Multiscale modeling of ductile failure in metallic alloys;Modélisation multi-échelle de la rupture ductile des alliages métalliques

Comptes Rendus Physique

Volumn 11, Issue 3-4, 2010, Pages 326-345

  Pardoen, Thomas ^a   Scheyvaerts, Florence ^a   Simar, Aude ^a   Tekǒlu, Cihan ^a   Onck, Patrick R ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Damage; Ductile fracture; Ductility; Fracture toughness; Multiscale modelling; Voids

Indexed keywords

EID: 77957021595     PISSN: 16310705     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crhy.2010.07.012     Document Type: Short Survey

References (118)

1. Pineau A. Review of fracture micromechanisms and a local approach to predicting crack resistance in low strength steels. Advances in Fracture Research 1981, vol. 2:553-577. Pergamon. D. François (Ed.).
2. Tvergaard V. Material failure by void growth to coalescence. Adv. Appl. Mech. 1990, 27:83-151.
3. Pineau A., Pardoen T. Failure mechanisms of metals. Comprehensive Structural Integrity Encyclopedia 2007, vol. 2. Elsevier, Chap. 6, on-line.
4. A.A. Benzerga, J.-B. Leblond, Ductile fracture by void growth to coalescence, Adv. Appl. Mech. (2010), in press.
5. Tipper C.F. The fracture of metals. Metallurgica 1949, 39:133-137.
6. Puttick K.E. Ductile fracture in metals. Philos. Mag. 1959, 4:964-969.
7. Rogers H.C. Tensile fracture of ductile metals. Trans. Metall. Soc. AIME 1960, 218:498-506.
8. Beachem C.D. An electron fractographic study of the influence of plastic strain conditions upon ductile rupture processes in metals. Trans. ASM 1963, 56:318.
9. Gurland J., Plateau J. The mechanism of ductile rupture of metals containing inclusions. Trans. ASM 1963, 56:442-454.
10. McClintock F.A. A criterion for ductile fracture by the growth of holes. J. Appl. Mech. 1968, 35:363-371.
11. Rice J.R., Tracey D.M. On the ductile enlargement of voids in triaxial stress. J. Mech. Phys. Solids 1969, 17:201-217.
12. D'Escatha Y., Devaux J.C. Numerical study of initiation, stable crack growth and maximum load with a ductile fracture criterion based on the growth of holes. ASTM STP 1979, vol. 668:229-248. American Society for Testing and Materials, Philadelphia. J.D. Landes, J.A. Begley, G.A. Clarke (Eds.).
13. Needleman A., Tvergaard V. An analysis of ductile rupture modes at a crack tip. J. Mech. Phys. Solids 1987, 35:151-183.
14. Xia L., Shih C.F., Hutchinson J. A computational approach to ductile crack growth under large scale yielding conditions. J. Mech. Phys. Solids 1995, 43:389-413.
15. Brocks W., Klingbeil D., Kunecke G., Sun D.-Z. Application of the Gurson model to ductile tearing resistance. ASTM STP 1995, vol. 1244:232. American Society for Testing and Materials, Philadelphia. M. Kirk, A. Bakker (Eds.).
16. Koppenhoefer K.C., Dodds R.H. Ductile crack growth in pre-cracked CVN specimens: numerical studies. Nuclear Eng. Design 1998, 180:221-241.
17. McMeeking R.M. Finite deformation analysis of crack-tip opening in elastic-plastic materials and implication for fracture. J. Mech. Phys. Solids 1977, 25:357-381.
18. Brunet M., Morestin F., Walter H. Damage identification for anisotropic sheet-metals using a non-local damage model. Int. J. Damage Mech. 2004, 13:35-57.
19. Lassance D., Fabrègue D., Delannay F., Pardoen T. Micromechanics of room and high temperature fracture in 6xxx Al alloys. Prog. Mater. Sci. 2007, 52:62-129.
20. Pardoen T. Numerical simulation of low stress triaxiality ductile fracture. Comput. Struct. 2006, 84:1641-1650.
21. Chéhab B., Bréchet Y., Véron M., Jacques P.J., Parry G., Glez J.-C., Mithieux J.-D., Pardoen T. Micromechanics of the high temperature damage in a dual phase stainless steel. Acta Mater. 2010, 58:626-637.
