A MULTISCALE MODELING APPROACH FOR THE PROGRESSIVE FAILURE ANALYSIS OF TEXTILE COMPOSITES MAO JIAZHEN NATIONAL UNIVERSITY OF SINGAPORE 2014 A MULTISCALE MODELING APPROACH FOR THE PROGRESSIVE FAILURE ANALYSIS OF TEXTILE COMPOSITES MAO JIA ZHEN (B.Eng. (Hons)), NUS A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Mao Jia Zhen 22 Mar 2014 Acknowledgement Acknowledgement This thesis is submitted in fulfilment of the requirement for award of the degree of Doctorate of Philosophy. The research has been carried out at the Department of Mechancial Engineering, National University of Singapore, during the period of Augest 2009 to July 2013. I am deeply indebted to Professor Tay Tong Earn for giving me the opportunity and supervising this work. Especially during the most challenging period of finalising my thesis, without his all-around support and guidance, this work would have never been accomplished. I would also like to thank A/Prof. Vincent Tan Beng Chye, for his invaluable help. The numerous discussions are important to this work. I am very grateful to Doctor Muhammad Ridha and Doctor Sun Xiu Shan for their advices and help. I am truly thankful to Mr. Chiam Tow Jong, Mr. Low Chee Wah and Mr. Abdul Malik Bin Baba for assisting me in my experiments. Lastly, I would like to deeply thank Ms. Wang Xuan, my daughter Mao Dou Dou, my father Mao Cheng Ming and mother Yang Pei Zhi for their love, support and encouragement throughout my life. You are the reason of this work. i Table of Contents Table of Contents Acknowledgement i Table of Content ii Summary…… vi Nonmenclature…… viii List of Figures…… . xiii List of Tables…… xxiii Chapter Introduction and Literature Review 1.1 Introduction to Textile Structural Composites 1.2 Review of Mechanical Modeling of Textile Composites . 1.3 Review of Damage Modeling of Textile Composites . 27 1.3.1 Failure Criteria . 28 1.3.2 Progressive Damage Modeling Techniques . 32 1.4 Aim of the Study . 40 1.5 Scope and Outline . 40 Chapter Multiscale Modeling Approach 42 2.1 Material Property Homogenization Method . 45 2.1.1 Periodic Boundary Conditions . 46 2.1.2 Effective Material Properties . 49 2.1.3 PBC Modeling to a 3D RVE Model 52 2.2 Micro-Mechanical Failure (MMF) Theory . 57 2.2.1 Stress Amplification Method . 57 2.2.1.1 Micro Stresses Calculated from Meso Stresses . 58 2.2.1.2 Meso Stresses Calculated from Macro Stresses 61 2.2.2 Fiber Failure Criterion . 64 2.2.3 Matrix Failure Criterion . 65 2.3 Progressive Damage Modeling . 66 ii Table of Contents 2.3.1 Energe-based Continuum Damage Mechanic Model 69 2.4 Flow Chart 73 2.5 Conclusion 76 Chapter Progressive Failure Analysis of Plain Woven Composites . 77 3.1 Modeling Strategy . 77 3.2 Micromechanical Model . 78 3.3 Mesomechanical Model 85 3.3.1 Geometric Modeling 87 3.3.2 Stress Analysis. 92 3.3.3 Progressive Failure Analysis 100 3.3.4 Validation by Experiment 105 3.4 Macromechanical Model 110 3.4.1 FE Modeling… 110 3.4.2 Simulation Result… . 112 3.4.3 Validation by Experiment… 114 3.5 Conclusion 119 Chapter Progressive Failure Analysis of NCF Composites 121 4.1 Introduction to NCF composites . 121 4.2 Nonlinear Mechanical Modeling of NCF composites 123 4.2.1 Modeling of Elastoplasticity for Epoxy Resin . 124 4.2.1.1 Elastoplastic Constitutive Model 126 4.2.1.2 Parameter Identification . 129 4.2.2 Nonlinear Stress Amplification Method 131 4.2.2.1 Method to Determine Nonlinear Coefficient . 134 4.2.3 Implementation of Nonlinear Multiscale Modeling 135 4.3 Micromechanical Model . 136 4.4 Mesomechanical Model 145 4.4.1 Case degree Laminate . 146 iii Table of Contents 4.4.2 Case Biaxial Laminates 156 4.4.2.1 Simulation Results… . 162 4.4.3 Experimental Verfication . 168 4.5 Macromechanical Model 173 4.5.1 Macroscopic Modeling 173 4.5.2 Simulation Results . 175 4.5.3 Experimental Verification 184 4.6 Conclusion 188 Chapter Extension to Mechanics of Defects in NCF Composites . 