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Ductile failure modeling

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An Erratum to this article was published on 17 October 2016

Abstract

Ductile fracture of structural metals occurs mainly by the nucleation, growth and coalescence of voids. Here an overview of continuum models for this type of failure is given. The most widely used current framework is described and its limitations discussed. Much work has focused on extending void growth models to account for non-spherical initial void shapes and for shape changes during growth. This includes cases of very low stress triaxiality, where the voids can close up to micro-cracks during the failure process. The void growth models have also been extended to consider the effect of plastic anisotropy, or the influence of nonlocal effects that bring a material size scale into the models. Often the voids are not present in the material from the beginning, and realistic nucleation models are important. The final failure process by coalescence of neighboring voids is an issue that has been given much attention recently. At ductile fracture, localization of plastic flow is often important, leading to failure by a void-sheet mechanism. Various applications are presented to illustrate the models, including welded specimens, shear tests on butterfly specimens, and analyses of crack growth.

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Notes

  1. An alternative limit-analysis based on velocity fields orthogonal to these spheroids was proposed by Garajeu et al. (2000).

  2. There is a slight gap between numerical and theoretical results for the orientation angle \(\theta \); but this gap is present from the very start of the loading (and not compensated afterwards), which indicates that it may be due to the difficulty, when examining the numerical results, of defining an orientation angle for an almost spherical, but not strictly ellipsoidal cavity.

  3. That softening models have their roots in homogenization is very often only implicit, but in the case of Gurson-type models quite clear and explicit.

  4. This means that the homogenization procedure based on such boundary conditions intrinsically remains a model, in contrast with other procedures using rigorous, for instance periodic, boundary conditions.

  5. The price to pay is, unfortunately, a larger bandwidth of the stiffness matrix than for a first-gradient model, because this matrix does not only “connect” first-neighbor nodes (contained in the same element), but also “third-neighbor” ones (having first neighbors lying in the same element).

  6. The emphasis is ours.

  7. Perrin’s work elaborated on earlier work by Yamamoto (1978) by accounting for deformation-induced anisotropy, consistent with the results of Koplik and Needleman (1988), and revisiting the Rice–Rudnicki localization condition (Rudnicki and Rice 1975); see Perrin and Leblond (1993).

References

  • Agoras M, Ponte Castañeda P (2013) Iterated linear comparison bounds for viscoplastic porous materials with ellipsoidal microstructures. J Mech Phys Solids 61:701–725

    Article  Google Scholar 

  • Agoras M, Ponte Castañeda P (2014) Anisotropic finite-strain models for porous viscoplastic materials with microstructure evolution. Int J Solids Struct 51:981–1002

    Article  Google Scholar 

  • Argon AS, Im J, Safoglu R (1975) Cavity formation from inclusions in ductile fracture. Met Trans A 6A:825–837

    Article  Google Scholar 

  • Arriaga M, McAuliffe C, Waisman H (2015) Onset of shear band localization by a local generalized eigenvalue analysis. Comput Methods Appl Mech Eng 289:179–208

    Article  Google Scholar 

  • Babout L, Bréchet Y, Maire E, Fougères R (2004) On the competition between particle fracture and particle decohesion in metal matrix composites. Acta Mater 52:4517–4525

    Article  Google Scholar 

  • Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98

    Article  Google Scholar 

  • Barsoum I, Faleskog J (2007a) Rupture mechanisms in combined tension and shear-experiments. Int J Solids Struct 44:1768–1786

    Article  Google Scholar 

  • Barsoum I, Faleskog J (2007b) Rupture mechanisms in combined tension and shear-micromechanics. Int J Solids Struct 44:5481–5498

    Article  Google Scholar 

  • Barsoum I, Faleskog J (2011) Micromechanical analysis on the influence of the lode parameter on void growth and coalescence. Int J Solids Struct 48:925–938

    Article  Google Scholar 

  • Beachem CD (1963) An electron fractographic study of the influence of plastic strain conditions upon ductile rupture processes in metals. Trans ASM 56:318–326

    Google Scholar 

  • Becker R, Needleman A (1986) Effect of yield surface curvature on necking and failure in porous solids. J Appl Mech 53:491–499

    Article  Google Scholar 

  • Benallal A, Desmorat R, Fournage M (2014) An assessment of the role of the third stress invariant in the Gurson approach for ductile fracture. Eur J Mech A/Solids 47:400–414

    Article  Google Scholar 

  • Benzerga AA (2000) Rupture ductile des tôles anisotropes. PhD thesis, Ecole Nationale Supérieure des Mines de Paris

  • Benzerga AA (2002) Micromechanics of coalescence in ductile fracture. J Mech Phys Solids 50:1331–1362

