An investigation was performed to study the mechanics of delamination growth in fiber-reinforced laminated composites resulting from transverse concentrated loads. The effect of matrix cracking on delamination propagation was the primary focus of the study. For simplicity's sake, only cross-ply laminates were investigated. An analytical model was proposed for determining the response of the laminates containing a matrix crack-induced delamination and subjected to a concentrated load through a spherical indenter. Two types of matrix cracks were considered in the model: a surfacebending crack and an internal shear crack. The model consists of three parts: a stress analysis, a contact analysis, and a failure analysis. A nonlinear three-dimensional finite element model based on an updated Lagrange formulation was developed for calculating stresses and strains in composites. An augmented Lagrangian method was utilized to simulate the interfacial contact condition of the embedded delamination and the indentation between the composite and the indenter. Fracture mechanics was applied to predict the delamination growth in three dimensions.
In order to verify the model, results of the calculations from the analysis were compared with the existing solutions and test data available in the literature. Experiments were also conducted to further substantiate the model and the predictions from the analysis. Overall, the predictions agreed well with the existing solutions and the test data.
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References
1.
1. Finn, S. R. and G. S. Springer. 1991. Composite Plates Impact Damage: An Atlas. Lancaster, PA: Technomic Publishing Co., Inc.
2.
2. Sjoblom, P. O., J. T. Hartness and T. M. Cordell. 1988. "On Low-Velocity Impact Testing of Composite Materials,"J. of Composite Materials, 22:30-52.
3.
3. Wu, H. T. and G. S. Springer. 1988. "Measurements of Matrix Cracking and Delamination Caused by Impact on Composite Plates,"J. of Composite Materials, 22:518-532.
4.
4. Gosse, J. H. and P. B. Y. Mori. 1988. "Impact Damage Characterization of Graphite/Epoxy Laminates,"Proceedings of the Third Technical Conference of the American Society for Composites, Seattle, WA, pp. 334-353.
5.
5. Joshi, S. P. 1988. "Impact-Induced Damage Initiation Analysis: An Experimental Study,"Proceedings of the Third Technical Conference of the American Society for Composites, Seattle, WA, pp. 325-333.
6.
6. Joshi, S. P. and C. T. Sun. 1986. "Impact-Induced Fracture in Quasi-Isotropic Laminate,"J. of Composite Technology and Research, 19:40-46.
7.
7. Choi, H. Y., R. J. Downs and F. K. Chang. 1991. "A New Approach toward Understanding Damage Mechanisms and Mechanics of Laminated Composites Due to Low-Velocity Impact, Part I-Experiments,"J. of Composite Materials, 25(8):992-1011.
8.
8. Poe, C. C., Jr.1988. "Simulated Impact Damage in a Thick Graphite/Epoxy Laminate Using Spherical Indenters," NASA TM-100539.
9.
9. Sun, C. T. and S. Rechak. 1988. "Effect of Adhesive Layers on Impact Damage in Composite Laminates," in Composite Materials: Testing and Design (Eighth Conference), J. D. Whitcomb, ed., ASIM STP 972, Philadelphia, PA: American Society for Testing and Materials, pp. 97-123.
10.
10. Liu, D. and L. E. Malvern. 1987. "Matrix Cracking in Impacted Glass/Epoxy Plates,"J. of Computers and Structures, 21:594-609.
11.
11. Malvern, L. E., R. L. Sierakowski, L. A. Ross and N. Cristescu. 1978. "Impact Failure Mechanisms in Fiber-Reinforced Composite Plates," in High Velocity Deformation of Solids, Kawata and Shiori, eds., Berlin: Springer-Verlag, pp. 120-130.
12.
12. Jones, S., J. Paul, T. E. Tay and J. F. Williams. 1988. "Assessment of the Effect of Impact Damage in Composites: Some Problems and Answers,"Composite Structures, 10:51-73.
13.
13. Sun, C. T. and J. E. Grady. 1988. "Dynamic Delamination Fracture Toughness of a Graphite/ Epoxy Laminate under Impact,"Composite Science and Technology, 31:55-72.
14.
14. Guynn, E. G. and T. K. O'Brien. 1985. "The Influence of Lay-up and Thickness on Composite Impact Damage and Compression Strength,"Proceedings of AIAA/ASME/ASCE/AHS, 26th Structure, Structural Dynamics and Materials Conference, Orlando, FL, pp. 187-196.
15.
15. Choi, H. T., H. Y. T. Wu and F. K. Chang. 1991. "A New Approach toward Understanding Damage Mechanisms and Mechanics of Laminated Composites Due to Low-Velocity Impact, Part II-Analysis,"J. of Composite Materials, 25(8):1012-1038.
16.
16. Choi, H. Y., H. S. Wang and F. K. Chang. 1992. "Effect of Laminate Configuration and Impactor's Mass on the Initial Impact Damage of Composite Plates Due to Line-Loading Impact,"J. of Composite Materials, 26(6):804-827.
17.
17. Choi, H. Y. 1991. "Effect of Transversely Low-Velocity Impact on Graphite/Epoxy Laminated Composites," Ph.D. thesis, Department of Mechanical Engineering, Stanford University.
18.
18. Sun, C. T. and M. G. Manoharan. 1989. "Growth of Delamination Cracks Due to Bending in a [905/05/90501 Laminate,"Composite Science and Technology, 34:365-377.
19.
19. Martin, R. H. and W. C. Jackson. 1991. "Damage Prediction in Cross-Plied Curved Composite Laminates;" NASA Technical Memorandum 104089.
20.
20. Salpekar, S. A.1991. "Analysis of Delamination in Cross Ply Laminates Initiating from Impact Induced Matrix Cracking," NASA Contract Report 187594.