189 5.1 Introduction to Defects Mechanics of Composite Materials 189 5.2 Study the Influence of Defects in NCF composites 194 5.2.1 Linear Analysis on Single Laminate 195 5.2.2 Failure Analysis on Biaxial Laminates 200 5.2.2.1 Defect Characterization 200 5.2.2.2 Case [0/90] 2s Laminates . 203 5.2.2.3 Case [±45]2s Laminates . 207 5.3 Conclusion 212 Chapter Conclusions and Recommendations . 214 6.1 Conclusions . 214 6.2 Recommendations for Future Work 217 References . 220 Appendix A Plain Woven Composites Study 243 A.1 Mesh Convergency Study for Plain Woven RVE Model . 243 A.2 Sensitivity Study for Plain Woven Composites 243 iv Table of Contents Appendix B NCF Composites Study 246 B.1 Mesh Convergency Study for NCF RVE Model 246 B.2 Nonlinear COfficients for Meso-to-Micro Stress Amplification 248 B.3 Nonlinear COfficients for Macro-to-Meso Stress Amplification . 251 B.4 Sensitivity Study for NCF Composites . 255 Article by the author Mao J Z, Sun X S, Ridha M, Tan V B C, and Tay T E. A modeling approach across length scales for progressive failure analysis of woven composites. Applied Composite Materials, 20: 213-231, 2013. . v Summary Summary Recent advances in textile composites require the development of a holistic modeling tool, which involves more than one length scale. Over the past decades, a large number of modeling techniques, capable of predicting accurately the mechanical performance of composite materials covering wider range of length scales are available. However, there is still a strong demand for a computational approach to implement the mechanical analysis for a macroscopic structure based on the micro-physical phenomena. With the rapid development of computer power, it is possible to integrate the available modeling tools into a holistic multiscale framework capable of simulating, designing and analyzing the performance of composite materials. In this thesis, a multiscale modeling approach to model the progressive damage in textile composites has been developed. The hierarchical models of textile composites at three different length scales (micro, meso, and macro) are developed with a novel two-way multiscale coupling technique. In this manner, the multiscale stress analysis is performed and the damage mechanisms can be captured within one finite element. Appropriate failure criteria are carefully selected in the present study. In addition, a continuum damage mechanics (CDM) method is used to model the post-failure behavior of the damaged element. The proposed multiscale method is first applied to predict the material stiffness, tensile strength and damage patterns of a central open-hole plain woven laminates. Tensile experiment is conducted to verify the analysis result. Consequently, the progressive vi Summary failure analysis based on a nonlinear multiscale modeling approach is implemented for the non-crimp stitched textile composites considering the material nonlinearity of epoxy resin. The global mechanical analysis of unnotched quasi-isotropic laminates has been performed and validated by the experiment. Finally, the proposed progressive failure analysis is extended to the defect mechanics of non-crimp stitched composite laminates. The parametric study based on defect modeling indicates the correlation between the void contents and mechanical properties. The numerical analysis result is validated by the experimental data. vii References mechanical properties of carbon/epoxy laminates. Composites; 26: 509–15, 1995. 164. Varna J, Joffe R, Berglund L A and Lundstr T S. Effect of voids on failure mechanisms in RTM laminates. Composites Science Technology; 53: 241–9, 1995. 165. Wisnom M R, Reynolds T and Gwilliam N. Reduction in interlaminar shear strengthby discrete and distributed voids. Composites Science Technology; 56:93– 101, 1996. 