Micromechanics of room and high temperature fracture in 6xxx Al alloys

Progress in Materials Science

Volumn 52, Issue 1, 2007, Pages 62-129

  Lassance, D ^a   Fabregue D ^a   Delannay, F ^a   Pardoen, T ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

6XXX AL ALLOYS; DAMAGE RESISTANCE; MULTIPLE LENGTHS SCALES; STRUCTURAL INTEGRITY ANALYSIS;

COMPOSITE MICROMECHANICS; DUCTILE FRACTURE; DUCTILITY; EXTRUSION; MATHEMATICAL MODELS; STRUCTURAL ANALYSIS;

ALUMINUM ALLOYS;

EID: 33749641676     PISSN: 00796425     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pmatsci.2006.06.001     Document Type: Review

References (168)

1. McClintock F.A. A criterion for ductile fracture by the growth of holes. J Appl Mech 35 (1968) 353-371
2. McClintock F.A. Local criteria for ductile fracture. Int J Fract 4 (1968) 103-130
3. Rice J.R., and Tracey D.M. On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17 (1969) 201-217
4. McClintock F.A. Plasticity aspects of fracture. In: Liebowitz H. (Ed). Fracture - an advanced treatise vol. 3 (1971), Academic Press 47-225
5. Needleman A. Void growth in an elastic-plastic medium. J Appl Mech 39 (1972) 964-970
6. Brown LM, Embury JD. The initiation and growth of voids at second phase particles. In: Proceedings of the third international conference on the strength of metals and alloys, ICSMA 3, Cambridge, England, 1973, p. 164-9.
7. Argon A.S., Im J., and Safoglu R. Cavity formation from inclusions in ductile fracture. Metall Trans A 6 (1975) 825-837
8. Argon A.S., and Im J. Separation of second phase particles in spheroidized 1045 steel, Cu-0.6pct Cr alloy and maraging steel in plastic straining. Metall Trans A 6 (1975) 839-851
9. Rudnicki J.W., and Rice J.R. Conditions for localisation of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23 (1975) 371-394
10. Argon A.S. Formation of cavities from non-deformable second-phase particles in low temperature ductile fracture. J Eng Mater Tech 98 (1976) 60-68
11. Yamamoto H. Conditions for shear localisation in the ductile fracture of void-containing materials. Int J Fract 14 (1978) 347-365
12. Goods S.H., and Brown L.M. The nucleation of cavities by plastic deformation. Acta Metall 27 (1979) 1-15
13. 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 Eng Mater Tech 99 (1977) 2-15
14. Chu C.C., and Needleman A. Void nucleation effects in biaxially stretched sheets. J Eng Mater Tech 102 (1980) 249-256
15. Beremin F.M. Cavity formation from inclusions in ductile fracture of A508 steel. Metall Trans A 12 (1981) 723-731
16. Lautridou J.C., and Pineau A. Crack initiation and stable crack growth resistance in A508 steels in relation to inclusion distribution. Eng Fract Mech 15 (1981) 55-71
17. Le Roy G., Embury J.D., Edward G., and Ashby M.F. A model of ductile fracture based on the nucleation and growth of voids. Acta Metall 29 (1981) 1509-1522
18. Pineau A. Review of fracture micromechanisms and a local approach to predicting crack resistance in low strength steels. In: François D., et al. (Ed). Advanced in fracture research, ICF 5 vol. 2 (1981), Pergamon 553-577
19. Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17 (1981) 389-407
20. Budiansky B., Hutchinson J.W., and Slutsky S. Void growth and collapse in viscous solids. In: Hopkins H.G., and Sewell M.J. (Eds). Mechanics of solids (1982), Pergamon Press 13-45 The Rodney Hill 60th anniversary volume
21. Tvergaard V. On localisation in ductile materials containing voids. Int J Fract 18 (1982) 237-251
22. Saje M., Pan J., and Needleman A. Void nucleation effects on shear localisation in porous plastic solids. Int J Fract 19 (1982) 163-182
23. Pineau A., and Pardoen T. Failure mechanisms of metals. Comprehensive structural integrity. 2nd ed. vol. 2 (2006), Elsevier [chapter 6]
24. Dons A.L. The Alstruc homogenisation model for industrial aluminium alloys. J Light Met 1 (2001) 133
25. Kalu P.N., and Humphreys F.J. Proc Conf Alumin Technol, vol. 86 (1986), The Institute of Metals, London 197-203
26. Zajac S., Hutchinson B., Johansson A., and Gullman L.-O. Microstructure control and extrudability of Al-Mg-Si alloys microalloyed with manganese. Mater Sci Technol 10 (1994) 323-333
27. Agarwal H., Gokhale A.-M., Graham S., and Horstmeyer M.-F. Void growth in 6061 aluminum alloy under triaxial stress state. Mater Sci Technol 341 1-2 (2003) 35-42
