A Gurson-type layer model for ductile porous solids with isotropic and kinematic hardening

Abstract

The aim of this work is to propose a Gurson-type model for ductile porous solids exhibiting isotropic and kinematic hardening. The derivation is based on a "sequential limit-analysis" of a hollow sphere made of a rigid-hardenable material. The heterogeneity of hardening is accounted for by discretizing the cell into a finite number of spherical layers in each of which the quantities characterizing hardening are considered as homogeneous. A simplified version of the model is also proposed, which permits to extend the previous works of Leblond et al. (1995) andLacroix et al. (2016) for isotropic hardening to mixed isotropic/kinematic hardening. The model is finally assessed through comparison of its predictions with the results of some micromechanical finite element simulations of the same cell. First, the numerical and theoretical overall yield loci are compared for given distributions of isotropic and kinematic pre-hardening. Then the predictions of the model are investigated in evolution problems in which both isotropic and kinematic hardening parameters vary in time. A very good agreement between model predictions and numerical results is found in both cases.

Void coalescence in porous ductile solids containing two populations of cavities

“…• The distribution of the second population of cavities and the yield limit was supposed to be uniform in the present work. In order to provide a better description of the local fields, it would be interesting to consider an heterogeneous distribution of the second population of cavities and hardening, using the framework of sequential limit-analysis (Morin et al, 2017;Leblond et al, 2018).…”

“…This model, based on the limit-analysis of a spherical cell containing a spherical void and made of a von Mises material, has permitted to describe accurately the effective behavior of porous materials for high values of the stress triaxiality (Tvergaard and Needleman, 1984). Due to its intrinsic limitations, this growth model has been widely extended to account for more realistic microstructures, notably through ellipsoidal voids (Gologanu et al, 1993;Madou and Leblond, 2012), plastic anisotropy of the matrix (Monchiet et al, 2008;Keralavarma and Benzerga, 2010;Morin et al, 2015b) and strain hardening effects (Leblond et al, 1995;Morin et al, 2017). Another framework, based on non-linear homogenization (Ponte Castaneda, 1991;Willis, 1991), has also been developed to derive micromechanical void growth models for spherical (Michel and Suquet, 1992) and ellipsoidal (Kailasam and Ponte Castaneda, 1998;Danas and Ponte Castaeda, 2009) cavities.…”

Benchmark Analysis of Ductile Fracture Simulation for Circumferentially Cracked Pipes Subjected to Bending

“…The particle model is shown in Fig. 20 [31] to introduce hardening effects has been improved in order to also take into account the effect of elasticity. The model is obtained by sequential limit analysis [32] where the representative volume element is a hollow sphere radially discretized into N concentric spheres of radii r i ; i ¼ 1 to N. The macroscopic yield function, taking into account mixed kinematic/isotropic hardening, is the following:…”

A strain gradient plasticity model of porous single crystal ductile fracture

“…Gurson originally considered an isotropic rigid perfectly plastic matrix material. Gurson's approach was later generalized to take isotropic hardening and kinematic hardening into account (Mear and Hutchinson, 1985;Besson and Guillemer-Neel, 2003;Morin et al, 2017). 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).…”