166. Costa M L, Almeida S F M, and Rezende M C. The influence of porosity on theinterlaminarshear strength of carbon/epoxy and carbon/bismaleimide fabriclaminates. Composites Science Technology; 61:2101–8. 2001. 167. Bureau M N and Denault J. Fatigue resistance of continuous glass fiber/polypropylene composites: consolidation dependence. Composites Science Technology, 64:1785–94, 2004. 168. Hagstrand P O, Bonjour F M and Manson J A E. The influence of void content on the structural flexural performance of unidirectional glass fibre reinforced polyprolylene composites. Composites: Part A; 36:705–14, 2005. 169. Chambers A R, Earl J S, Squires C A and Suhot M A. The effect of voids on the flexural fatigue performance of unidirectional carbon fibre composites developed for wind turbine applications. International Journal of Fatigue; 28:1389–98, 2006. 170. Liu L, Zhang B M, Wang D F and Wu Z J. Effects of cure cycles on void content and mechanical properties of composite laminates. Composites Structure; 73:303–9, 2006. 171. Little J E, Yuan X W and Jones M. Characterisation of voids in fibre reinforced composite materials. NDT&E International; 46:122–127, 2012. 240 References 172. Kosek M and Sejak P. Visualization of voids in actual C/C woven composite structure. Composites Science and Technology; 69: 1465–1469, 2009. 173. Jeong H. Effects of Voids on the mechanical strength and ultrasonic attenuation of laminated composites. Journal of Composite Materials; 31: 276 – 292, 1997. 174. Lundstrom T S and Gebart B R.Influence from process parameters on void formation in resin transfer molding. Polymer Composites, February; 15:25-33, 1994. 175. Howe C A, Paton R J and Goodwin A. A comparison between voids in RTM and prepreg carbon/epoxy laminates. In: ICCM-11 Conference proceedings, Gold Coast, Queensland, Australia; 4:46–51, 1997. 176. Goodwin A, Howe C A and Paton R J. The role of voids in reducing the interlaminar shear strength in RTM laminates. In: ICCM-11 conference proceedings, Gold Coast, Australia; 4:11-9, 1997. 177. Stone D E W and Clarke B. Ultrasonic attenuation as a measure of void content in carbon-fibre reinforced plastics. Non-destructive Testing June; 137-145, 1975. 178. Hu J L, Liu Y and Shao X M. Study on void formation in multi-layer woven fabrics. Composites: Part A; 35:595–603, 2004. 179. Rubin A M and Jerina K L. Evaluation of porosity in composite aircraft structures. Composites Engineering; 3:601-618, 1993. 180. Schell J S U, Deleglise M, Binetruy C, Krawczak P, Emanni P and Numerical prediction and experimental characterization of meso-scale-voids in liquid composite moulding. Composites Part A: Applied Science and Manufacturing; 241 References 38:2460-2470, 2007. 181. Chao L P and Huang J H. Prediction of elastic moduli of porous materials with equivalent inclusion method. Journal of Reinforced Plastics Composites; 18:592– 605, 1999. 182. Madsen B and Lilholta H. Physical and mechanical properties of unidirectional plant fibrecomposites—an evaluation of the influence of porosity. Composites Science and Technology; 63:1265–1272, 2003. 183. Huang H and Talreja R. Effects of void geometry on elastic properties of unidirectional reinforced composites. Composites Science Technology; 65:1964–81, 2005. 242 Appendix A – Plain Woven Composites Study Appendix A-1 Mesh Convergency Study for Plain Woven RVE Model Linear elastic stress analysis is performed to the plain woven mesoscale model to validate the mesh convergency. The longitudinal displacement Uxx = l is applied to the FE model where l is the length of the RVE. Four different mesh densities are used in this study. The result is presented in Fig. A1 and Table A1. Figure A1 Mesh convergency study result for mesoscale plain woven RVE model 243 Table A1 Mesh Convergency Study Results for Plain Woven Mesoscale RVE model Mesh A Mesh B Mesh C Mesh D