applied loads using LEFM equations. It was found that the shape of the COD and CSD over the first 400 microns behind the crack tip was described by an rm distribution, under both mode I and mode n, as -26-C h a p t e r 2 L i t e r a t u re R e v i e w predicted by LEFM. The magnitudes of the crack opening displacements in pure mode I were found to be lower than predicted, while the mode Et crack shear displacements were generally larger. Ferguson explained these discrepancies by local effects such as fibre bridging and variations in fibre volume fraction. The addition of a mode I load to a mode Et load increases the magnitude of the crack shear displacements. This effect was explained by the removal of frictional forces between the two half beams. Addition of a mode Et load to a mode I load did not have a consistent effect on the COD profile. Bannister et al. (1992) have measured the crack opening profile from scanning electron micrographs in ceramic matrix specimens under double torsion loading and with a fibre bridging zone fully developed (Figure 2.14). They found that the measured profile was in-between the profiles expected for the initiation and the propagation values of the applied stress intensity factor, meaning that the fibre bridges are restraining the opening of the crack tip faces. As can be seen in Figure 2.14, the COD's are measured at a distance from the crack tip greater than 1 mm, and are 1 mm apart from each other: this is not close enough to the crack tip to represent the local crack tip behaviour. Davidson (1993) used a stereoimaging technique to determine the displacements and strains from scanning electron microscope photographs (Figure 2.15). The automated image processing system requires fine surface details to compute the differences due to deformations between two images taken at different load or time. The appropriate surface texture is obtained by chemical, thermal or ion etching or by deposition of particles. Minimum displacements of 0.25 (xm can be measured on photographs at 4000x magnification, but the size of the area studied is then very limited (less than 20 |4,m). The hydraulic loading stage, designed to fit inside a scanning electron -27-C h a p t e r 2 L i t e r a tu re R e v i e w microscope, can apply a cyclic load up to 4 Hz and temperatures up to 800°C can be applied. The system has been used to study fatigue crack closure and fatigue crack growth under mode I loading in metals and metal matrix composites. Farqhuar et al. (1994) have measured the crack opening displacements profiles in ceramic materials under mode I loading, in order to study the influence of particle size and volume fraction (Figure 2.16). They compared these measurements with the results from a finite element computation, to determine the bridging tractions. The global applied loads and displacements were not measured and the specimen is not a standard geometry. In summary, several methods have been developed for the quantitative study of crack tip displacements. However, not many experiments have been conducted due to the very time consuming techniques used. The resolution of the measurements is also a limiting factor. The size and geometry of the specimens is often limited by the space available in the jig. The applied load and displacement is often not measured. Finally, few experiments have been conducted on polymer matrix specimens and delamination cracks. 2.3 Literature review summary A summary of the literature review is presented in Table 2.1. As we have seen, the macroscopic approach consists in measuring the global parameters and calculating the crack driving force using LEFM. It has been extensively used to determine the fracture toughness of materials under various conditions. It reveals that some factors have an effect on resistance to delamination: type of resin, insert, precrack, fibre bridging, friction, mixed-mode ratio. Several of these factors have an effect localized at the crack tip. Thus a study of micromechanisms is necessary. -28-C h a p t e r 2 L i t e r a t u r e R e v i e w Several studies have been conducted on qualitative in-situ observation of delamination behaviour and provided useful information, but now quantitative measurements of the crack tip behavior are needed. Some authors have presented techniques to measure local crack tip parameters such as strain fields and COD, but most have some limitations: the global load or displacement is not measured, the specimen is not standard size, the zone where the measurements are taken is too far from the crack tip or too limited in size, there are few tests or measurements, the loading is limited to mode I only, etc. Ferguson is the only one who took extensive measurements of both COD and CSD profiles on the full distance from the crack tip where the rm singularity applies, under mode I, mode II and mixed-mode loading, and measured the applied displacement as well. This allowed him to compare the global and local behaviour under different loading conditions. The present thesis builds on the technique and results developed by Ferguson (1991), by improving the testing and analysis method. -29-Chapter 2 Literature Review 2 c e E o U 8 2 s o> u W 2-1 H u ss u U 13 u o S3 •§ CS CU p , f3 Q .Ji O "E 8^ o. S o> u n. 1/3 go a .a 0> c > -a •s o = 2 e e -£ , 3 o H 5 u u e E •c a x W 50 JD 0 « 1 I 2 C a. — "2 "O b c = E •a o IS s = * 2 G E b = C C3 O) u s 0) M C M 0) as <3 2 -O N a O N N O D J O N oo — O N U _ C3 73 ^5 oo w _i; X) -O .3 T3 ( O l l U f f l o u -30-C3 60 00 ^ H oo o ^ CO C VI ~ aj oj (D Q £ Q •C 'C m CQ b b O N S O N 2> — f*~. O N CQ S*C" 00 Chapter 2 Literature Review 2.5 Figures </> in a> c sz O) 3 o 2500 2000 --I 1500 --1000 brittle tough in o Q. E o u 500 -F o-K B + • • • • • Mode I • Mode II Composite toughness = Resin Toughness + + + + + 1000 2000 3000 4000 5000 6000 7000 8000 9000 Neat Resin Toughness (J/m ) Figure 2.1 Variation of Mode I and Mode II delamination fracture toughness with the neat resin toughness, for a variety of composites, from (Bradley, 1989). B. Ductile Resin Figure 2.2 Damage zone size difference in a brittle and ductile resin composite (Bradley and Cohen, 1985). -31-Chapter 2 Literature Review stress diagram for pure mod* I I loading principal normal stress plane -for c o a l e s c e n c e o f t h e m i c r o c r a c k s _ b e g i n n i n g a t t h e u p p e r r e s i n / f i b i n t e r - f a c e 3* r • delamination crack t ip mlcrocracking , the principal i stress plane r ich regi between fibers h a c k l e r o t a t i o n due S m i c r o c r a c k s t o s h e a r 1 o a d i ng b e f o r e r e s i n / f i b e r • f i n a l m i c r o c r a c k c o a l e s c e n c e Figure 2.4 (a) (b) Principal normal stresses ahead of a crack tip in the resin-rich region between plies created by the mode II loading (a), coalescence of microcracks and rotation of hackles due to shear loading (b) (Hibbs and Bradley, 1987) -32-C h a p t e r 2 L i t e r a t u re R e v i e w • i l 6.9 MPa -6.9 MPa. 20.7 MPa -', 13.8 MPa 1 — - — •-» 2.5 mm Ahead crack —» Behind crack 2.5 mo (a) Syy = S 2, mode I. 6.9 MPa 9 MPa —' 0 Pa 13.8 MPa . 0 Pa 9 MPa 2.5 Ahead crack Behind crack 2.5 (b) Sxy - Sy, mode I I . Figure 2.5 Finite element stress contour plots at the crack tip in an orthotropic, elastic split laminate (Corleto et al., 1987). Figure 2.6 Fibre bridging -33-Chapter 2 Literature Review O O O midplane o <2> (a) Lay-up before curing (b) Laminate after curing Figure 2.7 Intermingling of plies during cure in a unidirectional composite (Johnson and Mangalgiri, 1987). ^ f i b e r m u s t b r i d g e Figure 2.8 Formation of fibre bridging by initiation of a defect in the plastic zone in the ply above the original delamination (Johnson and Mangalgiri, 1987). -34-C h a p t e r 2 L i t e r a t u re R e v i e w 140 T 90 4 1 1 1 1 1 1 1 1 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 Crack Length (m) Figure 2.9 Example of a R-curve for a AS4/3501 specimen (Ferguson, 1992). M Figure 2.10 Delaminated specimen with damage zone, stress-displacement damage response and delamination R-curve (Suo et al., 1992). -35-C h a p t e r 2 L i t e r a t u re R e v i e w O'Brien [3] Arcan, Hashin, & Voloshin [6] (a) Cracked lap shear. P > P (b) Edge delamination tension. (c) Arcan. 1 1 __1 Bradley & Cohen ml (d) Asymmetric DCB. Hashemi. Kinloch, Russell ic Street [8] ' & Williams [10] (e) Mixed-mode flexure. (f) Variable mixed-mode. Figure 2.11 Mixed-mode test configurations (Crews and Reeder, 1988) 1 r kJ /m Figure 2.12 Mixed mode delamination criterion for AS4/3501-6 (O'Brien, 1997), from (Reeder, 1994). -36-Chapter 2 Literature Review r (microns) Figure 2.13 Plot of COD Vs r for an applied G 7 of 34.9 J /m 2 (Ferguson, 1992). Figure 2.14 Crack opening displacement measured in fully bridged glass-lead composite. The solid line shows displacement calculated using the measured applied stress intensity factors at initiation (K=0A) and propagation (K=0.9) (Bannister et al., 1992). -37-Chapter 2 Literature Review 0 1 2 3 4 5 6 Vd, pm Figure 2.15 Crack opening displacements as a function of the distance from the crack tip. The solid line shows the square root dependence (Davidson, 1993). 0.5 0.4 0.3 E <o 0.2 0.1 0.0 r + 10 -0 -13 O 2 0 - D - 1 3 • • • • ,o • • •• o o • o • • • 0 OT> o I P © o O C D e o ° % e e © 50 100 r [/xm] 150 Figure 2.16 Crack opening displacements in zinc sulfide containing 10% and 20% of diamond particles (Farquhar, 1994). The applied K is not known. -38-Chapter 3 Experimental Method In order to study the relationship between global applied conditions and local crack tip behaviour, an experimental set-up has been developed (Figure 3.1). The quantitative study of the crack tip is made possible by a loading stage designed to fit inside the chamber of Hitachi S-2300 scanning electron microscope. This permits in-situ observation of the crack tip while a load is being applied. This loading stage is also instrumented to provide measurements of the global applied loads and displacements. The combination of both local and global approaches in this experimental set-up allows us to compare them and establish a relationship. The complete experimental system is composed of a mechanical loading jig, an electronic control system, a data acquisition and analysis system and an image acquisition and analysis system (Figure 3.2). Extensive testing of each component has been performed to ensure their proper operation. 3.1 Specimen preparation A split laminate specimen, also called a double cantilever beam (DCB), is used for mode I, mode II and mixed mode testing (Figure 3.3). Under mode Et loading, this type of specimen is also commonly called an end-notched cantilever beam (ENCB). The stage geometry is designed to accommodate standard size specimens, despite the limitations of the SEM chamber size. The specimen width B is 25.4 mm or less. The length L can be as long as 160 mm in mode I and 70 mm in mode Et and mixed mode. In order for the crack tip to be visible in the scanning electron microscope, the crack length, a, has to be between 5 and 50 mm. The minimum specimen thickness, 2h, is 3.07 mm, corresponding to the minimum loading arms spacing. In deciding the specimen dimensions, care has to be taken that the maximum load and displacement -39-Chapter 3 Experimental Method required will not exceed the load cell and displacement sensor limitations, which will be described later. Nevertheless, all these specifications are well within the ASTM standard guidelines and a regular size specimen can be tested. A typical specimen includes a Teflon crack starter, embedded during manufacture, that acts as a delamination starter crack. The specimen preparation is detailed in Appendix A. Loading blocks are adhesively bonded at the cracked end (Figure 3.3). In the case of mode II or mixed mode loadings, stiffening tabs are also bonded to the specimen in the clamping zone, to prevent the deformation of the specimen. All the tabs are bonded using a jig that ensures good alignment. AF-126 epoxy film adhesive is used and cured at 120°C for 2 hours. Then, the specimen edge is polished using standard metallographic techniques (120, 180, 320, 600 grit); the final stage consists in an aqueous suspension of 0.06 u.m alumina. In order to measure displacements at the crack tip, reference points are needed on the specimen edge and the finer the grid of reference points, the more accurate the measurements will be. For the best combination of accuracy and simplicity of use, we have opted for the deposition of gold through a fine mesh. Copper mesh with 500, 1000 and 2000 openings per inch have been used, which give a grid spacing of roughly 50.8, 25.4 and 12.7 \im respectively. The copper mesh is positioned on the specimen edge. A jig is used to maintain a good contact between the copper mesh and the specimen edge, otherwise the gold can slip under the mesh and the resulting grid is blurred. The assembly is placed in a vacuum evaporator, where a vacuum of 510"5 torr is established and gold is evaporated on the specimen through the mesh. The copper mesh is removed, leaving a gold grid on the specimen edge. -40-Chapter 3 Experimental Method For some tests performed, polysterene latex microspheres of 1 micron diameter were also deposited on the specimen edge, to provide additional and more closely spaced reference points. The specimen is then placed in the loading stage. 3.2 Mechanical testing Photographs of the loading stage are presented in Figure 3.4. One of the principal goals and design criteria was to accommodate a standard size DCB specimen, which was a challenge considering the limited dimensions of the SEM chamber. For this reason, an aluminium vacuum-proof box extends the size of the chamber. The platform can move in two horizontal directions, longitudinal (X) and transverse (Y), so that the crack tip can be localized in the SEM beam. Two knobs are used to control the X and Y movements of the platform. The test is operated in displacement control. The displacements are applied by stepper motors through a gear reduction system. Each of the two loading arms is controlled by a stepper motor. Due to the space limitation, the stepper motors are placed outside the chamber and the shafts go through a sealed lead-through. Universal joints have to be used to accommodate the platform X and Y movements. 3.2.1 Superposition principle Although no mixed mode tests have been conducted for this work, the design of the loading jig allows the simultaneous application of mode I and mode II loads. This is achieved by having two independent loading arms and using the superposition principle (Bradley and Cohen, 1985) illustrated in Figure 3.5. Mode I loads are applied by a symmetric deflection on each arm. Mode II loads are induced by applying a displacement to one end of a DCB specimen while the -41-Chapter 3 Experimental Method other end is clamped (see Figure 3.5). To avoid axial loads, the clamped end has to be free to move axially, and thus, roller bearings are used (see Figure 3.5). Due to space constraints and high load bearing requirements, the number of roller bearings are limited. There are only two contact points on each side of the specimen, which is not enough to ensure a rigid clamp. To provide an effective clamping condition (i.e, no specimen deformation in the clamping zone), steel stiffening tabs are bonded on each side of the specimen. The clamping system has been tested to check that there is no axial strain. A specimen was instrumented with two strain gauges close to the clamping point, on the tensile and compressive sides and loaded up to 100 N in mode TJ. The test was repeated several times and Figure 3.6 shows a typical result. The axial strain, given by (ecompression + £tension) 12, never exceeded 15 microstrains, which is very small compared to the bending strains, which are of the order of 1500 microstrains. 3.2.2 Calculation of the strain energy release rate The superposition of the two loadings results in a mixed mode load. The ratio of mode I and mode II depends on the amplitude of the symmetric and asymmetric components of the deflections. Using the principle of superposition (Bradley and Cohen, 1985), we can separate the mode I and mode II contributions. We then have: P,= {PR + PL). ; Sj={sR+sL) (3.1) 2 PU={PR-PL ); (SRSL) (3.2) 2 -42-Chapter 3 Experimental Method where PR and PL are the right and left arm loads and SR and SL the right and left arm displacements and are experimentally measured. Equations (3.1) and (3.2) can then be used to calculate Pi, Pu, 8} and Sn. Using LEFM, the local conditions in the crack tip area can be predicted from the global parameters such as applied load or deflection, geometry, crack length and material compliance. For an orthotropic DCB specimen under mode I load or mode II load (see Figure 3.5), the expression for the strain energy release rate has been obtained using finite element analysis in conjunction with analytical considerations (Hutchinson and Suo, 1992). We call them GIG and GUG, to indicate that they are calculated from the global values: 3P,S[ (3.3) (3.4) where (3.5) (3.6) Y,{p) = 0.677 + 0.149(p -1) - 0.013(p - \f (3.7) -43-Chapter 3 Experimental Method YI} (p) = 0.206 + 0.078(p -1) - 0.008(p -1) 2 (3.8) where a\y are the plane stress elastic compliance constants for the laminate: all= — ,a22= — -vn 1 M2 , a 6 6 = ; B is the specimen width and other terms are defined in Figure 3.5. '12 The expression for Gu in equation (3.4) does not take into account the machine compliance Co, which is independent of crack length. To obtain the total measured compliance C, we add the machine compliance Co to the expression of the specimen compliance obtained by Hutchinson and Suo (1992): L3 + 3a3(\ + Yir{p)A-V4-C=C0+- V lEBV (3.9) where E is the laminate flexural modulus. Since and P = S/C, we obtain f2_dC_ IB da (3.10) 9PlI8lIa2\\ + YII{p)V a) AEB2h3Cn + 2B L 3 +3a 3 (3.11) In mode II loading, a significant machine compliance is observed. Co can be obtained experimentally by loading a specimen in mode n, and measuring the compliance, C , for different crack lengths a (Russell and Street, 1987). Since the geometry induces unstable mode II crack -44-Chapter 3 Experimental Method growth, the increments in crack lengths were obtained by unloading the specimen and growing the crack in mode I, then reloading in mode JJ. As observed in Figure 3.7, there is indeed a linear relationship between C and L3 + 3a3^ + YII(p)A~i/4 ^j, which agrees with equation (3.9). Thus Co being equal to the y-intercept, we obtain a value of 4.8-10"3 mm/N. The term EBh3 is evaluated on each specimen from the measured compliance at the initial crack length using equation (3.9). 