28. Agarwal H., Gokhale A.-M., Graham S., and Horstmeyer M.F. Quantitative characterization of three-dimensional damage evolution in a wrought Al-alloy under tension and compression. Metall Mater Trans A 33A (2002) 2599-2606
29. Kobayashi T. Strength and fracture of aluminium alloys. Mater Sci Forum 426-432 (2003) 67-74
30. Toda H., and Kobayashi T. Damage behaviors of various coarse Al-Fe-Si particles in model wrought alloys. Mater Sci Forum 426-432 (2003) 393-398
31. Kuijpers N.C.W., Tirel J., Hanlon D.N., and Van der Zwaag S. Quantification of the evolution of the 3D intermetallic structure in a 6005A aluminium alloy during a homogenisation treatment. Mater Character 48 (2002) 379-392
32. Hancock J.W., and Mackenzie A.C. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J Mech Phys Solids 14 (1977) 147-169
33. Thomason P.F. Ductile fracture of metals (1990), Pergamon Press, Oxford
34. Mcallen P., and Phelan P. Ductile fracture by central bursts in drawn 2011 aluminium wire. Int J Fract 135 (2005) 19-33
35. Lassance D., Ryelandt L., Dille J., Delplancke J.L., Pardoen T., and Delannay F. Effet of the homogenisation conditions on the extrudability and high temperature resistance of an AA6063 aluminium alloy. Mater Sci Forum 426-432 (2003) 447-452
36. Lassance D., Scheyvaerts F., and Pardoen T. Growth and coalescence of penny-shaped voids in metallic alloys. Eng Fract Mech 73 (2006) 1009-1034
37. Montheillet F, Moussy F, editors. Physique et Mécanique de l'Endommagement, 1986, GRECO, Les Editions de Physique, les Ulis, France.
38. Becker R., Smelser E., Richmond O., and Appleby E. The effect of void shape on void growth and ductility in axisymmetric tension tests. Met Trans A 20 (1989) 853-861
39. Becker R., Smelser E., and Richmond O. The effect of void shape on the development of damage and fracture in plane-strain tension. J Mech Phys Solids 37 (1989) 111-129
40. Hom C.L., and McMeeking R.M. Void growth in elastic-plastic materials. J Appl Mech 56 (1989) 309-317
41. Hom C.L., and McMeeking R.M. Three-dimensional void growth before a blunting crack tip. J Mech Phys Solids 37 (1989) 395-415
42. Gologanu M., Leblond J.B., and Devaux J. Approximate models for ductile metals containing non-spherical voids - case of axisymmetric prolate ellipsoidal cavities. J Mech Phys Solids 41 (1993) 1723-1754
43. Gologanu M., Leblond J.B., and Devaux J. Approximate models for ductile metals containing non-spherical voids - case of axisymmetric oblate ellipsoidal cavities. ASME J Eng Mater Technol 116 (1994) 290-297
44. Gologanu M., Leblond J.B., Perrin G., and Devaux J. Recent extensions of Gurson's model for porous ductile metals. In: Suquet P. (Ed). Continuum micromechanics. CISM lectures series (1997), Springer 61-130
45. Pardoen T., and Hutchinson J.W. An extended model for void growth and coalescence. J Mech Phys Solids 48 (2000) 2467-2512
46. Benzerga A.A., Besson J., and Pineau A. Anisotropic ductile fracture - Part I: experiments. Acta Mater 52 (2004) 4623-4638
47. Benzerga A.A., Besson J., and Pineau A. Anisotropic ductile fracture - Part II: theory. Acta Mater 52 (2004) 4639-4650
48. Thomason P.F. Three-dimensional models for the plastic limit-load at incipient failure of the intervoid matrix in ductile porous solids. Acta Metall 33 (1985) 1079-1085
49. Thomason P.F. A three-dimensional model for ductile fracture by the growth and coalescence of microvoids. Acta Metall 33 (1985) 1087-1095
50. Koplik J., and Needleman A. Void growth and coalescence in porous plastic solids. Int J Solids Struct 24 (1988) 835-853
51. Pardoen T., Doghri I., and 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 46 (1998) 541-552
52. Gologanu M., Leblond J.B., Perrin G., et al. Theoretical models for void coalescence in porous ductile solids. I. Coalescence "in layers". Int J Solids Struct 38 (2001) 5581-5594
53. Benzerga A. Micromechanics of coalescence in ductile fracture. J Mech Phys Solids 50 (2002) 1331-1362
54. Faleskog J., and Shih C. Micromechanics of coalescence - I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids. J Mech Phys Solids 45 (1997) 21-45
55. Fabrègue D, Pardoen T. A constitutive model for elastoplastic solids containing primary and secondary voids, submitted for publication.
