Abstract
Numerical simulations based on the bifurcation and imperfection versions of the strain localization theory are used in this paper to predict the failure loci of metals and applied to an advanced high strength steel subjected to proportional loading paths. The results are evaluated against the 3D unit cell analyses of Dunand and Mohr (J Mech Phys Solids 66(1):133–153, 2014. doi:10.1016/j.jmps.2014.01.008) available in the literature. The Gurson porous plasticity model (Gurson in J Eng Mater Technol 99(1):2–15, 1977. doi:10.1115/1.344340) is used to induce strain softening and drive the localization process. The effects of the void growth, void nucleation and void softening in shear are investigated over a large range of stress triaxialities and Lode parameters. A correlation between the imperfection and bifurcation results is established.
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References
Aravas N (1987) On the numerical integration of a class of pressure dependent plasticity models. Int J Numer Methods 24:1395–1416. doi:10.1002/nme.1620240713
Bai Y, Wierzbicki T (2010) Application of extended Mohr–Coulomb criterion to ductile fracture. Int J Fract 161(1):1–20. doi:10.1007/s10704-009-9422-8
Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46(1):81–98. doi:10.1016/j.ijmecsci.2004.02.006
Barsoum I, Faleskog J (2007) Rupture mechanisms in combined tension and shear-micromechanics. Int J Solids Struct 44(17):5481–5498. doi:10.1016/j.ijsolstr.2007.01.010
Barsoum I, Faleskog J (2011) Micromechanical analysis on the influence of the Lode parameter on void growth and coalescence. Int J Solids Struct 48(6):925–938. doi:10.1016/j.ijsolstr.2010.11.028
Basu S, Benzerga AA (2015) On the path-dependence of the fracture locus in ductile materials: experiments. Int J Solids Struct 71:79–90. doi:10.1016/j.ijsolstr.2015.06.003
Benallal A (2017) Constitutive equations for porous solids with matrix behaviour dependent on the second and third stress invariants. Int J Impact Eng. doi:10.1016/j.ijimpeng.2017.05.004
Benallal A, Comi C (1996) Localization analysis via a geometrical method. Int J Solids Struct 33(1):99–119. doi:10.1016/0020-7683(95)00018-6
Benzerga A, Surovik D, Keralavarma S (2012) On the path-dependence of the fracture locus in ductile materials analysis. Int J Plast 37:157–170. doi:10.1016/j.ijplas.2012.05.003
Besson J, Steglich D, Brocks W (2001) Modeling of crack growth in round bars and plane strain specimens. Int J Solids Struct 38(46–47):8259–8284. doi:10.1016/S0020-7683(01)00167-6
Bryhni Dæhli LE, Børvik T, Hopperstad OS (2016) Influence of loading path on ductile fracture of tensile specimens made from aluminium alloys. Int J Solids Struct 88–89:17–34. doi:10.1016/j.ijsolstr.2016.03.028
Chalal H, Abed-Meraim F (2015) Hardening effects on strain localization predictions in porous ductile materials using the bifurcation approach. Mech Mater 91(Part 1):152–166. doi:10.1016/j.mechmat.2015.07.012
Chocron S, Erice B, Anderson CE (2011) A new plasticity and failure model for ballistic application. Int J Impact Eng 38(8–9):755–764. doi:10.1016/j.ijimpeng.2011.03.006
Chu CC, Needleman A (1980) Void nucleation effects in biaxially stretched sheets. J Eng Mater Technol 102(3):249. doi:10.1115/1.3224807
Desmorat R, Kane A, Seyedi M, Sermage J (2007) Two scale damage model and related numerical issues for thermo-mechanical High Cycle Fatigue. Eur J Mech A/Solids 26(6):909–935. doi:10.1016/j.euromechsol.2007.01.002
Di Y, Lixun C, Chen B (2016) A new fracture criterion for ductile materials based on a finite element aided testing method. Mater Sci Eng A. doi:10.1016/j.msea.2016.06.076
Dunand M, Mohr D (2014) Effect of Lode parameter on plastic flow localization after proportional loading at low stress triaxialities. J Mech Phys Solids 66(1):133–153. doi:10.1016/j.jmps.2014.01.008
Faleskog J, Gao X, Shih CF (1998) Cell model for nonlinear fracture analysis—I. Micromechanics calibration. Int J Fract 89(4):355–373. doi:10.1023/A:1007421420901
Ghahremaninezhad A, Ravi-Chandar K (2013) Ductile failure behavior of polycrystalline Al 6061-T6 under shear dominant loading. Int J Fract 180(1):23–39. doi:10.1007/s10704-012-9793-0
Gruben G, Fagerholt E, Hopperstad OS, Børvik T (2011) Fracture characteristics of a cold-rolled dual-phase steel. Eur J Mech A/Solids 30(3):204–218. doi:10.1016/j.euromechsol.2011.01.004
Gruben G, Vysochinskiy D, Coudert T, Reyes A, Lademo OG (2013) Determination of ductile fracture parameters of a dual-phase steel by optical measurements. Strain 49(3):221–232. doi:10.1111/str.12030
Gruben G, Morin D, Langseth M, Hopperstad O (2017) Strain localization and ductile fracture in advanced high-strength steel sheets. Eur J Mech A/Solids 61:315–329. doi:10.1016/j.euromechsol.2016.09.014