3.3 Crack tip faces displacements For a cracked anisotropic material, Sih, Paris and Irwin (1965) presented equations to relate the displacements to the stress intensity factor, as well as a relationship between the strain energy release rate and the stress intensity factor, both in mode I and mode U. Thus the crack face displacements in an orthotropic material can be related to the strain energy release rate. The detailed determination of the equations is presented in Appendix B: Equations (3.12) and (3.13) have been derived considering only the first term of the elastic stress singularity, and far from the crack tip, higher order terms will become significant. Note that this first term is a function of rm, whereas the stress and strain singularities are of the order of r'm. (3.12) (3.13) -45-Chapter 3 Experimental Method Equations (3.12) and (3.13) are used to evaluate the local values of Gj and Gu that gives the best fit to the COD and CSD profiles measured experimentally on the SEM images. These values are called Gu and GUL to indicate that they are calculated from the local crack tip conditions. 3.4 Data acquisition and test control During the loading, the applied loads, PR and P L , and deflections, SR and 8L, are continuously measured with a data acquisition system. Four strain gauges are bonded on each load cell (Figure 3.8) and wired in a Wheastone full-bridge connection. The load cells are then calibrated with weights (see Appendix C). The maximum allowable load is 890 N and the minimum measurable load is 0.5 N (accuracy 0.06% FS). The maximum distance that each loading arm can travel is 15 mm from the centre position (Figure 3.9). This gives a maximum applied displacement of 30 mm in pure mode I and 15 mm in pure mode II. Each displacement sensor (see Figure 3.8) is a beryllium-copper cantilever beam in contact with the loading pins. Four strain gauges are bonded on the beam and wired in a Wheastone full-bridge connection. The sensors are then calibrated with a Linear Voltage Displacement Transducer (LVDT) (see Appendix C). They are designed for a maximum displacement of 25 mm and the minimum measurable displacement is 1.5-10"2 mm (accuracy 0.06% FS). An LVDT with 50 mm range is used to measure the position along the crack direction (Figure 3.4). It is attached to the loading stage and thus records the change in the longitudinal position of the stage. At the beginning of the test, readings are taken from a ruler on the jig (see Figure 3.4) which is at a known distance from the loading point. Thus, at any moment, the distance between the loading point and the observed point is known. -46-Chapter 3 Experimental Method During the test, the applied load and displacement as well as the longitudinal position are recorded through a data acquisition board. The stepper motors (see Figure 3.4) are controlled using a stepper motor board and controller. The data acquisition and motor control are accomplished simultaneously in one program, written using the National Instruments Lab View graphical programming language (Figure 3.10). 3.5 Image acquisition Simultaneously with the stepper motor control and the data acquisition, the image of the crack tip provided by the SEM is grabbed in the computer and overlaid with the measurements of the applied conditions (load, displacement, strain energy release rate, position from crack tip, time), using a Coreco Occulus frame grabbing board. The overlaid image is then recorded on videotape (Figure 3.11). In the loading path, small pauses are incorporated in order to ensure a stable image. After the test, the video images of interest can be digitised with the computer, and analysed. Regularly, the loading is paused and the SEM image is recorded using a slow scan digital imaging system, PCI version 4, developed by Quartz Imaging Corporation. The images are then saved onto the computer hard disk. A magnification of 500x is usually used since it provides a good compromise between resolution and size of the viewed area. The resulting images have a significantly better resolution than the video images (1024 x 840 pixels vs. 640 x 484 pixels): for a magnification of 500x, this corresponds approximately to a viewing area of 240 x 200 fim, and one pixel is .24 u.m. However, the process takes more time and memory. The slow scan images are used to obtain the best accuracy in the crack tip displacement at certain load levels. A series -47-Chapter 3 Experimental Method of contiguous images are taken, starting well in front of the visible crack tip and extending to at least 600 pm behind, in order to provide the entire crack tip profile. The video images are used to follow what is happening between these load levels and very close to the critical load where failure will occur very quickly. Since events unfold rapidly, there is no time to take images of the entire crack profile. Instead, we concentrate on one position behind the crack tip. For the same magnification, the viewed area is the same as for the slow scan image. However, since the image is 490 x 470 pixels, the resolution is lower: for a magnification of 500x, a pixel is 0.5 pm. Moreover, the image is noisier. 3.6 Image analysis An image analysis software has been developed to measure on the image the crack opening and crack shear displacements as a function of distance behind the crack tip (Figure 3.12). The LabView graphical programming software was used together with the Concept Vi image analysis library from Graftek Inc. The slow scan images taken at any load level are assembled in a montage using the Ulead PhotoImpact stitching capability (Figure 3.13). The COD cannot be measured directly from the crack faces because the crack faces are often obscured. Thus the increase in distance between gold squares on each side of the crack is monitored instead. The vertical distance between the centroids of two squares on the zero load image is measured and subtracted from the distance between the same squares under load (Figure 3.14). The same technique is used to measure the CSD, with the horizontal distance being used. -48-Chapter 3 Experimental Method The montage is rotated to make sure that the crack is horizontal and cropped to keep only the area of interest. Then the image is thresholded in order to select the squares. Some processing steps are then taken to filter out some small features, leaving only the squares of interest. The centroids of every square is then calculated. The effect of thresholding, processing and calculating the centroids is presented in Figure 3.15. A printout of the screen showing the image analysis software during the thresholding operation is shown in Figure 3.16. The calibration of the image is done by using the distance between 2 centroids which are at least 10 grid spaces apart. A printout of the screen during the calibration operation is shown in Figure 3.17. For the early tests presented in this work, analyzed before the automatic technique for determining the centroids of the square was developed, the calibration was done using the line overlaid on the image by the SEM. It was found that in some instances this line was inaccurate by up to 5% and the results were recalibrated where necessary, using the distance between centroids. Once the calibration is done, the actual measurements can be taken. Using the mouse, 2 squares on each side of the crack can be selected and the horizontal and vertical distance between their centroids is calculated and recorded. A printout of the screen showing the selection of the centroids is shown in Figure 3.18. The measurement can be repeated for other pairs of squares at a different location along the crack. Errors in the measurements are of the order of one pixel, which, for a magnification of 500x, represents 0.24 um. Close to the crack tip, where the strains are high, taking measurements away from the crack faces introduces errors. This error is bigger in mode II since the horizontal displacements close to the crack face are large, while in mode I the vertical displacements close to the crack face are -49-Chapter 3 Experimental Method smaller. Thus, the measurements have to be taken as close as possible to the crack faces, and in an area very close to the crack tip (r < 100 |im), surface features such as dust particles or deposited microspheres are used as reference points, rather than the squares. This requires finding such features and manually selecting them on the unloaded and loaded images: it is very time consuming. This method was used for the first few tests performed. Another solution was therefore adopted: a mesh with increased openings per inch is used to obtain a smaller distance between the squares, which reduces the error. This involves technical difficulties during the grid deposition: since the grid is finer and thinner, it is very fragile and can be easily torn or wrinkled; careful manipulation and improvement to the gold deposition jig were necessary to obtain a good grid definition. The finer available mesh, 2000 opening per inch, resulting in square spacing of 12.7 microns, is used for the later tests. The squares are then close enough to the crack faces that the material displacements are negligible compared to the crack face displacements. 3.7 Summary An experimental method for measuring crack opening and shear displacement has been developed. An instrumented loading jig designed to fit inside a SEM was built. The specimen is a standard size DCB specimen. Mode I, mode TJ and mixed-mode load can be applied. The applied loads and displacements are measured. Using LEFM, the COD and CSD profiles can be calculated from those global values. A gold grid deposited on the specimen edges provides reference points for measuring the crack tip displacements. On the SEM images, the COD and CSD profiles are measured using a semi--50-Chapter 3 Experimental Method automatic image analysis method. These measurements can then be compared with the LEFM analytical predictions. -51-Chapter 3 Experimental Method 3.8 Figures image analysis 1=1! u • V C R H image marked with data image data acquisition test control loading stage SEM Figure 3.2 Schematic of the experimental system -52-Chapter 3 Experimental Method loading tab gold grid clamping tab (b) Figure 3.3 Configuration of the specimens used for (a) mode I and (b) mode II and mixed mode. Figure 3.4 Photograph of the loading jig -53-Chapter 3 Experimental Method Mixed Mode I 1 Figure 3.5 Superposition of mode I and mode II on a D C B specimen. 1500 •ST 1000 c '5 I 500 _^ o 1 w o "<5 co -500 c ri c m -1000 -1500 r* •Compressive bending strain AY A A Tensile bending strain A axial 350 c '5 -5 ~ o o -10 I 'to •"5 X < -20 -25 time (s) Figure 3.6 Results from a strain gauged specimen loaded under mode II. The lines show the compressive and tensile bending strains while the markers show the axial strains. -54-Chapter 3 Experimental Method 0.06 T 0 -I 1 1 1 1 1 1 1 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 L 3+3a 3(1+Y„r 1 / 4h/a) 3 (m 3) Figure 3.7 Relationship between specimen compliance and crack length for determination of machine compliance Co. Figure 3.8 Photograph of the load cells and displacement sensors. -55-Chapter 3 Experimental Method X o o o o o maximum mode I maximum mode II Figure 3.9 Schematic of the loading arms maximum displacements. -56-Chapter 3 Experimental Method Figure 3.10 Algorithm for the Labview control and data acquisition program. -57-Chapter 3 Experimental Method Chapter 3 Experimental Method Initialization Main Menu Exit Open Images File Rotate Image Save Image File Calibrate Image Manual Processing Automatic Processing Manual Measurement Gray Processing ! j Image Threshold [ 1 r Point Measurement Binary Imag e Processing [ 1 > r Angle Measurement ; j Automatic Measurement Figure 3.12 Algorithm showing the usual sequence of processing and analysis steps in the Labview image analysis program. -59-Chapter 3 Experimental Method Chapter 3 Experimental Method UNLOADED LOADED COD = syL-oYu 20 microns CSD = §xL-5Xu Figure 3.14 Measurement of the COD and CSD by the difference in distance between the centroid co-ordinates from the loaded to unloaded image. -61-Chapter 3 Experimental Method -62-Chapter 3 Experimental Method ^jstatt] j|gFtaolmpact Capture - WcfjlahVIEW | | E \5pcc»wi RlNKl pipe j jgJE ASpecjrcm R1\R1 proc j ^Thi^ hoki:.'vt [ gjj 1&55AM Figure 3.16 Printout of the screen showing the image analysis software during the thresholding of the image. Figure 3.17 Printout of the screen showing the image analysis software during the calibration of the image. -63-Chapter 3 Experimental Method Figure 3.18 Printout of the screen showing the image analysis software during the measurements of the COD. -64-Chapter 4 Mode I Results The objectives of the mode I tests are: • to observe the expected square root singularity in the COD profiles close to the crack tip; • to compare GJL to GIG, for starter film and propagated crack tips, for brittle and tough materials, and to propose an explanation for any discrepancies; • to compare the measured CODs with the results of a finite element model, along the entire length of the crack • to study the local crack tip behaviour when there is an increased resistance with crack growth and fibre bridging; in particular, measure Gu for increasing crack lengths and compare it to GIG', if the fibre bridging acts by shielding the crack tip elastically, GIL will be constant with crack length, or if its effect is to increase the resistance to crack growth by dissipating energy during fibre pullout, GIL and GIG will be equal, and increasing. 4.1 Verification of global/local agreement in a brittle material The purpose of this series of tests is to measure the local crack tip displacement field and global applied parameters, during mode I loading, up to and including failure, for a given crack length. The SEM images of a delamination crack tip under different mode I load levels are analyzed to obtain the COD profiles and GIL is determined. By using a brittle material and very short precracks with no fibre bridging, a good agreement between GIL and GIG is expected. 4.1.1 Test description Results are presented for the mode I testing of a DCB specimen of a 24-layer unidirectional AS4/3501-6 CFRP laminate, identified as specimen B l . The COD profiles have been measured -65-Chapter 4 Mode I Resul ts for 10 G /G levels covering 3 crack lengths (insert and small crack growths). The material properties used in the analytical calculations are presented in Table 4.1. The determination of these material properties is presented in Appendix D. The loading path is described in Figure 4.1. The specimen with the initial Teflon starter crack was loaded, until a small amount of crack growth occurred. Thus, the crack was grown by 600 pm in order to create a sharp crack tip without developing fibre bridging. The initial crack length (Teflon insert) is denoted by ai, while the second crack length is called a2. The load was then removed to take images of the unloaded crack a2. Then the crack was loaded again, until crack growth occurred, resulting in a crack length a3. Images were taken at crack lengths ai, a2 and a3, to compare the behaviour of a Teflon film crack tip and sharp crack tips, and during both unloading and loading phases, to study the effect of loading direction and history on the crack tip behaviour. Slow scan images from the SEM were recorded at the following G/G levels, in chronological order: 0, 30, 72, 0 and 69 J/m2 for crack a h 92, 40, 0, 35and 72 J/m2 for crack a2 and 38, 81, 41 and 0 J/m2 for crack a3. After the test, these images were assembled in a montage: a typical image is shown in Figure 4.2. Some of the profile montages are presented in larger size in Appendix F. From these images, the COD versus r profiles were obtained as described previously. 4.1.2 Results COD profiles were generated for ten load levels covering 3 crack lengths (Figure 4.3 to Figure 4.12). Then, equations 3.12 and 3.13 are used to calculate GIL- if it is equal to G /G , the calculated -66-Chapter 4 Mode I Results profile is plotted as a solid line, otherwise, it is plotted as a dashed line. It should be noticed that in all cases, no measurable CSDs were observed, thus only pure mode I is present at the crack tip. The load-displacement curves are presented in Appendix E and they are linear. 4.1.2.1 Square root profile: shape and magnitude Presented in Figure 4.13 is the plot of the COD2 vs. r for an applied G /G of 69 J/m2, demonstrating that the COD varies linearly with the square root of r. All the other nine load levels give the same linear relationship between COD2 and r. all the plots are presented in Appendix E. The data starts deviating from the predicted square root profile at approximately 500 pm behind the crack tip. Beyond this, the higher order terms begin to dominate the profile. This is in agreement with the observations of Ferguson (1992) and Poursartip, Gambone and Fernlund(1996). Moreover, for Figure 4.4 to Figure 4.12, GIL equals G/G. Therefore, for this brittle material and no fibre bridging, all of the applied load is transmitted to the crack tip and there is no local effect not accounted for by the analytical equations. It also confirms that this technique works very well. 4.1.2.2 Effect of insert In Figure 4.3, GIL is roughly half of G/G. This is the very first loading of the specimen and G /G is still low (30 J/m2). Therefore, we believe that the starter film is still sticking to the crack faces, preventing them from opening freely. When the load is increased to 72 J/m2 (Figure 4.4), the sticking force is overcome and GIL equals G /G--67-Chapter 4 Mode I Results However, once a higher load has already been applied, the sticking behaviour is definitively removed, as shown by Figure 4.8 for example. Observing the B l ai images, we can see that, at the insert fibre bundle, some transverse insert fibres are interlocked with the epoxy matrix (Figure 4.14). When the load is increased, they are freed. This effect is even more visible on Figure E.22 (Appendix E). Apart from this initial low load sticking, the insert seems to have no effect on the transmission of the applied loads to the crack tip. There is the same good global/local behaviour agreement for the ai, a2 and a3 sets of results, therefore the insert behaves similarly as a sharp precrack. This agrees with what has been reported in the literature: in mode I, for insert thicknesses greater than 13 microns, the toughness increases with insert thickness, and this is normally associated with the crack tip being more blunt. However, below 13 microns, the toughness stabilizes and is the same as the toughness obtained from a small precrack. Moreover, Ferguson (1992) measured the local COD profiles for specimens where no crack growth had occurred and he found that they were better fit by a linear relationship with r than with rU2. He explained this result by the fact that the insert tip acts as a blunt crack tip and therefore the typical stress singularity is not formed in front of the crack tip. The Teflon insert used by Ferguson was 25 microns thick, which is greater than the 13 microns limit above which the film tip bluntness affects the fracture toughness. The Teflon insert used in this work is 13 microns thick at the tip and therefore the COD profiles follow a rU2 relation and there is good global/local agreement. 