56. Gallais C, Simar A, Fabrègue D, Denquin A, Lapasset G, Meester B, et al. Multiscale analysis of the strength and ductility of friction stir welded 6056 Al joints, submitted for publication.
57. Marini B., Mudry F., and Pineau A. Experimental study of cavity growth in ductile rupture. Eng Fract Mech 6 (1985) 989-996
58. Becker R., Needleman A., Richmond O., and Tvergaard V. Void growth and failure in notched bars. J Mech Phys Solids 36 (1988) 317-351
59. Pardoen T., and Delannay F. On the coalescence of voids in prestrained notched round copper bars. Fatigue Fract Eng Mater Struct 21 (1998) 1459-1472
60. Besson J, editor. Local approach to fracture. Collective book, Presses de l'Ecole des Mines de Paris, 2004.
61. Huber G., Brechet Y., and Pardoen T. Void growth and void nucleation controlled ductility in quasi eutectic cast aluminium alloys. Acta Mater 53 (2005) 2739-2749
62. Bridgman P.W. Studies in large plastic flow and fracture (1952), McGraw-Hill, New-York
63. Norris D.M., Moran B., Scudder J.K., and Quinones D.F. A computer simulation of the tension test. J Mech Phys Solids 26 (1978) 1-19
64. Pardoen T., and Delannay F. Assessment of void growth models from porosity measurements in cold drawn copper bars. Metall Mater Trans A 29A (1998) 1895-1909
65. Zhang Z.L., Odegard J., Sovik O.P., and Thaulow C. A study on determining true stress-strain curve for anisotropic materials with rectangular tensile bars. Int J Solids Struct 38 (2001) 4489-4505
66. Blaz L., and Evangelista E. Strain rate sensitivity of hot deformed Al and AlMgSi alloy. Mater Sci Eng A 207 2 (1996) 195-201
67. Spigarelli S., Evangelista E., and McQueen H.J. Study of hot workability of a heat treated AA6082 aluminum alloy. Scr Mater 49 (2003) 179-193
68. Hosford W.F., and Caddell R.M. Metal forming - mechanics and metallurgy (1993), Prentice Hall
69. Lagneborg R., Zajac S., and Hutchinson B. Scr Metall Mater 29 (1993) 159-164
70. Hutchinson J.W., and Neale K.W. Influence of strain-rate sensitivity on necking under uniaxial tension. Acta Metall 25 (1977) 839-846
71. Hutchinson J.W. Survey of some recent work on the mechanics of necking (1979), Western Periodicals Co, North Holywood p. 87-98
72. Babout L., Maire E., Buffière J.Y., and Fougères R. Characterisation by X-ray computed tomography of decohesion, porosity growth and coalescence in model metal matrix composites. Acta Mater 49 (2001) 2055-2063
73. Babout L., Brechet Y., Maire E., and Fougères R. On the competition between particle fracture and particle decohesion in metal matrix composites. Acta Mater 52 (2004) 4517-4525
74. Babout L., Maire E., and Fougères R. Damage initiation in model metallic materials: X-ray tomography and modelling. Acta Mater 52 (2004) 2475-2487
75. Wang Q.J. Microstructural effects on the tensile and fracture behavior of aluminium casting alloys A356/357. Metall Mater Trans A 34 (2003) 2887-2899
76. Wang Q.J., Caceres C.H., and Griffiths J.R. Damage by eutectic cracking in aluminium casting alloys A356/357. Metall Mater Trans A 34A (2003) 2901-2912