Element No. 110356 15464 4629 3970 σ11 (GPa) 39.34 39.07 36.97 35.16 CPU time 33hrs12min 5hrs 2hrs25min 1hrs45min Linear elastic stress analysis is also performed to the plain woven macro model to validate the mesh convergency. Four different mesh densities are used in this study. The result is presented in Fig. A2 and Table A2. Figure A2 Mesh convergency study result for macroscale plain woven RVE model 244 Table A2 Mesh Convergency Study Results for Plain Woven Macroscale RVE model Mesh A Mesh B Mesh C Mesh D Element No. 3706 5876 16452 57968 σ11 (GPa) 32.16 34.68 38.1 38.27 In addtion, another meso density criterion is applied here. For a given mesh density, the difference of maximum stresses (σ11 in this case) between the element-average and element-non-average methods is less than 5%. The values of the maximum stress can be easily obtained from the stress analysis result. Appendix A-2 Sensitivity Study for Plain Woven Composite Table A3 Sensitivity Study Data for Plain Woven Composites Parameter Mode I Fiber fracture toughness, kJ/m2 56.35 112.7 225.4 Selection Range of Reference Points 0.1% 0.5% 1.0% Studied Performance Ultimate tensile stress of Plain woven OHT sample, MPa 269.3 301.2 357.4 Ultimate tensile stress of Plain woven OHT sample, MPa 305.1 301.2 297.8 245 Appendix B – NCF Composites Study Appendix B-1 Mesh Convergency Study for NCF RVE Model Linear elastic stress analysis is performed to the NCF mesoscale model to validate the mesh convergency. The longitudinal displacement Uxx = l is applied to the FE model where l is the length of the RVE. Four different mesh densities are used in this study. The result is presented in Fig. B1 and Table B1. Figure B1 Mesh convergency study result for mesoscale NCF RVE model 246 Table B1 Mesh Convergency Study Results for NCF Mesoscale RVE model Mesh A Mesh B Mesh C Mesh D Element No. 12447 7984 3224 1530 σ11 (GPa) 97.01 96.74 90.34 87.07 CPU time 2hrs30min 2hrs 1hrs15min 45min Linear elastic stress analysis is performed to the NCF macroscale model to validate the mesh convergency. Four different mesh densities are used in this study. The result is presented in Fig. B2 and Table B2. Figure B2 Mesh convergency study result for macro NCF RVE model 247 Table B2 Mesh Convergency Study Results for NCF Macroscale RVE model Mesh A Mesh B Mesh C Mesh D Element No. 6742 12510 27982 50248 σ11 (GPa) 28.04 30.48 34.56 35.1 In addition, another meso density criterion is applied here. For a given mesh density, the difference of maximum stresses (σ11 in this case) between the element-average and element-non-average methods is less than 5%. The values of the maximum stress can be easily obtained from the stress analysis result. Appendix B-2 Nonlinear Cofficients for Meso-to-Micro Stress Amplification Recalling that in the multiscale modeling method for NCF composites, the components in the nonlinear stress amplification matrix is calculated, which is a function of global stress tensor. As presented in Eq. 4.20, the value of the amplification factors can be obtained by multiply the nonlinear coefficient D j ( j G ) , j = 1-6, to the initial amplification matrix M j . The nonlinear coefficient D j ( j m ) presents how the meso-to-micro amplification factors for epoxy region are changed with the increase of the meso loads. 