    Article  Google Scholar 

  • Benzerga AA, Besson J (2001) Plastic potentials for anisotropic porous solids. Eur J Mech A/Solids 20:397–434

    Article  Google Scholar 

  • Benzerga AA, Leblond JB (2010) Ductile fracture by void growth to coalescence. Adv Appl Mech 44:169–305

    Article  Google Scholar 

  • Benzerga AA, Leblond JB (2014) Effective yield criterion accounting for microvoid coalescence. J Appl Mech 81(3):031009

    Article  Google Scholar 

  • Benzerga AA, Besson J, Pineau A (1999) Coalescence-controlled anisotropic ductile fracture. J Eng Mat Tech 121:221–229

    Article  Google Scholar 

  • Benzerga AA, Besson J, Batisse R, Pineau A (2002a) Synergistic effects of plastic anisotropy and void coalescence on fracture mode in plane strain. Modell Simul Mater Sci Eng 10:73–102

    Article  Google Scholar 

  • Benzerga AA, Tvergaard V, Needleman A (2002b) Size effects in the Charpy V-notch test. Int J Frac 116:275–296

    Article  Google Scholar 

  • Benzerga AA, Besson J, Pineau A (2004) Anisotropic ductile fracture. Part II: theory. Acta Mater 52:4639–4650

    Article  Google Scholar 

  • Beremin FM, Pineau A, Mudry F, Devaux J, DEscatha Y, Ledermann P (1981a) Experimental and numerical study of the different stages in ductile rupture: application to crack initiation and stable crack growth. In: Nemat-Nasser S (ed) Three-dimensional constitutive relations of damage and fracture. Pergamon Press, North Holland, pp 157–172

    Google Scholar 

  • Beremin FM, Pineau A, Mudry F, Devaux J, DEscatha Y, Ledermann P (1981b) Cavity formation from inclusions in ductile fracture. Met Trans A 12A:723–731

    Article  Google Scholar 

  • Bergheau JM, Leblond JB, Perrin G (2014) A new numerical implementation of a second-gradient model for plastic porous solids, with an application to the simulation of ductile rupture tests. Comput Methods Appl Mech Eng 268:105–125

    Article  Google Scholar 

  • Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19:3–52

    Article  Google Scholar 

  • Besson J, McCowan CN, Drexler ES (2013) Modeling flat to slant fracture transition using the computational cell methodology. Eng Frac Mech 104:80–95

    Article  Google Scholar 

  • Bishop RF, Hill R, Mott NF (1945) The theory of indentation and hardness tests. Proc Phys Soc Lond 57:147–159

    Article  Google Scholar 

  • Bouchaud E, Lapasset G, Planes J (1990) Fractal dimension of fractured surfaces: a universal value? Eur Phys Lett 13:73–79

    Article  Google Scholar 

  • Budiansky B, Hutchinson JW, Slutsky S (1982) Void growth and collapse in viscous solids. In: Hopkins HG, Sowell MJ (eds) Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, Pergamon Press, North Holland, pp 13–45

  • Cazacu O, Revil-Baudard B, Chandola N, Kondo D (2014) New analytical criterion for porous solids with Tresca matrix under axisymmetric loadings. Int J Solids Struct 51:861–874

    Article  Google Scholar 

  • Chu C, Needleman A (1980) Void nucleation effects in biaxially stretched sheets. J Eng Mat Tech 102:249–256

    Article  Google Scholar 

  • Cox TB, Low JR (1974) An investigation of the plastic fracture of AISI 4340 and 18 nickel-200 grade maraging steels. Met Trans 5:1457–1470

    Article  Google Scholar 

  • Dahl J, Nielsen KL, Tvergaard V (2012) Effect of contact conditions on void coalescence at low stress triaxiality shearing. J Appl Mech 79(021):003

    Google Scholar 

  • Danas K, Ponte Castañeda P (2009a) A finite-strain model for anisotropic viscoplastic porous media: I-theory. Eur J Mech A/Solids 28:387–401

    Article  Google Scholar 

  • Danas K, Ponte Castañeda P (2009b) A finite-strain model for anisotropic viscoplastic porous media: II-applications. Eur J Mech A/Solids 28:402–416

    Article  Google Scholar 

  • Danas K, Ponte Castañeda P (2012) Influence of the Lode parameter and the stress triaxiality on the failure of elasto-plastic porous materials. Int J Solids Struct 49:1325–1342

    Article  Google Scholar 

  • Dunand M, Mohr D (2011a) On the predictive capabilities of the shear modified gurson and the modified Mohr–Coulomb fracture models over a wide range of stress triaxialities and lode angles. J Mech Phys Solids 59:1374–1394