77. Deschamps A., Peron S., Brechet Y., Ehrström J.-C., and Poizat L. High temperature cleavage fracture in 5383 aluminum alloy. Mater Sci Eng A 319-321 (2001) 583-586
78. Nagaumi H., and Umeda T. Study of the crack sensitivity of 6xxx and 7xxx aluminum alloys. Mater Sci Forum 426-432 (2003) 465-470
79. Colley L.J., Wells M.A., and Maijer D.M. Tensile properties of as-cast aluminium alloy AA5182 close to the solidus temperature. Mater Sci Eng A 386 1-2 (2004) 140-148
80. Doghri I., and Ouaar A. Homogenisation of two-phase elasto-plastic composite materials and structures - Study of tangent operators, cyclic plasticity and numerical algorithms. Int J Solids Struct 40 (2003) 1681-1712
81. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc Roy Soc London, Ser A 241 (1957) 376-396
82. Berveiller M., and Zaoui A. An extension of the self-consistent scheme to plastically flowing polycrystrals. J Mech Phys Solids 26 (1979) 325-340
83. Kroon M., and Faleskog J. Micromechanisms of cleavage fracture initiation in ferritic steels by carbide cracking. J Mech Phys Solids 53 (2005) 171-196
84. Needleman A. A continuum model for void nucleation by inclusion debonding. J Appl Mech 54 (1987) 525-531
85. Needleman A. Analysis of tensile decohesion along an interface. J Mech Phys Solids 38 (1990) 289-324
86. Christman T., Needleman A., Nutt S., and Suresh S. On microstructural evolution and micromechanical modeling of deformation of a whisker-reinforced metal-matrix composite. Mater Sci Eng A 107 (1989) 49-61
87. Llorca J., Needleman A., and Suresh S. An analysis of the effects of matrix void growth on deformation and ductility in metal-ceramic composites. Acta Metall Mater 39 (1991) 2317-2335
88. Tvergaard V. Model studies of fibre breakage and debonding in a metal reinforced by short fibers. J Mech Phys Solids 41 (1993) 1309-1326
89. Shabrov M.N., and Needleman A. An analysis of inclusion morphology effects on void nucleation. Modell Simul Mater Sci Eng 10 (2002) 163-183
90. Lee B.J., and Mear M.E. Stress concentration induced by an elastic spheroidal particle in a plastically deforming solid. J Mech Phys Solids 47 (1999) 1301-1336
91. Pardoen T., and Hutchinson J.W. Micromechanics-based model for trends in toughness of ductile metals. Acta Mater 51 (2003) 133-148
92. Scheyvaerts F, Onck PR, Bréchet Y, Pardoen T. A multiscale model for the cracking resistance of 7000 Al. In: Besson J, Moinereau D, Steglich D, editors. Proceedings of the 9th European mechanics of materials conference on local approach to fracture, Euromech - Mecamat 2006. Moret-sur-Loing, 9-12 May 2006, France, Les Presses de l'Ecole des Mines de Paris, p. 447-52.
93. Klöcker H., and Tvergaard V. Growth and coalescence of non-spherical voids in metals deformed at elevated temperature. Int J Mech Sci 25 (2003) 1283-1308
94. Hutchinson JW, Tvergaard V. Softening due to void nucleation in metals. In: Fracture mechanics: twentieth symposium, 1989. p. 61-83.