248 Table B1 Table of nonlinear coefficient D2 ( yy ) for meso/micro stress amplification  yy (MPa) D2  yy (MPa) D2 0.00 2.55 5.10 7.66 10.21 12.76 15.30 17.87 20.43 22.98 25.53 28.09 30.64 33.19 35.75 38.30 1.00 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 40.85 43.41 45.96 48.51 51.07 53.62 56.17 58.73 61.28 63.83 66.39 68.94 71.49 73.98 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.52 Table B2 Table of nonlinear coefficient D3 ( zz ) for meso/micro stress amplification  zz (MPa) D3  zz (MPa) D3 0.00 2.55 5.10 7.66 10.21 12.76 15.30 17.87 20.43 22.98 25.53 28.09 30.64 33.19 35.75 38.30 1.00 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 40.85 43.41 45.96 48.51 51.07 53.62 56.17 58.73 61.28 63.83 66.39 68.94 71.49 73.98 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.52 249 Table B3 Table of nonlinear coefficient D4 ( xy ) for meso/micro stress amplification  xy 0.00 1.56 3.11 4.66 6.22 7.77 9.33 10.88 12.44 13.99 15.55 17.10 D4 1.00 1.00 1.00 1.00 1.11 1.12 1.13 1.15 1.17 1.19 1.21 1.23 Table B4 Table of nonlinear coefficient D5 ( xz ) for meso/micro stress amplification  xz 0.00 1.56 3.11 4.66 6.22 7.77 9.33 10.88 12.44 13.99 15.55 17.10 D5 1.00 1.00 1.00 1.00 1.11 1.12 1.13 1.15 1.17 1.19 1.21 1.23 Table B5 Table of nonlinear coefficient D6 ( yz ) for meso/micro stress amplification  yz D6 0.00 1.60 3.20 4.80 6.40 8.00 1.00 1.00 1.00 1.00 1.08 1.14 250 9.60 11.20 12.80 14.40 1.15 1.15 1.17 1.18 Appendix B-3 Nonlinear Cofficients for Macro-to-Meso Stress Amplification The nonlinear coefficient D j ( j M ) presents how the macro-to-meso amplification factors for fiber yarn are changed with the increase of the applied macro-loads. Table B6 Table of nonlinear coefficient D2 ( yy ) for macro/meso stress amplification  yy (MPa) 0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40 4.80 5.20 5.60 6.00 6.40 6.80 7.20 7.60 D2 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  yy (MPa) 9.20 9.60 10.00 10.40 10.80 11.20 11.58 11.96 12.34 12.71 13.07 13.43 13.79 14.15 14.49 14.84 15.17 15.51 15.85 16.19 251 D2 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.01 1.01 1.01 1.01 1.02 1.02 1.02 1.03 1.03 1.03 1.04 1.04  yy (MPa) 17.48 17.80 18.12 19.43 19.75 20.07 20.38 21.69 22.00 22.30 23.60 23.90 24.19 25.49 25.79 27.09 27.38 28.68 28.98 29.28 D2 1.05 1.06 1.06 1.06 1.07 1.07 1.07 1.08 1.08 1.09 1.09 1.09 1.10 1.10 1.10 1.11 1.11 1.11 1.12 1.12 Table B7 Table of nonlinear coefficient D3 ( zz ) for macro/meso stress amplification  zz (MPa) 0.00 0.42 0.83 1.25 1.66 2.08 2.49 2.91 3.32 3.73 4.15 4.56 4.98 5.39 5.81 6.22 6.64 7.05 7.47 7.88 8.30 8.71 9.13 9.54 D3 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  zz (MPa) 9.96 10.37 10.77 11.16 11.56 11.93 12.31 12.69 13.06 13.44 13.79 14.15 14.51 14.87 15.22 15.57 15.90 16.24 16.58 16.91 17.25 17.58 17.92 18.25  zz (MPa) 18.57 18.89 19.20 19.51 19.83 20.14 20.45 20.76 21.08 21.39 21.70 22.00 22.30 22.60 22.90 23.19 23.47 23.75 24.01 24.28 24.55 24.82 25.09 25.36 D3 1.00 1.00 1.00 1.00 1.01 1.01 1.01 1.01 1.02 1.02 1.02 1.03 1.03 1.03 1.04 1.04 1.04 1.05 1.05 1.06 1.06 1.06 1.07 1.07 D3 1.07 1.08 1.08 1.08 1.09 1.09 1.10 1.10 1.10 1.11 1.11 1.11 1.12 1.12 1.12 1.13 1.13 1.14 1.14 1.15 1.15 1.15 1.16 1.16  zz (MPa) 25.62 25.91 26.15 26.42 26.68 26.92 27.17 27.39 27.65 27.89 28.13 28.38 28.61 28.85 29.05 29.18 29.21 D3 1.17 1.17 1.17 1.18 1.18 1.19 1.19 1.20 1.20 1.21 1.21 1.21 1.22 1.22 1.23 1.24 1.25 Table B8 Table of nonlinear coefficient D4 ( xy ) for macro/meso stress amplification  xy (MPa) D4  xy (MPa) D4  xy (MPa) D4  xy (MPa) D4  xy (MPa) D4 0.00 0.29 0.58 0.87 1.16 1.45 1.74 2.03 2.32 2.61 2.90 3.19 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0 12.51 12.78 13.05 13.32 13.59 13.86 14.13 14.39 14.66 14.93 15.19 15.46 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 3 23.99 24.24 24.48 24.73 24.97 25.22 25.47 25.72 25.96 26.19 26.42 26.64 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 33.00 33.11 33.22 33.32 33.42 33.52 33.60 33.67 33.73 33.79 33.83 33.88 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 2 35.50 35.58 35.65 35.73 35.80 35.87 35.93 36.01 36.08 36.15 36.23 36.29 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 9 252 3.48 3.77 4.06 4.34 4.63 4.92 5.21 5.50 5.79 6.08 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0 15.72 15.99 16.25 16.52 16.78 17.05 17.31 17.57 17.84 18.10 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 