Homogenization-based continuum plasticity-damage model for ductile failure of materials containing heterogeneities

Journal of the Mechanics and Physics of Solids

Volumn 57, Issue 7, 2009, Pages 1017-1044

  Ghosh, Somnath ^a   Bai, Jie ^a   Paquet, Daniel ^a  

^a Ohio State University   (United States)

Author keywords

Anisotropic continuum plasticity damage model; Ductile fracture; Gurson Tvergaard Needleman model; Homogenization; LE VCFEM

Indexed keywords

ANISOTROPIC CONTINUUM PLASTICITY-DAMAGE MODEL; CAST ALLOYS; CHARACTERISTIC LENGTH; COMPUTATIONALLY EFFICIENT; CONTINUUM PLASTICITY; DAMAGE MODEL; DEFORMATION HISTORY; DUCTILE FAILURES; DUCTILE MATERIALS; EFFECTIVE TOOL; GURSON-TVERGAARD-NEEDLEMAN MODEL; HOMOGENIZATION; LE-VCFEM; LENGTH SCALE; MACROSCOPIC ANALYSIS; MACROSCOPIC DAMAGE; MATRIX CRACKING; METAL MATRIX COMPOSITES; MICRO MECHANICS MODEL; MICRO-MECHANICAL ANALYSIS; MICROMECHANICAL DAMAGE; MICROSTRUCTURAL COMPOSITION; MODEL PARAMETERS; NONLOCAL CONSTITUTIVE MODELS; NONUNIFORM; PRINCIPAL COORDINATES; REPRESENTATIVE VOLUME ELEMENTS; VOID NUCLEATION; VORONOI CELL FINITE ELEMENT;

ALUMINA; ANISOTROPY; DUCTILE FRACTURE; DUCTILITY; FAILURE ANALYSIS; INCLUSIONS; MATERIALS; METALLIC MATRIX COMPOSITES; MICROMECHANICS; MICROSTRUCTURE; MOSFET DEVICES; PLASTICITY; QUALITY ASSURANCE; VOLUME MEASUREMENT;

FINITE ELEMENT METHOD;

EID: 67349115751     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2009.04.002     Document Type: Article

References (50)