    Article  Google Scholar 

  • Dunand M, Mohr D (2011b) Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading. Eng Frac Mech 78:2919–2934

    Article  Google Scholar 

  • Enakoutsa K, Leblond JB (2009) Numerical implementation and assessment of the GLPD micromorphic model of ductile rupture. Eur J Mech A/Solids 28:445–460

    Article  Google Scholar 

  • Fleck NA, Hutchinson JW, Tvergaard V (1989) Softening by void nucleation and growth in tension and shear. J Mech Phys Solids 37:515–540

    Article  Google Scholar 

  • François D, Pineau A (2002) From Charpy to present impact testing. Elsevier, Oxford

    Google Scholar 

  • Gao X, Shih CF, Tvergaard V, Needleman A (1996) Constraint effects on the ductile–brittle transition in small scale yielding. J Mech Phys Solids 44:1255–1282

    Article  Google Scholar 

  • Garajeu M, Michel JC, Suquet P (2000) A micromechanical approach of damage in viscoplastic materials by evolution in size, shape and distribution of voids. Comput Methods Appl Mech Eng 183:223–246

    Article  Google Scholar 

  • Garrison WM, Moody NR (1987) Ductile fracture. J Phys Chem Solids 48:1035–1074

    Article  Google Scholar 

  • Gologanu M (1997) Etude de quelques problèmes de rupture ductile des métaux. PhD thesis, Université Paris 6

  • Gologanu M, Leblond JB, Devaux J (1993) Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities. J Mech Phys Solids 41:1723–1754

    Article  Google Scholar 

  • Gologanu M, Leblond JB, Devaux J (1994) Approximate models for ductile metals containing non-spherical voids—case of axisymmetric oblate ellipsoidal cavities. J Eng Mat Tech 116:290–297

    Article  Google Scholar 

  • Gologanu M, Leblond JB, Perrin G, Devaux J (1997) Recent extensions of Gurson’s model for porous ductile metals. CISM lectures series. In: Suquet P (ed) Continuum micromechanics. Springer, New York, pp 61–130

    Chapter  Google Scholar 

  • Gologanu M, Leblond JB, Perrin G, Devaux J (2001a) Theoretical models for void coalescence in porous ductile solids—I: coalescence in “layers”. Int J Solids Struct 38:5581–5594

    Article  Google Scholar 

  • Gologanu M, Leblond JB, Perrin G, Devaux J (2001b) Theoretical models for void coalescence in porous ductile solids–II: coalescence in “columns”. Int J Solids Struct 38:5595–5604

    Article  Google Scholar 

  • Goods SH, Brown LM (1979) The nucleation of cavities by plastic deformation. Acta Metal 27:1–15

    Article  Google Scholar 

  • Gurland J, Plateau J (1963) The mechanism of ductile rupture of metals containing inclusions. Trans ASM 56:442–454

    Google Scholar 

  • Gurson AL (1975) Plastic flow and fracture behavior of ductile materials incorporating void nucleation, growth and interaction. PhD thesis, Brown University, Providence

  • Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media. J Eng Mat Tech 99:2–15

    Article  Google Scholar 

  • Hadamard J (1903) Leçons sur la propagation des ondes et les équations de l’hydrodynamique, Librairie Scientifique, A. Herrmann, Paris, chap 6

  • Haltom SS, Kyriakides S, Ravi-Chandar K (2013) Ductile failure under combined shear and tension. Int J Solids Struct 50:1507–1522

    Article  Google Scholar 

  • Han X, Besson J, Forest S, Tanguy B, Bugat S (2013) A yield function for single crystals containing voids. Int J Solids Struct 50:2115–2131

    Article  Google Scholar 

  • Hill R (1948) A theory of yielding and plastic flow of anisotropic solids. Proc R Soc Lond A 193:281–297

    Article  Google Scholar 

  • Hill R (1958) A general theory of uniqueness and stability in elastic–plastic solids. J Mech Phys Solids 6:236–249

    Article  Google Scholar 

  • Hill R (1962) Acceleration waves in solids. J Mech Phys Solids 10:1–16

    Article  Google Scholar 

  • Hill R (1967) The essential structure of constitutive laws for metal composites and polycrystals. J Mech Phys Solids 15:79–95

    Article  Google Scholar 

  • Hom CL, McMeeking RM (1989) Three-dimensional void growth before a blunting crack tip. J Mech Phys Solids 37:395–415

    Article  Google Scholar 

  • Horstemeyer MF, Gokhale AM (1999) A void-crack nucleation model for ductile metals. Int J Solids Struct 36:5029–5055

    Article  Google Scholar 

  • Hu C, Ghosh S (2008) Locally enhanced voronoi cell finite element model (LE-VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions. Int J Numer Meths Eng 76:1955–1992