22. Devillers-Guerville L., Besson J., Pineau A. Notch fracture toughness of a cast duplex stainless steel: modelling of experimental scatter and size effects. Nuclear Eng. Design 1997, 168:211-225.
23. Bugat S., Besson J., Pineau A. Micromechanical modeling of the behavior of duplex stainless steels. Comput. Mater. Sci. 1999, 16:158-166.
24. Rivalin F., Besson J., Di Fant M., Pineau A. Ductile tearing of pipeline-steel wide plates: II. Modeling of in-plane crack propagation. Eng. Fract. Mech. 2001, 68:347-364.
25. Pardoen T., Dumont D., Deschamps A., Bréchet Y. Grain boundary versus transgranular ductile failure. J. Mech. Phys. Solids 2003, 51:637-665.
26. Gologanu M., Leblond J.-B., Perrin G., Devaux J. Recent extensions of Gurson's model for porous ductile metals. CISM Lectures Series 1997, 61. Springer, New York. P. Suquet (Ed.).
27. Pardoen T., Marchal Y., Delannay F. Thickness dependence of cracking initiation criteria in thin aluminum plates. J. Mech. Phys. Solids 1999, 47:2093-2123.
28. Pardoen T., Hachez F., Marchioni B., Blyth H., Atkins A.G. Mode I fracture of sheet metal. J. Mech. Phys. Solids 2004, 52:423-452.
29. Lacroix G., Pardoen T., Jacques P.J. On the fracture toughness of TRIP-assisted multiphase steels. Acta Mater. 2008, 56:3900-3913.
30. N. Clément, Phase transformations and mechanical properties of the Ti-5553 β-metastable titanium alloy, Ph.D. thesis, Université catholique de Louvain, 2009.
31. Argon A.S., Im J., Safoglu R. Cavity formation from inclusions in ductile fracture. Metall. Trans. A 1975, 6:825-837.
32. Shabrov M.N., Sylven E., Kim S., Sherman D.H., Chuzhoy L., Briant C.L., Needleman A. Void nucleation by inclusion cracking. Metall. Mater. Trans. A 2004, 35:1745-1755.
33. Budiansky B., Hutchinson J.W., Slutsky S. Void growth and collapse in viscous solids. Mechanics of Solids. The Rodney Hill 60th Anniversary Volume 1982, 13. Pergamon Press, Oxford. H.G. Hopkins, M.J. Sewell (Eds.).
34. Huber G., Brechet Y., Pardoen T. Void growth and void nucleation controlled ductility in quasi eutectic cast aluminium alloys. Acta Mater. 2005, 53:2739-2749.
35. Lassance D., Scheyvaerts F., Pardoen T. Growth and coalescence of penny-shaped voids in metallic alloys. Eng. Fract. Mech. 2006, 73:1009-1034.
36. Liao K.C., Pan J., Tang S.C. Approximate yield criteria for anisotropic porous ductile sheet metals. Mech. Mater. 1997, 26:213-226.
37. Bron F., Besson J., Pineau A. Ductile rupture in thin sheets of two grades of 2024 aluminum alloy. Mater. Sci. Eng. A 2004, 380:356-364.
38. A Benzerga A., Besson J., Pineau A. Anisotropic ductile fracture - Part I: experiments. Acta Mater. 2004, 52:4623-4638.
39. Benzerga A.A., Besson J., Pineau A. Anisotropic ductile fracture - Part II: theory. Acta Mater. 2004, 52:4639-4650.
40. Needleman A., Kushner A.S. An analysis of void distribution effects on plastic flow in porous solids. Eur. J. Mech. A/Solids 1990, 9:193-206.
41. Tvergaard V. Interaction of very small voids with larger voids. Int. J. Solids Struct. 1998, 35:3989-4000.
42. Thomason P.F. Ductile Fracture of Metals 1990, Pergamon Press, Oxford.
43. Worswick M.J., Chen Z.T., Pilkey A.K., Lloyd D., Court S. Damage characterization and damage percolation modeling in aluminum alloy sheet. Acta Mater. 2001, 49:2791-2803.
44. Tekǒlu C., Pardoen T. A micromechanics based damage model for composite materials. Int. J. Plast. 2010, 26:549-569.
45. Cox T.B., Low J.R. An investigation of the plastic fracture of AISI 4340 and 18 nickel-200 grade maraging steels. Metall. Trans. A 1974, 5:1457-1470.
46. Perrin G., Leblond J.B. Accelerated void growth in porous ductile solids containing two populations of cavities. Int. J. Plast. 2000, 16:91-120.