Gurson A (1977) 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 99(1):2–15. doi:10.1115/1.344340
Haddag B, Abed-Meraim F, Balan T (2009) Strain localization analysis using a large deformation anisotropic elastic–plastic model coupled with damage. Int J Plast 25(10):1970–1996. doi:10.1016/j.ijplas.2008.12.013
Haltom S, Kyriakides S, Ravi-Chandar K (2013) Ductile failure under combined shear and tension. Int J Solids Struct 50(10):1507–1522. doi:10.1016/j.ijsolstr.2012.12.009
Hutchinson J, Tvergaard V (1981) Shear band formation in plane strain. doi:10.1016/0020-7683(81)90053-6
Jia Y, Bai Y (2016) Ductile fracture prediction for metal sheets using all-strain-based anisotropic eMMC model. Int J Mech Sci. doi:10.1016/j.ijmecsci.2016.07.022
Lemaitre J, Desmorat R (2005) Engineering damage mechanics: ductile, creep, fatigue and brittle failures. Springer, Berlin/Heidelberg. doi:10.1007/b138882, arXiv:1011.1669v3
Madou K, Leblond JB (2012) A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voidsI: limit-analysis of some representative cell. J Mech Phys Solids 60(5):1020–1036. doi:10.1016/j.jmps.2011.11.008
Marciniak Z, Kuczynski K (1967) Limit strains in the processes of stretch-forming sheet metal. Int J Mech Sci 9(9):609–620. doi:10.1016/0020-7403(67)90066-5
Mear ME, Hutchinson JW (1985) Influence of yield surface curvature on flow localization in dilatant plasticity. doi:10.1016/0167-6636(85)90035-3
Mohr D, Marcadet SJ (2015) Micromechanically-motivated phenomenological Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities. Int J Solids Struct 67–68:40–55. doi:10.1016/j.ijsolstr.2015.02.024
Morin L, Leblond JB, Tvergaard V (2016) Application of a model of plastic porous materials including void shape effects to the prediction of ductile failure under shear-dominated loadings. J Mech Phys Solids 94:148–166. doi:10.1016/j.jmps.2016.04.032
Nahshon K, Hutchinson JW (2008) Modification of the Gurson model for shear failure. Eur J Mech A/Solids 27(1):1–17. doi:10.1016/j.euromechsol.2007.08.002
Needleman A, Rice JR (1978) Limits to ductility set by plastic flow localization. Mech Sheet Metal form 237–267. doi:10.1007/978-1-4613-2880-3_10
Nielsen KL, Tvergaard V (2010) Ductile shear failure or plug failure of spot welds modelled by modified Gurson model. Eng Fract Mech 77(7):1031–1047. doi:10.1016/j.engfracmech.2010.02.031
Papasidero J, Doquet V, Mohr D (2014) Determination of the effect of stress state on the onset of ductile fracture through tension-torsion experiments. Exp Mech 54(2):137–151. doi:10.1007/s11340-013-9788-4
Rice JR (1976) The localization of plastic deformation. In: 14th International congress of theoretical and applied mechanics, pp 207–220
Roth CC, Mohr D (2015) Ductile fracture experiments with locally proportional loading histories. Int J Plast 79:328–354. doi:10.1016/j.ijplas.2015.08.004
Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23(6):371–394. doi:10.1016/0022-5096(75)90001-0
Saje M, Pan J, Needleman A (1982) Void nucleation effects on shear localization in porous plastic solids. Int J Fract 19(3):163–182. doi:10.1007/BF00017128
Tvergaard V (1981) Influence of voids on shear band instabilities under plane strain conditions. Int J Fract 17(4):389–407. doi:10.1007/BF00036191
Tvergaard V (2015) Study of localization in a void-sheet under stress states near pure shear. Int J Solids Struct 75–76:134–142. doi:10.1016/j.ijsolstr.2015.08.008
Xue L, Wierzbicki T (2008) Ductile fracture initiation and propagation modeling using damage plasticity theory. Eng Fract Mech 75(11):3276–3293. doi:10.1016/j.engfracmech.2007.08.012
Yamamoto H (1978) Conditions for shear localization in the ductile fracture of void-containing materials. Int J Fract 14(4):347–365. doi:10.1007/BF00015989
Acknowledgements
O.S.H. and D.M. would like to acknowledge the financial support from the Centre for Advanced Structural Analysis (CASA) (Project No. 237885) as well as the FractAl project (Project No. 250553) funded by the Research Council of Norway and NTNU. Part of this work was performed when A.B. was a guest of the Structural Impact Laboratory at the Department of Structural Engineering at NTNU. A.B. also gratefully acknowledges the FractAl project for the financial support during his stay in Trondheim.
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Morin, D., Hopperstad, O.S. & Benallal, A. On the description of ductile fracture in metals by the strain localization theory. Int J Fract 209, 27–51 (2018). https://doi.org/10.1007/s10704-017-0236-9
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DOI: https://doi.org/10.1007/s10704-017-0236-9