1. Argon A., Im J., and Sofoglu R. Cavity formation from inclusions in ductile fracture. Metall. Trans. A 6A (1975) 825-837
2. Benssousan A., Lions J., and Papanicoulau G. Asymptotic Analysis for Periodic Structures (1978), North-Holland, Amsterdam
3. Benzerga A., Besson J., and Pineau A. Anisotropic ductile fracture Part II: theory. Acta Metall. 52 (2004) 4639-4650
4. Caceres C. Particle cracking and the tensile ductility of a model Al-Si-Mg composite system. Alum. Trans. 1 (1999) 1-13
5. Chu C., and Needleman A. Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Technol. 102 (1980) 249-256
6. Devaux J., Gologanu M., and Leblond J. Recent extension of Gurson's model for porous ductile metals. Continuum Micromech. 377 (1997) 197-264
7. Feyel F., and Chaboche J. FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fiber SiC/Ti composite materials. Comput. Methods Appl. Mech. Eng. 183 (2000) 309-330
8. Fish J., Yu Q., and Shek K. Computational damage mechanics for composite materials based on mathematical homogenization. Int. J. Numer. Methods Eng. 45 (1999) 1657-1679
9. Garajeu M., and Suquet P. Effective properties of porous ideally plastic or viscoplastic materials containing rigid particles. J. Mech. Phys. Solids 45 (1997) 873-902
10. Ghosh S. Multiscale Modeling and Simulation of Composite Materials and Structures (2008), Springer, Berlin pp. 83-164
11. Ghosh S., Bai J., and Raghavan P. Concurrent multi-level model for damage evolution in microstructurally debonding composites. Mech. Mater. 39 (2007) 241-266
12. Ghosh S., Lee K., and Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element model. Int. J. Solids Struct. 32 (1995) 27-62
13. Ghosh S., Lee K., and Moorthy S. Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model. Comput. Methods Appl. Mech. Eng. 132 (1996) 63-116
14. Ghosh S., Lee K., and Raghavan P. A multi-level computational model for multi-scale damage analysis in composite and porous materials. Int. J. Solids Struct. 38 (2001) 2335-2385
15. Ghosh S., and Moorthy S. Particle cracking simulation in non-uniform microstructures of metal-matrix composites. Acta Metall. Mater. 46 (1998) 965-982
16. Ghosh S., Nowak Z., and Lee K. Quantitative characterization and modeling of composite microstructures by Voronoi cells. Acta Mater. 45 (1997) 2215-2234
17. Ghosh S., Nowak Z., and Lee K. Tesselation based computational methods for the characterization and analysis of heterogeneous microstructures. Comput. Sci. Technol. 57 (1997) 1187-1210
18. Grange M., Besson J., and Andrieu E. An anisotropic Gurson type model to represent the ductile rupture of hydrided Zircaloy-4 sheets. Int. J. Fract. 105 (2000) 273-293
19. Guedes J.M., and Kikuchi N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput. Methods Appl. Mech. Eng. 83 (1990) 143-198
20. Gurson A. Continuum theory of ductile rupture by void nucleation and growth: Part I. Yield criteria and flow rule for porous ductile media. ASME J. Eng. Mater. Technol. 99 (1977) 2-15
21. Hashin Z. The elastic moduli of heterogeneous material. J. Appl. Mech. 29 (1962) 143-150
22. Hill R. A theory of yielding and plastic flow of anisotropic metals. Proc. R. Soc. London 193 (1948) 281-297
23. Hu C., Bai J., and Ghosh S. Micromechanical and macroscopic models of ductile fracture in particle reinforced metallic materials. Modeling Simulation Mater. Sci. Eng. 15 (2007) 377-392
24. Hu C., and Ghosh S. Locally enhanced Voronoi cell finite element model (LE-VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions. Int. J. Numer. Methods Eng. 76 12 (2008) 1955-1992
25. Jain J.R., and Ghosh S. A 3D continuum damage mechanics model from micromechanical analysis of fiber reinforced composites with interfacial damage. ASME J. Appl. Mech. 75 3 (2008) 031011-1-031011-15
26. Jain, J.R., Ghosh, S., 2008b. Damage evolution in composites with a homogenization based continuum damage mechanics model. Int. J. Damage Mech., doi:10.1177/1056789508091563.
27. Kouznetsova V., Brekelmans W., and Baaijens F. An approach to micro-macro modeling of hetergeneous materials. Comput. Mech. 27 (2001) 37-48
28. Li M., Ghosh S., and Richmond O. An experimental-computational approach to the investigation of damage evolution in discontinuously reinforced aluminum matrix composite. Acta Mater. 47 (1999) 3515-3532
29. Liao K., Pan J., and Tang S. Approximate yield criterion for anisotropic porous ductile sheet metals. Mech. Mater. 26 (1997) 213-226
30. Llorca J., and Gonzalez C. Microstructural factors controlling the strength and ductility of particle-reinforced metal-matrix composites. J. Mech. Phys. Solids 46 (1998) 1-28
31. Moorthy S., and Ghosh S. A Voronoi cell finite element model for particle cracking in elastic-plastic composite materials. Comput. Methods Appl. Mech. Eng. 151 (1998) 377-400
32. Moorthy S., and Ghosh S. Adaptivity and convergence in the Voronoi cell finite element model for analyzing heterogeneous materials. Comput. Methods Appl. Mech. Eng. 185 (2000) 37-74
33. Mori T., and Tanaka K. Average stress in the matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21 (1973) 571-574
34. Moulinec H., and Suquet P. A numerical method for computing the overall response of nonlinear composites with complex microstructures. Comput. Methods Appl. Mech. Eng. 157 (1998) 69-94
35. Moulinec H., and Suquet P. A computational scheme for linear and nonlinear composites with arbitrary phase contrasts. Int. J. Numer. Methods Eng. 52 (2001) 139-160
36. Pardoen T., and Hutchinson J. An extended model for void growth and coalescence. J. Mech. Phys. Solids 48 (2000) 2467-2512
37. Ponte Castaneda P., and Suquet P. Nonlinear composites. Adv. Appl. Mech. 34 (1998) 171-302
38. Pyrz R. Quantitative description of the microstructure of composites: I. Morphology of unidirectional composite systems. Compos. Sci. Technol. 50 (1994) 197-208
39. Raghavan P., and Ghosh S. A continuum damage mechanics model for unidirectional composites undergoing interfacial debonding. Mech. Mater. 37 (2005) 955-979
40. Sanchez-Palencia E. Non-homogeneous Media and Vibration Theory, Lecture Notes in Physics (1980), Springer, Berlin, Heidelberg
41. Siruguet K., and Leblond J. Effect of void locking by inclusion upon the plastic behaviour of porous ductile solids. Int. J. Plasticity 20 (2004) 225-268
42. Terada K., and Kikuchi N. Nonlinear Homogenization Method for Practical Applications, vol. 62 (1995), ASME, New York pp. 1-16
43. Terada K., and Kikuchi N. A class of general algorithm for multi-scale analysis of heterogeneous media. Comput. Methods Appl. Mech. Eng. 190 (2001) 5427-5464
44. Tvergaard V. On localization in ductile materials containing voids. Int. J. Fract. 18 (1982) 237-251
45. Tvergaard V., and Needleman A. Analysis of cup-cone fracture in round tensile bar. Acta Metall. 32 (1984) 157-169
46. Tvergaard V., and Needleman A. Effects of nonlocal damage in porous plastic solids. Int. J. Solids Struct. 32 (1995) 1063-1077
47. Vernerey F., Liu W., Moran B., and Olson G. A micromorphic model for the multiple scale failure of heterogeneous materials. J. Mech. Phys. Solids 56 (2008) 1320-1347
48. Wang D., Pan J., and Liu S. An anisotropic Gurson yield criterion for porous ductile sheet metals with planar anisotropy. Int. J. Damage Mech. 13 (2004) 7-33
49. Wang Q. Microstructural effects on the tensile and fracture behavior of aluminum casting alloys A356/357. Metall. Mater. Trans. A 34A (2003) 2887-2899
50. Willis J. Variational and related methods for the overall properties of composites. Adv. Appl. Mech. 21 (1981) 1-78