4.1.2.3 Effect of decreasing and increasing loads The results for 40 J/m2 (decreasing load, Figure 4.7) and 35 J/m2 (increasing load, Figure 4.8) for 2 2 a2 and for 38 J/m (increasing load, Figure 4.10) and 41 J/m (decreasing load, Figure 4.12) for a3 -68-Chapter 4 Mode I Results are similar and consistent: there is good agreement both in terms of shape and magnitude between the LEFM predictions and the local measurements. Therefore, the loading direction seems to have no effect on the crack tip behaviour. 4.1.2.4 Behaviour at failure After a G /G level of 72 J/m for crack a2, the applied displacement was increased until crack growth occurred, and the SEM images were recorded on videotape. Because events unfold rapidly, there is no time to monitor the same length of crack, so we focused on an area 430 pm behind the crack tip. The measured CODs at r = 430 pm for G /G levels of 109 and 126 J/m2 are plotted in Figure 4.15 and show good agreement with the global predicted magnitudes. Unstable crack growth occurred just after the image at 126 J/m2 was taken. An alternative view is presented in Figure 4.16, which shows the variation of the COD at r = 430 pm with increasing applied displacement. As can be seen, the COD increases linearly with the applied displacement, which indicates linear elastic behaviour right up to failure. 4.1.3 Comparison between global and local behaviour Figure 4.17 presents the relation between Gu and G /G for all loading cases and crack lengths of specimen B l , which summarizes the findings described previously. As we can see, there is a one to one relation between Gu and G / G up to failure. The only exception is for the very first loading, where the insert is believed to stick to the composite, restraining the opening of the crack. -69-C h a p t e r 4 M o d e I R e s u l t s 4.1.4 Comparison with F E M model Because the analytical prediction is only valid very close to the crack tip, a finite element analysis was performed in order to compare the measured crack opening displacements with the FEM predictions along the full length of the crack. The DCB specimen was modeled using the finite element code ANSYS® (version 5.3). A static linear analysis using 6 noded triangular plane stress elements was performed. Due to the stress singularity at the crack tip, the mesh was refined at the crack tip. Figure 4.18 shows the finite element mesh of the upper half of the specimen. The edge length of the elements at the crack tip is 2 pm and the model consists of 1342 elements in total. To model the singularity at the crack tip, the elements around the crack tip had their midside node displaced to the quarter point. This ensures a stress singularity of the form l / V r , in accordance with linear elastic fracture mechanics. Due to the symmetric nature of mode I loading, a symmetry boundary condition was imposed at the midplane of the mesh and the experimentally measured load was applied as two point loads. The model was also run with an applied displacement equal to the experimentally measured one. The material properties are the same as the ones used for the analytical curves (see Table 4.1). The resulting displacements, Uy, at the crack face were used to calculate the CODs as a function of r. They were then compared to the CODs measured on specimen B1 a3 for the same applied load. For the purpose of this comparison, the CODs were measured in a zone extending far from the crack tip, until there was no more grid. The resulting curves are presented in Figure 4.19 for the complete crack and in Figure 4.20 for the crack tip area. We can see that the measured COD are between the COD obtained from the FEM model for the cases of applied load and applied -70-Chapter 4 Mode I Results displacement. The difference between the FEM is probably due to some inaccuracies in the material properties. Nevertheless, they are very close. Figure 4.20 includes the analytical LEFM COD curve, which is valid only close to the crack tip since higher order terms are neglected. As seen, the FEM and analytical curves are very close below 300 microns and start to diverge noticeably at around 400 to 500 microns, which is an indication of the size of the singular zone. This confirms the results from the comparison between experimental measurements and analytical curve mentioned previously, where a singular zone of roughly 500 microns was observed. The model was also run for plane strain conditions, for both the applied load and applied displacement cases. The difference in CODs with plane stress conditions is less than 0.3%, and therefore, negligible. At the edge of the specimen, where we take our COD measurements, plane stress prevails, while the center of the specimen is in plane strain. Since the FEM results show that there is almost no difference in the CODs between plane stress and plane strain conditions, we conclude that the CODs measured on the edge of the specimen are representative of the CODs experienced at the center of the specimen. 4.2 Behaviour of a tougher material A tougher material was tested in order to study the relationship between the increase in toughness and the local crack tip behaviour. Bradley (1989) has explained the increase in toughness in some materials by observing the failure micromechanisms. He observed more microcracking in front of the crack tip in tougher materials. This larger damage zone would yield more load redistribution in front of the crack tip and thus a lower strain at the crack tip. Therefore, a higher -71-Chapter 4 Mode I Results load can be applied before failure occurs. If there is such a load redistribution, the COD profile behind the crack tip would be affected and would not agree with the LEFM prediction. 4.2.1 Test description A IM7/8551-7 unidirectional CFRP laminate, called T4, was tested. This resin is a toughened epoxy, with rubber particles at the interfaces between plies. The material properties used in the analytical calculations are presented in Table 4.1 and their determination is described in Appendix D. The loading path is described in Figure 4.21. In this test, no precrack was created, so the crack tip is directly at the end of the Teflon. Slow scan images were recorded at the following G/G levels: 92, 175, 257 and 340 J/m2. 4.2.2 Results From these images, the COD profiles were obtained as described previously. They are presented in Figure 4.23 to Figure 4.26. The load-displacement curves are presented in Appendix E and they are linear. As we can see, the shape of the COD profiles follows a square root dependency. This is better illustrated by Figure 4.27, where the square of the COD is plotted as a function of r for the lowest and highest load levels: there is indeed a linear relationship between COD2 and r. However, we can see that G/L is slightly lower than G/G (Figure 4.28). This difference is more pronounced for the lower loads, and this might be linked to the sticking behaviour of the insert during initial loading mentioned in the previous section. Also, the elastic properties of this material are not as well established as the ones for AS4/3501, which could mean some error in the calculations of G/G and G/L. -72-C h a p t e r 4 M o d e I R e s u l t s The only other explanation for this slightly lower magnitude of the COD profiles is the development of a damage zone in front of the crack tip. In Figure 4.29, we can see that, above 257 J/m , some small microcracks develop in front of the crack tip prior to the main crack growth. This was not observed on the brittle specimen B1. However, even at 340 J/m2, those microcracks are still small and limited. They translate on the COD profiles (Figure 4.25 and Figure 4.26) by small COD measurements in front of the crack tip. The fact that the extent of this microcracking is small can be linked to the small reduction in the magnitude of the COD profiles. However, microcracking and reduction in COD magnitude are not enough to explain the high toughness of this material, which is almost 4 times the toughness of AS4/3501: the effect on the COD profiles should be much bigger. For example, at 340 J/m2, the COD profile corresponds to a local G / of 290 J/m , which is still much higher than the toughness of a brittle material such as AS4/3501. Therefore, we must conclude that the high toughness of this material is due for the most part to the capacity of the resin to sustain higher strains, rather than crack tip blunting due to microcracking. 4.3 Mode I resistance curve The objective of this test is to study the relationship between the increase in G / C G due to crack growth and the local crack tip behaviour. More precisely, we would like to see if the increase in GicG is due to a reduction in the crack driving force or to an increase in the energy consumed in crack propagation, which are the left hand side and right hand side terms in the following condition for crack growth equation: -73-Chapter 4 Mode I Results GlL = GIcL (4.1) where Gu is the local strain energy release rate obtained from the COD profile and GUL the local critical strain energy release rate, both for the actual, fibre bridged system. Globally, we also have, at failure: GlG=GIcG (4.2) where G/G is the global strain energy release rate and G/ C G the value of G/G at failure. In the first case, when the fibre bridging reduces the crack driving force, we get from the superposition of displacements principle (see Chapter 1, equation 1.8): 4G7L=4G~^-4GTB (4.3) where G/G is the global strain energy release rate and G/B is the strain energy release rate due to fibre bridging. This stress approach implies an elastic behaviour of the fibre bridges. In the second case, when the energy consumed in crack propagation increases, we obtain from an energy balance, GIcL=G0+TB (4.4) where Go is the strain energy release rate for the initial crack with no bridging and TB is the energy consumed by fibre bridging breakage and pullout. This energy approach corresponds to a dissipative behaviour of the fibre bridges. If the fibre bridging behaviour is purely elastic, FB is zero and the criterion for crack growth becomes: -74-C h a p t e r 4 M o d e I R e s u l t s o (4.5) and GicL is constant with crack growth, which means that the COD profile at failure is the same, whatever the crack length. This behaviour is represented by a dashed line in Figure 4.30. When the fibre bridging only dissipates energy, GIB is zero and the criterion for crack growth' becomes: which is represented by the solid line in Figure 4.30. A combination of both is possible, and in that case the failure points will fall in between the two bounding cases. 4.3.1 Test description It has been shown (Russell, 1986) that a specimen with a higher volume fraction will have a greater increase in resistance to fracture with crack growth because, as the plies are closer together, more fibre bridging occurs. Several methods yield a higher volume fraction material, but the simplest way is to bleed out more resin during the cure by using more bleeder1 layers (Russell, 1986). Therefore an AS4-3501/6 specimen with 26 plies manufactured using 15 bleeder plies was used here. It is identified as R l . The specimen was loaded in mode I until crack growth was observed in the SEM, then immediately partially unloaded. This process was repeated until the crack growth had reached 47 mm. For 5 crack lengths, called ci to C5, slow scan images are recorded, at G/G levels L i Layer of absorbing material placed around the laminate to absord any excess resin during processing. GIL ~ GIcL ~ G IG (4.6) -75-Chapter 4 Mode I Results (=80 J/m2), L 2 (-260 J/m2) and L 3 (=400 J/m2), when possible (see Table 4.3). After the test, the COD profiles are measured from the slow scan images. With the superposition principle (see Figure 1.5), GIG is the global energy release rate calculated for the unbridged case (Pi, SW) rather than the actual measured (Pi, S,). Since we do not have 5W, we have calculated GIG for this test using Pt only (Hutchinson and Suo, 1991), instead of equation (3.3): UP'a'h + YAp)^4)2 GIG= 2 \ (4-7> 4.3.2 Results The R-curve obtained is presented in Figure 4.32. It can be seen that there is a clear increase of GicG with crack growth: it is multiplied by almost 6. The toughness increases very steeply at first, then less and less steeply until it reaches a plateau. The load-displacement curve, typical of mode I propagation tests, is presented in Appendix E. The COD profiles for crack lengths C i to C5 are presented in Figure 4.33 to Figure 4.37. Each series of dots corresponds to one level of GIG applied. When there was good agreement between Gu and GIG, the COD profile predicted analytically is plotted as a solid line. Otherwise, the dotted lines represent the same equation, but the value of GIL is adjusted to obtain a better fit to the COD values. Table 4.3 shows the values of GIL for the different crack lengths and applied, or global, GIG levels. -76-C h a p t e r 4 M o d e I R e s u l t s For the crack length C i (Figure 4.33), which is directly at the Teflon tip, the COD profile is in good agreement with the analytical curve for GIL=GIG=19 J/m2, both in terms of shape and magnitude. All the load is transmitted to the crack tip, since there is no fibre bridging. For C2 and c3 (Figure 4.34 and Figure 4.35), we can see that at L i , Gu is close to GIG- Thus, up to L i , all the applied load is transmitted to the crack tip. However, as G/c is increased to L2 and L3, we have GH<GIG- This means that fibre bridging is restraining the crack tip opening. For C4 and C5, the reduction is even greater. First, at L i , there is already a reduction in GIL- AS GIG increases to L 2 and L 3 , GIL is barely increasing. For c2, c 4 and c5, some fibre bridging is observable directly on the images. A close-up of these fibre bridges has been included on Figure 4.34, Figure 4.36 and Figure 4.37, with an arrow indicating the position of the fibre bridge. The COD profiles invariably show an inflection point right at the position of the fibre bridge: behind it, the COD profiles open up. 4.3.3 Behaviour close to failure The results for specimen B l (no bridging) and for the 5 crack lengths of specimen RI are presented as a plot of GiL vs. GIG in Figure 4.38. GicL is obtained from video images (failure points, hollow markers) and therefore have less precision, thus error bars showing the standard deviations are included. Since events unfold rapidly at failure, the video images concentrate on one position behind the crack tip of the crack and we do not see if the crack is growing at the crack tip. Therefore, it is difficult to determine the exact moment of failure: the COD might be measured on an image where the crack is already growing, and therefore is overestimated. In the present case, we know that this is more likely for -77-Chapter 4 Mode I Results the short crack cases (c2 and c3) where the events occurred more rapidly. Especially, G /L c for c 2 might be higher than the real value. As we can see on Figure 4.38, for C 3 , c 4 and C 5 , those last points seem to continue the almost linear trend set by the GUJGIG relationship obtained for lower loads. Moreover, as the crack length increases, the curve is moved downward: the longer the crack length, the lower the Gu at which there is deviation from a GIL=GIG relation and the closer G / C L is to Go. Therefore, for longer crack length, failure points are similar to the elastic fibre bridge behaviour illustrated in Figure 4.30 and the dominant effect is the elastic shielding from the fibre bridges. 4.3.4 Specimens with smaller increase in toughness with crack growth Two AS4/3501 specimens similar to R l , but with less volume fraction, and therefore less increase in toughness with crack growth, were also tested (see Appendix E). The resistance curve increase was much less than with the R l specimen. A difference between G/G and Gu was also noticed, but only for the longest crack length on one specimen. This is not surprising, since there is less increase in toughness and therefore less fibre bridging and the applied G/G levels are not very high. Thus the reduction in Gu is less noticeable. 4.4 Summary Mode I tests were conducted on an AS4/3501-6 unidirectional material, and, as expected from LEFM, the crack tip CODs exhibited a square root shape, for roughly 500 pm behind the crack tip. Good agreement was obtained between G/L and G/G- The only exception is for the first loading from the insert, at low loads, where G/L is smaller than expected because the insert is sticking to the crack faces. For this material, the behaviour remains linear elastic up to fracture. -78-Chapter 4 Mode I Results Also, the COD profiles agreed well with the results from a finite element model along the entire crack length. A specimen with a higher fracture toughness was also studied. The GIL is slightly lower than the GIG- This result can be linked to the fact that some microcracking develops in front of the crack tip, redistributing the loads in front of the crack tip. However, it is not enough to account for the significantly high toughness of this material, which might simply be due to the capacity of the resin to undergo higher strains. The increase in resistance with crack growth was also studied and correlated with the local crack tip behaviour. Up to an applied GIG around 80 J/m2, GIG and GIL agree well, for small amounts of crack growth. When G/c is further increased, GIL does not increase as much, and for longer crack growth, it barely increases. This confirms that fibre bridges act by keeping the crack closed. Thus the global applied loads are deviated from the crack tip and a higher load can be applied before crack growth occurs. The longer the crack growth, the closer the local GICL is to the initiation toughness Go and, therefore, the more the effect of fibre bridging is due to elastic behaviour rather than dissipative behaviour. -79-C h a p t e r 4 M o d e I R e s u l t s 4.5 Tables Table 4.1 Material properties of AS4/3501-6 and IM7/8551-7 unidirectional laminate Properties AS4/3501-6 IM7/8551-7 Ej 102 GPa 130 GPa E2 9GPa 8.3 GPa vI2 0.3 0.34 Gl2 7.1 GPa 4.85 GPa Table 4.2 Characteristics of specimens B l , T4 and R l Specimen B l Specimen T4 Specimen R l material AS4/3501-6 IM7/8551-7 AS4/3501-6 V>(%) 59 61 67 grid spacing (pm) 50.8 50.8 25.4 h (mm) 1.77 2.08 1.71 B (mm) 19.36 22.95 18.86 L (mm) 145.5 137.5 131.5 a (mm) 18.8 (ai) 21.7 19.5 (C l) 19.4 (a2) 22.2 (c2) 21.4 (a3) 26.7 (c3) 35.2 (c4) 47.0 (c5) Table 4.3 G/L (J/m2) for the five crack lengths and the three levels of G/G (J/m2) Crack length (mm) GlcG (J/m2) GIG GIG = L 2 GIG ~ L 3 GIG G/L GIG GIL G/G G/L 19.5 (ci) 105 79 80 22.2 (c2) 333 82 70 250 100 26.7 (c3) 458 85 80 252 110 380 160 35.2 (c4) 556 94 70 263 80 400 95 47.0 (c5) 637 99 55 277 60 426 75 -80-C h a p t e r 4 M o d e I R e s u l t s 4.6 Figures a1 S P E C I M E N B1 L O A D I N G a2 a3 crack growth G|C G=96 J /m 2 crack growth iG, c G=126 J /m 2 G,6=81 J /m 2 G l f i=72 J /m 2 =41 J /m 2 Figure 4.1 Description of specimen B l loading path for the tests presented in Figure 4.3 to Figure 4.20. The horizontal steps show where the loading was held constant to perform slow scans in the SEM. Figure 4.2 Montage of the SEM crack tip images for specimen B l (crack a2), for G /G = 72 J/m2. -81-C h a p t e r 4 M o d e I R e s u l t s (A C o o o o -100 8 j 7 --6 --5 --• G|Q = 30 J/m 2 G , L = G , G G L L 100 200 300 400 r ( m i c r o n s ) 500 600 700 800 Figure 4.3 Plot of COD vs. r (distance from the crack tip) for GIG = 30 J/m 2 on specimen B l (ai). Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit. (A C o Q o O -100 8 j 7 --6 --5 4 + • G | G = 72J/m G | L = G | G 100 200 300 400 r ( m i c r o n s ) 500 600 700 800 Figure 4.4 Plot of COD vs. r (distance from the crack tip) for GIG = 72 J/m on specimen B l (ai). Solid line shows COD profile calculated from GIL = GIG--82-C h a p t e r 4 M o d e I R e s u l t s in c o Q O O -100 8 j 7 --6 ---1 - L • G | G = 69 J/m : G| L = G | G 300 400 r ( m i c r o n s ) 500 600 800 Figure 4.5 Plot of COD vs. r (distance from the crack tip) for G/G = 69 J/m 2 on specimen B l (ai). Solid line shows COD profile calculated from GIL = GIG-(A C o Q O O -100 100 200 300 400 r ( m i c r o n s ) 500 600 700 800 Figure 4.6 Plot of COD vs. r (distance from the crack tip) for G/G = 92 J/m on specimen B l (a2). Solid line shows COD profile calculated from GIL = GIG--83-Chapter 4 Mode I Results -84-Chapter 4 Mode I Results Figure 4.10 Plot of COD vs. r (distance from the crack tip) for GIG = 38 J/m 2 on specimen B l (a3). Solid line shows COD profile calculated from GIL = GIG--85-Chapter 4 Mode I Results r (microns) Figure 4.11 Plot of COD vs. r (distance from the crack tip) for G/G = 81 J/m 2 on specimen B l (83). Solid line shows COD profile calculated from GIL = G/G. -86-Chapter 4 Mode I Results -87 -Chapter 4 Mode I Results £ — Crack tip 200 microns G,G= 30 J/m2 G,, = 15 J/m2 -88-Chapter 4 Mode I Results c o Q O O 18 T 16 14 --12 --10 --8 --6 --4 --• G| G= 74 J/m14 A G|G = 109 J/m 2 • G|G = 126J/m 2 G|L= G|Q O unstable A unstable fai lure -100 100 200 300 r (microns) 400 500 600 700 Figure 4.15 Plot of COD vs. r (distance from the crack tip) for G / G values of 74, 109 and 126 J /m 2 on specimen B l (a2). Solid lines show COD profile calculated from GIL = GIG. Figure 4.16 Plot of COD versus applied 8/ at r = 430 pm for specimen B l (a2). -89-C h a p t e r 4 M o d e I R e s u l t s £ a 140 -r 120 + 100 + 80 + 60 + 40 + 20 + 0 - K crack growth G|L=G|G / ' / / / / / Insert sticking 20 40 60 80 GIG (J/m2) from video B1 H 1 100 120 140 Figure 4.17 Plot of Gu vs. G/G for specimen B l , showing that GIL=GIG for all cases but one. The exception occurs for the first loading from the insert and might be explained by the insert sticking effect. -90-Chapter 4 Mode I Results Figure 4.18 Finite element mesh of the mode I DCB specimen, showing the upper half of the specimen, which is symmetric, and 2 successive enlargement of the crack tip area. -91-Chapter 4 Mode I Results 600 j 500 --400 ---100 -1-•FEM, applied load FEM, applied displacement experimental 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 r (microns) Figure 4.19 Comparison between COD profile obtained experimentally on specimen B l (a3) and by finite element method, for applied load and applied displacement conditions. 10 x r (microns) Figure 4.20 Comparison between COD profile obtained experimentally on specimen B l (a3) and by finite element method, in the region close to the crack tip. -92-C h a p t e r 4 M o d e I R e s u l t s 5, S P E C I M E N T4 LOADING crack growth G i c G=435 J/m2 t Figure 4.21 Description of specimen T4 dimensions and loading path of tests presented in Figure 4.23 to Figure 4.27. The horizontal steps show where the loading was held constant to perform slow scans in the SEM. Figure 4.22 Montage of the SEM crack tip images for specimen T4, for G/G = 92 J/m 2 -93-Chapter 4 Mode I Results 14 T 12 + 10 + (0 c o Q O O -100 -2 -L • G| Q = 92 J/m 2 G|L= G| G G, L 600 700 r (microns) Figure 4.23 Plot of COD vs. r (distance from the crack tip) for GIG = 92 J/m 2 on specimen T4. Solid line shows COD profile calculated from GIL = G/G- Dashed line shows COD profile calculated from GIL that gives the best fit. Figure 4.24 Plot of COD vs. r (distance from the crack tip) for GIG = 175 J/m 2 on specimen T4. Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit. -94-C h a p t e r 4 M o d e I R e s u l t s 1 4 T I e-l 1 1 1 1 1 1 1 -100 0 100 200 300 400 500 600 700 r ( m i c r o n s ) Figure 4.25 Plot of COD vs. r (distance from the crack tip) for G/G = 257 J/m 2 on specimen T 4 . Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit. -100 0 100 200 300 400 500 600 700 r ( m i c r o n s ) Figure 4.26 Plot of COD vs. r (distance from the crack tip) for G/G = 340 J/m 2 on specimen T 4 . Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit. -95-C h a p t e r 4 M o d e I R e s u l t s 200 180 160 140 N1o 120 c o o 100 E 80 60 40 20 0 -20 C i o o • G | G = 92 J / m 2 • G i G = 3 4 0 J / m 2 60 J/nri ^ 290 J /m _ • • _ • • T4 1 0 0 200 300 400 r (microns) 500 600 700 Figure 4.27 Plot of COD vs. r for GIG values of 92 and 340 J/m2 on specimen T4 showing the square root dependence over the first 500 microns. 350 j 300 --250 --200 --$ 150 + 100 --50 --0 G,L=G IG T 4 0 50 100 150 200 250 300 350 G I G (J/m2) Figure 4.28 Plot of Gu vs. GIG for specimen T4 showing GIL<GIG in all cases. -96-C h a p t e r 4 M o d e I R e s u l t s GIG=257 J/m2 GIG=340 J/m 2 GIG=GlcG=435 J/m2 50 microns T4 Figure 4.29 SEM images of specimen T4 showing the formation of microcracks in front of the Teflon crack tip. -97-Chapter 4 Mode I Results Figure 4.31 Montage of the SEM crack tip images for specimen RI (crack c5), for GIG = 277 J/m 2. -98-C h a p t e r 4 M o d e I R e s u l t s 680 + 580 + 480 + ~ 380 + O u 280 + 180 + 0.015 0.02 0.025 0.03 0.035 C r a c k l e n g t h (m) 0.04 0.045 0.05 Figure 4.32 R-curve measured for high fibre volume specimen R l . It shows a clear increase of GUG as a function of crack growth. (0 c o Q O U -100 100 200 300 400 r ( m i c r o n s ) 500 600 700 800 Figure 4.33 Plot of COD vs. r (distance from the crack tip) for G / G = 79 J/m 2 on specimen R l (ci). Solid line shows COD profile calculated from Gu = GIG--99-Chapter 4 Mode I Results w c o i_ o I Q O O 10 j 9 --8 --7 --6 --5 --4 --3 --2 --1 l . A - - * * ^ ^ A A 100 J / m 2 * 70 J / m 2 A^ A G | G = 250 J/m1" • G | G = 82 J/m 2 G||_ G | C G = 333 J/m R1 c 2 —<— 500 —I— 600 —I 700 -100 100 200 300 r (microns) 400 Figure 4.34 Plot of COD vs. r (distance from the crack tip) for G/G values of 82 and 250 J/m2 on specimen R l (c2). Dashed line shows COD profile calculated from GIL that gives the best fit. 12 x w c o o I D O O 10 --8 --6 --4 --A • • 1 -100 .1 • G | G = 380 JmT G I G = 252 J/m 2 G | G = 85 J/m 2 •G|L = G | G 160 J/m 2 G|L -AT - — """"" A . " A — A - * " * 110 J/i / r r r* • 85 J/rrf G | C G = 458 J/m 2 Rl c3 100 200 300 400 500 600 700 800 r (microns) Figure 4.35 Plot of COD vs. r (distance from the crack tip) for G / G values of 85, 252 and 380 J/m2 on specimen R l ( C 3 ) . Solid line shows COD profile calculated from GIL = GIG- Dashed line shows COD profile calculated from GIL that gives the best fit. -100-Chapter 4 Mode I Results c o o I Q O O 12 T 10 + 8 + 6 + 4 + 2 + A • _i_9_ Ar -t">-^ . - ' _ . _ - 9 5 J/m" - " " _ - • 80 J/m2 • - " " " 7 0 J/m 2 m G I G = 400 J/m" A G | G = 263 J/m2 • G | G = 94 J/m2 Gu. + + G | C G = 556 J/m R1 c4 — I 1 -100 100 200 300 400 r (microns) 500 600 700 800 Figure 4.36 Plot of COD vs. r (distance from the crack tip) for GIG values of 94, 263 and 400 J/m2 on specimen RI (c4). Dashed line shows COD profile calculated from GIL that gives the best fit. trt C o Q o o 11 A * A A A • 1 A • • • H A • HI n A A 1 A 75 J/mz 60 J/m2 _ nr-"-""' " 55 J/m2 • G IG = 426 J/m2 .4 • G , G GIL GIG = 277 J/mz 99 J/m" G , C G = 6 3 7 J/m' R1 c5 r— 200 300 400 r (microns) ' t f -100 X 500 600 700 Figure 4.37 Plot of COD vs. r (distance from the crack tip) for GIG values of 99, 277 and 426 J/m 2 on specimen RI (c5). Dashed line shows COD profile calculated from GIL that gives the best fit. -101-Chapter 4 Mode I Results 700 600 + 500 4-400 4-E 300 4-200 4-100 + -#~R1 c1 HK-R1 c2 -A - R 1 c3 -•—R1 c4 -•—R1 c5 + B1 o R1 d failure • R1 c2 failure A R1 c3 failure o R1 c4 failure O R1 c5 failure / G I L = G IG difficult to determine if G ! L increasing or crack already growing 100 200 300 400 500 600 700 G I G (J/m2) Figure 4.38 Plot of GJL vs. GIG for specimen RI. Dotted line represents a one-to-one correspondence. Dashed line represents Go. Clear marker are obtained from video images and standard deviation is shown as error bar. -102-Chapter 5 Mode II Results The objective of this series of tests was to compare the GUG and GUL for a brittle material, from the insert and from a grown crack. As shown previously, GUG is calculated from the applied conditions while GUL is obtained from the CSD profile. If all the applied load is transmitted to the crack tip, we should have: GIIG=GIIL Local crack tip phenomena, such as extensive microcracking and significant mode I openings, were observed. Therefore, the effect of these micromechanisms were studied in more detail and quantified. 5.1 Tests description Results are presented for 20 applied GUG levels distributed over 5 crack lengths and three DCB specimens of 24 layer unidirectional AS4/3501-6 CFRP laminate. The loading paths are described in Figure 5.1 to Figure 5.3 and the specimens dimensions, in Table 5.1. The loading is paused at regular GUG intervals to take slow scan images. 5.1.1 Test from the insert and short crack growth A specimen with an insert (B8 a0, was first loaded to GUG levels of 122 and 225 J/m2 and unloaded. The crack was grown 600 um from the insert under mode I loading and then loaded at GUG levels of 225, 326, 363, 423, 480 and 550 J/m2 (B8 a2). The crack was extended 4900 um from the insert and loaded at the following GUG levels: 112, 210, 269, 324, 432, 543, 648 and 770 J/m2 (B8 a3). Finally, the crack was loaded up to failure, which occurred at a GUG of 880 J/m2. -103-Chapter 5 Mode II Results 5.1.2 Test from the insert A specimen ( B l l aO was loaded, from the insert, to GUG levels of 104, 297, 494 and 695 J/m2. Unstable crack growth occurred at 978 J/m . The principal goal was to study the effect of loading from the insert by comparing the results from tests from the insert (B8 ai and B l l aj) with the ones with a grown crack (B8 a2, B8 a3 and B13 ai). 5.1.3 Long precrack test A specimen (B13) with a long crack grown in mode I (ai=44.64 mm) was loaded at GUG levels of 103, 306, 499, 603 and 721 J/m2. Then, unstable crack growth occurred, at a GUG of 833 J/m2. The goal is to study the effect of a large starter crack on the crack tip behaviour. For all tests, slow scan images from the SEM are recorded at the indicated GUG levels, at a magnification of 500x and a resolution of 1024 x 840 pixels. After the test, these images are assembled in a montage: a typical image is shown in Figure 5.4. More montages are shown in Appendix F. From these images, the COD and CSD versus r profiles are obtained as described previously. 5.2 Crack tip behaviour On all three specimens, matrix microcracks (Figure 5.5) are formed ahead of the crack tip in the resin rich region between the fibres as mode II is applied, which is what has been reported in the literature (Hibbs and Bradley, 1987; O'Brien et al., 1989). These microcracks form at a 45° angle to the fibre direction, which is the plane of principal normal stress for a pure mode II loading. Between two microcracks a ligament is created. As the mode II load is increased, the -104-Chapter 5 Mode II Results angle between microcracks and the fibre direction increases. Finally the microcracked zone grows by coalescence of the microcracks at the fibre/matrix interface, either at the top or bottom of the matrix region (Figure 5.5 and Figure 5.6). All these findings are in agreement with studies found in the literature (Russell and Street, 1985; Hibbs and Bradley, 1987; O'Brien et al. 1989). In Figure 5.5, the difference between the zone containing microcracks and the one where the microcracks have coalesced is quite visible: in the first zone, called the damaged zone, the shear displacements are continuous, while they are discontinuous in the coalesced zone. In Figure 5.7, we define the length of the zone grown by coalescence from the initial crack length ao to be rc. The length of the zone containing microcracks that have not coalesced is called Lj. One difficulty encountered was the determination of the crack tip position, because of the presence of the damage zone. In theory, the crack faces' shear displacements should be zero at the crack tip. However, we measured significant shear displacements in front of the crack tip. The damage zone in front of the crack tip makes the crack behave as if it were longer: if we shift the analytical LEFM CSD profile towards the damage zone to a new crack length aeg, we can find a position for which there is a good agreement with the shear displacement measurements. The effective crack size, aeff, is equal to the sum of the initial crack length a0, the coalesced zone length rc and a damage radius that we will call rj (see Figure 5.7): aeff =a0+rc + rd (5-2) The GUG levels were recalculated using aeg instead of a0: the difference was usually small. Nevertheless, all the GUG values presented in this chapter are corrected to take into account Aa = rd+rc. -105-Chapter 5 Mode II Results Since the crack tip position is advancing, it is not possible to plot the CSD as a function of r, the distance from the crack tip. Instead, the CSDs are plotted as a function of x, the position along the crack with an arbitrary origin, the same for all load levels. 5.2.1 CSD profiles CSD profiles were generated for the indicated GUG levels at crack lengths of 18.4 mm (aO, 19.1 mm (a2) and 23.3 mm (a3) for specimen B8 (Figure 5.8 to Figure 5.9) and for specimen B l l ai (Figure 5.10) and B13 ai (Figure 5.11).The grid used for specimen B l l and B13 is four times finer than for specimen B8, thus providing much more accurate measurements. Note that in the damage zone ahead of the crack tip, where there are no well defined crack faces, the crack face shear displacements have to be measured between points just above and below the damage zone. Since the strains in this area are very large, errors can be introduced if the measurements are not taken just above and below the damage. Due to the coarse mesh used for specimen B8, the displacements of the square centroids (see section 3.6) include elastic deformation of the undamaged material. Thus manual measurements very close above and below the damage were used close to the crack tip. At a certain distance behind the crack tip, the magnitude of the manually measured CSDs matched the automatic ones, and the latter were used for the rest of the profile. Since manual measurements require finding appropriate surface features, automatic measurements are more uniform: this explains why part of the CSD profiles for specimen B8 are more irregular. For specimens B l l and B13, the mesh was fine enough to use only the automatic method, and the profiles are smoother. -106-Chapter 5 Mode II Results In Figure 5.8, for some load levels, not enough images were taken in the damage area. This lack of measurements makes the determination of the effective crack tip more hazardous and, in those cases, the local Gu line is not shown. For the GUG levels lower than 200 J/m2, for all specimens, the measured CSD profiles are in very good agreement with the analytical LEFM predictions, both in terms of shape of the curve and in magnitude (Figure 5.8 to Figure 5.11). The good agreement between GUG and GUL indicates that all the load is transmitted to the crack tip and there is no effect from friction. As can be seen, the data starts deviating from the predicted square root profile at approximately 1000 um behind the crack tip. Beyond this, the higher order terms begin to dominate the profile. The length of the zone were the measurements and theoretical curve coincide is reduced for higher GUG levels, since there is more damage, affecting the displacement field. 5.2.2 CSD at failure With specimen B8 a3, the load was increased up to failure and images were recorded on video. Since events unfold rapidly, we focused at one position r behind the crack tip. The measured CSD for Gu levels of 767 and 880 J/m are shown in Figure 5.12. It is not possible to measure the aeffat failure, therefore it is determined using equation (5.2), approximating r</ and rc by linear extrapolation (the linear increase of rj and rc with GUG will be shown later). The analytical predictions obtained fit the experimental measurements reasonably well, demonstrating that the model developed is valid up to failure. -107-Chapter 5 Mode II Results 5.2.3 COD profiles The COD profiles were measured for the indicated GUG levels at crack lengths of 18.4 mm (aO, 19.1 mm (a2) and 23.3 mm (a3) on specimen B8 (Figure 5.13 and Figure 5.14) and for specimens B l 1 ai (Figure 5.15) and B13 ai (Figure 5.16). For a pure mode U test, the COD are expected to be 0. However, all the figures show that this is not the case. There is a significant amount of mode I opening observed. Careful observation of the SEM images suggests that local opening displacements are created by surface roughness features sliding on top of each other (Figure 5.17). LEFM analytical profiles are back calculated from the COD measurements in Figure 5.13 to Figure 5.16, by adjusting the value of GIL until there is good agreement. On all the figures, we notice that the measurements agree well with a square root singularity for a length of roughly 1 mm from the crack tip. Then the CODs seems to reach a plateau. This can be explained by the fact that, at a certain distance behind the crack tip, a maximum surface roughness has been reached and the height of these bumps is roughly constant. On Figure 5.14 (a3), it can be seen that initially, with no mode II load, a mode I component of roughly 7 J/m2 is present. Since the crack has been grown 4 mm from the insert, there is debris preventing it from shutting closed. 