47. Faleskog J., Shih C.F. Micromechanics of coalescence - I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids. J. Mech. Phys. Solids 1997, 45:21-45.
48. Fabrègue D., Pardoen T. A constitutive model for elastoplastic solids containing primary and secondary voids. J. Mech. Phys. Solids. J. Mech. Phys. Solids 2009, 57:869-870. Corrigendum to "A constitutive model for elastoplastic solids containing primary and secondary voids".
49. Thomason P.F. Three-dimensional models for the plastic limit-load at incipient failure of the intervoid matrix in ductile porous solids. Acta Metall. 1985, 33:1079-1085.
50. Pardoen T., Doghri I., Delannay F. Experimental and numerical comparison of void growth models and void coalescence criteria for the prediction of ductile fracture in copper bars. Acta Mater. 1998, 46:541-552.
51. Scheyvaerts F., Onck P.R., Pardoen T. A new model for void coalescence by internal necking. Int. J. Damage Mech. 2010, 19:95-126.
52. Hancock J.W., Mackenzie A.C. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J. Mech. Phys. Solids 1977, 14:147-169.
53. Marini B., Mudry F., Pineau A. Experimental study of cavity growth in ductile rupture. Eng. Fract. Mech. 1985, 6:989-996.
54. Simar A., Nielsen K.L., de Meester B., Tvergaard V., Pardoen T. Micro-mechanical modelling of ductile failure in 6005A aluminium using a physics based strain hardening law including stage IV. Eng. Fract. Mech. 2010, 77:2491-2503.
55. Tvergaard V., Hutchinson J.W. Two mechanisms of ductile fracture: void by void growth versus multiple void interaction. Int. J. Solids Struct. 2002, 39:3581-3597.
56. Needleman A., Tvergaard V. An analysis of ductile rupture in notched bars. J. Mech. Phys. Solids 1984, 32:461-490.
57. Besson J., Steglich D., Brocks W. Modelling of plane strain ductile rupture. Int. J. Plast. 2003, 19:1517-1541.
58. Pardoen T., Hutchinson J.W. Micromechanics-based model for trends in toughness of ductile metals. Acta Mater. 2003, 51:133-148.
59. Gurson A. Continuum theory of ductile rupture by void nucleation and growth: part I - Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 1977, 99:2-15.
60. Gologanu M., Leblond J.B., Devaux J. Approximate models for ductile metals containing non-spherical voids - case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 1993, 41:1723-1754.
61. Gologanu M., Leblond J.B., Devaux J. Approximate models for ductile metals containing non-spherical voids - case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Technol. 1994, 116:290-297.
62. Monchiet V., Cazacu O., Charkaluk E., Kondo D. Macroscopic yield criteria for plastic anisotropic materials containing spheroidal voids. Int. J. Plast. 2008, 24:1158-1189.
63. Pardoen T., Hutchinson J.W. An extended model for void growth and coalescence. J. Mech. Phys. Solids 2000, 48:2467-2512.
64. Pierard O., Doghri I. A study of various estimates of the macroscopic tangent operator in the incremental homogenization of elasto-plastic composites. Int. J. Multiscale Comput. Eng. 2006, 4:521-543.
65. Doghri I., Friebel C. Effective elasto-plastic properties of inclusion-reinforced composites study of shape, orientation and cyclic response. Mech. Mater. 2005, 37:45-68.
66. Doghri I., Ouaar A. Homogenization of two-phase elasto-plastic composite materials and structures - study of tangent operators, cyclic plasticity and numerical algorithms. Int. J. Solids Struct. 2003, 40:1681-1712.
67. Bornert M., Bretheau T., Gilormini P. Homogénéisation en mécanique des matériaux, 1. Matériaux aléatoires élastiques et milieux périodiques 2001, HERMES Science, Paris.
68. Chu C., Needleman A. Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Technol. 1980, 102:249-256.
69. Beremin F.M. Cavity formation from inclusions in ductile fracture of A508 steel. Metall. Trans. A 1981, 12:723-731.
70. Leblond J.B., Perrin G., Devaux J. An improved Gurson-type model for hardenable ductile metals. Eur. J. Mech. A/Solids 1995, 14:499-527.
71. Klöcker H., Tvergaard V. Growth and coalescence of non-spherical voids in metals deformed at elevated temperature. Int. J. Mech. Sci. 2003, 25:1283-1308.
