A comparison among several recent criteria for the failure analysis of composites

Journal of Advanced Materials

Volumn 40, Issue 4, 2008, Pages 73-111

  Icardi, Ugo ^a   Ferrero, L ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FORECASTING; QUALITY ASSURANCE; REINFORCEMENT; RELIABILITY; SAFETY FACTOR;

ACCURATE PREDICTIONS; CONSTITUENT MATERIALS; CONTINUOUS REINFORCEMENTS; DESIGN PARAMETERS; DISCRETIZATION; FAILURE CRITERIONS; FAILURE THEORIES; INTERLAMINAR STRESSES; LEVELS OF ANALYSIS; LOADING CONFIGURATIONS; PHYSICALLY BASED; SOLID ELEMENTS; SPECIFIC CLASSES;

FAILURE ANALYSIS;

EID: 55849106602     PISSN: 10709789     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (136)

1. R.E. Rowlands, Strength (Failure) Theories and Their Experimental Correlations, Handbook of Composites 1985; Elsevier Science Publ. 3: 71-125.
2. M.N. Nahas, Survey of Failure and Post-failure Theories of Laminated Fibre Reinforced Composites, Jnl. of Composite Technology & Research 1986; 8: 138-153.
3. J.F. Echaabi, F. Trochu F, Review of Failure Criteria of Fibrous Composite Materials, Polymer Composites 1996; 17: 786-798.
4. F. Paris, A Study of Failure Criteria of Fibrous Composite Materials, NASA/CR-2001-210661, 2001.
5. R.C. Tennyson, G.E. Wharam, Evaluation of Failure Criterion for Graphite-epoxy, NASA CR-172547 1985.
6. L. Tong, An Assessment of Failure Criteria to Predict the Strength of Adhesively Bonded Composite Double Lap Joints, Jnl. of Reinforced Plastics and Composites 1997; 16, 8: 698-713.
7. M.J. Hinton, P.D. Soden, Predicting Failure in Composite Laminates: The Background to the Exercise, Composites. Sci.& Technol. 1998; 58: 1001-1010.
8. P.D. Soden, M.J. Hinton, A.S Kaddour, Lamina Properties, Lay-up Configurations and Loading Conditions for a Wide Range of Fibre Reinforced Composite Laminates, Composites Sci. & Technol. 1998; 58: 1011-1224.
9. P.D. Soden, M.J. Hinton, A.S Kaddour, A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates, Composites Sci. & Technol. 1998; 58: 1225-1254.
10. P.D. Soden, M.J. Hinton, A.S Kaddour, Biaxial Test Results for Strength and Deformation of a Range of E-glass and Carbon Fibre Reinforced Composite Laminates: Failure Exercise Benchmark Data, Composites Sci. & Technol. 2002; 62: 1489-1514.
11. M.J. Hinton, A.S Kaddour, P.D. Soden, A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates, Judged Against Experimental Evidence, Composites Sci. & Technol. 2002; 62: 1725-1797.
12. U. Icardi, a. Atzori, Simple, Efficient Mixed Solid Element for Accurate Analysis of Local Effects in Laminated and Sandwich Composites, Advances in Engineering Software 2004; 32 (12): 843-859.
13. S.W. Tsai, E.M. Wu, A General Theory of Strength for Anisotropic Materials, Jnl. of Composite Materials 1971; 5: 58-80.
14. W. Tsai, Theory of Composite Design, 1988. Dayton: Thin Composites 4th Ed.
15. Z. Hashin, A. Rotem, A Fatigue Failure Criterion for Fiber Reinforced Materials, Jnl. of Composite Materials 1973; 7: 448-464.
16. A. Rotem, Z. Hashin, Failure Modes of Angle-ply Laminates, Jnl. of Composite Materials 1975; 9: 191-206.
17. Z. Hashin, Failure Criteria for Unidirectional Fiber Composites, Jnl. of Applied Mechanics 1980; 47: 329-334.
18. Z. Hashin, Analysis of Orthogonally Cracked Laminates Under Tension, Jnl. of Applied Mechanics 1987; 54: 872-879.
19. S.E Yamada, C.T Sun, Analysis of Laminate Strength and Its Distribution, Jnl. of Composite Materials 1978; 12: 275-284.
