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Modelling progressive failure of fibre reinforced laminated composites: mesh objective calculations

Published online by Cambridge University Press:  27 January 2016

E. J. Pineda  and
A. M. Waas
E. J. Pineda*
Affiliation:
NASA Glenn Research Center, Cleveland, Ohio, USA
A. M. Waas*
Affiliation:
University of Michigan, Ann Arbor, Michigan, USA
*
[email protected]
[email protected]
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Abstract

A thermodynamically-based work potential theory for modelling progressive damage and failure in fibre-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory, utilises separate ISVs for modelling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed, matrix microdamage is the dominant damage mechanism in continuous, fibre-reinforced, polymer matrix laminates, and its evolution is captured with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. Typically, failure evolution (i.e. post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method numerical setting. Therefore, consistent characteristic element lengths are introduced into the formulation of of the three failure potentials. The theory is implemented into commercial FEM software. The model is verified against experimental results from a laminated, quasi-isotropic, T800/3900-2 panel containing a central notch. Global load versus displacement, global load versus local strain gauge data, and macroscopic failure paths obtained from the models are compared to the experiments. Finally, a sensitivity study is performed on the failure parameters used in the model.

Type
Research Article
Information
The Aeronautical Journal , Volume 116 , Issue 1186 , December 2012 , pp. 1221 - 1246
Copyright
Copyright © Royal Aeronautical Society 2012 