5.2.4 Relation between mode I and mode II For all the specimens, the magnitude of the CODs increases with the mode JI load, as the wavy crack surfaces oscillations slide over each other (Figure 5.17). This finding is confirmed in Figure 5.18, where the GIL is plotted against the GUG- When there is only an insert (B8 ai and -108-Chapter 5 Mode II Results B l l ai), Gu is much smaller for the same GUG- This can be explained by the fact that the Teflon insert is smoother than the crack grown in the material. GIL values as high as 33 J/m2 (B8 a3 and B13 aO are measured: this is 25% of G / c , therefore the mode I component is very significant. This would mean that what is thought to be a pure mode II loading is in fact a mixed-mode loading with a significant ratio of mode I. Thus the final failure might be due, at least partly, to the mode I component. Moreover, these high GIL values are measured before unstable failure is reached: GIL at failure is likely to be even higher. On Figure 5.18, the GIL values at failure have been evaluated by linear interpolation and plotted against GUCG (dashed lines) for the 3 cases were GHCG is known. Even though these values are not exact, they show a trend: the higher the GUCG, the lower the mode I component. This would confirm the findings by several authors that Guc from an insert is higher than from a precrack(0'Brien, 1997), since, as we have seen, GIL is lower due to less surface waviness. Figure 5.19 shows the effect, of not knowing that there is a mode I component on the mixed-mode failure envelope, for the 3 failure points shown in the previous graph. The pure mode I value comes from specimen B l (Chapter 4). If we neglect the mode I component, the G//c values are different and there seems to be significant scatter in the data. If the GIL values are included, then each data point is shifted up by a different amount and there is a linear relation between them rather than scatter. Similarly, O'Brien (1997) points out that the scatter in mixed-mode delamination test results for AS4/3501-6 increases significantly for high mode II ratios (Figure 5.20). These points do not take into account a possible local mode I component. According to our findings, the tests with lower Guc would have the highest mode I component. Moving those points to the left (more mode I), and up (addition of G / c) might bring them closer to each other. -109-Chapter 5 Mode II Results A simple model can be developed to model the relation between Gu and GUG (see inset in Figure 5.21), were the surface waviness is characterized by an angle 0. Using equations (3.12) and (3.13), we have the following equation: tan(0) = COD= AjjG^Jr^ CSD AJJ -\JG~JJQ -\[rjf (5.3) where 4 I •yJ7U * 2 2 2a ii a ii {aiia22 ) (5.4) 4Ja7, -A„ =^LdL24 4n 2a J2 + a66 2a + *22 l l l (5.5) and r/ and ru are the distances between the surface oscillations and the COD and CSD profile origins, respectively. We have rn=ri+rd (5.6) where the damage radius is obtained from the shift in CSD profile (r</ will be studied in more detail later) and it increases with GUG-Therefore IL ( A ^ V 1 + ^ tan20 V 'i J TIIG (5.7) -110-Chapter 5 Mode II Results The model is compared to the measurements in Figure 5.21 and the angles 0 giving the best agreement are represented on the surface waviness images in Figure 5.22. 5.3 Crack advance 5.3.1 Microcrack behaviour The angle that the microcracks make with the plane of the crack has been measured in the damage zone for each load level for specimen B8 a3, and is presented in Figure 5.23. We can see that when the microcracks appear, on the left of each curve, they make a 45° angle with the crack. As the load is increased, the microcrack angle increases, up to a maximum of roughly 90° (at the right of each curves), then they fail. Since the ligaments at the right are failing, the curves are moving to the left as the load increases. At the same time, they are becoming more spread out, as the damage zone is growing in length. In Figure 5.24, the microcrack angles are presented for the highest load level, together with the COD and CSD profiles. The CODs start where the microcracks have reached 90°: the crack can only open in mode I once the ligaments have coalesced. Also, the origin of the line of best fit is roughly at the middle of zone containing hackles. Moreover, this point seems to correspond to an inflexion in the hackle angle curve: the slope is less on the left. 5.3.2 Coalescence and damage zone measurements For the lower applied GUG loads, the COD profiles have the same origin with increasing mode II load, since the ligaments created by the microcracking can still withstand an opening load. However, at higher load levels, for specimen B8 (a2 and a3) and B13 ai, the origin of the COD -111-Chapter 5 Mode II Results profile is shifting: the crack is advancing by a distance rc because the microcracks are coalescing. A visual observation of the images confirms that the distance rc obtained from the shift in the COD profiles agrees very well with the length of the coalesced zone. Once the coalescence length rc has been determined from the advance in COD profile, the damage radius rj can be obtained from the effective crack size aeff, following equation (5.2): rd and rc are presented in Figure 5.25 to Figure 5.27 for specimens B8 a3, B l l ai and B13 ai respectively. From the observation of the damage zone on the images (B8 a3), the end of the damage zone has been measured and it can be observed (Figure 5.25) that the distance Ld between the end of the coalesced zone and the end of the damage zone is roughly twice the values rd from the CSD profiles: the damage radius is half of the damage zone length. Looking at Figure 5.28, the coalescence length rc can be compared for all three specimens. On this figure, the values for B8 ai and B8 a2 have been added, despite the lack of many data points and the lower GUG levels, to see if they follow the general trend observed in the other sets of results. We can see that for all of them there is almost no coalescence below 200 or 300 J/m , then there is a linear increase, but the rate of increase is very different for each specimen: high for B13 ai, less high for B8 a3 and B8 a2 and almost 0 for B l 1 aj. Also, if we look at Figure 5.18, we can see that B11 aj has the lowest Gu for the same GUG. For a lower surface waviness, Gu is lower and therefore the ligaments are less likely to reach the limit strain and coalesce. However, the coalescence rate is very different between B8 a2, B8 a3 and B13 ai (Figure 5.28), yet they have very similar Gu to GUG relationships (Figure 5.20). The main difference between them is that B13 ai has the longest precrack, followed by B8 a3 and B8 a2 and B l 1 ai has no precrack. -112-Chapter 5 Mode II Results Therefore, there is a correlation between crack length and rate of coalescence, but we have no explanation for this trend yet. On Figure 5.29, the damage radius is compared for all specimens. The trend is similar for all specimens: steady increase in rj, with a relatively similar rate of increase. The rate of increase is lower for higher GUG'- for B13 ai, rd becomes almost constant above 300 J/m2, for the other specimens, the slope is lower than at the beginning. 5.3.3 Damage zone size modelling By analogy with the plastic zone in metals (Irwin, 1960), Williams (1989) evaluated the damage size in mode I by assuming that the mode I stresses in the damage zone have reached a maximum of <7d, which would be equal to the damage stress measured in an unnotched tensile specimen. This damage stress is analogous to the yield stress in a metal. This approach can be applied to mode II loading: the shear stress in the damage zone is then equal to rd, the shear stress measured in an unnotched specimen loaded in bending when damage appears. This approach can be modified, as proposed by Irwin (1960), to redistribute the load not carried in the damage zone, by assuming that the presence of a damage zone makes the crack displacements larger and stiffness lower, as if the crack were longer, of size aeg = a0 + S (Figure 5.30). The elastic shear stress distribution at the tip of the effective crack size, in the plane 6 = 0°, is: * - = j £ < 5 ' 8 ) -113-C h a p t e r 5 M o d e II R e s u l t s The shear stress in the region 8+ X is limited to the damage stress rd (Figure 5.30). Hence, for r — X, = Td, and equation (5.8) becomes: TJ = rJL- or X = 4i7tX 2K (5.9) The load lost in region A must be carried by region B: (5.10) (8+X)rd=K„ 42nX K (5.11) Replacing rd according to equation (5.9), it follows that S+X = 2X (5.12) S=X = — 2K V Td J (5.13) Therefore 8 is half the length of the damage zone. Since this model does not take into account coalescence of the crack, 8 is the same as the previously defined damage radius (equation (5.2) with rc = 0) and: J _ 2K 'K. * \Td J (5.14) Sih, Paris and Irwin (1965) derived a relationship between Gu and Ku for an orthotropic material: G,r-KH -j= a22 2al2+a66 + -a ii 2a n (5.15) -114-Chapter 5 Mode II Results Thus, combining the Williams and Irwin approaches, we get: _ J _ G 7 / V 2 rd ~ a 2 2lZTd fl,. To evaluate zd, the shear damage stress, short beam shear tests were conducted (see Appendix D). A deviation from linearity on the load-displacement curve was obtained at 67 MPa and failure occured at 101 MPa. By comparison, Adams and Lewis obtained a shear failure strength for AS4/3501-6 of 106 MPa with the Short Beam Shear Test Method and 114 MPa with the Iosipescu Shear Test Method, values which are very close to ours. In the analogy with plastic zone in metals, the shear damage stress is the equivalent here of the yield stress. Therefore, the appropriate value to use for the shear damage stress Td in equation (5.16) is the point of deviation from linearity, with a value of 67 MPa. As mentioned previously, rd values have been obtained experimentally by measuring the shift needed to have agreement between the measured CSD profile and the analytical predictions. The values rd appeared to be roughly equal to half the length of the total damage zone Ld - S+X determined by visual inspection, which agrees well with equation (5.13). Figure 5.31 offers a comparison of the measured rd values with the model: the dashed lines are calculated using equation (5.16) and the elastic properties of AS4/3501-6, for the two bounding values of td obtained by the Short Beam Shear Test, at the deviation from linearity (Td=61 MPa) and at failure (rd=\0\ MPa). All specimens fall in the range between the two bounds. The slope of the model using the deviation from linearity (67 MPa) agrees well with the initial rising part of the A22 + 2a , 2 +#66 2an (5.16) -115-Chapter 5 Mode II Results measured ra, for most specimens. Above G//G=300 J/m2, rj increases with a smaller slope, which would agree better with a model using the failure value of td (101 MPa). 5.4 Delamination resistance curves Figure 5.32 shows the increase in toughness with crack growth (Aa = rd + rc). Up to a value Guo of 100 J/m2, the load increases with no damage. Then, as the load continues to increase, the damage increases and so does the resistance to crack growth. The increase in toughness is steeper for shorter initial cracks. Ideally, the R-curve is thought to be a material property and thus the same irrespective of the initial crack size (Broek, 1987). To illustrate this, on Figure 5.33, the crack extension Aa = rd +rc is plotted to the right and the crack length is plotted to the left. For a given P and S, Gu is plotted as a function of crack length, according to equations (3.3) and (3.11). For the points of final fracture (marked as an X), the value Aa = rd + rc is not known. It was approximated by linear extrapolation from the previous points. Final fracture should occur when (Broek, 1987): ^ - ^ ; G / / = G / / C (5.17) da da which is when the Gu line becomes tangent to the R-curve line (Figure 5.33). When the initial crack length is increased, the slope of the Gu lines is reduced, therefore it is expected that it would be possible to go further on the R-curve line. But as we can see on Figure 5.33, this is not what is happening in our case, since the R-curves are different for different crack lengths. The R-curve difference is due to the fact that Aa = rd + rc is higher for longer crack. As we have seen previously (Figure 5.28 and Figure 5.29), this is mainly due to rc being much higher. In the insert -116-Chapter 5 Mode II Results case ( B l l ai), we have previously pointed out that rc increases less, probably due to the lower G/L- However, the difference between the short and long precrack cases is harder to explain, since they have similar G/L. To characterize the resistance curve, the damage zone can be represented by a series of continuously distributed nonlinear springs (Hutchinson and Suo, 1992). The shear stress r is a function of the shear displacement 6S and this function is identical for each spring. When 8S reaches a maximum Ss0, the spring cannot withstand any load anymore. According to the J-integral conservation (Rice, 1968): where Ss is the shear displacement at the initial crack tip. According to Hutchinson and Suo (1992), differentiating (5.18) yields the spring law: A second order polynomial can be fitted to a curve of Gu vs. Ss and its derivative corresponds to the stress-displacement curve. Since specimen B11 ai experienced almost no coalescence, it is a good candidate to evaluate the t vs. Ss curve. Figure 5.34 shows the curve Gu vs. Ss (the end-opening at x=1080 microns, the initial crack tip) for specimen B l 1 ai. A linear fit through the 4 points gives a slope of 66 MPa. Thus, according to equation (5.19), r would be constant with 5S and equal to 66 MPa, corresponding to a rigid-plastic behaviour of the damaged material (Figure 5.35). This value is G0+^t(Ss)dSs (5.18) (5.19) -117-Chapter 5 Mode II Results extremely close to the value obtained for the deviation from linearity on the load-displacement curve from the short beam shear test. However, some experimental results are not accounted for by this model. In particular, it does not conform to the behaviour observed during coalescence of the microcracks. For example, from the crack growth observed from the COD profile of specimen B8 a3, it is noticed that the ligaments at the initial crack length coalesce at G//=211 J/m2 and Ss0=2 pm. According to equation (5.18), Gu reaches a steady state value when the ligament at the initial crack tip is submitted to its maximum displacement Ss0 and the entire area under the strain softening law has been observed. In our observation, Gu continues to increase after Ss0 has been reached at the initial crack tip. For this reason, it is not correct to take the derivative of the Gu versus Ss curve for specimens B8 a3 and B13 &\ (Figure 5.36) in the zone where coalescence is occurring, because the increase in Ss is due not only to the progression of damage but also to the advance of the crack by coalescence. In Figure 5.36, the slope of Gu versus 8S is effectively decreasing when coalescence starts to occur, confirming that 8S is increasing more rapidly due to microcracks coalescence. This is especially true for B13 ai, which, as we have shown previously, is experiencing considerably more coalescence. We are left with only the two first points of the Gu versus Ss to evaluate the derivative, which lacks precision. We get a constant material stress-displacement curve at a value of 90 MPa for B8 a3 and 65 MPa for B13 ai. The value for specimen B13 a( is very close to the one for specimen B l l ai described earlier, and agrees with the damage stress obtained from the Short Beam Shear Test (67 MPa). The value for B8 a3 is higher, but is still less than the shear strength obtained from the Short Beam Shear Test -118-Chapter 5 Mode II Results (101 MPa). We can see on Figure 5.36 that, below 600 J/m2, B8 a3 and B l l ai have overall a very similar Gu versus Ss curve. This is probably due to the fact that, below 600 J/m2, the coalescence in B8 a3 is still small. If we do a linear fit through the B8 a3 points below 600 J/m2, we get a slope of 52 MPa. We can therefore estimate that the constant material stress-displacement curve for B8 a3 is somewhere between 52 and 90 MPa. Contrary to what is predicted by the model, Gu continues to increase after Ss0 has been reached at the initial crack tip. At subsequent points of crack coalescence, we have measured a Ss0 which is increasing, on all the specimens. This contradicts the assumption for equation (5.18) stating that any point in the damage zone was experiencing the same strain softening law. The experimental results show that as the crack is growing, we are moving along the stress-displacement curve (Figure 5.35) and this has to be taken into account in the model. Thus, as the microcracks coalesce, more damage is created and the ligament can withstand a higher deformation. When we observed the images for B8 a3, we measured an increase in the height of the damage zone at the tail, hd, with the mode U load (Figure 5.37 and Figure 5.38). Thus the height of the damage is increasing, yielding more energy absorption, an increase in Gu and a bigger surface under the strain softening curve. We can also notice on Figure 5.38 that for the highest load, hd decreases while rd doesn't change and rc increases more rapidly: may be we are reaching the steady state point were rd and hd would be constant because all the area under the stress-displacement curve has been used. However, since unstable crack growth occurred right after, it is not possible to confirm this trend. Such an increase in damage height is not observed for B l 1 ai, since there is so little coalescence (the total length of coalescence is enclosed in Figure 5.37). We can consider Ss0 and therefore, -119-Chapter 5 Mode II Results the plateau zone in the R-curve, have not been reached yet and the model is applicable. The height of the damage zone at the tail, hd, is 17.3 microns. For specimen B13 ai, Figure 5.39 shows how hd and r</ are both almost constant for increasing Gn values above 300 J/m while rc is increasing rapidly. This is similar to what is happening for the highest load of B13 ai. At 300 J/m2, rj and hd have attained their steady state values and the damage zone is just moving without increasing in size. We do not know why G//c is still increasing then. 5.5 Summary • CSD profiles have been generated for specimens under pure mode JJ loading. For low applied Gu levels, a square root singularity has been observed for roughly 1000 (im from the crack tip. There is good agreement between GUG and GUL, therefore friction is not reducing the load transmitted to the crack tip. • When Gn increases, 45° microcracks appear in front of the crack tip, forming a long damage zone. At the tail of the damage zone, there is coalescence of the microcracks. The origin of the CSD profile is shifted ahead of the crack tip and goes down to 0 less rapidly: the square root behaviour is less and less pronounced for increasing Gn levels. • COD profiles have been measured, and