    Article  Google Scholar 

  • Huang Y (1991) Accurate dilatation rates for spherical voids in triaxial stress fields. J Appl Mech 58:1084–1085

    Article  Google Scholar 

  • Huespe A, Needleman A, Oliver J, Sánchez P (2012) A finite strain, finite band method for modeling ductile fracture. Int J Plast 28:53–69

    Article  Google Scholar 

  • Huespe AE, Needleman A, Oliver J, Sánchez PJ (2009) A finite thickness band method for ductile fracture analysis. Int J Plast 25:2349–2365

    Article  Google Scholar 

  • Hussein MI, Borg U, Niordson CF, Deshpande VS (2008) Plasticity size effects in voided crystals. J Mech Phys Solids 56:114–131

    Article  Google Scholar 

  • Idiart MI (2007) Nonlinear sequential laminates reproducing hollow sphere assemblages. C R Mecanique 335:363–368

    Article  Google Scholar 

  • Idiart MI (2008) Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates. J Mech Phys Solids 56:2599–2617

    Article  Google Scholar 

  • Jacques N, Mercier S, Molinari A (2012) Effects of microscale inertia on dynamic ductile crack growth. J Mech Phys Solids 60:665–690

    Article  Google Scholar 

  • Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Frac Mech 21:31–48

    Article  Google Scholar 

  • Joly P, Cozar R, Pineau A (1990) Effect of crystallographic orientation of austenite on the formation of cleavage cracks in ferrite in an aged duplex stainless steel. Scripta Metall Mater 24:2235–2240

    Article  Google Scholar 

  • Kailasam M, Ponte Castaneda P (1998) A general constitutive theory for linear and nonlinear particulate media with microstructure evolution. J Mech Phys Solids 46:427–465

    Article  Google Scholar 

  • Keralavarma SM, Benzerga AA (2008) An approximate yield criterion for anisotropic porous media. C R Mecanique 336:685–692

    Article  Google Scholar 

  • Keralavarma SM, Benzerga AA (2010) A constitutive model for plastically anisotropic solids with non-spherical voids. J Mech Phys Solids 58:874–901

    Article  Google Scholar 

  • Keralavarma SM, Chockalingam S (2016) A criterion for void coalescence in anisotropic ductile materials. Int J Plast (in press)

  • Kondori B, Benzerga AA (2014) Effect of stress triaxiality on the flow and fracture of Mg alloy AZ31. Metall Mater Trans A 45:3292–3307

    Article  Google Scholar 

  • Koplik J, Needleman A (1988) Void growth and coalescence in porous plastic solids. Int J Solids Struct 24:835–853

    Article  Google Scholar 

  • Lebensohn R, Cazacu O (2012) Effect of single-crystal plastic deformation mechanisms on the dilatational plastic response of porous polycrystals. Int J Solids Struct 49:3838–3852

    Article  Google Scholar 

  • Leblond JB, Gologanu M (2008) External estimate of the yield surface of an arbitrary ellipsoid containing a confocal void. C R Mecanique 336:813–819

    Article  Google Scholar 

  • Leblond JB, Mottet G (2008) A theoretical approach of strain localization within thin planar bands in porous ductile materials. C R Mecanique 336:176–189

    Article  Google Scholar 

  • Leblond JB, Morin L (2014) Gurson’s criterion and its derivation revisited. J Appl Mech 81(051):012

    Google Scholar 

  • Leblond JB, Perrin G, Devaux J (1994) Bifurcation effects in ductile metals with nonlocal damage. J Appl Mech 61:236–242

    Article  Google Scholar 

  • Leblond JB, Perrin G, Devaux J (1995) An improved Gurson-type model for hardenable ductile metals. Eur J Mech A/Solids 14:499–527

    Google Scholar 

  • Lee BJ, Mear ME (1992) Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids. J Mech Phys Solids 40:1805–1836

    Article  Google Scholar 

  • Lee BJ, Mear ME (1999) Stress concentration induced by an elastic spheroidal particle in a plastically deforming solid. J Mech Phys Solids 47:1301–1336

    Article  Google Scholar 

  • Madou K, Leblond JB (2012a) A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: limit-analysis of some representative cell. J Mech Phys Solids 60:1020–1036

    Article  Google Scholar 

  • Madou K, Leblond JB (2012b) A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—II: determination of yield criterion parameters. J Mech Phys Solids 60:1037–1058

    Article  Google Scholar 

  • Madou K, Leblond JB (2013) Numerical studies of porous ductile materials containing arbitrary ellipsoidal voids—I: yield surfaces of representative cells. Eur J Mech A/Solids 42:480–489