20. F.K. Chang, L. Lessard, Damage Tolerance of Laminated Composites Containing an Open Hole and Subjected to Compressive Loadings: Part I-Analysis. Jnl. of Composite Materials 1990; 25: 2-43.
21. F.K. Chang, M.H. Chen, The In Situ Ply Shear Strength Distributions in Graphite/Epoxy Laminated Composites, Jnl. of Composite Materials 1987; 21: 708-733.
22. H.T. Choi, H.Y.T. Wu, F.K. Chang, A New Approach Toward Understanding Damage Mechanism and Mechanics of Laminated Composites Due to Low-velocity Impact: Part II-Analysis, Jnl. of Composite Materials 1991; 25: 1012-1038.
23. H.Y. Choi, F.K. Chang, A Model for Predicting Damage in Graphite/Epoxy Laminated Composites Resulting from Low-velocity Point Impact, Jnl. of Composite Materials 1992; 26: 2134-2169.
24. H.Y. Choi, H.S. Wang, F.K. Chang, Effect of Laminate Configuration and Impactor's Mass on the Initial Impact Damage of Composite Plates Due to Line-loading Impact, Jnl. of Composite Materials 1992; 26: 804-827.
25. I. Shahid, F.K. Chang, An Accumulative Damage Model for Tensile and Shear Failures of Laminated Composite Plates, Jnl. of Composite Materials 1995; 29: 926-981.
26. H.T. Sun, F.K. Chang, X. Qing x, The Response of Composite Joints with Bolt-clamping Loads, Part I: Model Development, Jnl. of Composite Materials 2002; 36: 47-67.
27. P. Perugini, A. Riccio, F. Scaramuzzino, Three-dimensional Progressive Damage Analysis of Composite Joints, Paper 62, 8th International Conference on Civil and Structural Engineering Computing 2001.
28. S.G. Joo, C.S. Hong, C.G. Kim, Free Edge Effect of the Post Failure Behavior of Composite Laminates Under Tensile Loading, Jnl. of Reinforced Plastics and Composites 2001; 20: 191-222.
29. Y.J. Lee, C.H. Huang, Ultimate Strength and Failure Process of Composite Laminated Plates Subjected to Low-velocity Impact, Jnl. of Reinforced Plastics and Composites 1991; 10: 542-556.
30. C.Y. Wang, C.H. Yew, Impact Damage in Composite Laminates, Computers & Structures 1990; 37: 967-982.
31. U. Icardi, G. Zardo, CO Plate Element for Delamination Damage Analysis, Based on a Zig-zag Model and Strain Energy Updating, Int. Jnl. of Impact Engineering 2005; 31: 579-606.
32. D.W. Sleight, N.F. Knight, J.T. Wang, Evaluation of a Progressive Failure Analysis Methodology for Laminated Composite Structures, Proceedings of AIAA/ASME/ASCE/AHS/ASC 38th Structures, Structural Dynamics and Materials Conference, 1997, AIAA Paper 97-1187.
33. L.B. Lessard, M.M Shokrieh, Two-dimensional Modeling of Composite Pinned-joint Failure, Jnl. of Composite Materials 1995; 29: 671-697.
34. M.E. Pachajoa, M.K. Frances, J.D. Lee, Stress and Failure Analysis of Composite Structures, Engineering Fracture Mechanics 1995; 50: 883-902.
35. C.T. Sun, B.J. Quinn, D.W. Oplinger, An Accumulative Damage Model for Tensile and Shear Failures of Laminated Composite Plates, Jnl. of Composite Materials 1995; 29, 926-981.
36. A. Puck, Festigkeitsanalyse von faser-matrix-laminaten - Modelle fur die praxis, Carl Hanser Verlag, 1995.
37. A. Puck, Festigkeitsberechnung an glassfaser/kunstoff laminates bei zusammengesetzeter beanspruchung, Kunststoffe, 1969; 59: 780-787.
38. A. Puck, Calculating the Strength of Glass-fibre/Plastic Laminates Under Combined Load, Kunststoffe, German Plastics 1969; 55: 18-19.
39. A. Puck, Failure Criterion Shows the Direction, Kunststoffe, German Plastics 1992; 82: 29-32.
40. A. Puck, Fracture Criteria for Highly Stressed Fibre-plastic Composites Which Meet Requirements of Design Practice, Kunststoffe, German Plastics 1992; 82: 34-38.
41. A. Puck, H. Shurmann, Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models, Composites Sci.& Technol. 1998; 58: 1045-1067.