their magnitude is quite significant, even though a pure mode II is applied. These CODs are due to the waviness of the crack: as crack features slide over each other due to the mode II load, they open the crack. GIL is lower when the crack tip is at the end of the insert than when there is a crack, since there is less waviness. -120-Chapter 5 Mode II Results That could explain why initiation G//c values are found to be higher than propagation ones, since GIL is lower. The variable nature of surface waviness, and therefore, the variable amount of GIL, can also explain the higher scatter in the G//c data in the literature. • The point at which the COD become 0 indicates where the microcracks are intact and have not coalesced: this allows the determination of the length of coalescence,rc. The distance between the origin of the COD profile and the origin of the CSD profile determines the damage zone Above a threshold value of 200-300 J/m2, rc increases linearly. The rate of increase of rc with Gn is almost 0 when there is no precrack, since GIL is lower: coalescence might be provoked by reaching a certain level of crack opening. The rate of increase of rc is higher with longer precracks. As for rd, it increases with GUG in a relatively similar way for all specimens. • Two approaches are taken to try to model the damage zone: - In an analogy with Irwin's plastic zone in metals, it is assumed that the damage zone has the same effect as if the crack was longer and that the shear stress has reached a limit and is constant in the damage zone. The result is that rj should be proportional to Gu, and the rate of increase depends on the shear damage stress and the material elastic properties. The experimentally measured rd increase with Gu at a rate which correspond to a shear damage stress which is in a reasonable range, between the deviation from linearity stress and the failure stress obtained from short beam shear tests. -121-Chapter 5 Mode II Results Invoking the Dugdale model, the damage zone can also be represented by a series of non-linear springs having identical stress-displacement curves. According to the J-integral conservation, the spring law can be deduced from the derivative of the Gu versus CSD at the initial crack tip curve obtained experimentally. We obtained a rigid-plastic damage response with a shear stress of 66 MPa, which is equal to the value obtained from the deviation from linearity in the short beam shear test. -122-Chapter 5 Mode II Results 5.6 Tables Table 5.1 Characteristics of specimens B8, B l l and B13. Specimen B8 Specimen B l l Specimen B13 material AS4/3501-6 AS4/3501-6 AS4/3501-6 V>(%) 59 59 59 grid spacing (pm) 50.8 12.7 12.7 h (mm) 1.82 1.79 1.80 B (mm) 19.93 19.51 19.63 L (mm) 70.0 70.0 70.0 a (mm) 18.4(a,) 19.0 (a2) 23.3 (a3) 18.4 (a,) 44.64 (ai) -123-C h a p t e r 5 M o d e II R e s u l t s 5.7 Figures t \ mode I crack growth 600 pm mode I crack growth 4300 pm Figure 5.1 Description of specimen B8 loading path Specimen B11 unstable crack growth GN c=978 J /m 2 G n=695 J/m2 G M=494 J/m21 G„=297 J/m2 G „ = 1 0 4 J/m2 Figure 5.2 Description of specimen B l l loading path -124-Chapter 5 Mode II Results Specimen B13 unstable crack growth Gllc=833 J /m 2 G„=721 J/m2 71 G„=603 J/m2 j 1 GM=499 J/m2 J ' GM=306 J/m2 j Gi„=1:03 rf6mm/min x m o d e I crack growth Figure 5.3 Description of specimen B13 loading path ^ ™ - ^ ^ ^ ^ ^ 1 9 f i t TEFLON TIP GOLD GRID<^" TEFLON FILM \ " \ CSD —j p * 100 microns Figure 5.4 S E M crack tip image (B8 ai) for Gu = 225 J/m 2 Figure 5.5 S E M image showing microcracks: the damage and coalescence zones are delimited by a transition from displacement continuity across the crack plane to displacement discontinuity. -125-Chapter 5 Mode II Results B8 a , images zone G„ (J/m*) 45° microcracks onset \ w microcracks rotation coalescence 20 microns \ \ \ W ( l< , >! N—L *V 1_ J I;:.::-::- I 269 432 543 Figure 5.6 Mechanisms of microcracks creation, rotation and coalescence (in agreement with Russell and Street, 1985; Hibbs and Bradley, 1987; O'Brien et al. 1989) CSD COD *eff Figure 5.7 Definition of crack tip damage zone parameters. -126-Chapter 5 Mode II Results 20 j 18 -• 16 --14 --In % 1 2 -o ° ft --o 6 --4 --2 --• G|IG = 550 J/m 2 • G|IG = 480 J/m 2 X G|IG = 423 J/m2 • GlIG = 363 J/m 2 GlIG = 326 J/m 2 • GlIG = 225 J/m2 O G|IG = 225 J/m2 A G|IG = 122 J/m2 - GIIL = GIIG 500 1000 1500 x (microns) 2000 2500 Figure 5.8 Plot of CSD vs. x (longitudinal position) for specimen B 8 ( a i and a2). Lines show CSD profiles based on GUL equal to GUG-x (microns) Figure 5.9 Plot of CSD vs. JC (longitudinal position) for specimen B 8 a3. Lines show CSD profiles based on GUL equal to GUG-- 1 2 7 -Chapter 5 Mode II Results 16.0 j 14.0 --12.0 --« 10.0 + o 0.0 - G|| G = 695 J/m2 + G„G = 494 J/m2 X G„G = 297 J/m2 - G|| G = 104J/m 2 G||L = G|| G 500.0 1000.0 1500.0 x (microns) 2000.0 2500.0 Figure 5.10 Plot of CSD vs. x (longitudinal position) for specimen B l l ai. Lines show CSD profiles based on GUL equal to GUG-• GMG = 721 J/m2 x (microns) Figure 5.11 Plot of CSD vs. x (longitudinal position) for specimen B13 ai. Lines show CSD profiles based on GUL equal to GUG--128-C h a p t e r 5 M o d e II R e s u l t s 18 -r 17 --16 --15 --c 1 4 -o •g 1 3 -8 1 2 " O 11 --10 --9 --unstable failure 880 J/m' Aa=rd+rc=1316 u.m 770 J/m Aa=rd+rc=l 100 u.m A G| L G = 770 J / m 2 (Fig. 5.9) • G U G = 770 J / m 2 (video) A G | I G = 880 J / m 2 (video) G M L = G|| G B8 a 3 + + + + + 1500 1600 1700 1800 1900 2000 x ( m i c r o n s ) 2100 2200 2300 Figure 5.12 Plot of CSD vs. x (longitudinal position) for specimen B8 83. Unstable failure occurred at 880 J/m . Lines show orthotropic L E F M prediction based on G// values of 770 and 880 J/m 2. The value /v+rc for 880 J/m 2 has been estimated by linear extrapolation. -129-Chapter 5 Mode II Results £ O i _ u 1 Q O O 5 T 4 + 3 + 2 + 1 + -1 -L • G M G = 550 J/m2 • GUG = 225 J/m2 o G M G = 225 J/m2 A G I I G = 122J/m 2 - - G|i_ 25 J/m 2 • • 12 J/m 2 , ,4 J/m" / - Q H a — • u p ' B8 a 2 Teflon, O O O A 68 a! A A & 0 1000 •+-1*00 A 2000 2500 x (microns) Figure 5.13 Plot of COD vs. r (distance from the crack tip) for specimen B8 (a i and a2) loaded under pure mode II. Dashed lines show COD profiles for GIL that best fit the measurements. 8 -j-7 --6 --^ 5 --I < + E a o o 3 + 2 --1 --A • O • o A • GUG = 770 J/m2 G | I G = 648 J/m2 G N G = 543 J/m2 G N G = 432 J/m2 G , I G = 324 J/m2 G|,G = 269 J/m2 33 J/m 2 A 28 J/m" G l l G : GIL 0 J/m" A * * A A A * A A A £ A " 22 J/m2 J/m2 I r A 50D * #000 * ^  1500 2000 2500 5 J/m" B8 a, 3000 3500 x (microns) Figure 5.14 Plot of COD vs. r (distance from the crack tip) for specimen B8 as loaded under pure mode II. Dashed lines show COD profiles for GIL that best fit the measurements. -130-Chapter 5 Mode II Results 5.0 -r 20 J/m 2 12 J/m 2 8 J/m 2 2000.0 2500.0 x (microns) Figure 5.15 Plot of COD vs. r (distance from the crack tip) for specimen B l l a i loaded under pure mode II. Dashed lines show COD profiles for GIL that best fit the measurements. :i 6 £ 5 + o o E 4 + • G„G = 721 J/m" X G „ G = 603 J/m X G„G = 499 J/rri + GUG = 306 J/m GUG = 306 J/m G, L 26 J/m" 33 J/m" 22 J/m 2 28 J/m 2 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 x (microns) Figure 5.16 Plot of COD vs. r (distance from the crack tip) for specimen B13 ai loaded under pure mode II. Dashed lines show COD profiles for GIL that best fit the measurements. -131-Chapter 5 Mode II Results 50 microns no load M global shear load Figure 5.17 Local opening displacement created under global shear loading -132-Chapter 5 Mode II Results Figure 5.18 Plot of GIL vs. GUG global for specimen B8, B l l and B13. Hollow markers indicate test from insert. The x markers show values at failure (GILC evaluated by linear extrapolation). 140 120 100 80 60 40 20 I 9-S • including opening o neglecting opening B8 a 3, B11 a 1 t B13 a. real G He O fth,, O--100 100 300 500 700 900 1100 1300 -20 -1-G„ (J/m2) apparent G M c Figure 5.19 Effect of neglecting the mode I opening due to surface waviness on the mixed mode failure envelope. -133-C h a p t e r 5 M o d e II R e s u l t s G, k J / m 2 Figure 5.20 Mixed mode failure criterion for A S 4 / 3 5 0 1 (O'Brien, 1997). The arrows show where the data points would move if some local mode I opening due to surface roughness is taken into account. 0 100 200 300 400 500 600 700 G I I G (J/m2) Figure 5.21 Plot of GIL VS. G//G. Dashed lines represent the model. -134-Chapter 5 Mode II Results Chapter 5 Mode II Results 2000 x (microns) Figure 5.23 Microcracks angle for increasing GUG (specimen B8 83). The solid trendlines extremities correspond to the visible edges of the damage zone, while their inflection point is positioned at the origin of the CSD profile. x (microns) Figure 5.24 Relationships between microcrack angle and crack faces displacements. -136-Chapter 5 Mode II Results Figure 5.25 Plot of the coalesced zone length rc, damage radius rd and zone length Ld vs. GUG for specimen B8 83. Figure 5.26 Plot of the coalesced zone length rc and damage radius rd vs. Gn for specimen B l l a i . -137-Chapter 5 Mode II Results 0 100 200 300 400 500 600 700 800 G, I G (J/m2) Figure 5.27 Plot of the coalesced zone length rc and damage radius r<j vs. GUG for specimen B13 ai. 1600 -r 1400 --1200 --~ 1000 -c o o 800 -£, 600 -400 -200 -0 i-0.0 •B11 a1 •B8 a1 -B8 a2 -B8 a3 •B13a1 100.0 a=44.6 mm (crack) a=23.3 mm (crack) a=18.4 mm (insert) 200.0 300.0 400.0 500.0 G„ G (J/m2) 600.0 700.0 800.0 Figure 5.28 Plot of coalesced zone length rc vs. GUG obtained from the shifts in the measured COD profiles from specimens B8, B l l and B13. Hollow markers indicate tests from the insert. -138-Chapter 5 Mode II Results 600 T 900 Figure 5.29 Plot of damage radius r& vs. Gu obtained from the shifts in the measured COD and CSD profiles from specimens B8, B l l and B13. Hollow markers indicate tests from insert. Figure 5.30 Estimate of damage zone size -139-Chapter 5 Mode II Results Figure 5.31 Plot of r</ vs. Gn for specimens B8, B l l and B13. The dashed lines represent the Irwin-Williams model for T4 values of 67 MPa (deviation from linearity) and 101 MPa (failure). Hollow markers indicate test from insert. 0.000 0.001 0.001 0.002 0.002 0 .003 0 .003 Aa=r d+r c (m) Figure 5.32 R-curve for specimen B l l a i , B8 and B13 a i . -140-Chapter 5 Mode II Results Chapter 5 Mode II Results 70 j 60 --50 ---5-40 + Q. ,? 30 --20 --10 + 0 104 J/m" + 297 J/m" A — 494 J/m" A — 695 J/rrf A + A failure displacement § s 0 B11 a! + + 0.000002 0.000004 0.000006 5 s ( m ) 0.000008 0.00001 0.000012 Figure 5.35 Stress-displacement curve characterizing the damaged material in specimen B l l a i . 200 + 100 + -B11 a1 -B8 a3 -B13a1 -no coalescence coalescence + 0.000000 0.000005 0.000010 0.000015 5S (m) 1 0.000020 0.000025 Figure 5.36 Plot of Gu vs. SS at the tail of the damage zone for specimen B8 a3, B l l a i and B13 a i . Specimen B l l a i showed almost no coalescence. -142-Chapter 5 Mode II Results G„=210 J/m 2 G„=269 J/m2 G„=324 J/m2 B8 a, G„=432J/m 2 G„=543J/m 2 G„=648J/m 2 G„=770J/m 2 G,,=306J/m2 G„=499J/m 2 G„=603J/m 2 G„=721 J/m2 B13a, • m B11 a, G„=695 J/m 2 20 microns Figure 5.37 Damage zone height, at the tail of the damage zone (B8 a3, B l l a i and B13 a i ) -143-Chapter 5 Mode II Results 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 G , (J/m 2) Figure 5.38 Damage zone height at the tail of the damage zone, hd, as a function of Gu, for specimen B8 a3. Figure 5.39 Damage zone height at the tail of the damage zone, hd, as a function of Gn, for specimen B13 ai. -144-Chapter 6 Conclusions and Further Work The main objective of this work was to study and understand delamination crack tip behaviour. To achieve this objective, the local crack tip behaviour was quantified and compared to the global behaviour. The conclusions that can be drawn from this work are presented in this chapter, as well as recommendations for future work. 6.1 Conclusions • An in-situ S E M experimental method has been developed. Full size standard delamination specimens can be loaded up to failure in mode I, mode II and mixed mode inside a SEM. The globally applied conditions and the local crack tip displacements can be simultaneously measured and compared. This experimental method is not meant to become a common testing method: the goal is to use it to further the understanding of delamination behaviour. This knowledge can be used to help in defining standard tests for failure criterion determination, to develop tougher materials and to establish design procedures. • The classic L E F M prediction corresponds to the local behaviour for a brittle material with minimal fibre bridging under mode I loading. Extensive testing has been conducted: COD profiles have been measured for 10 G / G levels covering 3 crack lengths (insert and small crack growths) for a brittle material and 4 G / G levels and 1 crack length (insert) for a tougher material. The square root dependency of the CODs for the first 500 pm behind the crack tip has been observed repeatedly. The -145-Chapter 6 Conclusions and Further Work magnitudes of the COD profiles for the brittle material correspond to what is expected from the global applied conditions, right up to failure. The measured C O D profile all the way to the loading points has also been compared to the calculated displacement from a finite element model and the agreement is very good. • The increase in crack resistance with mode I crack growth is explained. The C O D profiles have been measured for 12 G /c levels covering 5 increasing crack lengths. With crack growth, the COD profiles have a lower magnitude than expected due to the closing action of fibre bridges on the crack tip. Therefore, more load can be applied before crack growth occurs and G / C G increases significantly. It appears that crack growth occurs when the COD profile reaches the same magnitude as the critical COD profile of the initial crack with no fibre bridging, and therefore, the behaviour of the fibre bridging is elastic rather than dissipative. • The mode II crack tip behaviour and damage development has been quantified. The C S D and C O D profiles have been measured for 20 GUG levels over 5 crack lengths. The development and coalescence of microcracks in front of the crack tip under mode II loading has been observed and measured. The damage zone size and damaged material stress-displacement behaviour have been modelled. -146-C h a p t e r 6 C o n c l u s i o n s a n d F u r t h e r W o r k • The presence of local mode I under pure mode II loading has significant consequences for material characterization and design. Significant CODs have been measured when the global loading is nominally pure mode U. Their presence can be explained by the roughness of the crack faces. They are reduced when the starter crack consists of the starter film with no precrack. This finding has significant consequences on the development of a standard pure mode U test for the determination of Gnc. Furthermore, the crack waviness should be taken into account at the design stage, and more studies are needed to be able to do this modelling. Manufacturing issues are also involved: the smaller the fibre waviness, the smaller the mode I component induced by the pure mode U loading and the more load the part will be able to withstand. 6.2 Further work Two main areas can be the object of further work: improvements to the experimental method and the use of the method to study other problems of interest. • Several improvements to the experimental method could make the measurements simpler, faster and more accurate. In particular, the video images quality could be increased by removing the present noise and distortions. This would provide valuable quantitative measurements just before failure. • More tests should be conducted to study the effect of various parameters. Tests on tough materials could help explain the mechanisms leading to higher resistance to delamination. -147-Chapter 6 Conclusions and Further Work As a first step, this work has concentrated on unidirectional materials, but real parts have more complicated lay-ups and it would be useful to conduct tests on specimen with various fibre orientations and lay-ups. Finally, as the precrack characteristics has a big influence on the determination of delaminated material toughness, tests should be conducted on specimens with varying insert thickness. • Mixed-mode tests for a series of mode I to mode It ratios should be conducted to study the mixed-mode failure envelopes. In particular, this would provide a crucial knowledge of how the globally applied loads are related to the local mode I and mode II components. As we have seen from the pure mode II tests, the local mode I and mode II components can be different from what is expected from the globally applied conditions. This can have serious consequences on the mixed mode failure envelope, which might explain the widely different failure envelopes presented in the literature. The determination of the failure envelope is essential for design purposes. • Finally, the effect of path dependency (i.e. mode I loading applied before a mode II loading, and vice-versa) on the local crack tip behaviour could also be explored. -148-References Bannister, M. , Shercliff, H., Ashby, M.F., et al, "Toughening in Brittle Systems by Ductile Bridging Ligaments", Acta Metallurgia et Materialia, Vol. 40, No. 7, 1992, pp. 1531-1537. Bradley, W.L., "Relationship of Matrix Toughness to Interlaminar Fracture Toughness", In: Application of Fracture Mechanics to Composite Materials, ed. K. Friedrich, Elsevier Science Publisher, Amsterdam, The Netherlands, 1989, pp. 159-187. Bradley, W.L. and Cohen, R.N., "Matrix Deformation and Fracture in Graphite-Reinforced Epoxies", In: Delamination and Debonding of Materials, ASTM STP 876, ed. W.S. Johnson, ASTM, Philadelphia, PA, USA, 1985, pp. 389-410. Broek, D., "Elementary Engineering Fracture Mechanics", Martinus Nijhoff Publishers, Dordrecht, 1986. Carlsson, L.A. and Gillespie, J.W., Jr., "Mode-U Interlaminar Fracture of Composites", In: Application of Fracture Mechanics to Composite Materials, ed. K. Friedrich, Elsevier Science Publishers, Amsterdam, 1989, pp. 113-157. Corleto, C , Bradley, W. and Henriksen, M. , "Correspondence Between Stress Fields and Damage Zones Ahead of Crack Tip of Composites Under Mode I and Mode TJ Delamination", Sixth International Conference on Composite Materials and Second European Conference on Composite Materials (ICCM & ECCM), London, UK, Vol. 3, 1987, pp. 3.378-3.387. Crews, J.H. and Reeder, J.R., "A Mixed-Mode Bending Apparatus for Delamination Testing", Technical Memorandum, NASA TM-100662, NASA, Langley Research Center, Hampton, Va, 1988. Davidson, D.L., "Micromechanics Measurement Techniques for Fracture", In: Experimental Techniques in Fracture, ed. J.S. Epstein, VCH