4 26.87 27.11 27.34 27.57 27.79 28.00 28.21 28.43 28.65 28.86 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 9 33.91 33.91 33.81 33.70 33.65 33.66 33.70 33.78 33.86 33.94 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 36.33 36.38 36.41 36.44 36.47 36.50 36.52 36.55 36.58 36.61 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 Table B9 Table of nonlinear coefficient D5 ( xz ) for macro/meso stress amplification  xz (MPa) 0.00 0.12 4.73 4.85 4.97 5.09 5.21 5.33 5.44 5.56 5.67 5.79 5.90 6.01 6.12 6.23 6.34 6.45 6.56 6.67 6.77 6.88 D5 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.01 1.01 1.01 1.01 1.01 1.01 1.02 1.02 1.02 1.02 1.02  xz (MPa) 9.15 9.25 9.34 9.44 9.53 9.62 9.72 9.81 9.90 9.99 10.09 10.18 10.27 10.36 10.45 10.54 10.63 10.72 10.81 10.90 10.99 11.08 D5 1.07 1.08 1.08 1.08 1.08 1.08 1.09 1.09 1.09 1.09 1.09 1.10 1.10 1.10 1.10 1.10 1.11 1.11 1.11 1.11 1.11 1.12  xz (MPa) 12.67 12.73 12.79 12.85 12.91 12.97 13.03 13.09 13.15 13.21 13.27 13.32 13.37 13.43 13.48 13.54 13.60 13.65 13.71 13.76 13.82 13.87 253 D5 1.20 1.20 1.20 1.21 1.21 1.22 1.22 1.22 1.23 1.23 1.23 1.24 1.24 1.25 1.25 1.25 1.26 1.26 1.27 1.27 1.27 1.28  xz (MPa) 13.92 13.98 14.03 14.09 14.14 14.19 14.23 14.28 14.33 14.37 14.41 14.46 14.50 14.54 14.59 14.64 14.69 14.74 14.78 14.82 14.86 14.89 D5 1.28 1.28 1.29 1.29 1.30 1.30 1.30 1.31 1.31 1.32 1.32 1.33 1.33 1.33 1.34 1.34 1.35 1.35 1.35 1.36 1.36 1.37  xz (MPa) 14.93 14.97 15.00 15.03 15.06 15.09 15.12 15.14 15.16 15.19 15.23 15.28 15.34 15.41 15.48 15.55 D5 1.37 1.38 1.38 1.39 1.39 1.40 1.40 1.41 1.42 1.42 1.43 1.43 1.43 1.43 1.43 1.44 Table B10 Table of nonlinear coefficient D6 ( yz ) for macro/meso stress amplification  yz (MPa) D6 0.00 0.13 0.26 0.38 0.51 0.64 0.77 0.89 1.02 1.15 1.28 1.41 1.53 1.66 1.79 1.92 2.04 2.17 2.30 2.43 2.56 2.68 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  yz (MPa) D6 5.49 5.60 5.72 5.83 5.95 6.06 6.18 6.29 6.41 6.52 6.63 6.75 6.86 6.98 7.09 7.20 7.31 7.43 7.54 7.65 7.76 7.87 1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05  yz (MPa) D6 7.99 8.10 8.21 8.32 8.43 8.54 8.65 8.76 8.87 8.98 9.09 9.20 9.31 9.42 9.53 9.64 9.75 9.86 9.97 10.08 10.19 10.30 254 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.08 1.08 1.08 1.08 1.08  yz (MPa) D6 10.41 10.52 10.63 10.73 10.84 10.95 11.06 11.17 11.27 11.38 11.49 11.60 11.71 11.81 11.92 12.03 12.14 12.24 12.35 12.46 12.57 12.68 1.08 1.08 1.08 1.08 1.08 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.10 1.10 1.10 1.10 1.10 1.10  yz (MPa) D6 12.78 12.89 13.00 13.11 13.21 13.32 13.42 13.51 13.59 13.64 13.67 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.11 1.11 1.11 1.12 Appendix B-4 Sensitivity Study for NCF Composite Table B11 Sensitivity Study Data for Plain Woven Composites Parameter Mix-mode fracture toughness for delamination Gn, Gs and Gt, kJ/m2 0.1, 0.5, 0.5 0.2, 1.0, 1.0 0.4, 2.0, 2.0 Throug-thickness stitching peak load, N 9.82 19.63 39.27 Studied Performance Ultimate tensile stress of NCF [±45o] sample, MPa 93.45 104.90 133.78 Ultimate tensile stress of NCF [±45o] sample, MPa 104.97 104.90 104.33 255 [...]... together in the braided performs The tubular form is available in biaxial and triaxial architectures The triaxial braided fabric consists of inserting an axial yarn between the braided yarns in either longitudinal or vertical direction The angle between the bias axis and the braid axis is called braid angle, usually indicated as θ (see Fig.1.3) Figure 1.3 Braid angle in biaxial braided fabric [2] Similar to... previous analysis, appropriate failure criteria are used to determine whether the damage occurs In 2 Chapter 1: Introduction and Literature Review progressive damage, the last step of the failure analysis involves a stiffness reduction model to simulate a loss in the load-carrying capability of the damaged parts For the study of