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References

1. Lamborn, M.J. and Schapery, R.A. An investigation of deformation path-independence of mechanical work in fiber-reinforced plastics, Proceedings of the Fourth Japan-US Conference on Composite Materials, Technomic Publishing Co, Lancaster, PA, USA, 1988.Google Scholar
2. Schapery, R.A. Mechanical characterization and analysis of inelastic composite laminates with growing damage, Mechanics & Materials Center Report5762-89-10, Texas A & M University, College Station, TX 77804, 1989.Google Scholar
3. Schapery, R.A. A theory of mechanical behaviour of elastic media with growing damage and other changes in structure, J Mech Phys Solids, 38, (2), 1990, pp 1725–1797.Google Scholar
4. Lamborn, M.J. and Schapery, R.A. An investigation of the existence of a work potential for fiberre-inforced plastic, J Compos Mater, 1993, 27, pp 352–382.Google Scholar
5. Sicking, D.L. Mechanical Characterization of Nonlinear Laminated Composites with Transverse Crack Growth, Ph.D. thesis, Texas A&M University, College Station, TX, USA, 1992.Google Scholar
6. Schapery, R.A. and Sicking, D.L. A Theory Of Mechanical Behaviour Of Elastic Media With Growing Damage And Other Changes In Structure, Mechanical Behaviour of Materials, edited by Bakker, A. Delft University Press, Delft, The Netherlands, 1995, pp 45–76.Google Scholar
7. Bazant, Z. and Cedolin, L. Blunt crack band propagation in finite element analysis, J Eng Mech Div.-ASCE, 1979, 105, pp 297–315.Google Scholar
8. Pietruszczak, S. and Mroz, Z. Finite element analysis of deformation of strain-softening materials, Int J Numer Methods Eng, 1981, 17, pp 327–334.Google Scholar
9. Pineda, E.J., Waas, A.M., Bednarcyk, B.A. and Collier, C.S. Computational implementation of a thermodynamically based work potential model for progressive microdamage and transverse cracking in fiber-reinforced laminates, 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL, USA, 12-15 April 2010.Google Scholar
10. Bazant, Z.P. and Oh, B.H. Crack band theory for fracture of concrete, Mater and Struct, 1983, 16, pp 155–77.Google Scholar
11. de Borst, R. and Nauta, P. Non-orthogonal cracks in a smeared finite element model, Eng Comput, 1985, 2, pp 35–46.Google Scholar
12. Talreja, R. A continuum mechanics characterization of damage in composite materials, P. Roy. Soc. Lond. A Mat, 1985, 4, pp 335–375.Google Scholar
13. Dvorak, G.J., Laws, N. and Hejazi, M. Analysis of progressive matrix cracking in composite laminates I. Thermoelastic properties of a ply with cracks, J Compos Mater, 1985, 19, pp 216–234.Google Scholar
14. Allen, D.H., Harris, C.E. and Groves, S.E. A thermomechanical constitutive theory for elastic composites with distributed damage I. Theoretical development, Int J Solids Struct, 1987, 23, (9), pp 1301–1318.Google Scholar
15. Lemaitre, J. and Chaboche, J.-L. Mechanics of Solid Materials, Cambridge University Press, 1994.Google Scholar
16. McCartney, L.N. Predicting transverse crack formation in cross-ply laminates, Compos Sci Technology, 1998, 58, pp 1069–1081.Google Scholar
17. Talreja, R. (ed), 9 of Composite Materials Series, Elsevier Science B.V., Amsterdam, The Netherlands, 1994.Google Scholar
18. Matzenmiller, A., Lubliner, J. and Taylor, R.L. A constitutive model for anisotropic damage in fiber composites, Mech Mater, 1995, (20), 2, pp 125–152.Google Scholar
19. Bednarcyk, B.A., Aboudi, J. and Arnold, S.M. Micromechanics modelling of composites subjected to multiaxial progressive damage in the constituents, AIAA J, 2010, 48, pp 1367–1378.Google Scholar
20. Pineda, E.J. A Novel Multiscale Physics-Based Progressive Damage and Failure Modelling Tool for Advanced Composite Structures, Ph.D. thesis, Universtiy of Michigan, Ann Arbor, MI, USA, 2012.Google Scholar
21. Pineda, E.J. and Waas, A.M. Numerical implementation of a multiple-ISV thermodynamicallybased work potential theory for modelling progressive damage and failure in fiber-reinforced laminates, NASA/TM 2011-217401, 2011.Google Scholar
22. Bogert, P.B., Satyanarayana, A. and Chunchu, P.B. Comparison of damage path predicions for composite laminates by explicit and standard finite element analysis tool, 47 AIAA Structures, Structural Dynamics, and Materials Conference, 1-4 May 2006.Google Scholar
23. Satyanarayana, A., Bogert, P.B. and Chunchu, P.B. The effect of delamination on damage path and failure load prediction for notched composite laminates, 48th AIAA Structures, Structural Dynamics, and Materials Conference, 23-26 April 2007.Google Scholar