42. L. Kroll, W. Hufenbach, Physically Based Failure Criterion for Dimensioning of Thick-walled Laminates, Applied Composite Materials 1997; 4: 321-332.
43. S.J. Mayes, A.C. Hansen, Multicontinuum Failure Analysis of Composite Structural Laminates, Mechanics of Composite Materials and Structures 2001; 8: 249-262.
44. R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, 1950.
45. R. Hill, Elastic Properties of Reinforced Solids: Some Theoretical Principles, Jnl. Mech. Phys. Solids 1963; 11: 357-372.
46. C.G. Davila, P.P. Camanho, Failure Criteria for FRP Laminates in Plane Stress, NASA/TM-2003-212663, 2003.
47. A.K. Noor, Computational Structures Technology-leap Frogging into the Twenty-first Century, Advances in Computational Structures Technology, 1996; Civil-Comp Press: 1-18.
48. A.K. Noor, W.S. Burton, C.W. Bert, Computational Models for Sandwich Panels and Shells, Appl. Mech. Rev. 1996; 49 (3): 155-199.
49. J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd Edition, CRC Press, Boca Raton, FL., 2003.
50. L.T. Tenek, J. Argyris, Finite Element Analysis for Composite Structures, Kluwer Academic Publ., 1998.
51. V.R. Aitharaju, R.C Averill, Zig-zag Kinematic Displacement Models for the Analysis of Laminated Composites, Mech. of Comp. Mater. and Struct. 1999; 6 (1): 31-56.
52. U. Icardi, Application of Zig-zag Theories to Sandwich Beams, Mech. of Advan. Mater. and Struct. 2003; 10: 77-97.
53. R. Thornburgh, A. Chattopadhyay, Unified Approach to Modeling Matrix Cracking and Delamination in Laminated Composite Structures, AIAA J. 2001; 39 (1): 153-160.
54. S.V. Hoa, W. Feng, Hybrid Finite Element Method for Stress Analysis of Laminated Composites, Kluwer Academic Publ., 1998.
55. I. Babuska, The Finite Element Method with Lagrange Multipliers, Num. Math 1973; 20: 179-192.
56. F. Brezzi, On the Existence, Uniqueness and Approximation of Saddle Point Problems Arising from Lagrangian Multipliers, RAIRO 1974; 8-R2: 129-151.
57. M.D. Olson, The Mixed Finite Element Method in Elasticity and Elastic Contact Problems, In S.N. Atluri, R.H. Gallagher, O.C. Zienkiewicz eds., Hybrid and Mixed Finite Element Methods, John Wiley & Sons: 19-49, 1983.
58. S. Nakazawa, Mixed Finite Elements and Iterative Solution Procedures, Iterative Methods in Non-Linear Problems, Pineridge, 1984.
59. C. Loubignac, C. Cantin, C. Touzot, Continuous Stress Fields in Finite Element Analysis, AIAA Journal 15, 1978: 1645-1647.
60. I. Gol'demblat, V.A. Kopnov, Strength of Glass-reinforced Plastics in the Complex Stress State, Polymer Mechanics 1965; 1: 54-59.
61. A.K. Malmeister, Theories of Strength, Polymer Mechanics 1966; 2:324-331.
62. C.B. Norris, Strength of Orthotropic Materials Subjected to Combined Stress, U.S. Forest Products Laboratory Report 1816, 1950.
63. L. Fisher, How to Predict Structural Behavior of Reinforced Plastic Laminates, Modern Plastics 1960; 37: 121-128, 208-209.
64. E.K. Ashkenazi, Problems of the Anisotropy of Strength, Polymer Mechanics 1965; 1, 60-70.
65. O. Hoffman, The Brittle Strength of Ortothropic Materials, Jnl. of Composite Materials 1965; 1: 200-206.
66. S.C. Cowin, On the Strength Anisotropy of Bone and Wood, ASME Jnl. of Applied Mechanics 1979; 46: 832-838.
67. V.D. Azzi, S.W. Tsai, Anisotropic Strength of Composites, Experimental Mechanics 1965; 5: 283-288.
68. R.C. Tennyson, A.P. Nayaro, G.E. Wharam, Application of the Cubic Polynomial Strength Criteria to the Failure Analysis of Composite Materials, Jnl. of Composite Materials 1980; 14: 28-41.
