DAMAGE PROGRESSION IN OPEN-HOLE TENSION COMPOSITE LAMINATES BY THE ELEMENTFAILURE METHOD LIU GUANGYAN NATIONAL UNIVERSITY OF SINGAPORE 2007 DAMAGE PROGRESSION IN OPEN-HOLE TENSION COMPOSITE LAMINATES BY THE ELEMENTFAILURE METHOD LIU GUANGYAN (M.ENG) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 Acknowledgement Acknowledgement The author would like to express his sincere gratitude to all of the kindhearted individuals for their precious advice, guidance, encouragement and support, without which the successful completion of this thesis would not have been possible. Special thanks to the author’s supervisor A/Prof. Tay Tong-Earn and A/Prof. Vincent Tan Beng Chye, whom the author has the utmost privilege and honor to work with. Their instruction makes the exploration in damage of composite materials a wonderful journey. Their profound knowledge on mechanics and strict attitude towards academic research will benefit the author’s whole life. The author would also like to thank Dr Serena Tan, Dr Shen Feng, Dr Li Jianzhong, Mr Arief Yudhanto and Mr Tan Kwek Tze for their invaluable help. Many thanks to his friends Dr Zhang Bing, Mr Mohammad Zahid Hossain and Mr Zhou Chong for making the research environment a lively place. The author extends heartfelt thanks to his flatmates, who make him feel at home after one-day working. Last but not least, the author expresses his utmost love and gratitude to his parents and sister for their understanding and support during the course of this project. i Table of Contents Table of Contents Acknowledgement i Table of Contents .ii Summary v Publications vii Nomenclature viii List of Figures . xi List of Tables xvi Chapter Introduction and Literature Review 1.1 Introduction 1.2 Review of Failure Theories for Fibrous Composite Materials 1.3 1.2.1 Non-Interactive Failure Theories . 1.2.2 Interactive Failure Theories . Review of Damage Modeling Techniques for Fibrous Composite Materials… 10 1.3.1 Material Property Degradation Method (MPDM) . 11 1.3.1.1 MPDM Applied to Lamination Theory . 11 1.3.1.2 MPDM Applied to Finite Elements . 13 1.3.2 Fracture Mechanics Approach . 18 1.3.3 Decohesion Element Method 21 1.3.3.1 Point Decohesion Element Method . 22 1.3.3.2 Line Decohesion Element Method . 25 1.3.3.3 Plane Decohesion Element Method . 28 1.3.4 Element-Delete Approach . 31 1.3.5 Element-Failure Approach 32 1.4 Problem Statement . 33 1.5 Scope of Study . 35 Chapter Element-Failure Method and Strain Invariant Failure Theory 37 ii Table of Contents 2.1 Element-failure Method (EFM) . 37 2.1.1 Principles of the EFM 37 2.1.2 Validation of the EFM . 43 2.1.3 2.2 Formulas of the EFM . 47 Strain Invariant Failure Theory 54 2.2.1 SIFT . 55 Chapter Damage Prediction in Unidirectional and Cross-Ply Composite Laminates . 64 3.1 Implementation of the EFM and SIFT . 64 3.2 Damage Prediction in Unidirectional Laminates . 68 3.3 Damage Prediction in Cross-Ply Laminates 73 3.4 Conclusion . 76 Chapter Damage Prediction in Quasi-Isotropic Composite Laminates 77 4.1 Model Strategy . 77 4.1.1 Final Failure Criterion 77 4.1.2 Delamination Criterion 78 4.2 Problem Description 81 4.3 Results and Discussion 82 4.3.1 Damage in [±45/90/0]s OHT Laminate 82 4.3.2 Damage in [45/0/-45/90]s OHT Laminate . 93 4.4 Conclusion . 104 Chapter Hole Size Effect 106 5.1 Comparison with Sihn [Private Communication]’s Experimental Data . 106 5.1.1 Description of Specimens 107 5.1.2 Finite Element Analysis . 108 5.2 Comparison with Daniel [1978]’s Experimental Data . 115 5.2.1 Description of Specimens 115 5.2.2 Finite Element Analysis . 116 iii Table of Contents 5.3 Conclusion . 119 Chapter Conclusions and Recommendations . 120 6.1 Conclusions 120 6.2 Recommendations for Future Work . 123 References . 124 Appendix . 141 iv Summary Summary Damage propagation in composite laminates is traditionally modeled by the material property degradation method (MPDM), which assumes that a damaged material can be replaced by an equivalent material with degraded properties. For the MPDM, the stiffness matrix of composite laminates needs to be reformulated and inverted after modifying material properties of damaged elements. This is a computationally intensive process, especially for a finite element model with a fine mesh. There is also a possibility that by reducing the material properties, the stiffness matrix of the damaged finite element becomes ill-conditioned and convergence to a solution is not