textile composites, due to the complex textile architectures and material system,... permeability of fabrics and deteriorate the mechanical performance of composite structures 1.2 Review of Multiscale Modeling of Textile Composites In the past two decades, numerous solutions for structural analysis were developed with the increasing application of textile composite In this section, modeling approaches for mechanical analysis across different length scales of textile composite are presented... according to their geometrical and material heterogeneities The design procedure of composites structures usually includes failure analysis A typical progressive failure analysis involves a model for damage initiation and propagation In the first place, the stress or strain analysis is carried out by applying certain loading and boundary condition According to stress or strain distribution obtained from... .174 Figure 4.3 1a Predicted damages from macromechanical analysis at applied strain 0.18% 176 Figure 4.31b Predicted damages from macromechanical analysis at applied strain 0.33% 177 Figure 4.31c Predicted damages from macromechanical analysis at applied strain 0.38% 179 Figure 4.31d Predicted damages from macromechanical analysis at applied strain 0.65% ... Woven composites provide superior out -of- plane performance to the UD composites because of the strong interlocking of the fiber bundles They are widely used in military and aerospace industries for their high delamination and impact resistance On the other hand, the interlocking causes the crimp of the fiber yarns, which complicates the modeling for analysis and design Besides, the crimp regions of woven... Firstly, modeling techniques for textile composites are briefly introduced from the analytical to the numerical method Then, the finite element (FE) based modeling at different length scales are discussed respectively Finally, the existing multiscale modeling approaches are introduced The limitations of those multiscale methods are also identified In the beginning, a number of analytical approaches have... yarns result in the deterioration of the in-plane properties For instance, woven composites have a lower inplane compressive strength than the other textile composites 4 Chapter 1: Introduction and Literature Review Braided fabric can be regarded as the combination of filament winding and weaving It is normally integrated as a tubular form over a cylindrical mandrel Fiber yarns are interwound together... properties and low weight In the past century, they have been one of the most widely used materials in aerospace, civil, automotive, and marine applications Meanwhile, products of composite materials also start to popularize in sports and leisure industry in recent years Among the variety of composites, textile reinforced composite form an essential part of this large family, which is defined as the combination... [10-13] to establish the constitutive equation of the textile composite material They were usually used as analysis codes to predict the overall properties and the mechanical response The simplest method is based on the rule of mixture and Classical Laminate Theory (CLT) In this method, the composite laminates are treated as homogenized materials Thus the stress or strain distributions within the textile . A MULTISCALE MODELING APPROACH FOR THE PROGRESSIVE FAILURE ANALYSIS OF TEXTILE COMPOSITES MAO JIAZHEN NATIONAL UNIVERSITY OF SINGAPORE 2014 A MULTISCALE. length scales are available. However, there is still a strong demand for a computational approach to implement the mechanical analysis for a macroscopic structure based on the micro-physical phenomena the performance of composite materials. In this thesis, a multiscale modeling approach to model the progressive damage in textile composites has been developed. The hierarchical models of textile