On analysis of the elasto-viscoplastic response of single crystals with anisotropic damage: Constitutive modelling and computational aspects

International Journal for Numerical Methods in Engineering

Volumn 61, Issue 3, 2004, Pages 406-432

  Feng, Lu ^a   Zhang, Guang ^b   Zhang, Ke Shi ^b   Xu, J Q ^a   Yu, Hai Dong ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Anisotropic damage; Consistent algorithmic tangent stiffness; Continuum damage mechanics; Crystal plasticity; Newton Raphson iterative scheme; Plastic anisotropy

Indexed keywords

ANISOTROPY; CRYSTAL DEFECTS; ELASTICITY; ITERATIVE METHODS; MICROSTRUCTURE; THERMODYNAMIC PROPERTIES; VISCOELASTICITY;

ANISOTROPIC DAMAGE; DAMAGE MECHANICS; LATTICE ORIENTATION;

SINGLE CRYSTALS;

CRYSTAL; VISCOELASTICITY;

EID: 4644312466     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1072     Document Type: Article

References (43)

1. Yang C, Kumar AV. Investigation of strain hardening in NiAl single crystals using three dimensional FEA models. Journal of Engineering Materials and Technology 2001; 123:20-27.
2. Kumar AV, Yang C. Study of work hardening models for single crystals using three dimensional finite element analysis. International Journal of Plasticity 1999; 15:737-754.
3. Marin EB, Dawson PR. On modelling the elasto-viscoplastic response of metals using polycrystal plasticity. Computer Methods in Applied Mechanics and Engineering 1998; 165:1-21.
4. Peirce D, Asaro RJ, Needleman A. Material rate dependence and localized deformation in crystalline solids. Acta Metallurgica 1983; 31:(12):1951-1976.
5. Peirce D, Asaro RJ, Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metallurgica 1982; 30:1087-1119.
6. Kachanov L. Time of the rupture process under creep conditions. Izvestiya Akademii Nauk SSR 1958; 8:26-31.
7. Rabotnov Y. Creep rupture. In Applied Mechanics, Hetenyi M, Vincenti W. (eds), Proceedings of the 12th International Congress of Applied Mechanics, 26-31 August 1968, Stanford. Springer: Berlin, 1968; 342-349.
8. Chaboche J, Lesne P. A non-linear continuous fatigue damage model. Fatigue and Fracture of Engineering Materials and Structures 1988; 11:1-17.
9. Dufailly J, Lemaitre J. Modeling very low cycle fatigue. International Journal of Damage Mechanics 1995; 4:153-170.
10. Hayhurst D. Creep rupture under multiaxial states of stress. Journal of the Mechanics and Physics of Solids 1972; 20:381-390.
11. Cocks A, Leckie F. Creep constitutive equations for damaged materials. Advances in Applied Mechanics 1987; 25:239-294.
12. Lemaitre J. A continuous damage mechanics model for ductile fracture. Journal of Engineering Materials and Technology 1985; 107:83-89.
13. Rousselier G. Ductile fracture models and their potential in local approach of fracture. Nuclear Engineering and Design 1987; 105:97-111.
14. Lämmer H, Tsakmakis Ch. Discussion of coupled elastoplasticity and damage constitutive equations for small and finite deformations. International Journal of Plasticity 2000; 16:495-523.
15. Vaz Jr M, Owen DRJ. Aspects of ductile fracture and adaptive mesh refinement in damaged elasto-plastic materials. International Journal for Numerical Methods in Engineering 2001; 50:29-54.
16. Murakami S, Ohno N. A continuum theory of creep and creep damage. In 3rd IUTAM Symposium on Creep in Structures, Ponter ARS, Hayhurst DR (eds). Springer: Berlin, 1981; 422-444.
17. Chow CL, Wang J. An anisotropic theory of continuum damage mechanics for ductile fracture. Engineering Fracture Mechanics 1987a; 27(5):547-558.
18. Chow CL, Wang J. An anisotropic theory of elasticity for continuum damage mechanics. International Journal of Fracture 1987b; 33:3-16.
19. Qi W, Brocks W. Simulation of anisotropic creep damage in engineering components. ECCOMAS 2000; 1-14.