72. Grange M., Besson J., Andrieu E. An anisotropic Gurson model to represent the ductile rupture of hydrided Zircaloy-4 sheets. Int. J. Fract. 2000, 105:273-293.
73. Benzerga A.A., Besson J., Batisse R., Pineau A. Synergistic effects of plastic anisotropy and void coalescence on fracture mode in plane strain. Mod. Simul. Mater. Sci. Eng. 2002, 10:73-102.
74. Keralavarma S.M., Benzerga A. An approximate yield criterion for anisotropic porous media. C. R. Mécanique 2008, 336:685-692.
75. Mear M., Hutchinson J.W. Influence of yield surface curvature on flow localization in dilatant plasticity. Mech. Mater. 1985, 4:395-407.
76. Besson J., Guillemer-Neel C. An extension of the Green and Gurson models to kinematic hardening. Mech. Mater. 2003, 35:1-18.
77. Mühlich U., Brocks W. On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening. Comput. Mech. 2003, 31:479-488.
78. Nahshon K., Hutchinson J.W. Modification of the Gurson Model for shear failure. Eur. J. Mech. A/Solids 2008, 27:1-17.
79. Thomason P.F. A theory for ductile fracture by internal necking of cavities. J. Institute Metals 1968, 96:360-365.
80. Thomason P.F. A three-dimensional model for ductile fracture by the growth and coalescence of microvoids. Acta Metall. 1985, 33:1087-1095.
81. F. Scheyvaerts, P.R. Onck, T. Pardoen, Multiscale modelling of ductile fracture in heterogeneous metallic alloys, Ph.D. thesis, Universite catholique de Louvain, 2009.
82. Kaisalam M., Ponte-Castañeda P. A general constitutive theory for linear and nonlinear particulate media with microstructure evolution. J. Mech. Phys. Solids 1998, 46:427-465.
83. Yerra S.K., Tekǒlu C., Scheyvaerts F., Delannay L., Van Bael A., Van Houtte P., Pardoen T. Void growth and coalescence in single crystals. Int. J. Solids Struct. 2010, 47:1016-1029.
84. Brocks W., Sun D.Z., Hönig A. Verification of the transferability of micromechanical parameters by cell model calculations with viscoplastic materials. Int. J. Plast. 1995, 11:971-989.
85. Gao X., Kim J. Modelling of ductile fracture: significance of void coalescence. Int. J. Solids Struct. 2006, 43:6277-6293.
86. Koplik J., Needleman A. Void growth and coalescence in porous plastic solids. Int. J. Solids Struct. 1988, 24:835-853.
87. Benzerga A.A. Micromechanics of coalescence in ductile fracture. J. Mech. Phys. Solids 2002, 50:1331-1362.
88. Tvergaard V. Studies of void growth in a thin ductile layer between ceramics. Comput. Mech. 1997, 20:186-191.
89. Leblond J.B., Mottet G. A theoretical approach of strain localization within thin planar bands in porous ductile materials. C. R. Mécanique 2008, 336:176-189.
90. Fleck N.A., Hutchinson J.W. Strain gradient plasticity. Adv. Appl. Mech. 1997, 33:295-361.
91. Wen J., Huang Y., Hwang K.C., Liu C., Li M. The modified Gurson model accounting for the void size effect. Int. J. Plast. 2005, 21:381-395.
92. Niordson C.F. Strain gradient plasticity effects in whisker-reinforced metals. J. Mech. Phys. Solids 2003, 51:1863-1883.
93. Rice J.R. The localization of plastic deformation. Theoretical and Applied Mechanics 1976, 207-220. North-Holland Publ. Co. W.T. Koiter (Ed.).
94. Needleman A., Rice J.R. Limits to ductility set by plastic flow localization. Mechanics of Sheet Metal Forming 1978, 237. Plenum Press, New York. D.P. Koistinen, N.M. Wang (Eds.).
95. Needleman A., Tvergaard V. Analyses of plastic flow localization in metals. Appl. Mech. Rev. 1992, 45:S3-S18.
96. Yamamoto H. Conditions for shear localization in the ductile fracture of void-containing materials. Int. J. Fract. 1978, 14:347-365.
97. L.M. Brown, J.D. Embury, The initiation and growth of voids at second phase particles, in: Proc. Third Int. Conf. on the Strength of Metals and Alloys, ICSMA 3, Cambridge, England, 1973, p. 164.