    Article  Google Scholar 

  • Madou K, Leblond JB, Morin L (2013) Numerical studies of porous ductile materials containing arbitrary ellipsoidal voids—II: evolution of the length and orientation of the void axes. Eur J Mech A/Solids 42:490–507

    Article  Google Scholar 

  • Mandel J (1964) Contribution théorique à l’étude de l’écrouissage et des lois d’écoulement plastique. 11th international congress on applied mechanics. Springer, Berlin, pp 502–509

    Google Scholar 

  • Mandel J (1966) Conditions de stabilité et postulat de Drucker. In: Krautchenko J, Sirieys PM (eds) Rheology and soil mechanics. Springer, Berlin, pp 58–68

    Google Scholar 

  • Mansouri LZ, Chalal H, Abed-Meraim F (2014) Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis. Mech Mater 76:64–92

    Article  Google Scholar 

  • Mathur KK, Needleman A, Tvergaard V (1996) Three dimensional analysis of dynamic ductile crack growth in a thin plate. J Mech Phys Solids 44:439–464

    Article  Google Scholar 

  • McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech 35:363–371

    Article  Google Scholar 

  • McClintock FA, Kaplan SM, Berg CA (1966) Ductile fracture by hole growth in shear bands. Int J Frac Mech 2:614–627

  • McMeeking RM (1977) Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture. J Mech Phys Solids 25:357–381

    Article  Google Scholar 

  • Mear ME, Hutchinson JW (1985) Influence of yield surface curvature on flow localization in dilatant plasticity. Mech Mater 4:395–407

    Article  Google Scholar 

  • Michel JC, Suquet P (1992) The constitutive law of nonlinear viscous and porous materials. J Mech Phys Solids 40:783–812

    Article  Google Scholar 

  • Monchiet V, Gruescu C, Charkaluk E, Kondo D (2006) Approximate yield criteria for anisotropic metals with prolate or oblate voids. C R Mecanique 334:431–439

    Article  Google Scholar 

  • Monchiet V, Cazacu O, Charkaluk E, Kondo D (2008) Macroscopic yield criteria for plastic anisotropic materials containing spheroidal voids. Int J Plast 24:1158–1189

    Article  Google Scholar 

  • Monchiet V, Charkaluk E, Kondo D (2011) A micromechanics-based modification of the gurson criterion by using Eshelby-like velocity fields. Eur J Mech A/Solids 30:940–949

  • Morin L (2015) Influence des effets de forme et de taille des cavités, et de l’anisotropie plastique sur la rupture ductile. PhD thesis, Université Pierre et Marie Curie—Paris VI

  • Morin L, Madou K, Leblond JB, Kondo D (2014) A new technique for finite element limit-analysis of Hill materials, with an application to the assessment of criteria for anisotropic plastic porous solids. Int J Eng Sci 74:65–79

    Article  Google Scholar 

  • Morin L, Leblond JB, Benzerga AA (2015a) Coalescence of voids by internal necking: theoretical estimates and numerical results. J Mech Phys Solids 75:140–158

    Article  Google Scholar 

  • Morin L, Leblond JB, Kondo D (2015b) A Gurson-type criterion for plastically anisotropic solids containing arbitrary ellipsoidal voids. Int J Solids Struct 77:86–101

    Article  Google Scholar 

  • Morin L, Leblond JB, Benzerga AA, Kondo D (2016) A unified criterion for the growth and coalescence of microvoids. J Mech Phys Solids (in press)

  • Nahshon K, Hutchinson JW (2008) Modification of the Gurson model for shear failure. Eur J Mech A/Solids 27:1–17

    Article  Google Scholar 

  • Needleman A (1972) A numerical study of necking in circular cylindrical bars. J Mech Phys Solids 20:111–127

    Article  Google Scholar 

  • Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54:525

    Article  Google Scholar 

  • Needleman A (2015) The effect of rate dependence on localization of deformation and failure in softening solids. J Appl Mech 82(021):002

    Google Scholar 

  • Needleman A, Rice JR (1978) Limits to ductility set by plastic flow localization. In: Koistinen DP, Wang NM (eds) Mechanics of sheet metal forming. Plenum Press, Berlin, pp 237–267

  • Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32:461–490

    Article  Google Scholar 

  • Needleman A, Tvergaard V (1991) A numerical study of void distribution effects on dynamic, ductile crack growth. Eng Frac Mech 38:157–173

    Article  Google Scholar 

  • Needleman A, Tvergaard V (1994) Mesh effects in the analysis of dynamic ductile crack growth. Eng Frac Mech 47:75–91

    Article  Google Scholar 

  • Nielsen KL (2008a) 3D modelling of plug failure in resistance spot welded shear-lab specimens (DP600-steel). Int J Frac 153:125–139

