Abstract
Ductile fracture consists of the nucleation, growth, and coalescence of microvoids observed as dimples on the fracture surface. Typical alloys contain diverse heterogeneities that are stochastically distributed, so that void nucleation is essentially heterogeneous and statistical. The scenarios of homogeneous vs. stochastic heterogeneous void nucleation are systematically compared under simple shear deformation in two limiting cases: (1) a uniform sheet that can be viewed as representing the initial stages of plastic deformation, and (2) the same sheet with an embedded central pore, the latter representing the prevailing situation for which large voids have already nucleated and grown. The homogeneous case provides a reference to which the statistically heterogeneous cases are compared. In the uniform sheet model, heterogeneous void nucleation decreases the porosity accumulation and the stress triaxiality. However, when embedding a geometrical pore at the center of the simulation cell, the averaged triaxiality increases irrespective of the void nucleation heterogeneity. The overall ductile failure process can be thought of as a gradual evolution from the initial stage (1) of a homogeneous sheet with heterogeneous void nucleation towards the final stage of a similar void-containing sheet (2), with the associated evolutions of the stress and porosity fields presented here.
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References
Andersen RG, Tekoğlu C, Nielsen KL (2020) Cohesive traction–separation relations for tearing of ductile plates with randomly distributed void nucleation sites. Int J Fract. https://doi.org/10.1007/s10704-020-00454-2
Bandstra JP, Goto DM, Koss DA (1998) Ductile failure as a result of a void-sheet instability: experiment and computational modeling. Mater Sci Eng A 249(1–2):46–54. https://doi.org/10.1016/S0921-5093(98)00562-0
Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46(1):81–98
Barsoum I, Faleskog J (2007) Rupture mechanisms in combined tension and shear-experiments. Int J Solids Struct 44(6):1768–1786. https://doi.org/10.1016/j.ijsolstr.2006.09.031
Benseddiq N, Imad A (2008) A ductile fracture analysis using a local damage model. Int J Press Vessels Pip 85(4):219–227. https://doi.org/10.1016/j.ijpvp.2007.09.003
Benzerga AA et al (2016) Ductile failure modeling. Int J Fract. https://doi.org/10.1007/s10704-016-0142-6
Berdin C et al (2004) Local approach to fracture. http://blog.livedoor.jp/kachin_shan/
Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech. https://doi.org/10.1177/1056789509103482
Bourih A et al (2018) Effective yield surface of porous media with random overlapping identical spherical voids. J Mater Res Technol 7(2):103–117. https://doi.org/10.1016/j.jmrt.2017.01.002
Chen S, Osovski S (2019a) Damage evolution around shear loaded intervoid ligaments in plane strain and plane stress. Eur J Mech A/Solids. https://doi.org/10.1016/j.euromechsol.2019.103909
Chen S, Osovski S (2019b) The effect of internal pressure in gas pores containing materials on their mechanical stability under shear. Mech Res Commun 98:37–41. https://doi.org/10.1016/j.mechrescom.2019.05.008
Chen S, Osovski S (2020) Damage evolution around an embedded pore in quasi-static shear dominant compression and tension specimens. Mech Mater. https://doi.org/10.1016/j.mechmat.2020.103513
Fadida R, Shirizly A, Rittel D (2020) Static and dynamic shear-compression response of additively manufactured Ti6Al4V specimens with embedded voids. Mech Mater. https://doi.org/10.1016/j.mechmat.2020.103413
Fisher JR, Gurland J (1981) Void nucleation in spheroidized carbon steels—1. Experimental. Met Sci 15(5):185–192. https://doi.org/10.1179/030634581790426633
Fleck NA, Hutchinson JW (1986) Void growth in shear. Proc R Soc a: Math Phys Eng Sci 407(1833):435–458. https://doi.org/10.1098/rspa.1986.0104
François D, Pineau A, Zaoui A (2012) Mechanical behaviour of materials: volume II: fracture mechanics and damage. Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki. https://doi.org/10.1007/978-94-007-4930-6
Goods SH, Brown LM (1979) Overview No. 1. The nucleation of cavities by plastic deformation. Acta Metall 27(1):1–15. https://doi.org/10.1016/0001-6160(79)90051-8
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 Mater Technol 99(1):2–15. https://doi.org/10.1115/1.3443401
Kiran R, Khandelwal K (2014) Gurson model parameters for ductile fracture simulation in ASTM A992 steels. Fatigue Fract Eng Mater Struct 37(2):171–183. https://doi.org/10.1111/ffe.12097
Koplik J, Needleman A (1988) Void growth and coalescence in porous plastic solids. Int J Solids Struct 24(8):835–853
Longère P, Bhogaraju S, Craciun D (2015) Void collapse / growth in solid materials under overall shear loading. Mech Res Commun 69:1–7. https://doi.org/10.1016/j.mechrescom.2015.05.009
Nahshon K, Hutchinson JW (2008) Modification of the Gurson model for shear failure. Eur J Mech A/Solids 27(August 2007):1–17. https://doi.org/10.1016/j.euromechsol.2007.08.002
Needleman A (1987) Continuum model for void nucleation by inclusion debonding. Am Soc Mech Eng (pap) 54(1):525–531
Nielsen KL, Dahl J, Tvergaard V (2012) Collapse and coalescence of spherical voids subject to intense shearing: studied in full 3D. Int J Fract 177(2):97–108. https://doi.org/10.1007/s10704-012-9757-4
Noell PJ, Carroll JD, Boyce BL (2018) The mechanisms of ductile rupture. Acta Mater 161:83–98. https://doi.org/10.1016/j.actamat.2018.09.006
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. https://doi.org/10.1016/j.ijsolstr.2015.05.006
Simulia DS (2020) ‘Abaqus 2020’, Abaqus Analysis User’s Guide.
Torki ME, Benzerga AA (2018) A mechanism of failure in shear bands. Extreme Mech Lett 23:67–71. https://doi.org/10.1016/j.eml.2018.06.008
Tvergaard V (2009) Behaviour of voids in a shear field. Int J Fract 158(1):41–49. https://doi.org/10.1007/s10704-009-9364-1
Tvergaard V (2015) Study of localization in a void-sheet under stress states near pure shear. Int J Solids Struct 75–76:134–142. https://doi.org/10.1016/j.ijsolstr.2015.08.008
Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32(1):157–169
Verleysen P, Peirs J (2017) Quasi-static and high strain rate fracture behaviour of Ti6Al4V. Int J Impact Eng 108:370–388. https://doi.org/10.1016/j.ijimpeng.2017.03.001
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Sincere appreciation is acknowledged to Professor D. Rittel for the enjoyable brainstorming discussions.
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Chen, S. The effect of statistically heterogeneous void nucleation on metal failure in shear. Int J Fract 235, 267–278 (2022). https://doi.org/10.1007/s10704-022-00636-0
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DOI: https://doi.org/10.1007/s10704-022-00636-0