Investigation of a gradient enriched Gurson-Tvergaard model for porous strain hardening materials

Abstract

Size effects in a strain hardening porous solid are investigated using the Gurson-Tvergaard (GT) model enriched by a constitutive length parameter, as proposed by Niordson and Tvergaard [C.F. Niordson, V. Tvergaard, A homogenised model for size effects in porous metals, J. Mech. Phys. Solids ( 2019)]. The results are compared with unit cell calculations of regularly distributed voids embedded in a strain gradient enhanced matrix material. The strain gradient plasticity theory proposed by Fleck and Willis [N.A. Fleck, J.R. Willis, A mathematical basis for strain gradient plasticity theory. Part II: tensorial plastic multiplier, J. Mech. Phys. Solids 57 ( 2009) 1045-1057], extended to finite strains, is adopted for the cell model, consistent with the gradient enriched Gurson model. The gradient model allows for a material length parameter to enter the constitutive framework for dimensional consistency, while the enriched GT model has the same length parameter introduced through prefactors of the usual q 1 and q 2 factors. The continuum model featuring size-dependent Tvergaard-constants is used to investigate a strain hardening material with the strain gradient plasticity enriched cell model as reference. The two models are compared for three triaxialities, three initial void volume fractions, and three hardening exponents. The enriched GT model captures the effect of elevated yield point and suppressed void growth with increasing length parameter for all the cases investigated. The agreement between the models is good until severe void distortion or plastic flow localisation between neighbouring voids. The response curves and void growth curves for the enriched GT model deviate from those of the cell model at high axial strains. Void shape plots, which are only available for the cell model, show that the length parameter influences the shape of the void which in turn has impact on the material response curves and the void evolution. This is not captured by the enriched GT model as the voids are accounted for solely through a volume fraction parameter.

Ductile fracture of hydrostatic‐stress‐insensitive metals using a coupled damage‐plasticity model

“…Meanwhile, to reduce the pathological mesh dependency issue on damage softening in the coupled damage‐plasticity model, a rate‐dependent component, , is proposed following the consistency viscoplastic regularization method 31 . Comparing with the non‐local 32,33 and strain‐gradient 34 approaches, the consistency viscoplastic regularization method is more convenient, satisfies the Kuhn–Tucker conditions and can implicitly introduce a length‐scale measure that limits damage and strain localization in quasistatic problems 31,35,36 …”

A strain gradient plasticity model of porous single crystal ductile fracture

“…Other studies focused on deriving effective yield criteria of porous materials with a plastic anisotropic matrix material (Benzerga and Besson, 2001;Morin et al, 2015;Keralavarma and Chockalingam, 2016). Recent studies also investigate the role of size-effects in porous metals (Monchiet and Kondo, 2013;Holte et al, 2019;Niordson and Tvergaard, 2019;.…”

3D study of plastic flow localization at a void-sheet

“…The behavior of such voids in a cyclic shear field has been analyzed in [14]. There has also been recent studies of strain gradient effects on void growth to coalescence by Holte et al [15].…”