Publishers, Inc., USA, 1993, pp. 41-59. Davies, P. and Benzeggah, M.L., "Interlaminar Mode-I Fracture Testing", In: Application of Fracture Mechanics to Composite Materials, ed. K. Friedrich, Elsevier Science Publishers, Amsterdam, 1989, pp. 81-112. Davies, P., Moulin, C , and Kausch, H.H., "Measurement of Gic and Gnc in Carbon/Epoxy Composites", Composites Science and Technology, Vol. 39, 1990, pp. 193-205. Dugdale, D., "Yielding of Steel Sheets Containing Slits", J. Mech. Phys. Solids, Vol. 8, 1960, pp. 100-108. Farquhar, D.S., Phoenix, S.L., and Raj, R., "Determination of Fracture Toughness and Bridging Fractions From Crack- Opening Displacement Measurements in Particulate Composites of Diamond in Zinc Sulfide", Acta Metallurgica et Materialia, Vol. 42, 1994, pp. 65-75. -149-References Ferguson, J.S., 1992, "Measurement of Delamination Crack Tip Displacements in G/E Laminates Using Scanning Electron Microscopy", M . A. Sc. thesis, The University of British Columbia, Vancouver, BC, Canada. Ferguson, J.S., Gambone, L.R. and Poursartip, A., "The Influence of Mode of Loading on the Local Crack Tip Behaviour of Delaminations", First Canadian International Composites Conference and Exhibition (CANCOM '91), 1991. Garg, A.C., "Delamination - a Damage Mode in Composite Structures", Engineering Fracture Mechanics, Vol. 29, 1988, pp. 557-584. Gillespie, J.W., Jr., Carlsson, L A . , and Pipes, R.B., "Finite Element Analysis of the End Notched Flexure Specimen for Measuring Mode Ii Fracture Toughness", Composites Science and Technology, Vol. 27, 1986, pp. 177-197. Hashemi, S., Kinloch, A. and Williams, G., "Mixed-Mode Fracture in Fiber-Polymer Composite Laminates", In: ASTM Special Technical Publication 1110, Anonymous, ASTM, Philadelphia, PA, USA, 1991, pp. 143-168. Hibbs, M.F. and Bradley, W.L., "Correlations Between Micromechanical Failure Processes and the Delamination Toughness of Graphite/Epoxy System", In: Fractography of Modem Engineering Materials: Composites and Metals, ASTM STP 948, eds. J.E. Masters and J.J. Au, ASTM, Philadelphia, 1987, pp. 68-97. Hutchinson, J.W. and Suo, Z., "Mixed Mode Cracking in Layered Materials", In: Advances in Applied Mechanics, Anonymous, 1992, pp. 63-191. Irwin, G.R., "Plastic Zone Near a Crack and Fracture Toughness", Proc. 7th Sagamore Conf., 1960, pp. IV-63. Johnson, W.S. and Mangalgiri, P.D., "Investigation of Fiber Bridging in Double Cantilever Beam Specimens", ASTM J. Compos. Technol. Res., Vol. 9, No. 1, 1987, pp. 10-13. Kaute, D.W., Shercliff, H.R., and Ashby, M.F., "Delamination, Fibre Bridging and Toughness of Ceramic Matrix Composites", Acta Metallurgica et Materialia, Vol. 42, No. 7, 1993, pp. 1959-1970. Kohyama, A. and Sato, S., "In Situ Observation of Deformation and Fracture Process for Fiber Reinforced Composites Under SEM", Proceedings of the Ninth International Conference on Composite Materials (ICCM/9), Madrid, Spain, Vol. V (Composites Behaviour), 1993, pp. 903-912. Kortschot, M.T., "High Resolution Strain Measurements by Direct Observation in the Scanning Electron Microscope", Journal of Materials Science, Vol. 23, 1988, pp. 3970-3972. Lee, S. M. , "Mode II Delamination Failure Mechanisms of Polymer Matrix Composites", Journal of Materials Science, Vol. 32, No. 5, 1997, pp. 1287-1295. -150-References Mao, T.H., Beaumont, P.W.R., and Nixon, W.C., "Direct Observations of Crack Propagation in Brittle Materials", Journal of Materials Science Letters, Vol. 2, 1983, pp. 613-616. Martin, R.H., "Composites Structures: A Dual Approach to Design", Materials World., Vol. 3, No. 7, 1995, pp. 320-322. Murri, G.B., Salpekar, S.A. and O'Brien, T.K., "Fatigue Delamination Onset Prediction in Unidirectional Tapered Laminates", In: Composite Materials: Fatigue and Fracture. Third Volume. ASTM STP 1110. Anonymous, Philadelphia, 1991, pp. 312-339. O' Brien, T.K. and Martin, R.H., "Round Robin Testing for Mode I Interlaminar Fracture Toughness of Composite Materials", Journal of Composites Technology and Research, Vol. 15, No. 4, 1993, pp. 269-281. O'Brien, T.K., "Composite Interlaminar Shear Fracture Toughness, Gnc: Shear Measurement or Sheer Myth?", Technical Memorandum, NASA TM-110280, NASA Langley Research Center, January 1997. O'Brien, T.K., Murri, G.B. and Salpekar, S.A., "Interlaminar Shear Fracture Toughness and Fatigue Thresholds for Composite Materials", In: Composite Materials: Fatigue and Fracture. Second Volume. ASTM STP 1012. ed. P.A. Lagace, ASTM, Philadelphia, 1989, pp. 222-250. Poursartip, A., Gambone, L.R., and Fernlund, G., "In-Situ SEM Measurements of Crack Tip Displacements in Composite Laminates to Determine G in Mode I and Mode JJ", Engineering Fracture Mechanics, 1997. Prel, Y.J., Davies, P., Benzeggah, M.L., et al. "Mode I and Mode JJ Delamination of Thermosetting and Thermoplastic Composites", In: Composite Materials: Fatigue and Fracture, ASTM STP 1012. ed. P.A. Lagace, ASTM, Philadelphia, 1989, pp. 251-269. Reeder, J.R., "A Bilinear Failure Criterion for Mixed-Mode Delamination", In: Composite Materials: Testing and Design, Eleventh Volume, ASTM STP 1206, Anonymous, Philadelphia, 1994, pp.303-322. Rice, J.R., "A Path Independant Integral and Approximation Analysis of Strain Concentration by Notches and Cracks", J. of Applied Mechanics, Vol. 35, 1968, pp. 379-386. Russell, A.J., "Micromechanisms of Interlaminar Fracture and Fatigue", NRCC/IMRI Symposium "Composites '86", 1986. Russell, A.J., "Initiation and Growth of Mode JJ Delamination in Toughened Composites", In: Composite Materials: Fatigue and Fracture. Third Volume. ASTM STP 1110. ed. K.R. O' Brien, ASTM, Philadelphia, 1991, pp. 226-242. Russell, A.J. and Street, K.N., "Factors Affecting the Interlaminar Fracture Energy of Graphite/Epoxy Laminates", Proceedings of the Fourth International Conference on Composite Materials (ICCM-IV), 1982, pp. 279-286. -151-References Russell, A.J. and Street, K.N., "Moisture and Temperature Effects on the Mixed-Mode Delamination Fracture of Unidirectional Graphite/Epoxy", In: Delamination and Debonding of Materials, ASTM STP 876, ed. W.S. Johnson, ASTM, Philadelphia, PA, USA, 1985, pp. 349-370. Russell, A.J. and Street, K.N., "The Effect of Matrix Toughness on Delamination: Static and Fatigue Fracture Under Mode II Shear Loading of Graphite Fiber Composites", In: Toughened Composites, ASTM STP 937. ed. N.J. Johnston, ASTM, Philadelphia, 1987, pp. 275-294. Shercliff, FL, Vekinis, G., and Beaumont, P.W.R., "Direct Observation of the Fracture of Cas-Glass/Sic Composites. Part I. Delamination", Journal of Materials Science, Vol. 29, 1994, pp. 3643-3652. Sih, G.C., Paris, P.C, and Irwin, G.R., "On Cracks in Rectilinearly Anisotropic Bodies", International Journal of Fracture Mechanics, Vol. 1, 1965, pp. 189-202. Smith, P.A., Gilbert, D.G., and Poursartip, A., "Matrix Cracking of Composites Inside a Scanning Electron Microscope", Journal of Materials Science Letters, Vol. 4, 1985, pp. 845-847. Spearing, S.M. and Evans, A.G., "The Role of Fiber Bridging in the Delamination Resistance of Fiber-Reinforced Composites", Acta Metallurgica et Materialia, Vol. 40, No. 9, 1992, pp. 2191-2199. Sun, Y.Q., Tian, J. and Anderson, T.L., "In Situ Observation of Delamination Fracture Test in Graphite /Epoxy Composite During Mode II Loading Inside a SEM", Proceedings of the Ninth International Conference on Composite Materials (ICCM/9), Madrid, Spain, Madrid, Spain, Vol. V (Composites Behaviour), 1993, pp. 834-841. Sun, Y.Q., Tian, J., Wang, J.B., et al, "In Situ SEM Study of Microcracking Behavior in Crack Tip Damage Zone of Polymer Matrix Composite", Proceedings of the Tenth International Conference on Composite Materials, Whistler, British Columbia, Canada, Vol. I (Fatigue and Fracture), 1995, pp. 343-350. Suo, Z., Bao, G., and Fan, B., "Delamination R-Curve Phenomena Due to Damage", Journal of the Mechanics and Physics of Solids (UK), Vol. 40, No. 1, 1992, pp. 1-16. Theocaris, P.S., "Elastic Field Around the Crack Tip Measured by Scanning Electromicroscopy", Engineering Fracture Mechanics, Vol. 37, 1990, pp. 739-751. Theocaris, P.S., Stassinakis, C.A., and Kytopoulos, V., "Stress Intensity Factors and Cods Defined by in-Plane Displacements Measured by Scanning Electron Microscopy", Journal of Materials Science, Vol. 23, 1988, pp. 3992-3996. Williams, J.G., "On the Calculation of Energy Release Rates for Cracked Laminates", International Journal of Fracture, Vol. 36, 1988, pp. 101-119. -152-References Williams, J.G., "Fracture Mechanics of Delamination Tests", Journal of Strain Analysis for Engineering Design, Vol. 24, 1989, pp. 207-214. Williams, J.G., "Fracture Mechanics of Composites Failure", Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science, Vol. 204, 1990, pp. 209-218. -153-APPENDIX A Specimen Preparation The specimen preparation involves three major steps: the bonding of the tabs, the polishing of the edge and the deposition of the gold grid. A. 1 Bonding of the loading and clamping tabs Once the specimen is cut to the desired dimensions, loading tabs and, in the case of mode II and mixed-mode, clamping tabs must be bonded to it. A jig is used to ensure a good alignment of the tabs with the specimen (Figure A.l) . The first step is to prepare the jig by cleaning it and applying a mold release agent for epoxy. The bonding surfaces, on the tabs and on the specimen are scrubbed with sandpaper (grit 400) and cleaned with acetone. A piece of adhesive epoxy film (AF-126) is cut to the tab dimension and bonded to it. Then the tabs and the specimen are placed in the jig. After closing the jig, pressure is applied on the assembly by the use of C-clamps. The adhesive is cured in the oven at 250°F (120-125°C) during two hours. The assembly is allowed to cool down before being opened carefully, to avoid propagating the crack. The clamping tabs need to be milled to ensure that the total thickness of the composite, adhesive and tabs just fit in between the clamping rollers. The required thickness is 0.55 inch. A.2 Polishing The edge of the specimen has to remain flat during polishing. Two Plexiglas blocks are placed on each side of the specimen and they are clamped together with a c-clamp. -154-Appendix A Spec imen Preparation Standard metallographic techniques are used for polishing the edge. Sandpaper wheels of grit 120, 180, 320 and 600 grit are successively used. The specimen is rotated by 180° between each step, to be able to see if sanding mark have changed direction, indicating that a finer grit can then be used. The final stage of the polishing is an aqueous suspension of 0.06 pm alumina. Finally, the specimen is cleaned with acetone. The specimen edge is then carbon coated to avoid charging in the SEM of the areas uncovered by the gold grid. The deposition is done in a vacuum evaporator for twenty seconds. The goal of the polishing is to obtain a smooth, scratch free surface which will give uniform SEM images. Overpolishing might create a corrugated surface where the fibers stick out and their edges become very bright on the SEM images. These bright edges are undesirable because they interfere with the image analysis. A.3 Gold grid deposition The goal of this operation is to evaporate gold through a copper mesh placed on the edge of the specimen and obtain a gold grid when the mesh is removed. The difficulty is to ensure a good contact between the mesh and the specimen. Otherwise, the gold slips under the mesh, resulting in an indistinct grid. However, the mesh is very fragile and has to be manipulated careful. A special jig is designed for this purpose (Figure A.2). The specimen is centered in the lower part of the jig, using the shims and side screws. Two bottom screws are used to lift the specimen up. The centering of the specimen with respect to the slot in the top plate is checked. -155-Appendix A Specimen Preparation A curved slotted plate holds the mesh, applying pressure on the mesh edges and stretching the mesh very gently when it is pressed down and flattened. Silicone rubber pieces 1 mm thick are placed on each side of the slot, on the concave side. They stick easily to the slotted plate and to the mesh, yet the bond is not too strong. Since they are compressible, they also ensure a more uniform contact and pressure on the mesh. The mesh, protected by plastic film, is cut into a 3x35mm piece with a scalpel. Using tweezers, it is then placed carefully on the slotted plate silicone rubber, avoiding wrinkle. Then the plate is placed on the lower part of the jig, with the mesh touching the sample. The roof plate is placed above and lightly screwed (the slotted plate remains bent). Then the specimen is pushed up with the bottom screws, slowly bending the slotted plate, until there is contact. The jig is then placed in the vacuum evaporator and gold is deposited during 15 seconds at 30 Amps. Finally, the sample is carefully removed of the jig by unscrewing the bottom screws, lowering the sample and removing the top plates. -156-Appendix A Spec imen Preparation A.4 Figures Figure A . l Photograph of the tab bonding jig. -157-Appendix A Spec imen Preparation CURVED SLOTED METAL PLATE Figure A.2 Photograph of the gold deposition jig. -158-APPENDIX B Derivation of COD and CSD Othotropic Equations Sih et al. (1965) have derived the expressions for the displacement fields in an area close to the crack tip and, for the case of plane problems; they obtained, for the model: iKfixp2^cosd+fi2 sin6-ju2Piyjcosd + pl sinf?) Mi ~Mi (BA) v = K,42rRe [MIQIyl^os6 + p2sind -jl2qx~Jcosd + pl sin#) //, - Mi (B.2) and, for the mode II: u = KH-yj2r Re| 1 Mi-Mi (p2yjcosd + fl2 sin# - pljcosd + p: sin#) (B.3) v = K„42r Rel (q2^JcosO + jU2 sin6?-ql*Jcos8 + px sin6?) Mi ~ Mi (B.4) where Pj=anMj +ai2-al6pj a ii 1j=aiiMj+ — -ai6 (B.5) (B.6) the complex numbers Pj are the roots of the characteristic equation: anp4 -2a 1 6 / / 3 +(2au +a66)ju2 -2a26ju + a22 = 0 (B.7) and ajj(i,j= 1,2,6) are the 6 independent elastic constants. -159-Appendix B Derivation of the COD and CSD orthotopic equations The expressions for jx^ have been obtained by Ferguson (1992) for the case of unidirectional composites. These materials are specially orthotropic, therefore the elastic constants and a 2 6 are zero and equation (B.7) becomes: anju4+(2an+a66)ju2 +a22 =0 (B.8) where a\\=\IE\, a 2 2 =l /£2, a\2=-\nlE\ and a^=Gn for plane stress. Equation (B.8) has two complex and two wholly imaginary roots: / * , = ± ^ ± £ (B.9) A 2a, M 2 = ± , - ^ (B.10) \ 2a, where d = 2a 1 2 + a 6 6 and e = -\j(2al2 +a 6 6) 2 - 4 a n a 2 2 . Ferguson (1992) then derived the equations for the displacements on the crack faces, behind the crack tip, at 0=180°. In mode I, u=0 at #=180°. Substituting equation(B.6), where a 2 6 is zero, into (B.2) and simplifying yields: v^Kjyflr'R.e V1+M2 ju{ju2 a22i (B.ll) Ferguson (1992) has shown that selecting both negative or positive roots of jix and ju2 will not always give real solutions. Therefore, one root must be positive and the other negative, and, after simplifications: -160-Appendix B Derivation of the COD and CSD orthotopic equations tlx+fl2=. -2. A22 2a 1 2+ a 6 6 all a, (B.12) M1M2 = A , 2 2 Ml (B.13) v = K, 2^rana22 2au + a 6 6 a22 a 11 (B.14) Similarly, in mode II, v=0 and 0=180° and : = K„24ran 2al2+a66^ a22 2a 11 V a i i (B.15) Sih et al. (1965) also derived the relationships between the stress intensity factor and strain energy release rate for an orthotropic material: G, = nKj 2 \ana22 ja22 | 2a, 2+a 6 6 an 2au (B.16) 42~ A22 + 2a 1 2 +a66 Mi 2a,, (B.17) Therefore, the COD and CSD can be expressed as a function of the applied G: COD = 2v = -j=2A(ana22y a22 | 2an+a66 au 2an '4T~4g, (B.18) CSD = 2u = ^±L21 4n W22 | 2 A 1 2 + A 6 6 au 2a,, 4r^G^j (B.19) -161-APPENDIX C Load Cells and Displacement Sensors Calibrations C.I Load cells The load cell is attached to a vertical surface in the same way it is attached to the jig. Then increasing weights are suspended to the loading pin and the voltage is recorded. The loading and unloading was repeated 4 times for each load cells. The resulting curves are shown for the left and right load cell in Figure C l and Figure C.2. We can see that the calibration curves are very much linear and repeatable. C.2 Displacement sensors The displacement sensors calibration curves were measured after installation in the jig. The load cell was moved to different position and a LVDT was used to measure the load cell displacement while the displacement sensor voltage was measured. The loading and unloading was repeated twice. The resulting curves are shown for the left and right displacement sensors in Figure C.3 and Figure C.4. The calibration curves are very linear and repeatable. -162-Appendix C Load Cells and Displacement Sensors Calibrations C.3 Figures 700 T 0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600 Voltage (V) Figure C l Calibration curve for the left load cell. 700 x 0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600 Voltage (V) Figure C.2 Calibration curve for the right load cell. -163-Appendix C Load Cells and Displacement Sensors Calibrations 16.00 T 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 Displacement sensor (V) Figure C.3 Calibration curve for the left displacement sensor. 