assured. In this thesis, a new damage-modeling technique known as the elementfailure method (EFM) is proposed, which is based on the idea that the nodal forces of a finite element of a damaged composite material can be modified to achieve the reduction of load-carrying capacity and reflect the general damage state. Hence, there should be savings in computational efforts since each change in damage state is achieved by modifying modal forces of damaged elements only, and reformulation and inversion of stiffness matrix is not required. Because the stiffness matrix of the element is not altered, computational convergence can always be guaranteed. Employed with a recently-proposed failure criterion called the strain invariant failure theory (SIFT) and the fiber ultimate strain, the EFM is implemented in a 3D implicit finite element code to model the damage propagation in open-hole tension composite laminates. By predicting damage patterns and ultimate strengths of two v Summary quasi-isotropic composite laminates, the mesh dependency and stacking sequence effect are investigated. It is found that both coarse mesh and fine mesh give quite similar damage patterns, and laminates with different lay-ups show different ultimate strengths. The simulation results predicted by this progressive damage model agree very well with the experimental observations. In addition, the hole-size effect of open-hole tension composite laminates is also investigated by the developed progressive damage model. After comparing the ultimate strengths of laminates with the same lengths, widths and lay-ups but different hole sizes, it is found that laminates with smaller holes have higher tensile strength than those with larger holes. The hole-size effect is correctly captured by the progressive damage model. vi Publications Publications Tay, T.E., Liu, G. and Tan, V.B.C. (2006), Damage Progression in open-hole tension laminates by the SIFT-EFM approach, Journal of Composite Materials, 40(11), pp. 971-992. Tay, T.E., Liu, G., Yudhanto, A. and Tan, V.B.C., A Multi-scale approach to modeling progressive damage in composite structures, International Journal of Damage Mechanics (accepted) Tay, T.E., Tan, V.B.C. and Liu, G. (2006), A new integrated micro-macro approach to damage and fracture of composites, Materials Science and Engineering B, 132(12), pp. 138-142. Liu, G., Li, J.Z., Shen, F., Tan, V.B.C. and Tay, T.E. (2006), Analysis of composite fan blades with v-joints using the element-failure method (EFM) and strain invariant failure theory. 35th solid mechanics conference, Krakow, Poland, 4-8 September 2006. Tay, T.E., Tan, V.B.C. and Liu, G. (2005), A novel approach to damage progression: the element-failure method (EFM), Advances in Multi-scale Modeling of Composite Material Systems & Components, Cannery Row, Monterey Bay, California, USA, 25-30 September 2005. vii Nomenclature Nomenclature K Element stiffness matrix u Nodal displacement vector of an element f Nodal force vector of an element C Material stiffness matrix B Strain-displacement matrix Subscripts 1,2,3 Directions of material coordinate system where refers to the fiber direction Subscripts x, y, z Directions of global coordinate system E1 , E2 , E3 Young’s moduli in material coordinate system E x , E y , Ez Young’s moduli in global coordinate system ν12 , ν13 , ν 23 Poisson’s ratios in material coordinate system ν xy , ν xz , ν yz Poisson’s ratios in global coordinate system G12 , G13 , G23 Shear moduli in material coordinate system G xy , G xz , G yz Shear moduli in global coordinate system α ,α ,α Coefficients of thermal expansion in material coordinate system E Elastic modulus of the rod A Cross-section area of the rod L One-third of the length of the rod Fint Internal nodal force of elements Fd Desired nodal force of elements R(i) Residual nodal force of elements at the ith iteration viii References [91] Reddy, Y.S.N., Moorthy C.M.D. and Reddy J.N. 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(2004), On impact damage of composite shells by a low-velocity projectile, Journal of Composite Materials, 38(14), pp. 12311254. 140 Appendix Appendix The appendix presented here, depicts the additional simulation results for the two quasi-isotropic composite laminates studied in Chapter 4. 141 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). -45o ply (c). 90o ply (d). 