24. Schapery, R.A. Prediction of compressive strength and kink bands in composites using a work potential, Int J Solids Structures, 1995, 32, (6), pp 739–765.Google Scholar
25. Basu, S., Waas, A.M. and Ambur, D.R. Prediction of progressive failure in multidirectional composite laminated panels, Int J Solids Structures, 2007, 44, (9), pp 2648–2676.Google Scholar
26. Pineda, E.J., Waas, A.M., Bednarcyk, B.A., Collier, C.S. and Yarrington, P.W. Progressive damage and faiure modelling in notched laminated fiber reinforced composites, Int J Fract, 2009, 158, pp 125–143.Google Scholar
27. Hinterhoelzl, A. and Schapery, R.A. FEM implementation of a three-dimensional visoelastic constitutive model for particulate composites with damage growth, Mech Time-Depend Mat, 2004, 8, (1), pp 65–94.Google Scholar
28. Rice, J.R. Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, J Mech Phys Solids, 19, 1971, pp 433–455, bon fiber composites, J Compos Mater, 2006, 40, (22).Google Scholar
29. Hashin, Z. and Rotem, A. A fatigue failure criterion for fiber reinforced composite materials, J Composite Materials, 1973, 7, pp 448–464.Google Scholar
30. Dugdale, D.S. Yielding of steel sheets containing slits, J Mech Phys Solids, 1960, 8, pp 100–108.Google Scholar
31. Barenblatt, G.I. The mathematical theory of equilibrium cracks in brittle fracture, Adv Appl Mech, 7, 1962, pp 55–129.Google Scholar
32. Gustafson, P.A. and Waas, A.M. The influence of adhesive constitutive parameters in cohesive zone finite element models of adhesively bonded joints, Int J Solids Struct, 2009, pp 2201–2215.Google Scholar
33. Ortiz, M. and Pandolfi, A. Finite-deformation irreversible cohesive elements for three dimensional crack-propagation analysis, Int J Numer Meth, 1999, 44, pp 1267–1282.Google Scholar
34. Camanho, P.P. and Dâvila, C.G. Mixed-mode decohesion finite elements for the simulation of delamination in composite materials, NASA/TM 2002-211737, 2002.Google Scholar
35. Xie, D.E., Salvi, A., Sun, C.E., Waas, A.M. and Caliskan, A. Discrete cohesive zone model to simulate static fracture in 2-D triaxially braided carbon fiber composites, J Compos Mater, 2006, 40, (22).Google Scholar
36. Gustafson, P.A. Analytical and Experimental Methods for Adhesively Bonded Joints Subjected to High Temperatures, PhD. thesis, University of Michigan, Ann Arbor, MI, USA, 2008.Google Scholar
37. Turon, A., Camanho, P.P., Costa, J. and Davila, C.G. A damage model for the simulation of delamination in advanced composites under variable-mode loading, Mech Mater, 2006, 38, (11).Google Scholar
38. Ranatunga, V., Bednarcyk, B.A. and Arnold, S.M. Modelling progressive damage using local displacement discontinuities with the FEAMAC multiscale modelling framework, NASA/TM 2010-216825, 2010.Google Scholar
39. Budiansky, B. and Fleck, N.A. Compressive failure of fiber composites, J Mech Phys Solids, 1993, 41, (1), pp 183–211.Google Scholar
40. Basu, S., Waas, A.M. and Ambur, D.R. Compressive failure of fiber composites under multiaxial loading, J Mech Phys Solids, 2006, 54, (3), pp 611–634.Google Scholar
41. Hoek, E. and Bieniawski, Z.T. Brittle rock fracture propagation in rock under compression, Int J Fract, 1965, 1, (3), pp 137–155.Google Scholar
42. Puck, A. and Schǖrmann, H. Failure analysis of FRP laminates by means of physically based phenomenological models, Comps Sci Technol, 1998, 58, pp 1045–1067.Google Scholar
43. Liechti, K. and Hanson, E. Non-linear effects in mixed-mode interfacial delaminations, Int J Fract, 1988, 36, pp 199–217.Google Scholar
44. Benzeggagh, M. and Kenane, M. Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus, Compos Sci Technol, 1996, 56, pp 439–449.Google Scholar
45. Bažant, Z.P. Crack band model for fracture of geomaterials, Proceedings of the 4th International Conference on Numerical Methods in Geomechanics, Edmonton, Canada, 1982.Google Scholar
46. Rots, J.G. and de Borst, R. Analysis of mixedmode fracture in concrete, J Eng Mech, 1987, 113, (11), pp 1739–1758.Google Scholar
47. Abaqus, , Abaqus User’s Manual,1-3, Version 6.10-1, Dassault Systemes Simulia Corp, Providence, RI, USA, 2008.Google Scholar
48. Basu, S. Computational Modelling of Progrssive Failure and Damage in Composite Laminates, PhD. thesis, University of Michigan, Ann Arbor, MI, USA, 2005.Google Scholar
49. Camanho, P.P., Dâvila, C.G., Pinho, S.T., Iannucci, L. and Robinson, P. Prediction of in situ strenghts and matrix cracking in composites under transverse tension and in-plane shear, Composites: Part A, 2006, 37, pp 165–176.Google Scholar