95. Steglich D., and Brocks W. Micromechanical modeling of the behavior of ductile materials including particles. Comput Mater Sci 9 (1997) 7-17
96. Siruguet K., and Leblond J.-B. Effect of void locking by inclusions upon the plastic behavior of porous ductile solids - I: theoretical modeling and numerical study of void growth. Int J Plast 20 (2004) 225-254
97. Maire E., Bordreuil C., Babout L., and Boyer J.C. Damage initiation and growth in metals. Comparison between modeling and tomography experiments. J Mech Phys Solids 53 (2005) 2411-2434
98. Cox T.B., and Low J.R. An investigation of the plastic fracture of AISI 4340 and 18 nickel-200 grade maraging steels. Metall Trans A 5 (1974) 1457-1470
99. Van Stone R.H., Cox T.B., Low J.R., and Psioda J.A. Microstructural aspects of fracture by dimpled rupture. Int Met Rev 30 (1985) 157-179
100. Perrin G., and Leblond J.-B. Analytical study of a hollow sphere made of plastic porous material and subjected to hydrostatic tension - application to some problems in ductile fracture of metals. Int J Plast 6 (1990) 677-699
101. Tvergaard V. Interaction of very small voids with larger voids. Int J Solids Struct 35 (1998) 3989-4000
102. Perrin G., and Leblond J.-B. Accelerated void growth in porous ductile solids containing two populations of cavities. Int J Plast 16 (2000) 91-120
103. Enakoutsa K, Leblond J-B, Audoly B. Influence of continuous nucleation of secondary voids upon growth and coalescence of cavities in porous ductile metals. In: Carpinteri A, editor. Proceedings of the 11th international conference on fracture, March 20-25, Turin, Italy, CD-Rom, 2005.
104. Xia L., Shih C.F., and Hutchinson J.W. A computational approach to ductile crack growth under large scale yielding conditions. J Mech Phys Solids 43 (1995) 389-413
105. Xia L., and Shih C.F. Ductile crack growth - I. A numerical study using computational cells with microstructurally based length scales. J Mech Phys Solids 43 (1995) 233-259
106. Xia L., and Shih C.F. Ductile crack growth - II. Void nucleation and geometry effects on macroscopic fracture behavior. J Mech Phys Solids 43 (1995) 1953-1981
107. Ruggieri C., Panontin T.L., and Dodds Jr. R.H. Numerical modeling of ductile crack growth in 3-D using computational cell elements. Int J Fract 82 (1996) 67-95
108. Gao X., Faleskog J., and Shih C.F. Cell model for nonlinear fracture analysis - II. Fracture-process calibration and verification. Int J Fract 89 (1998) 374-386
109. Gullerud A.S., Gao X., Dodds Jr. R.H., and Haj-Ali R. Simulation of ductile crack growth using computational cells: numerical aspects. Eng Fract Mech 66 (2000) 65-92
110. Besson J., Steglich D., and Brocks W. Modelling of plane strain ductile rupture. Int J Plast 19 (2003) 1517-1541
111. Needleman A., and Tvergaard V. An analysis of ductile rupture in notched bars. J Mech Phys Solids 32 (1984) 461-490
112. Needleman A., and Tvergaard V. Analysis of the cup and cone fracture in a round tensile bar. Acta Metall 32 (1984) 157-169
113. Lassance D, Schmitz M, Delannay F, Pardoen T. Linking microstructure and high temperature ductility in aluminium alloys 6xxx. In: Carpinteri A, editor. Proceedings of ICF11 - 11th international conference on fracture, 20-25 March 2005, Turin, Italy, CD-Rom - 5079.
114. Pardoen T., Marchal Y., and Delannay F. Thickness dependence of cracking initiation criteria in thin aluminum plates. J Mech Phys Solids 47 (1999) 2093-2123
115. Pardoen T., Hachez F., Marchioni B., Blyth H., and Atkins A.G. Mode I fracture of sheet metal. J Mech Phys Solids 52 (2004) 423-452
116. Pardoen T., Dumont D., Deschamps A., and Brechet Y. Grain boundary versus transgranular ductile failure. J Mech Phys Solids 51 (2003) 637-665
117. Pardoen T. Numerical simulation of low stress triaxiality ductile fracture. Comput Struct 84 (2006) 1641-1650
118. Walsh J.A., Jata K.V., and Starke E.A. The influence of Mn dispersoid content and stress state on ductile fracture of 2134 type Al alloys. Acta Metall 37 (1989) 2861-2871