0o ply Figure A.1 Damage maps of [±45/90/0]s laminate just after the first major load drop ( C delam = 0.1, ε nominal = 9.97×10-3). delamination (a). 45o/-45o interface (b). -45o/90o interface (c). 90o/0o interface Figure A.2 Delamination in [±45/90/0]s laminate just after the first major load drop ( C delam = 0.1, ε nominal = 9.97×10-3). 142 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). -45o ply (c). 90o ply (d). 0o ply Figure A.3 Damage maps of [±45/90/0]s laminate just after the first major load drop ( C delam = 0.3, ε nominal = 1.02×10-2). delamination (a). 45o/-45o interface (b). -45o/90o interface (c). 90o/0o interface Figure A.4 Delamination in [±45/90/0]s laminate just after the first major load drop ( C delam = 0.3, ε nominal = 1.02×10-2). 143 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). -45o ply (c). 90o ply (d). 0o ply Figure A.5 Damage maps of [±45/90/0]s laminate just after the first major load drop ( C delam = 0.8, ε nominal = 1.01×10-2). delamination (a). 45o/-45o interface (b). -45o/90o interface (c). 90o/0o interface Figure A.6 Delamination in [±45/90/0]s laminate just after the first major load drop ( C delam = 0.8, ε nominal = 1.01×10-2). 144 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). -45o ply (c). 90o ply (d). 0o ply Figure A.7 Damage maps of [±45/90/0]s laminate just after the first major load drop ( C delam = 1.0, ε nominal = 9.84×10-3). delamination (a). 45o/-45o interface (b). -45o/90o interface (c). 90o/0o interface Figure A.8 Delamination in [±45/90/0]s laminate just after the first major load drop ( C delam = 1.0, ε nominal = 9.84×10-3). 145 Appendix 900.0 800.0 700.0 Stress(MPa) 600.0 500.0 400.0 300.0 Cdelam=0.1 Cdelam=0.3 Cdelam=0.5 Cdelam=0.8 Cdelam=1.0 200.0 100.0 0.0 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 Strain Figure A.9 Stress-strain curves of [±45/90/0]s laminate predicted by using different values of Cdelam. Table A.1 Predicted strength of [±45/90/0]s laminate by different values of Cdelam. Cdelam 0.1 0.3 0.5 0.8 1.0 Predicted strength (MPa) 557.3 568.4 561.3 564.6 550.3 146 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). 0o ply (c). -45o ply (d). 90o ply Figure A.10 Damage maps of [45/0/-45/90]s laminate just after the first major load drop ( C delam = 0.1, ε nominal = 7.68×10-3). delamination (a). 45o/0o interface (b). 0o/-45o interface (c). -45o/90o interface Figure A.11 Delamination in [45/0/-45/90]s laminate just after the first major load drop ( C delam = 0.1, ε nominal = 7.68×10-3). 147 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). 0o ply (c). -45o ply (d). 90o ply Figure A.12 Damage maps of [45/0/-45/90]s laminate just after the first major load drop ( C delam = 0.3, ε nominal = 7.55×10-3). delamination (a). 45o/0o interface (b). 0o/-45o interface (c). -45o/90o interface Figure A.13 Delamination in [45/0/-45/90]s laminate just after the first major load drop ( C delam = 0.3, ε nominal = 7.55×10-3). 148 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). 0o ply (c). -45o ply (d). 90o ply Figure A.14 Damage maps of [45/0/-45/90]s laminate just after the first major load drop ( C delam = 0.8, ε nominal = 7.68×10-3). delamination (a). 45o/0o interface (b). 0o/-45o interface (c). -45o/90o interface Figure A.15 Delamination in [45/0/-45/90]s laminate just after the first major load drop ( C delam = 0.8, ε nominal = 7.68×10-3). 149 Appendix J1 ε vmf m ε vm ε ult fiber (a). 45o ply (b). 0o ply (c). -45o ply (d). 90o ply Figure A.16 Damage maps of [45/0/-45/90]s laminate just after the first major load drop ( C delam = 1.0, ε nominal = 7.68×10-3). delamination (a). 45o/0o interface (b). 0o/-45o interface (c). -45o/90o interface Figure A.17 Delamination in [45/0/-45/90]s laminate just after the first major load drop ( C delam = 1.0, ε nominal = 7.68×10-3). 150 Appendix 800.0 700.0 Stress(MPa) 600.0 500.0 400.0 300.0 Cdelam=0.1 Cdelam=0.3 Cdelam=0.5 Cdelam=0.8 Cdelam=1.0 200.0 100.0 0.0 0.000 0.002 0.004 0.006 0.008 0.010 Strain 0.012 0.014 0.016 0.018 Figure A.18 Stress-strain curves of [45/0/-45/90]s laminate predicted by using different values of Cdelam. Table A.2 Predicted strength of [45/0/-45/90]s laminate by different values of Cdelam. Cdelam 0.1 0.3 0.5 0.8 1.0 Predicted strength (MPa) 437.2 430.1 437.4 437.3 437.3 151 [...]