A new decohesion element with the capability of dealing with crack propagation under mixed-mode loading is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and non-self-similar growth of delaminations in composite materials. A single relative displacement-based damage parameter is applied in a softening law to track the damage state of the interface and to prevent the restoration of the cohesive state during unloading. The softening law is applied in the three-parameter Benzeggagh-Kenane mode interaction criterion to predict mixed-mode delamination propagation. To demonstrate the accuracy of the predictions, steady-state delamination growth is simulated for quasi-static loading of various single mode and mixed-mode delamination test specimens and the results are compared with experimental data.
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References
1.
1. Whitney, J.M. and Nuismer, R.J. (1974). Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations , Journal of Composite Materials, 8: 253-265 .
2.
2. Kim, R.Y. and Soni, S.R. (1984). Experimental and Analytical Studies on the Onset of Delamination in Laminated Composites , Journal of Composite Materials, 18: 70-80 .
3.
3. Camanho, P.P. and Matthews, F.L. (1999). Delamination Onset Prediction in Mechanically Fastened Joints in Composite Laminates , Journal of Composite Materials, 33: 906-927 .
4.
4. Dávila, C.G. and Johnson, E.R. (1993). Analysis of Delamination Initiation in Postbuckled Dropped-Ply Laminates , AIAA Journal, 31(4): 721-727 .
5.
5. Schoeppner, G.A. and Pagano, N.J. (1998). Stress Fields and Energy Release Rates in Cross-ply Laminates , International Journal of Solids and Structures, 11: 1025-1055 .
6.
6. Sun, C.T. and Jih, C.J. (1987). On Strain-Energy Release Rates for Interfacial Cracks in Bi-Material Media , Engineering Fracture Mechanics, 28(1): 13-20 .
7.
7. Sun, C.T. and Manoharan, M.G. (1989). Strain Energy Release Rates of an Interfacial Crack Between Two Orthotropic Solids , Journal of Composite Materials, 23: 460-478 .
8.
8. Krueger, R. and O'Brien, T.K. (2001). A Shell/3D Modeling Technique for the Analysis of Delaminated Composite Laminates , Composites-Part A, 32: 25-44 .
9.
9. Li, J. and Sen, J.K. (2000). Analysis of Frame-to-Skin Joint Pull-Off Tests and Prediction of the Delamination Failure , 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Seattle, WA, USA.
10.
10. Li, J. (2000). Three-Dimensional Effects in the Prediction of Flange Delamination in Composite Skin-Stringer Pull-Off Specimens , 15th Conference of the American Society for Composites, Texas, USA.
11.
11. Krueger, R., Cvitkovich, M.K., O'Brien, T.K. and Minguet, P.J. (2000). Testing and Analysis of Composite Skin/Stringer Debonding Under Multi-Axial Loading , Journal of Composite Materials, 34(15): 1263-1300 .
12.
12. Köning, M., Krueger, R. and Rinderknecht, S. (1995). Numerical Simulation of Delamination Buckling and Growth , 10th International Conference on Composite Materials (ICCM-10), Whistler, Canada.
13.
13. Krueger, R. (1999). A Shell/3D Modeling Technique for Delamination in Composite Laminates , 14th Conference of the American Society for Composites, Ohio, USA.
14.
14. Krueger, R., Minguet, P.J. and O'Brien, T.K. (1999). A Method for Calculating Strain Energy Release Rates in Preliminary Design of Composite Skin/Stringer Debonding Under Multi-Axial Loading, NASA TM-1999-209365.
15.
15. Rybicki, E.F. and Kanninen, M.F. (1977). A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral , Engineering Fracture Mechanics, 9: 931-938 .
16.
16. Rinderknecht, S. and Kröplin, B. (1994). Calculation of Delamination Growth With Fracture and Damage Mechanics, Recent Developments in Finite Element Analysis, CIMNE, Barcelona, Spain .
17.
17. Dudgale, D.S. (1960). Yielding of Steel Sheets Containing Slits , Journal of Mechanics and Physics of Solids, 8: 100-104 .
18.
18. Barenblatt, G.I. (1962). Mathematical Theory of Equilibrium Cracks in Brittle Failure , Advances in Applied Mechanics, 7.