21.
21. Liu, S., Z. Kutlu and F. K. Chang. 1991. "Matrix Cracking and Delamination in Laminated Polymeric Composites Resulting from Transversely Concentrated Loadings,"Proceedings of the 1st International Conferences on Deformation and Fracture of Composites, Manchester, England, March 25-27, 1991, pp. 30/1 to 30/7.
22.
22. Liu, S., Z. Kutlu and F. K. Chang. 1993. "Matrix Cracking-Induced Delamination Propagation in Graphite/Epoxy Laminated Composites due to Transversely Concentrated Load," in Composite Materials: Fatigue and Fracture STP 1156 (4th Volume), Stinchcomb and Ashbaugh, eds.
23.
23. Liu, S., Z. Kutlu and F. K. Chang. 1993. "Matrix Cracking and Delamination in Laminated Composite Beams Subjected to a Transverse Concentrated Line Load,"Journal of Composite Materials, 27(5):436-470.
24.
24. Fung, Y. C.1965. Foundations of Solid Mechanics. New Jersey: Prentice-Hall, Inc.
25.
25. Bathe, K. J.1982. Finite Element Procedures in Engineering Analysis. New Jersey: Prentice-Hall.
26.
26. Luenberger, D. G.1984. Linear and Nonlinear Programming. Reading, MA: Addison-Wesley.
27.
27. Kikuchi, N. and J. T. Oden. 1988. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. Philadelphia: SIAM.
28.
28. Hestenes, M. R.1969. "Multiplier and Gradient Methods,"Journal of Optimization, Theory and Applications, 4:303-320.
29.
29. Powell, M. J. M."A Method for Nonlinear Constraints in Minimization Problems," in Optimization, R. Fletcher, ed., New York: Academic Press.
30.
30. Rockafellar, R. T.1969. "Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming;'SIAM Journal of Control, 12:268-285.
31.
31. Glowinsky, R. and P. LeTallec. 1984. "Finite Element Analysis in Nonlinear Incompressible Elasticity," in Finite Elements, Vol. V Special Problems in Solid Mechanics, J. T. Oden and G. F. Carey, eds., Englewood Cliffs, NJ: Prentice-Hall.
32.
32. Wriggers, P. and J. C. Simo. 1985. "A Note on Tangent Stiffness for Fully Nonlinear Contact Problems,"Communications in Applied Numerical Methods, 1:199-203.
33.
33. Simo, J. C. and T. A. Laursen. 1992. "An Augmented Lagrangian Treatment of Contact Problems Involving Friction,"Computers and Structures, 42(1):97-116.
34.
34. Rybicki, E. F. and M. F. Kanninen. 1977. "A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral,"Engineering Fracture Mechanics, 9:931-938.
35.
35. Kanninen, M. F. and C. H. Popelar. 1985. Advanced Fracture Mechanics, Oxford Engineering Science Series. Oxford University Press.
36.
36. Hahn, H. T.1983. "A Mixed-Mode Fracture Criterion for Composite Materials,"Composite Technology Review, 5:26-29.
37.
37. Lu, X. and D. Liu. 1989. "Strain Energy Release Rates at Delamination Front,"Proceedings of the American Society of Composites, Fourth Technical Conference, October 1989, pp. 277-286.
38.
38. Chai, H. 1989. "Mixed-Mode Fracture Behavior of Delaminated Films,"Proceedings of the American Society for Composites, Fourth Technical Conference, October 1989, pp. 815-825.
39.
39. Whitcomb, J. D.1988. "Instability-Related Delamination Growth of Embedded and Edge Delaminations," NASA Technical Memorandum 100655.
40.
40. Kutlu, Z. and F. K. Chang. 1992. "Modelling Compression Failure of Laminated Composites Containing Multiple through-the-Width Delaminations,"J. of Composite Materials, 26(3): 350-389.
41.
41. Liu, S. 1992. "Damage Mechanics of Cross-Ply Laminates Resulting from Transverse Concentrated Loads," Ph.D. dissertation, Department of Mechanical Engineering, Stanford University.
42.
42. Benson, D. J. and J. O. Hallquist. 1990. "A Single Surface Contact Algorithm for the Post-Buckling Analysis of Shell Structures,"Computer Methods in Applied Mechanics and Engineering, 78:141-163.
43.
43. Parisch, H.1989. "A Consistent Tangent Stiffness Matrix for Three-Dimensional Nonlinear Contact Analysis,"International J. for Numerical Methods in Engineering, 28:803-1812.
44.
44. Davidson, B. D.1990. "An Analytical Investigation of Delamination Front Curvature in Double Cantilever Beam Specimens"Journal of Composite Materials, 24:1124-1137.
45.
45. Crews, J. H., K. N. Shivakumar and I. S. Raju. 1991. "Strain Energy Release Rate Distribution for Double Cantilever Beam Specimen,"AIAA-Journal, 10:1686-1691.
46.
46. Timoshenko, S. P. and S. Woinowski-Krieger. 1959. Theory of Plates and Shells. McGraw-Hill.
47.
47. Sun, C. T. and S. H. Yang. 1980. "Contact Law and Impact Responses of Laminated Composites," NASA CR-159884, Washington, D.C.
48.
48. Tan, T. M. and C. T. Sun. 1985. "Use of Statical Indentation Laws in the Impact Analysis of Laminated Composite Plates,"Journal of Applied Mechanics, 52:6-12.
49.
49. Odagiri, N., H. Kishi and T. Nakae. 1989. "T800H/3900-2 Toughened Epoxy Prepreg System: Toughening Concepts and Mechanism,"34th Intenational SAMPE Symposium, pp. 43-52.