69. Z. Jiang, R.C. Tennyson, Closure of the Cubic Tensor Polynomial Failure Surface, Jnl. of Composite Materials 1989; 23: 208-231.
70. C.L.D. Huang, Strength Coefficients of the Cubic Criterion for Graphite Composites, Jnl. of Engineering Materials and Technology 1990; 112: 227-230.
71. H. Kilic, R. Haj-Ali, Progressive Damage and Nonlinear Analysis of Pultruded Composite Structures, Composites Part B: Engineering 2003; 34B: 235-250.
72. S. Huybrechts, A. Maji, J. Lao, P. Wegner, T. Meink, Validation of the Quadratic Composite Failure Criteria with Out-of-Plane Shear Terms, Jnl. of Composite Materials 2002; 36: 1879-1887.
73. J.N. Reddy, A.K. Pandey, A First-ply Failure Analysis of Composite Laminates, Computers and Structures 1987; 25: 371-393.
74. G.S. Padhi, R.A. Shenoi, S.S.J. Moy, G.L. Hawkins, Progressive Failure and Ultimate Collapse of Laminated Composite Plates in Bending, Composite Structures 1998; 40: 277-291.
75. B.G. Prusty, S.K. Satsangi, C. Ray, First-ply Failure Analysis of Laminated Panels under Transverse Loading, Jnl. of Reinforced Plastics and Composites 2001; 20: 671-687.
76. P. Pal, C. Ray, Progressive Failure Analysis of Laminated Composite Plates by Finite Element Method, Jnl. of Reinforced Plastics and Composites 2002; 21: 1505-1513.
77. T.Y. Kam, H.F. Sher, T.N. Chao, R.R. Chang, Prediction of Deflection and First-ply Failure Load of Thin Laminated Composite Plates via the Finite Element Approach, Int. Jnl. of Solids and Structures 1996; 33: 375-398.
78. T.Y. Kam, T.B. Jan, First-ply Failure Analysis of Laminated Composite Plates Based on the Layerwise Linear Displacement Theory, Composite Structures 1995; 32: 583-591.
79. H.Y. Yeh, W.L. Richards, Yeh-Stratton Criterion for Stress-concentrations on Fiber-reinforced Composite Materials, NASA CR-198054 1996.
80. H.Y. Yeh, W.L. Richards, Failure Study of Composite Materials by the Yeh-Stratton Criterion, NASA TM-113087 1997.
81. H.T. Hahn, A Mixed-mode Fracture Criterion for Composite Materials, Composites Tech. Rev. 1983; 5: 26-29.
82. F.K. Chang, R.A Scott, G.S. Springer, Failure Strength of Nonlinearly Elastic Composite Laminates Containing a Pin Loaded Hole, Jnl. of Composite Materials 1984; 18: 464-477.
83. R.S. Sandhu, Non Linear Behavior of Unidirectional and Angle Ply Laminates, Jnl. of Aircraft 1975; 13: 104-111.
84. H.T. Hahn, S.W. Tsai, On the Behavior of Composite Laminates after Initial Failures, Astronautics and Aeronautics 1983; 21: 58-62.
85. F.K. Chang, G.S. Springer, The Strengths of Fiber Reinforced Composite Bends, Jnl. of Composite Materials 1986; 20: 30-47.
86. R.K. Luo, E.R. Green, C.J. Morrison, An Approach to Evaluate the Impact Damage Initiation and Propagation in Composite Laminates, Composites Part B: Engineering 2001; 32B: 513-520.
87. F.K. Chang, K.Y. Chang, Post Failure Analysis of Bolted Composite Joints in Tension or Shearout Mode Failure, Jnl. of Composite Materials 1987; 21: 803-833.
88. F.K. Chang, K.Y. Chang, A Progressive Damage Model for Laminated Composites Containing Stress Concentrations, Jnl. of Composite Materials 1987; 21: 834-855.
89. Y. Zhang, S. Wang, B. Petersson, Large Deflection Analysis of Composite Laminates, Jnl. of Material Processing Technology 2003; 138: 34-40.
90. S. Liu, Z. Kutlu, F.K. Chang, Matrix Cracking and Delamination in Laminated Composite Beams Subjected to a Transverse Concentrated Line Load, Jnl. of Composite Materials 1993; 27: 436-470.
91. W.C. Hwang, C.T. Sun, Failure Analysis of Laminated Composites by Using Iterative Three-dimensional Finite Element Method, Computers & Structures 1989; 33: 41-47.