20. Qi W, Bertram A. Anisotropic continuum damage modelling for single crystals at high temperatures. International Journal of Plasticity 1999; 15:1197-1215.
21. Qi W, Bertram A. Damage modelling of the single crystal superalloy SRR99 under monotonous creep. Computational Materials Science 1998; 13:132-141.
22. Mathur KK, Dawson PR, Kocks UF. On modelling anisotropy in deformation processes involving textured polycrystals with distorted grain shape. Mechanics of Materials 1990; 10:183-202.
23. Beaudoin AJ, Dawson PR, Mathur KK, Kocks UF, Korzekwa DA. Application of polycrystal plasticity to sheet forming. Computer Methods in Applied Mechanics and Engineering 1994; 117:49-70.
24. Ortiz, Stainier L. The variational formulation of viscoplastic constitutive updates. Computer Methods in Applied Mechanics and Engineering 1999; 171:419-444.
25. Borja RI, Wren JR. Discrete micromechanics of elastoplastic crystals. International Journal for Numerical Methods in Engineering 1993; 36:3815-3840.
26. Anand L, Kothari M. A computational procedure for rate-independent crystal plasticity. Journal of the Mechanics and Physics of Solids 1996; 44:525-558.
27. Miehe C. Multisurface thermoplasticity for single crystals at large strains in terms of Eulerian vector updates. International Journal of Solids and Structures 1996; 33:1981-2004.
28. Miehe C. Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals. International Journal for Numerical Methods in Engineering 1996; 39:3367-3390.
29. Sarma G, Zacharia T. Integration algorithm for modelling the elastoviscoplastic response of polycrystalline materials. Journal of the Mechanics and Physics of Solids 1999; 47:1219-1238.
30. Lee EH. Elastic-plastic deformation at finite strains. Journal of Applied Mechanics and Engineering 1969; 36:1.
31. Cordebois JP, Sidoroff F. Damage induced elastic anisotropy. Mechanical Behaviour of Anisotropic Solids. Martinus Nijhoff Publishers: Boston, 761-774.
32. Miehe C, Stein E. A canonical model of multiplicative elasto-plasticity: formulation and aspects of the numerical implementation. European Journal of Mechanics - A/Solids 1992; 11:25-43.
33. Cuitino AM, Ortize M. Computational modelling of single crystals. Modelling and Simulation Materials Science and Engineering 1992; 1:255-263.
34. 2 intermetallic crystals. Materials Science and Engineering A 1993; 170:111-123.
35. Ortiz M, Repetto EA. Nonconvex energy minimization and dislocation structures in ductile single crystals. Journal of the Mechanics and Physics of Solids 1999.
36. Briottet L, Klöcker H, Montheillet F. Damage in a viscoplastic material-part II. Overall behaviour. International Journal of Plasticity 1998; 14(6):453-471.
37. Germain P, Nguyen QS, Suquet P. Continuum thermodynamics. Journal of Applied Mechanics 1983; 50: 1010-1020.
38. Krajcinovic D. Constitutive equations for damaging materials. Journal of Applied Mechanics 1983; 50(6): 355-360.
39. Murakami S, Ohno N. A continuum theory of creep damage. In Creep in Structure, Ponter ARS, Hayhurst DR (eds). Springer: Berlin; 422-444.
40. Miehe C, Schröder J, Schotte J. Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Computer Methods in Applied Mechanics and Engineering 1999; 171:387-418.
41. Radovitzky R, Ortiz M. Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering 1999; 172:203-240.
42. Miehe C, Schröder J. A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity. International Journal for Numerical Methods in Engineering 2001; 50:273-298.
43. Jeeho Lee, Fenves GL. A return-mapping algorithm for plastic-damage models 3-D and plane stress formulation. International Journal for Numerical Methods in Engineering 2001; 50:487-506.