119. Joly P., Meyzaud Y., and Pineau A. Micromechanisms of fracture of an aged duplex stainless steel containing a brittle and a ductile phase: development of a local criterion of fracture. Advances in local fracture/damage models for the analysis of engineering problems, AMD vol. 137 (1992), The American Society of Mechanical Engineers 151-180
120. Bugat S., Besson J., and Pineau A. Micromechanical modeling of the behavior of duplex stainless steels. Comput Mater Sci 16 (1999) 158-166
121. Kwon D., and Asaro R.J. A study of void nucleation, growth and coalescence in spheroidized 1518 steel. Metall Trans A 11 (1990) 91-101
122. Pineau A. Global and local approaches of fracture - transferability of laboratory test results to components. In: Argon A.S. (Ed). Topics in fracture and fatigue (1992), Springer 197-234
123. Tvergaard V. Material failure by void growth to coalescence. Adv Appl Mech 27 (1990) 83-151
124. Estrin Y. Dislocation-density-related constitutive modeling. In: Krausz A.S., and Krausz K. (Eds). Unified constitutive laws of plastic deformation (1996), Academic Press, New York 69-106
125. Nes E. Modelling of work hardening and stress saturation in FCC metals. Prog Mater Sc 41 (1998) 129-193
126. Kocks U.F., and Mecking H. Physics and phenomenology of strain hardening: the FCC case. Prog Mater Sci 48 (2003) 171-273
127. Ankem S., Margolin H., Greene C.A., Neuberger B.W., and Oberson P.G. Mechanical properties of alloys consisting of two ductile phases. Prog Mater Sc 51 (2006) 632-709
128. Gandin C.A., Brechet Y., Rappaz M., Canova G., Ashby M., and Shercliff H. Modelling of solidification and heat treatment for the prediction of yield stress of cast alloys. Acta Mater 50 (2002) 901
129. Brunet M., Morestin F., and Walter H. Damage identification for anisotropic sheet-metals using a non-local damage model. Int J Damage Mech 13 (2004) 35
130. Saanouni K., Mariage J.F., Cherouat A., and Lestriez P. Numerical prediction of discontinuous central bursting in axisymmetric forward extrusion by continuum damage mechanics. Comput Struct 82 (2004) 2309
131. Khelifa M., Badreddine H., Belamri N., Gahbiche M.A., Saanouni K., Cherouat A., et al. Effect of anisotropic plastic flow on the ductile damage evolution in hydrobulging test of thin sheet metal. Int J Forming Proc 8 (2005) 271
132. Huetink J., Vreede P.T., and van der Lugt J. Progress in mixed Eulerian-Lagrangian finite element simulation of forming processes. Int J Numer Methods Eng 30 (1990) 1441
133. Lof J. Elasto-viscoplastic FEM simulations of the aluminium flow in the bearing area for extrusion of thin-walled sections. J Mater Proc Tech 114 (2001) 174
134. Ponthot J.P., and Belytschko T. Arbitrary Lagrangian-Eulerian formulation for element-free Galerkin method. Comput Methods Appl Mech Eng 152 (1998) 19
135. Boman R., and Ponthot J.P. Finite element simulation of lubricated contact in rolling using the arbitrary Lagrangian-Eulerian formulation. Comput Methods Appl Mech Eng 193 (2004) 4323
136. Shercliff H.R., and Ashby M.F. A process model for age hardening of aluminium alloys - I. The model. Acta Metall Mater 38 (1990) 1789-1802
137. Shercliff H.R., and Ashby M.F. A process model for age hardening of aluminium alloys - II. Applications of the model. Acta Metall Mater 38 (1990) 1803-1812
138. Myhr O.R., and Grong O. Process modelling applied to 6082-T6 aluminium weldments - I. Reaction kinetics. Acta Metall Mater 39 (1991) 2693-2702
139. Myhr O.R., and Grong O. Process modelling applied to 6082-T6 aluminium weldments - II. Applications of the model. Acta Metall Mater 39 (1991) 2703-2708
140. Myhr O.R., and Grong O. Modelling of the age hardening behaviour of Al-Mg-Si alloys. Acta Mater 49 (2001) 65-75
141. Myhr O.R., Grong O., Fjaer H.G., and Marioara C.D. Modelling of the microstructure and strength evolution in Al-Mg-Si alloys during multistage thermal processing. Acta Mater 52 (2004) 4997-5008
142. Deschamps A., and Brechet Y. Influence of predeformation and ageing of an Al-Zn-Mg alloy - II. Modeling of the precipitation kinetics and yield stress. Acta Mater 47 (1999) 293-305