19.
19. Camanho, P.P., Dávila, C.G. and Ambur, D.R. (2001). Numerical Simulation of Delamination Growth in Composite Materials, NASA-TP-211041.
20.
20. de Moura, M.F., Gonçalves, J.P., Marques, A.T. and de Castro, P.T. (1997). Modeling Compression Failure After Low Velocity Impact on Laminated Composites Using Interface Elements , Journal of Composite Materials, 31: 1462-1479 .
21.
21. Goyal-Singhal, V., Johnson, E.R., Dávila, C.G, and Jaunky, N. (2002). An Irreversible Constitutive Law for Modeling the Delamination Process Using Interface Elements . 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Colorado, USA.
22.
22. Reddy Jr., E.D., Mello, F.J. and Guess, T.R. (1997). Modeling the Initiation and Growth of Delaminations in Composite Structures , Journal of Composite Materials, 31: 812-831 .
23.
23. Chen, J., Crisfield, M.A., Kinloch, A.J., Busso, E.P., Matthews, F.L., and Qiu, Y. (1999). Predicting Progressive Delamination of Composite Material Specimens Via Interface Elements , Mechanics of Composite Materials and Structures, 6: 301-317 .
24.
24. Petrossian, Z. and Wisnom, M.R. (1998). Prediction of Delamination Initiation and Growth From Discontinuous Plies Using Interface Elements , Composites-Part A, 29: 503-515 .
25.
25. Cui, W. and Wisnom, M.R. (1993). A Combined Stress-Based and Fracture Mechanics-Based Model for Predicting Delamination in Composites , Composites, 24(6): 467-474 .
26.
26. Shahwan, K.W. and Waas, A.M. (1997). Non-Self-Similar Decohesion Along a Finite Interface of Unilaterally Constrained Delaminations , Proceedings of the Royal Society of London, 453: 515-550 .
27.
27. Reeder, J.R. (1992). An Evaluation of Mixed-Mode Delamination Failure Criteria, NASA-TM-104210.
28.
28. Allix, O. and Corigliano, A. (1999). Geometrical and Interfacial Nonlinearities in the Analysis of Delamination in Composites , International Journal of Solids and Structures, 36: 2189-2216 .
29.
29. Ahmad, S., Irons, B.M. and Zienkiewicz, O.C. (1970). Analysis of Thick and Thin Shell Structures by Curved Finite Elements , International Journal for Numerical Methods in Engineering, 2: 419-451 .
30.
30. Beer, G. (1985). An Isoparametric Joint/Interface Element for Finite Element Analysis , International Journal for Numerical Methods in Engineering, 21: 585-600 .
31.
31. Daudeville, L., Allix, O. and Ladevèze, P. (1995). Delamination Analysis by Damage Mechanics: Some Applications , Composites Engineering, 5(1): 17-24 .
32.
32. Pinho, S.T. (2002). Crush Simulation and Energy Absorption of Composite Tubes, MSc Thesis, Faculty of Engineering, University of Porto, Portugal.
33.
33. Gonçalves, J.P., de Moura, M.F., de Castro, P.T. and Marques, A.T. (2000). Interface Element Including Point-to-Surface Constraints for Three-Dimensional Problems With Damage Propagation , Engineering Computations, 17(1): 28-47 .
34.
34. Mi, Y., Crisfield, M.A., Davies, G.A.O. and Hellweg, H.B. (1998). Progressive Delamination Using Interface Elements , Journal of Composite Materials, 32: 1246-1273 .
35.
35. Schellekens, J.C.J. and de Borst, R. (1991). Numerical Simulation of Free Edge Delamination in Graphite-Epoxy Laminates Under Uniaxial Tension , Proceedings of the 6th International Conference on Composite Structures.
36.
36. Schellekens, J.C.J. and de Borst, R. (1993). On the Numerical Integration of Interface Elements , International Journal for Numerical Methods in Engineering, 36: 43-66 .
37.
37. Schellekens, J.C.J. (1992). Computational Strategies for Composite Structures, PhD Thesis, Technical University of Delft, The Netherlands.
38.