92. S. Mohammadi, D.R.J. Owen, D. Peric D, A Combined Finite/Discrete Element Algorithm for Delamination Analysis of Composites, Finite Elements In Analysis and Design 1998; 28: 249-262.
93. J.P. Hou, N. Petrinic, C. Ruiz, S.R. Hallet, Prediction of Impact Damage in Composite Plates, Composites Sci. & Technol. 2000; 60: 273-281.
94. J.C. Brewer, P.A. Lagace, Quadratic Stress Criterion for Initiation of Delamination, Jnl. of Composite Materials 1988; 22: 1141-1155.
95. J.P Hou, N. Petrinic, C. Ruiz, A Delamination Criterion for Laminated Composites Under Low Velocity Impact, Composites Sci. & Technol. 2001; 61: 2069-2074.
96. R.M. Christensen, Tensor Transformations and Failure Criteria for the Analysis of Fiber Composite Materials, Jnl. of Composite Materials 1988; 22: 874-897.
97. R.M. Christensen, Stress Based Yield/Failure Criteria for Fiber Composites, Int. Jnl. of Solids and Structures 1997; 34: 529-543.
98. C.L. Hung, F.K. Chang, Bearing Failure of Bolted Composite Joints, Part II: Model and Verification, Jnl. of Composite Materials 1996; 30: 1359-1400.
99. I. Shahid, Progressive Failure Analysis of Laminated Composite Plates Subjected to In-plane Tensile and Shear Loads, Ph.D. Dissertation, Department of Civil Engineering, Stanford University, 1993.
100. G. Abu-Farsakh, New Material Models for Non-linear Stress-strain Behavior of Composite Materials, Composites 1989; 20: 349-360.
101. G. Abu-Farsakh, Y.A. Abdel-Jaward, A New Failure Criterion for Nonlinear Composite Materials, Jnl. of Composite Technology and Research 1994; 16: 138-145.
102. M.M. Shokrieh, L.B. Lessard, Multiaxial Fatigue Behavior of Unidirectional Plies Based on Uniaxial Fatigue Experiments, Part I: Modeling, Int. J. of Fatigue 1997; 19: 201-207.
103. M.M. Shokrieh, L.B. Lessard, Progressive Fatigue Damage Modeling of Composite Materials, Part I: Modeling, Jnl. of Composite Materials 2000; 34: 1056-1080.
104. M.L. Dano, G. Gendron, A. Picard, Stress and Failure of Mechanically Fastened Joints in Composite Laminates, Composite Structures 2000; 50: 287-296.
105. D. Cohen, M.W. Hyer, J. Stuart, O.H. Griffith, C. Prasad, S.R. Yalamanchili, Failure Criterion for Thick Multifastener Graphite-epoxy Composite Joints, Jnl. of Composite Technology and Research 1995; 17: 237-248.
106. J.N. Whitney, R.J. Nuismer, Stress Failure Criteria for Laminated Composites Containing Stress Concentrations, Jnl. of Composite Materials 1974; 8: 253-265.
107. J.F. Echaabi, F. Trochu, R. Gauvin, A General Strength Theory for Composite Materials Based on Dual Kriging Interpolation, Jnl. of Reinforced Plastics and Composites 1995; 14: 211-232.
108. J.R Echaabi, F. Trochu, Failure Mode Dependent Strength Criteria for Composite Laminates, Jnl. of Reinforced Plastics and Composites 1997; 16 (10): 926-945.
109. J. Echaabi, F. Trochu, A Methodology to Derive Failure Criteria of Fibrous Composite Laminates, Jnl. of Composite Materials 1996; 30: 1088-1114.
110. E.C. Edge, Stress Based Grant-Sanders Method for Predicting Failure of Composite Laminates, Composites Sci.& Technol. 1998; 58: 1033-1041.
111. R.C. Sanders, P. Grant, The Strength of Laminated Plates Under In-plane Loading, BAe Report SOR(P)130 1982.
112. I. Eriksson, C.G. Aronsson, Strength of Tensile Loaded Graphite/Epoxy Laminates Containing Cracks, Open and Filled Holes, Jnl. of Composite Materials 1991; 24: 456-482.