143. Nicolas M., and Deschamps A. Characterisation and modelling of precipitate evolution in an Al-Zn-Mg alloy during non-isothermal heat treatments. Acta Mater 51 (2003) 6077-6094
144. Esmaeili S., Lloyd D.J., and Poole W.J. Modeling of the precipitation hardening for the naturally aged Al-Mg-Si-Cu alloy AA6111. Acta Mater 51 (2003) 3467-3481
145. Faleskog J., Gao X., and Shih C.F. Cell model for nonlinear fracture analysis - I. Micromechanics calibration. Int J Fract 89 (1998) 355-373
146. Leblond J.-B., Perrin G., and Devaux J. An improved Gurson-type model for hardenable ductile metals. Eur J Mech A/Solids 14 (1995) 499-527
147. Mear M., and Hutchinson J.W. Influence of yield surface curvature on flow localization in dilatant plasticity. Mech Mater 4 (1985) 395-407
148. Arndt S., Svendsen B., and Klingbeil D. Modellierung der Eigenspannungen and der Rissspitze mit einem Schädigungsmodell. Tech Mech 17 (1997) 323-332
149. Besson J., and Guillemer-Neel C. An extension of the Green and Gurson models to kinematic hardening. Mech Mater 35 (2003) 1-18
150. Mühlich U., and Brocks W. On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening. Comput Mech 31 (2003) 479-488
151. Doege E., El-Dsoki T., and Seibert D. Prediction of necking and wrinkling in sheet-metal forming. J Mater Proc Tech 50 (1995) 197-206
152. Liao K.C., Pan J., and Tang S.C. Approximate yield criteria for anisotropic porous ductile sheet metals. Mech Mater 26 (1997) 213-226
153. Rivalin F., Besson J., Di Fant M., and Pineau A. Ductile tearing of pipeline-steel wide plates: II. Modeling of in-plane crack propagation. Eng Fract Mech 68 (2001) 347-364
154. Grange M., Besson J., and Andrieu E. An anisotropic Gurson model to represent the ductile rupture of hydrided Zircaloy-4 sheets. Int J Fract 105 (2000) 273-293
155. Benzerga A.A., Besson J., Batisse R., and Pineau A. A. Synergistic effects of plastic anisotropy and void coalescence on fracture mode in plane strain. Mod Simul Mater Sci Eng 10 (2002) 73-102
156. Wang D.A., Pan J., and Liu S.D. An anisotropic Gurson yield criterion for porous ductile sheet metals with planar anisotropy. Int J Damage Mech 13 (2004) 7-33
157. Hill R. A theory of the yielding and plastic flow of anisotropic metals. Proc Roy Soc London A 193 (1948) 1197-1232
158. Benzerga A., and Besson J. Plastic potentials for anisotropic porous solids. Eur J Mech A/Solids 20 (2001) 397-434
159. Kaisalam M., and Ponte Castañeda P. A general constitutive theory for linear and nonlinear particulate media with microstructure evolution. J Mech Phys Solids 46 (1998) 427-465
160. Peirce D., Shih C.F., and Needleman A. A tangent modulus method for rate dependent solids. Comput Struct 18 (1984) 875-887
161. Moran B., Asaro R.J., and Shih C.F. Effects of material rate sensitivity and void nucleation on fracture initiation in a circumferentially cracked bar. Metall Trans A 22 (1991) 161-170
162. Haghi M.L., and Anand L. A constitutive model for isotropic, porous, elastic-viscoplastic metals. Mech Mater 13 (1992) 37-53
163. Leblond J.-B., Perrin G., and Suquet P. Exact results and approximate models for porous viscoplastic solids. Int J Plast 10 (1994) 213-235
164. Flandi L., and Leblond J.-B. A new model for porous nonlinear viscous solids incorporating void shape effects - I: Theory. Euro. J Mech A/Solids 24 (2005) 537-551
165. Zhang Z.L., and Niemi E. A new failure criterion for the Gurson-Tvergaard dilational constitutive model. Int J Fract 70 (1995) 321-334
166. Needleman A., and Rice J.R. Limits to ductility set by plastic flow localization. In: Koistinen D.P., and Wang N.M. (Eds). Mechanics of sheet metal forming (1978), Plenum Press, New York 237-265
167. Gao H., Huang Y., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity - I. Theory. J. Mech. Phys. Solids 47 (1999) 1239-1263
168. Wen J., Huang Y., Hwang K.C., Liu C., and Li M. The modified Gurson model accounting for the void size effect. Int J Plast 21 (2005) 381-395