16.00 T -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 Displacement sensor (V) Figure C.4 Calibration curve for the right displacement sensor. -164-APPENDIX D Material Properties D. 1 Determination of the elastic properties A modified three-point bending test based on ASTM standard D790-90 (Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials) was used to determine simultaneously the Young's and shear moduli (Fisher et al., 1981). Different proportions of shear and bending deformations are present at different span-to-depth ratios (SDR): shear is predominant for short SDR while bending is more important for large SDR. Taking into account both bending and shear contributions, we have: 1 L 3 3L k 4E{ wh3 SwhGl2 where k is the slope of the load-displacement curve, L is the support span, h the specimen depth, w the specimen width, E/is the flexural modulus in the fibre direction and Gn is the in plane shear modulus. It is possible to determine E/ and Gn by measuring k for different Llh values. Some corrections have to be made to take into account the contribution of machine compliance and the local indentation of the specimen by the loading and reacting rollers to the specimen deflection. This contribution was determined by an indentation test were the deflection was due only to roller indentation and machine compliance, with no bending or shear stresses being applied. This is achieved placing the specimen on solid flat plate and applying a compressive stress with the loading roller. Therefore, since there is one loading roller and two reacting rollers, the corrected value kcorr to use in equation (D.l) is: -165-Appendix D Material Properties k. measured (D.2) corr 1- measured ^indent where kmeasured is the slope of the load-displacement curve obtained from the three-point bending test and kindent is the slope of the load-displacement curve obtained from the indentation test. The tests were conducted on two specimens from the same plates as the ones use in the delamination tests, AS4/3501-6 and IM7/8551 respectively. Each specimen was tested for 8 different spans, taking care in remaining in the elastic region and not introduce damage. Finally, an indentation test was performed on each specimen. The results for the flexural and shear modulus of AS4/3501 and IM7/8551 are presented in Table D . l . They can be compared with the values provided by the manufacturer (Table D.2). The difference is probably due to differences in the manufacturing: the properties are affected by differences in fibre volume fraction. Figure D.l shows the apparent modulus, calculated using only the first term in (D.l) and therefore neglecting the shear deformation, as a function of span-to-depth ratio. As expected, it is lower than the actual flexural modulus, especially at low span-to-depth ratios. The transverse modulus, E2 and the Poisson's ratio, Vn, used were the ones obtained from the manufacturer, Hercules (Table D.2) D.2 Determination of shear strength A short beam shear strength test has been conducted on 20 AS4/3501-6 specimens, according to the ASTM standard D2344-84 (Apparent Interlaminar Shear Strength of Parallel Fiber Composites by Short-Beam Method). The span-to-depth ratio was 4. For all 20 specimens, the -166-Appendix D Material Properties failure observed was a horizontal shear failure. The shear stress was calculated from two load values: the load at which deviation from linearity occurred and the failure load. The first value is called damage strength and the second is the shear strength. The results are presented in Table D.3. D.3 Determination of fibre volume fraction Table D.4 presents the fibre volume fractions for the material studied obtained by matrix digestion and image analysis. For the matrix digestion method, the fibre volume fraction was measured according to the ASTM D 3171-76 standard. For the image analysis method, Scanning Electron images of a cross-section of the material were taken in the Scanning Electron Microscope, at a magnification of x800. A total of 14 images (11 for TM7-8551) were taken at equal intervals through the thickness for each specimens. The number of fibres in each image was counted manually, then multiply by the fibre cross-section area and divided by the total area of the image. The fibre diameter was provided by the manufacturer. -167-Appendix D Material Properties DA Tables Table D . l Flexural and shear modulus obtained experimentally for AS4/3501 and IM7/8551. AS4/3501-6 IM7/8551 kindent (kN/mm) 42 49 E/ (GPa) 102 130 Gl2 (GPa) 7.1 4.85 Table D.2 Elastic properties for AS4/3501-6 and IM7/8551-7 provided by the manufacturer (Hercules). AS4/3501-6 IM7/8551 Ei (GPa) 138 142 E2 (GPa) 9.96 8.3 G 1 2 (GPa) 7.1 4.55 V l 2 0.3 0.34 -168-Appendix D Material Properties Table D.3 Apparent Interlaminar Damage and Shear Strength for AS4/3501-6 Average value Standard deviation Specimen thickness (mm) 3.53 Specimen width (mm) 6.39 Specimen length (mm) 21.5 Damage strength (MPa) 67.17 2.53 Shear strength (MPa) 101.01 3.15 Table D.4 Fibre volume fractions measured by matrix digestion and image analysis. Method AS4/3501-6 (specimens B) AS4/3501-6 (specimens R) IM7/8551 (specimens T) Vf 56.9 67.4 60.1 digestion (standard deviation) (1.00, 3 samples) (0.00, 2 samples) (2.33, 2 samples) image Fibre diameter 7 pm 7 pm 5 pm analysis 60.3 65.1 54.9 -169-Appendix D Material Properties D.5 Figures 140 -r 120 --100 --80 --£ 6 0 + 40 --20 --0.000 >Flexural modulus + 5.000 Apparent flexural modulus + + + 10.000 15.000 20.000 Span-to-depth ratio, Uh -AS4/3501-6 - ••- IM7/8551 1 25.000 1 30.000 Figure D . l Apparent flexural modulus for AS4/3501 and IM7/8551 as a function of span to depth ratio. The apparent modulus is lower than the actual value because the shear deformation has been neglected, especially at low span-to-depth ratios. -170-APPENDIX E Additional Results All the results not presented in the main body of the thesis because they were repetitious or inconclusive are included here. E. 1 Additional mode I results E . l . l Load-displacement curves The global load versus global displacement curves for specimens B1 (crack lengths ai, a2 and a3) and T4 are presented in Figure E. l to Figure E.5. The figures include the points where COD profiles were generated and the points at which delamination growth was observed in the SEM. These curves show a linear relationship between the load and displacement for both the brittle (Bl) and tough (T4) material. A abrupt drop in the load with crack growth is noticeable on Figure E.3, since the crack growth is large enough (2 mm) to have an effect. It is not noticeable on Figure E.2 and Figure E.5, since the amount of crack growth detected in the SEM is very small. The load-displacement curve for the mode I crack propagation test is shown in Figure E.6, with the points where COD profiles were generated and the points at which delamination growth was observed in the SEM. The result is typical of DCB crack propagation tests performed in a standard load frame. E.1.2 Singularity zone size in the brittle mode I test COD profiles were generated for 10 load levels covering 3 crack lengths on a brittle specimen, as presented in section 4.1. In order to show the singular zone size, the COD 2 vs. r can be plotted. Moreover, the CODs are proportional to the square root of GIL- Thus by normalizing the COD 2 -171-Append ix E Addi t ional Results with respect to GIL, all the profiles should fall on the same curve. Figure E.7 to Figure E.9 show plots of COD /GIL for crack lengths ai to a3. As seen from these figures, the plots are linear with r for a region that extends to approximately 500 microns behind the crack tip, for almost all GIG-For crack length a3 and GIG of 81 and 41 J/m , the region seems to be smaller: approximately 300 and 400 microns respectively. We can therefore conclude that for most profiles, the singularity zone is roughly 500 microns. E.1.3 Results of preliminary mode I resistance curve tests The objective of these tests is to study if the increase in mode I delamination toughness is related to a reduction in crack tip opening due to fibre bridging by to comparing G/G to Gn. E.l.3.1 Tests description The specimen was loaded in mode I until crack growth was observed in the SEM, then immediately partially unloaded. This process was repeated until the crack length was close to 40 mm. Two AS4/3501 specimens were tested: B3 and B5 (see Table E.l). For 3 crack lengths on B3 (ci to c3), and 6 crack lengths on B5 (ci to C6), slow scan images are recorded, at G/G levels varying between 74 and 84 J/m2. After the test, the COD profiles are measured from the slow scan images. E.l.3.2 Results The R-curve obtained for specimen B3 and B5 are presented in Figure E.10 and Figure E. l 1. We can see that there is an increase of G/ C G with crack growth, but it is less pronounced than the -172-Appendix E Additional Results increase observed in the high volume fraction specimen R l (see Chapter 4). The R-curve increase is more important for specimen B3 than for B5. The COD profiles are presented in Figure E.12 to Figure E.14 for crack lengths c i to C3 of specimen B3, and in Figure E.15 to Figure E.20 for crack lengths C i to C(, of specimen B5. Where there is good agreement between G/L and G / G , the COD profile predicted analytically is plotted as a solid line. Otherwise, the dotted lines represent the same equation, but the value of G/L is adjusted to obtain a better fit to the COD values. Table E .2 and Table E.3 shows the values of G/L and G /G for the different crack lengths, for specimen B3 and B5, respectively. Those values are presented graphically in Figure E.21. As we can see, we have good agreement between G/G and G/L in most cases, except B3 Ci and B3 C 3 . In the case of B3 C i , the crack has not been grown yet and therefore, there is no fibre bridging to explain the reduction in the G/L . However, we have seen previously with B1 a i (no crack growth) for G/c=30 J/m (see Chapter 4) that there was a similar reduction during the initial loading, and that it disappeared subsequently. This was attributed to the sticking of the starter film to the crack faces, preventing the crack from opening. Figure E.22 shows how fibre bundles in the Teflon insert are interlocked with the specimens matrix. This might reduce the opening until sufficient load is applied to overcome the interlocking forces. B3 C3 is the longest crack growth. Therefore, the effect of fibre bridging is maximum and it explains the difference between G/L and G/G-For all the other cases, G/G and G/L are equal. We would expect some difference to appear as crack growth increases. However, we observe that the increase in G / C G with crack growth is not -173-Appendix E Addi t ional Resul ts that pronounced, especially in B5. Moreover, the applied G / G is always less than 84 J/m2, and as we have seen with specimen RI (see Chapter 4), the difference between Gn and G / G becomes noticeable when G / G is higher. This is explained by the fact that the fibre bridges become tight only above a certain load level. E.1.3.3 Summary The effect of fibre bridging is noticeable, but not evident, in specimen B3 and not visible at all in B5. This is because the increase in toughness with crack growth is not steep enough. Also, the load levels that we can apply to take slow scan images are limited to the 80-90 J/m2 range, otherwise we get too close to G / C G and the crack might grow. Therefore, it was decided to use a specimen which exhibits more fibre bridging and toughness increase: specimen RI (see Chapter 4) has a higher volume fraction and therefore, more fibre bridging and a more pronounced R-curve. The results obtained with specimen B3 and B5 are consistent with the results obtained from specimen RI, but much less conclusive. E.2 Additional mode II results E.2.1 Load-displacement curves The global load versus global displacement curves for specimens B8 (crack lengths aj, a2 and a3), B l 1 and B13 are presented in Figure E.23 to Figure E.27. The figures include the points where CSD profiles were generated and the points at which unstable delamination growth was observed in the SEM. For specimen B8 and B l l , the curves show a linear relationship between the load and displacement. A abrupt drop in the load with crack growth is noticed when unstable crack -174-Appendix E Additional Results growth occurred. However, for specimen B13, there is a deviation from a linear load-displacement curve prior to unstable crack growth. This can be explained by the larger coalescence growth in this specimen, which reduces the compliance. -175-Appendix E Addi t ional Resul ts E.3 Tables Table E . l Characteristics of specimens B3 and B5 Specimen B3 Specimen B5 material AS4/3501-6 AS4/3501-6 V>(%) 59* 59* grid spacing (pm) 50.8 50.8 h (mm) 1.77 1.76 B (mm) 19.61 19.82 L (mm) 145.5 137.5 a (mm) 18.7 (c,) 18.7 ( c i ) 19.8 (c2) 19.4 ( c 2 ) 39.6 (c3) 22.0 (c3) 24.1 (c4) 29.6 (c5) 37.7 (c6) Vf determination methods described in Appendix D Table E.2 GIL (J/m2) for the three crack lengths of B3. Crack length (mm) G / c G (J /m 2 ) GIG (J/m2) G / L (J /m 2 ) 18.7 (c,) 105 83 50 19.8 (c2) 120 74 71 39.6 (c3) 173 81 60 -176-Appendix E Additional Results Table E.3 GIL (J/m2) for the five crack lengths of B5. Crack length (mm) G / c G (J /m 2 ) G / G (J/m2) G i L (J/m2) 18.7 (ci) 89 74 74 19.4 (c2) 114 72 72 22.0 (c3) 121 83 83 24.1 (c4) 135 75 75 29.6 (c5) 146 81 81 37.7 (c6) 160 84 84 -177-Appendix E Additional Results E.4 Figures 60 " 50 " 40 --13 30 + o 20 --10 --0 C O D profile GIG = 30 J/m 2 •V 4- 4- 4- 4- 4- 4-0.05 0.1 0.15 0.2 0.25 0.3 Displacement (mm) C O D profile GIG = 72 J/m 2 B1 a, 0.35 0.4 0.45 Figure E . l Load-displacement curve for specimen B l (aO showing the points where the C O D profiles were taken (first loading ramp on Figure 4.1). 70 --60 50 Z 40 •a TO 3 3 0 " 20 •-10 --o --crack growth, Aa = 0.6 mm Girr, = 96 J/m 2 +f : C O D profile B1 a * » C O D profile 2 „ .' B1 a, G | G = 9 2 J / m C O D profile g I G = 69 J /m 2 B1 a 2 GIG = 41 J /m 2 B1 ai, a 2 4- 4- 4- 4-0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Displacement (mm) Figure E.2 Load-displacement curve for specimen B l (ai, a2) showing the points where the C O D profiles were taken (second loading ramp on Figure 4.1). -178-Appendix E Additional Results 70 T 60 + 50 + S. 40 + T3 5 30 20 10 crack growth, Aa = 2 mm G , C G = 126 J/m2 | unloading C O D profile GIG = 74 J/m2 A > i C O D profile GIG = 35 J/m2 + + + B1 a 2 H 1 0.1 0.2 0.3 0.4 Displacement (mm) 0.5 0.6 Figure E.3 Load-displacement curve for specimen B l (a2) showing the points where the C O D profiles were taken (third loading ramp on Figure 4.1). 60 T 50 + 40 + 3 30 + o 20 + 10 + C O D profile GIG = 41 J/m2 *** C O D profile GIG = 81 J/m2 C O D profile GIG = 38 J/m2 + B1 a 3 0.1 0.2 0.3 0.4 Displacement (mm) 0.5 0.6 Figure E.4 Load-displacement curve for specimen B l (a3) showing the points where the C O D profiles were taken (fourth loading ramp on Figure 4.1). -179-Appendix E Additional Results 160 j 140 + 120 100 --%, 80 " •o cs ° 60 -40 -20 " 0 -20 crack growth, Aa = 0.7 mm G | C G = 435 J/m: C O D profile GIG = 340 J/m" '. C O D profile GIG = 257 J/m" C O D profile GIG = 175 J/m2 C O D profile GIG = 92 J/m2 0.2 0.4 0.6 0.8 T4 1.2 Displacement (mm) Figure E.5 Load-displacement curve for specimen T 4 showing the points where the C O D profiles were taken (loading ramp on Figure 4.23). -180-Appendix E Additional Results 100 T Displacement (mm) Figure E.6 Load-displacement curve for specimen R I showing the points where the C O D profiles were taken and were crack growth occurred. -181-Appendix E Addi t ional Resul ts -182-Appendix E Addi t ional Resul ts Appendix E Additional Results 1.6 x 1.4 1.2 + 1 + A + • GIG = 38 J/nrT A GIG =81 J/m 2 + G,G = 41J/m 2 —~" analytical L E F M + A + I— -100 0 100 200 300 400 500 600 700 800 900 1000 1100 r (microns) Figure E.9 Plot of C O D 2 / G I L for specimen B l a 3 showing the square root dependency zone. -184-Appendix E Additional Results Figure E.10 R-curve measured for specimen B3. 180 x 0.015 0.02 0.025 0.03 0.035 0.04 crack length (mm) Figure E . l l R-curve measured for specimen B5. -185-Appendix E Additional Results -100 8 j 7 - -6 - -5 - -4 - -3 - -2 - -• G | Q = 8 3 J/m G|L = G | G G|L 100 2 0 0 3 0 0 4 0 0 5 0 0 r (microns) 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 Figure E.12 Plot of COD vs. r (distance from the crack tip) for G / G = 83 J/m 2 on specimen B3 (ci). Solid line shows COD profile calculated from GIL = Gic Dashed line shows COD profile calculated from GIL that gives the best fit. -186-Appendix E Addi t ional Resul ts 7 T I 9*1 1 1 1 1 1 1 1 1 1 -100 0 100 200 300 400 500 600 700 800 900 r (microns) Figure E.14 Plot of COD vs. r (distance from the crack tip) for G/G = 81 J/m 2 on specimen B3 (c3). Solid line shows COD profile calculated from G1L = GIG. Dashed line shows COD profile calculated from GIL that gives the best fit. - 1 8 7 -Appendix E Additional Results -188-Appendix E Additional Results -2 -L r (microns) Figure E.19 Plot of COD vs. r (distance from the crack tip) for G/G = 81 J/m on specimen B5 ( C 5 ) . Solid line shows COD profile calculated from GIL = GIG. -189-Appendix E Additional Results -190-Appendix E Additional Results 100 T 90 + 80 + 70 + 60 + E 3 50 f O 40 + 30 + 20 + 10 + • B5 O B 3 G | L = G I G B3 c 2 B3 c 3 o B3 Ci Insert sticking 10 20 30 40 50 60 70 80 90 100 G,G (J/m2) Figure E.21 Plot of GIL VS. G/G for specimen B3 and B5. Dotted line represents a one-to one correspondence. -191-Appendix E Additional Results -192-Appendix E Additional Results Displacement (mm) Figure E.23 Load-displacement curve for specimen B8 (ai) showing the points where the C O D profiles were taken (loading ramp on Figure 5.1). 450 T Displacement (mm) Figure E.24 Load-displacement curve for specimen B8 (a2) showing the points where the C O D profiles were taken (loading ramp on Figure 5.1). -193-Appendix E Additional Results unstable crack growth Displacement (mm) Figure E.25 Load-displacement curve for specimen B8 (a3) showing the points where the C O D profiles were taken (loading ramp on Figure 5.1). 600 T unstable crack growth GMCG = 978 J/m 10 12 Displacement (mm) Figure E.26 Load-displacement curve for specimen B l l showing the points where the C O D profiles were taken (loading ramp on Figure 5.2). -194-Appendix E Additional Results 0 1 2 3 4 5 6 7 Displacement (mm) Figure E.27 Load-displacement curve for specimen B13 showing the points where the C O D profiles were taken (loading ramp on Figure 5.3). -195-> "TJ TJ m z g x o 3 «-»• Q> CQ CD (0 O CO o 3 CQ CD to > T J a 5" o 3 0) ca w o - I S) o 3 u W aro C •BP mmm mmW mmm u mam mmm mmm -a re O 3 re 3 s*o s WRwW^ I^ WI^ ^^  m^mmmw W f - a ^ ^ R 4^s^s^V f era 3 i re c 3 M T C re O «s M o ts re 03 ers re -! re re re 3 to o o era c - i re O 3 W n 7? 3 u JO rc S5 cn « ft ft 3 ro 3 ca c p o II ON vo (71 • • • • • • • • fl II ff 111 • 1 • • • • lin JB g S I s**^  m • ? if m • • • • i B • • -lM, fjg«f. • • • 1 1 1 • m • • • * mf m i n • • • l i l • • it • ^ • « s i s | • SP J M H P ISM INK WB m m m 111 m m m H I m I 1 I I I m m m mm* I I I Hi 1^ H j§ I I I IP t I I I • • M mum m m m i l l m m m m iii m m m m • • • I I I • • • I I I • • • I I I • I I • • • I M * • If • • i m i n n i 1 1 Bp I " j • J 1 V >«fc I • V * *%m 1 s • % i » £p • te | » *• • fel " f * • r ? | 1 £ • I • B ' l I Jfci P I • • • • I • • • • • • • « « I I I I • I B I I I I I I I 11 • I P P P P I I I H I | p | P P P P P P P P P mm* P P P P P M ppp m m m ppp Jfil Pf P « • • P P P -1 .y; P P P H I • P P i l l H I mm m 111 it p i • p • 111 • p • P P P H I • up n • • P ggjj: • I V I I I I I I • P I I I I Mil « I I • • II I I I P « • P P « ppa p p • p p i • • • erg e rt W o 3 s; JO ft C/3 « 3 JO re 1 I/! 13 re re  3 w c P n II V O | l l m I 1 1 1 • • a Si I P P I I I B P P • i HH iB H i a a • P H g" :^|: :|^: mm (M 111 • « • i i IH ws w m m I • I I I I P I P • • if I I I S • * • P I SP* * ™ I I I 111 I I I • 1 • i l l • I p R S I 111 111 • 11 - p r i ' i ^ 'H' w& I I I i i HI H : X IB *^ 111 gjg H & gp: lb ' HP I I i i l l mi ips n g g • i i • i i • • 1 • • i • ;•>•  ^ is H US 8 • • « JO c re "1 O 3 r»-69 JO ft O W o >-! &5 o 7T p JO re o5 1 "3 re re 3 re 3 CC 5 h P — S3 II O 3 • • • • • • I • • • • • • • • • « • • I P P I • • •I mm m m m ft mm fl^W' P • • • • IB (fc J(i JB P • • • • • • • « « • • P • • • • • p p p p p » P • • • • « « • i • • • P • • • • • • • • • • • P • • • • • p • • • • • • • • 1 1 1 ! 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