113. J. Bäcklund, Fracture Analysis of Notched Composites, Computers and Structures 1981; 13: 145-154.
114. W.W. Feng, A Failure Criterion for Composite Materials, Jnl. of Composite Materials 1991; 25: 88-100.
115. A.E. Green, J.E. Adkins, {\em Large Elastic Deformations and Non-Linear Continuum Mechanics}. Clarendon Press, Oxford, 1970.
116. L.J. Hart-Smith, A New Approach to Fibrous Composite Laminate Strength Prediction, 8th DOD/NASA/FAA Conference on Fibrous Composites in Structural Design, NASA CP-3087 1989; 663-693.
117. L.J. Hart-Smith, A Strain-based Maximum-shear-stress Failure Criterion for Fibrous Composite Laminates, Proc. 31st AIAA/ASME/ASCE/AHS/ASC Structural Dynamics and Materials Conf., Long Beach CA, April 2-4 1992, CP902; 2: 714-722.
118. L.J. Hart-Smith, Predicting the Strength of Fibrous Composites by an Orthotropic Generalization of the Maximum-Shear Stress (Tresca) Condition, Jnl. of Aerospace Eng. 1994; 208: 9-18.
119. L.N. McCartney, Predicting Transverse Crack Formation in Cross-Ply Laminates, Composites Sci. & Technol. 1998; 58: 1069-1081.
120. A. Rotem, H.G. Nelson, Fatigue Behavior of Graphite-epoxy Laminate at Elevated Temperatures, ASTM STP 723, 1981: 152-173.
121. A. Rotem, The Anisotropic Fatigue Behavior of Isotropic Composite Laminates, Int. Jnl of Fatigue 1994; 16: 266-272.
122. A. Rotem, Prediction of Laminate Failure with the Rotem Failure Criterion, Composites Sci. & Technol. 1998; 58: 1083-1094.
123. C.K. Kim, H.Y. Yeh, Development of a New Yielding Criterion: The Yeh-Stratton Criterion, Engineering Fracture Mechanics 1994; 47: 569-582.
124. H.Y. Yeh, C.K. Kim, The Yeh-Stratton Criterion for Composite Materials, Jnl. of Composite Materials 1994; 28: 927-939.
125. H.Y. Yeh, C.H. Kim, Effects of Interaction Component of the Generalized Yeh-Stratton Criterion, Jnl. of Reinforced Plastics and Composites 1994; 13: 793-802.
126. H.L. Yeh, H.Y. Yeh, A Sequential Fiber Failure Criterion for the Tensile Fracture in Notched Fiber Reinforced Composites, Jnl. of Reinforced Plastics and Composites 2003; 22: 463-478.
127. H.T Yeh, C. Kim, The Mixed Mode Crack Propagation by the Yeh-Stratton Criterion, Engineering Fracture Mechanics 1994; 48: 595-607.
128. Composite Materials Handbook - Polymer Matrix Composite Material Properties Vol. 2, MIL-HDBK-17-2F.
129. M.L. Benzeggagh, M. Kenane, Measurement of Mixed-mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites with Mixed-mode Bending Apparatus, Composite Science and Technology 1996; 56: 439-449.
130. L.J. Hart-Smith, Predictions of the Original and Truncated Maximum-strain Failure Modes for Certain Fibrous Composite Laminates, Composites Sci. & Technol. 1998; 58 (7): 1151-1178.
131. K.S. Liu, S.W. Tsai, A Progressive Quadratic Failure Criterion for a Laminate, Composites Sci. & Technol. 1998; 58: 1023-1032.
132. H.A. Whitworth, S.W. Yin, A Failure Criterion for Laminated Fiber-reinforced Composites, Composite Engineering 1991; 1: 61-67.
133. W.E. Wolfe, T.S. Butalia, A Strain Energy Based Failure Criterion for Non-linear Analysis of Composite Laminates Subjected to Biaxial Loading, Composites Sci. & Technol. 1998; 58: 1007-1124.
134. H.L. Yeh, Quadric Surfaces Criterion for Composite Materials, Jnl. of Reinforced Plastics and Composites 2003; 22: 517-532.
135. R.Y. Kim, S.R. Soni, Experimental and Analytical Studies on the Onset of Delamination in Laminated Composites, Jnl. of Composite Materials 1984; 18: 70-80.
136. T.Y. Kam, F.M. Lai, Experimental and Theoretical Predictions of First-ply Failure Strength of Laminated Composite Plates, Int. Jnl. of Solids and Structures 1999; 36: 2379-2395.