    Article  Google Scholar 

  • Nielsen KL (2008b) Ductile damage development in friction stir welded aluminum (AA2024) joints. Eng Frac Mech 75:2795–2811

    Article  Google Scholar 

  • Nielsen KL (2010) Predicting failure response of spot welded joints using recent extensions to the Gurson model. Comput Mater Sci 48:71–82

    Article  Google Scholar 

  • Nielsen KL, Tvergaard V (2009) Effect of a shear modified Gurson model on damage development in a few tensile specimen. Int J Solids Struct 46:587–601

    Article  Google Scholar 

  • Nielsen KL, Tvergaard V (2010) Ductile shear failure or plug failure of spot welds modelled by modified gurson model. Eng Frac Mech 77:1031–1047

    Article  Google Scholar 

  • Nielsen KL, Dahl J, Tvergaard V (2012) Collapse and coalescence of spherical voids subject to intense shearing: studied in full 3D. Int J Frac 177:97–108

    Article  Google Scholar 

  • Ortiz M, Molinari A (1992) Effect of strain hardening and rate sensitivity on the dynamic growth of a void in a plastic material. J Appl Mech 59:48–53

    Article  Google Scholar 

  • Osovski S, Srivastava A, Ponson L, Bouchaud E, Tvergaard V, Ravi-Chandar K, Needleman A (2015) The effect of loading rate on ductile fracture toughness and fracture surface roughness. J Mech Phys Solids 76:20–46

    Article  Google Scholar 

  • Pan J, Saje M, Needleman A (1983) Localization of deformation in rate sensitive porous plastic solids. Int J Frac 21:261–278

    Article  Google Scholar 

  • Papasidero J, Doquet V, Mohr D (2015) Ductile fracture of aluminum 2024–t351 under proportional and non-proportional multi-axial loading: Bao-wierzbicki results revisited. Int J Solids Struct 69–70:459–474

    Article  Google Scholar 

  • Pardoen T, Hutchinson JW (2000) An extended model for void growth and coalescence. J Mech Phys Solids 48:2467–2512

    Article  Google Scholar 

  • Paux J, Morin L, Brenner R, Kondo D (2015) An approximate yield criterion for porous single crystals. Eur J Mech A/Solids 51:1–10

    Article  Google Scholar 

  • Perrin G (1992) Contribution à l’étude théorique et numérique de la rupture ductile des métaux. PhD thesis, Ecole Polytechnique

  • Perrin G, Leblond JB (1990) 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 6:677–699

    Article  Google Scholar 

  • Perrin G, Leblond JB (1993) Rudnicki and Rice’s analysis of strain localization revisited. J Appl Mech 60:842–846

    Article  Google Scholar 

  • Pineau A, Benzerga AA, Pardoen T (2016) Failure of metals I. brittle and ductile fracture. Acta Mater 107:424–483

    Article  Google Scholar 

  • Ponte Castaneda P (1991) The effective mechanical properties of nonlinear composites. J Mech Phys Solids 39:45–71

    Article  Google Scholar 

  • Ponte Castañeda P, Zaidman M (1994) Constitutive models for porous materials with evolving microstructure. J Mech Phys Solids 42:1459–1495

    Article  Google Scholar 

  • Ponte Castaneda P (2002) Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory. J Mech Phys Solids 50:737–757

    Article  Google Scholar 

  • Ponte Castaneda P (2012) Bounds for nonlinear composites via iterated homogenization. J Mech Phys Solids 60:1583–1604

    Article  Google Scholar 

  • Puttick KE (1959) Ductile fracture in metals. Phil Mag 4:964–969

    Article  Google Scholar 

  • Raniecki B, Bruhns OT (1981) Bounds to bifurcation stresses in solids with non-associated plastic-flow law at finite strain. J Mech Phys Solids 29:153–172

    Article  Google Scholar 

  • Rice J (1976) The localization of plastic deformation. In: Koiter W (ed) 14th International congress theoretical and applied mechanics, North–Holland, Amsterdam, pp 207–220

  • Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35:379–386

    Article  Google Scholar 

  • Rice JR, Johnson MA (1970) The role of large crack tip geometry changes in plane strain fracture. In: Inelastic behavior of solids, Mc Graw Hill, New York, pp 641–672

  • Rice JR, Tracey DM (1969) On the enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217

    Article  Google Scholar 

  • Ritchie RO (1978) On the relationship between fracture toughness and Charpy V-Notch energy in ultrahigh strength steels. In: Rosenfield AR, Gegel HL, Hasson DF (eds) What does the Charpy test really tell us?. American Society for Metals, Metals Park, pp 54–73