... similar non-interactive failure theory is the maximum strain theory [Waddoups, 1967] Instead of stresses, strain components are used to express the failure conditions and failure occurs whenever any one of the strain components exceeds the corresponding ultimate strain However, the maximum strain theory also has its limitation because it ignores the strain interactions Despite their shortcomings, the maximum... determined 1.3 Review of Damage Modeling Techniques for Fibrous Composite Materials Once damage in composite materials is identified by a failure theory, a suitable damage modeling technique is needed to describe the effect of damage on the loadbearing capability of the material Besides failure theory studies, the development of damage modeling techniques is another important and exciting area of composite. .. is accounted for in the determination of these strength parameters The Tsai-Wu failure theory overcomes the shortcomings of previously mentioned failure theories It is still the most commonly used failure theory for composite materials A weakness on using the Tsai-Wu failure theory is that it can predict damage occurrence but cannot differentiate damage modes In order to determine damage modes, additional... Gosse, 2002] In this theory, matrix failure is determined by considering the 8 Chapter 1: Introduction and Literature Review criticality of three strain invariants These invariants have been “amplified” by thermo-mechanical amplification factors extracted from micromechanical finite element models The first of the invariants is related to J1 (the first strain invariant), the second related to the von Mises... Review In non-interactive failure theories, specific failure modes are predicted by comparing individual lamina stresses or strains with corresponding strengths or ultimate strains No interaction among different stress or strain components on failure is considered One of the earliest non-interactive failure theories is the so-called maximum stress theory [Jenkins, 1920] This theory is based on the assumption... 6 , then the damage mode is matrix cracking If the maximum value is due to σ 3 or σ 4 orσ 5 , then the damage mode is delamination A simplified 2D form, in which only fiber breakage and matrix cracking are determined, is used by Wolford and Hyer [2005] to predict the failure initiation and progression in internally-pressurized elliptical composite cylinders Another judgment for identifying damage modes... incorporating all of the stress components in one equation, some failure theories use several mathematical formulations and different formulation representing damage conditions for different damage modes This type of failure theories can also be called damage- mode-based theories One of the most popular damage- mode-based failure theories is the Hashin failure theory Considering that different failure. .. been proposed in the literature In an interactive failure theory, all or some of the stress or strain components are included in an equation representing the failure condition Tsai [1968] adapted the orthotropic yield criterion proposed by Hill [1950] to homogeneous, anisotropic materials and introduced the Tsai-Hill theory The TsaiHill theory is expressed in terms of a single criterion instead of multiple... al [2004] Based on the stress or strain expressions representing the failure conditions, failure theories for fibrous composite materials can be classified into two groups: non-interactive failure theories and interactive failure theories Some of the most representative and widely used failure theories are discussed in this section 1.2.1 Non-Interactive Failure Theories 3 Chapter 1: Introduction and... and Matthews [1999] to predict the damage progression and strength of mechanically fastened joints in carbon fiber-reinforced plastics that fail in bearing, net -tension and shear-out modes This progressive damage model relates the material elastic properties with internal state variables Di that are functions of the type of damage Four damage modes are assumed by using Hashin’s failure theory The effect . DAMAGE PROGRESSION IN OPEN- HOLE TENSION COMPOSITE LAMINATES BY THE ELEMENT- FAILURE METHOD LIU GUANGYAN NATIONAL UNIVERSITY OF SINGAPORE 2007 DAMAGE PROGRESSION. propagation in open- hole tension composite laminates. By predicting damage patterns and ultimate strengths of two v Summary quasi-isotropic composite laminates, the mesh dependency and stacking. predicted by this progressive damage model agree very well with the experimental observations. In addition, the hole- size effect of open- hole tension composite laminates is also investigated by the