98. Leblond J.-B., Perrin G., Devaux J. Bifurcation effects in ductile metals with nonlocal damage. J. Appl. Mech. 1994, 61:236-242.
99. Tvergaard V., Needleman A. Effects of non local damage in porous plastic solids. Int. J. Solids Struct. 1995, 32:1063-1077.
100. Reusch F., Svendsen B., Klingbeil D. Local and non-local Gurson-based ductile damage and failure modelling at large deformation. Eur. J. Mech. A/Solids 2003, 22:770-792.
101. Geers M.G.D. Finite strain logarithmic hyperelasto-plasticity with softening: a strongly nonlocal implicit gradient framework. Comput. Methods Appl. Mech. Eng. 2004, 193:3377-3401.
102. Mediavilla J., Peerlings R.H.J., Geers M.G.D. A nonlocal triaxiality-dependent ductile damage model for finite strain plasticity. Comput. Methods Appl. Mech. Eng. 2006, 66:661-688.
103. Huespe A.E., Needleman A., Oliver J., Sánchez P.J. A finite thickness band method for ductile fracture analysis. Int. J. Plast. 2009, 25:2349-2365.
104. Tvergaard V., Hutchinson J.W. The relationship between crack growth resistance and fracture process parameters in elastic plastic solids. J. Mech. Phys. Solids 1992, 40:1377-1397.
105. Steglich D., Brocks W., Heerens J., Pardoen T. Anisotropic ductile damage modelling of Al2024 alloys. Eng. Fract. Mech. 2008, 75:3692-3706.
106. Dumont D., Deschamps A., Bréchet Y. A model for predicting fracture mode and toughness in 7000 series aluminium alloys. Acta Mater. 2004, 52:2529-2540.
107. Morgeneyer T.F., Starink M.J., Wang S.C., Sinclair I. Quench sensitivity of toughness in an Al alloy: direct observation and analysis of failure initiation at the precipitate-free zone. Acta Mater. 2008, 56:2872-2884.
108. Krol T., Baither D., Nembach E. The formation of precipitate free zones along grain boundaries in a superalloy and the ensuing effects on its plastic deformation. Acta Mater. 2004, 52:2095-2108.
109. Pardoen T., Bréchet Y. Influence of microstructure driven strain localisation on ductile fracture of metallic alloys. Philos. Mag. 2004, 84(3-5):269-298.
110. Mishra R.S., Ma Z.Y. Friction stir welding and processing. Mater. Sci. Eng. R 2005, 50:1-78.
111. Nandan R., DebRoy T., Bhadeshia H.K.D.H. Recent advances in friction-stir welding - process, weldment structure and properties. Prog. Mater. Sci. 2008, 53:980-1023.
112. Threadgill P.L., Leonard A.J., Shercliff H.R., Withers P.J. Friction stir welding of aluminium alloys. Int. Mater. Rev. 2009, 54:49-93.
113. Simar A., Lecomte-Beckers J., Pardoen T., de Meester B. Effect of boundary conditions and heat source distribution on temperature distribution in friction stir welding. Sci. Technol. Weld. Joining 2006, 11:170-176.
114. Simar A., Pardoen T., de Meester B. Effect of rotational material flow on temperature distribution in friction stir welds. Sci. Technol. Weld. Joining 2007, 12(4):324-332.
115. Simar A., Bréchet Y., de Meester B., Denquin A., Pardoen T. Microstructure, local and global mechanical properties of friction stir welds in aluminium alloy 6005A-T6. Mater. Sci. Eng. A 2008, 486:85-95.
116. Simar A., Bréchet Y., de Meester B., Denquin A., Pardoen T. Sequential modelling of local precipitation, strength and strain hardening in friction stir welds of an aluminium alloy 6005A-T6. Acta Mater. 2007, 55:6133-6143.
117. Nielsen K.L., Pardoen T., Tvergaard V., de Meester B., Simar A. Modelling of plastic flow localisation and damage development in friction stir welded 6005A aluminium alloy using physics based strain hardening law. Int. J. Solids Struct. 2010, 47:2359-2370.
118. Gallais C., Simar A., Fabrègue D., Denquin A., Lapasset G., de Meester B., Bréchet Y., Pardoen T. Multiscale analysis of the strength and ductility of 6056 aluminium friction stir welds. Metall. Mater. Trans. A 2007, 38:964-981.