    Google Scholar 

  • Rodriguez AK, Ayoub GA, Mansoor B, Benzerga AA (2016) Effect of strain rate and temperature on fracture of AZ31B magnesium alloy. Acta Mater 112:194–208

  • Rogers HC (1960) Tensile fracture of ductile metals. Trans Met Soc AIME 218:498–506

    Google Scholar 

  • Rousselier G (1981) Finite deformation constitutive relations including ductile fracture damage. In: Nemat–Nasser (ed) Three-dimensional constitutive equations of damage and fracture. Pergamon Press, North Holland, pp 331–355

  • Rousselier G (1987) Ductile fracture models and their potential in local approach of fracture. Nucl Eng Design 105:97–111

    Article  Google Scholar 

  • Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure–sensitive dilatant materials. J Mech Phys Solids 23:371–394

  • Ruggieri C, Panontin TL, Dodds RH (1996) Numerical modeling of ductile crack growth in 3-D using computational cell elements. Int J Frac 82:67–95

    Article  Google Scholar 

  • Scheyvaerts F, Onck PR, Tekoglu C, Pardoen T (2011) The growth and coalescence of ellipsoidal voids in plane strain under combined shear and tension. J Mech Phys Solids 59:373–397

    Article  Google Scholar 

  • Segurado J, Llorca J (2009) An analysis of the size effect on void growth in single crystals using discrete dislocation dynamics. Acta Mater 57:1427–1436

    Article  Google Scholar 

  • Shabrov MN, Needleman A (2002) An analysis of inclusion morphology effects on void nucleation. Modell Simul Mater Sci Eng 10:163–183

    Article  Google Scholar 

  • Shima S, Oyane M (1976) Plasticity theory for porous metals. Int J Mech Sci 18:285–291

    Article  Google Scholar 

  • Shinohara Y, Madi Y, Besson J (2016) Anisotropic ductile failure of a high-strength line pipe steel. Int J Frac 197:127–145

  • Song D, Agoras M, Ponte Castaneda P (2015) The evolution of pore shape and orientation in plastically deforming metals: implications for macroscopic response and shear localization. Mech Mater 90:47–68

    Article  Google Scholar 

  • Srivastava A, Ponson L, Osovski S, Bouchaud E, Tvergaard V, Needleman A (2014) Effect of inclusion density on ductile fracture toughness and roughness. J Mech Phys Solids 63:62–79

    Article  Google Scholar 

  • Tang S, Kopacz AM, Chan O’Keeffe S, Olson GB, Liu WK (2013) Three-dimensional ductile fracture analysis with a hybrid multiresolution approach and microtomography. J Mech Phys Solids 61:2108–2124

    Article  Google Scholar 

  • Tang H, Fairchild DP, Cheng W, Kan W, Cook M, Macia ML (2015) Development of surface flaw interaction rules for strain-based pipelines. Int J Offshore Polar Eng 25:45–55

    Google Scholar 

  • Tanguy B, Besson J, Piques R, Pineau A (2005) Ductile to brittle transition of an A508 steel characterized by charpy impact test. Part II: modeling of the charpy transition curve. Eng Frac Mech 72:413–434

    Article  Google Scholar 

  • Tekoglu C, Leblond JB, Pardoen T (2012) A criterion for the onset of void coalescence under combined tension and shear. J Mech Phys Solids 60:1363–1381

    Article  Google Scholar 

  • Thomas TY (1961) Plastic flow and fracture in solids. Academic Press, New York

    Google Scholar 

  • Thomason PF (1985) Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids. Acta Metal 33:1079–1085

    Article  Google Scholar 

  • Tipper CF (1949) The fracture of metals. Metall 39:133–137

    Google Scholar 

  • Torki ME, Benzerga AA, Leblond JB (2015) On void coalescence under combined tension and shear. J Appl Mech 82(7):071005

    Article  Google Scholar 

  • Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Frac 17:389–407

    Article  Google Scholar 

  • Tvergaard V (1982a) Ductile fracture by cavity nucleation between larger voids. J Mech Phys Solids 30:265–286

    Article  Google Scholar 

  • Tvergaard V (1982b) On localization in ductile materials containing spherical voids. Int J Frac 18:237–252

    Google Scholar 

  • Tvergaard V (1987) Effect of yield surface curvature and void nucleation on plastic flow localization. J Mech Phys Solids 35:43–60

    Article  Google Scholar 

  • Tvergaard V (1990) Material failure by void growth to coalescence. Adv Appl Mech 27:83–151

    Article  Google Scholar 

  • Tvergaard V (2008) Shear deformation of voids with contact modeled by internal pressure. Int J Mech Sci 50:1459–1465

