Implicit integration procedure for viscoplastic Gurson materials

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 44-47, 2006, Pages 6146-6157

  Betegon C ^a   del Coz, J J ^a   Penuelas I ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Ductile fracture; Gurson material; Viscoplasticity

Indexed keywords

ALGORITHMS; DUCTILE FRACTURE; DUCTILITY; ELASTICITY; INTEGRATION; POROSITY; STRAIN RATE;

GURSON MATERIALS; GURSON YIELD FUNCTION; IMPLICIT INTEGRATION; VISCOPLASTIC MATERIALS;

VISCOPLASTICITY;

ALGORITHMS; DUCTILE FRACTURE; DUCTILITY; ELASTICITY; INTEGRATION; POROSITY; STRAIN RATE; VISCOPLASTICITY;

EID: 33746192371     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.12.015     Document Type: Article

References (37)

1. Gurson A.L. Continuum theory of ductile rupture by void nucleation and growth: part I - yield criteria and flow rules for porous ductile media. J. Engrg. Mater. Technol. 99 (1977) 2-15
2. Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions. Int. J. Fract. 17 (1981) 389-407
3. Tvergaard V. On localization in ductile materials containing spherical voids. Int. J. Fract. 18 (1982) 237-252
4. Tvergaard V., and Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 32 (1984) 57-169
5. Sun D.-Z., Kienzler R., Voss B., and Schmitt W. Application of micro-mechanical models to the prediction of ductile fracture. In: Atluri S.N., Newman Jr. J.C., Raju I.S., and Esptein J.S. (Eds). Fracture Mechanics, 22nd Symposium vol. II, ASTM STP 1131 (1992), American Society for Testing and Materials, Philadelphia 368-378
6. Koplik J., and Needleman A. Void growth and coalescence in porous plastic solids. Int. J. Solids Struct. 24 (1988) 835-853
7. Steilich D., and Brocks W. Micromechanical modelling of damage and fracture of ductile materials. Fatigue Fract. Engrg. Mater. Struct. 21 (1998) 1175-1188
8. Zhang Z.L., and Hauge M. On the Gurson parameters. In: Panontin T.L., and Sheppard S.D. (Eds). Fatigue and Fracture Mechanics vol. 29, ASTM STP 1321 (1998), American Society for Testing and Materials
9. Thomason P.F. Ductile Fracture of Metals (1990), Pergamon Press, Oxford
10. Thomason P.F. A three-dimensional model for ductile fracture by the growth and coalescence of micro-voids. Acta Metall. 33 (1985) 1087-1095
11. Thomason P.F. A view on ductile-fracture modelling. Fatigue Fract. Engrg. Mater. Struct. 21 (1998) 1105-1122
12. Zhang Z.L., Thaulow C., and Odegard J. A complete Gurson model approach for ductile fracture. Engrg. Fract. Mech. 67 (2000) 155-168
13. Pan J., Saje M., and Needleman A. Localization of deformation in rate sensitive porous plastic solids. Int. J. Fract. 21 (1983) 261-278
14. Pierce D., Shih C.F., and Needleman A. A tangent modulus method for rate dependent solids. Comput. Struct. 18 (1984) 875-887
15. Tvergaard V., and Needleman A. Effect of material rate sensitivity on failure modes in the Charpy V-notch test. J. Mech. Phys. Solids 34 (1986) 213-241
16. Worswick M.J., and Pelletier P. Numerical simulation of ductile fracture during high strain rate deformation. Eur. Phys. J. AP 4 (1998) 257-267
17. Koppenhoefer K.C., and Dodds Jr. R.H. Ductile crack growth in pre-cracked CVN specimens: numerical studies. Nucl. Engrg. Des. 180 (1998) 221-241
18. Besson J., Steglich D., and Brocks W. Modeling of cracks growth in round bars and plane strain specimens. Int. J. Solids Struct. 38 (2001) 8259-8284
19. Becker R. Ring fragmentation predictions using the Gurson model with material stability conditions as failure criteria. Int. J. Solids Struct. 39 (2002) 3555-3580
20. Borvik T., Hoppertad O.S., and Berstad T. On the influence of stress triaxiality and strain rate on the behavior of a structural steel. Part II. Numerical study. Eur. J. Mech. A/Solids 22 (2003) 15-32
21. Alfano G., De Angelis F., and Rosati L. General solution procedures in elasto/viscoplasticity. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5123-5147
22. Ponthot J.P. Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes. Int. J. Plast. 18 (2002) 91-126
23. Sloan S.W. Substepping schemes for the numerical integration of elastoplastic stress strain relations. Int. J. Numer. Methods Engrg. 24 (1987) 893-911
24. Ortiz M., and Simo J.C. An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int. J. Numer. Methods Engrg. 23 (1986) 353-366
25. Simo J.C., and Taylor R.L. Consistent tangent operator for rate-independent elasto-plasticity. Comput. Methods Appl. Mech. Engrg. 48 (1985) 101-118
26. Wallin M., and Ristinmaa M. Accurate stress updating algorithm based on constant strain rate assumption. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5583-5601
27. Buttner J., and Simeon B. Runge-Kutta methods in elastoplasticity. Appl. Numer. Math. 41 (2002) 443-458
28. Carosio A., William K., and Etse G. On the consistency of viscoplastic formulations. Int. J. Solids Struct. 37 (2000) 7349-7369
29. Wang W.M., and Sluys L.J. Formulation of an implicit algorithm for finite deformation viscoplasticity. Int. J. Solids Struct. 37 (2000) 7329-7348
30. Pardoen T., and Hutchinson J.W. An extended model for void growth and coalescence. J. Mech. Phys. Solids 48 (2000) 2467-2512
31. Pardoen T., and Hutchinson J.W. Micromechanics-based model for trends in toughness of ductile metals. Acta Mater. 51 (2003) 133-148
32. Chu C.C., and Needleman A. Void nucleation effects in biaxially stretched sheets. J Engrg. Mater. Technol. 102 (1980) 249-256
33. 0 rate-dependent effects in frictional contact and viscoplasticity. J. Mater. Proc. Tech. 80 (1998) 628-634
34. Sloan S.W., and Booker J.R. Integration of Tresca and Mohr-Coulomb constitutive relations in plane strain elastoplasticity. Int. J. Numer. Methods Engrg. 33 (1992) 163-196
35. Dorman J.R., and Prince P.J. A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6 (1980) 19-26
36. ABAQUS 6.4., Hibbit, Karlsson and Sorensen, Inc., Pawtucket, 2003.
37. Tvergaard V., and Hutchinson J.W. Effect of T-stress on mode I crack growth resistance in a ductile solid. Int. J. Solids Struct. 31 (1994) 823-833