38. de Borst, R. and Rots, J.G. (1989). Occurrence of Spurious Mechanisms in Computation of Strain-Softening Solids , Engineering Computations, 6: 272-280 .
39.
39. Alfano, G. and Crisfield, M.A. (2001). Finite Element Interface Models for the Delamination Analysis of Laminated Composites: Mechanical and Computational Issues , International Journal for Numerical Methods in Engineering, 50: 1701-1736 .
40.
40. Dodes, I.A. (1978). Numerical Analysis for Computer Science, North-Holland, New York, USA .
41.
41. Ungsuwarungsri, T. and Knauss, W.G. (1987). The Role of Damage-Softened Material Behaviour in the Fracture of Composites and Adhesives , International Journal of Fracture, 35: 221-241 .
42.
42. Needleman, A. (1987). A Continuum Model for Void Nucleation by Inclusion Debonding , Journal of Applied Mechanics, 54: 525-531 .
43.
43. Rice, J.R. (1968). A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks , Journal of Applied Mechanics, 31: 379-386 .
44.
44. Dávila, C.G., Camanho, P.P. and de Moura, M.F. (2001). Mixed-Mode Decohesion Elements for Analyses with Progressive Delamination , 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Seattle, Washington, USA.
45.
45. Krajcinovic, D. and Fonseka, G.U. (1981). The Continuous Damage Theory of Brittle Materials , Journal of Applied Mechanics, 48: 809-815 .
46.
46. Cui, W., Wisnom, M.R. and Jones, M. (1992). A Comparison of Failure Criteria to Predict Delamination of Unidirectional Glass/Epoxy Specimens Waisted Through the Thickness , Composites, 23(3): 158-166 .
47.
47. Mohammadi, S., Owen, D.R.J. and Peric, D. (1998). A Combined Finite/Discrete Element Algorithm for Delamination Analysis of Composites , Finite Elements in Analysis and Design, 28: 321-336 .
48.
48. Lee, S.M. (1993). An Edge Crack Torsion Method for Mode III Delamination Fracture Testing , Journal of Composites Technology & Research, 15(3): 193-201 .
49.
49. Benzeggagh, M.L. and Kenane, M. (1996). Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites With Mixed-Mode Bending Apparatus , Composites Science and Technology, 56: 439-449 .
50.
50. Wu, E.M. and Reuter Jr., R.C. (1965). Crack Extension in Fiberglass Reinforced Plastics, T. & AM Report No. 275, University of Illinois.
51.
51. Crisfield, M.A., Hellweg, H.B. and Davies, G.A.O. (1994). Failure Analysis of Composite Structures Using Interface Elements , NAFEMS Conference on Application of Finite Elements to Composite Materials, London, UK.
52.
52. Hellweg, H.B. (1994). Nonlinear Failure Simulation of Thick Composites, PhD Thesis, Imperial College of Science and Technology, University of London, UK.
53.
53. Hibbitt, Karlsson and Sorensen. (1996). ABAQUS 6.2 User's Manual. Pawtucket, USA .
54.
54. Crews, J.H. and Reeder, J.R. (1988). A Mixed-Mode Bending Apparatus for Delamination Testing, NASA-TM-100662.
55.
55. Reeder, J.R. and Crews, J.R. (1990). Mixed-Mode Bending Method for Delamination Testing , AIAA Journal, 28: 1270-1276 .
56.
56. Reeder, J.R. and Crews, J.H. (1991). Nonlinear Analysis and Redesign of the Mixed-Mode Bending Delamination Test, NASA-TM-102777.
57.
57. Test Method D6671-01. Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites, American Society for Testing and Materials (ASTM), West Conshohocken, PA, USA .
58.
58. Reeder, J.R. (2002). Load-displacement Relations for DCB, ENF and MMB AS4/PEEK Test Specimens. Private Communication.
59.
59. Mi, Y. and Crisfield, M.A. (1996). Analytical Derivation of Load-Displacement Relationship for the DCB and Proof of the FEA Formulation, Department of Aeronautics Report, Imperial College of Science and Technology, University of London, U.K.
60.
60. Reeder, J.R. (2000). Refinements to the Mixed-Mode Bending Test for Delamination Toughness , 15th Conference of the American Society for Composites, Texas, USA.