    Article  Google Scholar 

  • Tvergaard V (2009) Behaviour of voids in a shear field. Int J Frac 158:41–49

    Article  Google Scholar 

  • Tvergaard V (2012) Effect of stress-state and spacing on voids in a shear-field. Int J Solids Struct 49:3047–3054

    Article  Google Scholar 

  • Tvergaard V, Hutchinson JW (2002) Two mechanisms of ductile fracture: void by void growth versus multiple void interaction. Int J Solids Struct 39:3581–3597

    Article  Google Scholar 

  • Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metal 32:157–169

    Article  Google Scholar 

  • Tvergaard V, Needleman A (1986) Effect of material rate sensitivity on the failure modes in the Charpy V-notch test. J Mech Phys Solids 34:213–241

    Article  Google Scholar 

  • Tvergaard V, Needleman A (1988) An analysis of the temperature and rate dependence of Charpy V-notch energies for a high nitrogen steel. Int J Frac 37:197–215

    Article  Google Scholar 

  • Tvergaard V, Needleman A (1994) Effect of crack meandering on dynamic, ductile fracture. J Mech Phys Solids 38:447–471

    Google Scholar 

  • Tvergaard V, Needleman A (1995) Effects of nonlocal damage in porous plastic solids. Int J Solids Struct 32:1063–1077

    Article  Google Scholar 

  • Tvergaard V, Needleman A (2000) Analysis of the Charpy V-notch test for welds. Eng Frac Mech 65:627–643

    Article  Google Scholar 

  • Tvergaard V, Needleman A (2004) 3d analyses of the effect of weld orientation in Charpy specimens. Eng Frac Mech 71:2179–2195

    Article  Google Scholar 

  • Tvergaard V, Nielsen KL (2010) Relations between a micro-mechanical model and a damage model for ductile failure in shear. J Mech Phys Solids 58:1243–1252

    Article  Google Scholar 

  • Van Stone RH, Cox TB, Low JR, Psioda JA (1985) Microstructural aspects of fracture by dimpled rupture. Int Met Rev 30:157–179

    Article  Google Scholar 

  • Willis JR (1977) Bounds and self-consistent estimates for the overall properties of anisotropic composites. J Mech Phys Solids 25:185–202

    Article  Google Scholar 

  • Willis JR (1991) On methods for bounding the overall properties of nonlinear composites. J Mech Phys Solids 39:73–86

    Article  Google Scholar 

  • Wilner B (1988) Stress analysis of particles in metals. J Mech Phys Solids 36:141–165

    Article  Google Scholar 

  • Xu XP, Needleman A (1992) The influence of nucleation criterion on shear localization in rate-sensitive porous plastic solids. Int J Plast 8:315–330

    Article  Google Scholar 

  • Xu XP, Needleman A (1993) Void nucleation by inclusion debonding in a crystal matrix. Model Simul Mater Sci Eng 1:111–132

    Article  Google Scholar 

  • Xue L (2008) Constitutive modeling of void shearing effect in ductile fracture of porous materials. Eng Frac Mech 75:3343–3366

    Article  Google Scholar 

  • Xue Z, Faleskog J, Hutchinson JW (2013) Tension-torsion fracture experiments—Part II: simulations with the extended Gurson model and a ductile fracture criterion based on plastic strain. Int J Solids Struct 50:4258–4269

    Article  Google Scholar 

  • Yamamoto H (1978) Conditions for shear localization in the ductile fracture of void-containing materials. Int J Frac 14:347–365

    Article  Google Scholar 

  • Zhang ZL, Thaulow C, Odegard J (2000) A complete Gurson model approach for ductile fracture. Eng Frac Mech 67:155–168

    Article  Google Scholar 

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Acknowledgments

AAB acknowledges the support of the National Science Foundation under Grant Number CMMI-1405226. AN is grateful for the support provided by the National Science Foundation under Grant Number CMMI-1200203.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Texas A&M University, College Station, TX, USA

    Ahmed Amine Benzerga

  2. Institut Jean le Rond d’Alembert, Sorbonne Universités, Université Pierre et Marie Curie, Paris, France

    Jean-Baptiste Leblond

  3. Department of Materials Science and Engineering, Texas A&M University, College Station, TX, USA

    Alan Needleman

  4. Department of Mechanical Engineering, The Technical University of Denmark, Lyngby, Denmark

    Viggo Tvergaard

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  1. Ahmed Amine Benzerga
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  2. Jean-Baptiste Leblond
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  3. Alan Needleman
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  4. Viggo Tvergaard
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Correspondence to Alan Needleman.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10704-016-0159-x.

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Benzerga, A.A., Leblond, JB., Needleman, A. et al. Ductile failure modeling. Int J Fract 201, 29–80 (2016). https://doi.org/10.1007/s10704-016-0142-6

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