Application of a model of plastic porous materials including void shape effects to the prediction of ductile failure under shear-dominated loadings

International audienceAn extension of Gurson's famous model (Gurson, 1977) of porous plastic solids, incorporating void shape effects, has recently been proposed by Madou and Leblond (Madou and Leblond, 2012a,b, 2013; Madou et al., 2013). In this extension the voids are no longer modelled as spherical but ellipsoidal with three different axes, and changes of the magnitude and orientation of these axes are accounted for. The aim of this paper is to show that the new model is able to predict softening due essentially to such changes, in the absence of significant void growth. This is done in two steps. First, a numerical implementation of the model is proposed and incorporated into the SYSTUS and ABAQUS finite element programmes (through some freely available UMAT (Leblond, 2015) in the second case). Second, the implementation in SYSTUS is used to simulate previous " numerical experiments " of Tvergaard and coworkers (Tvergaard, 2008, 2009; Dahl et al., 2012; Nielsen et al., 2012; Tvergaard, 2012, 2015a) involving the shear loading of elementary porous cells, where softening due to changes of the void shape and orientation was very apparent. It is found that with a simple, heuristic modelling of the phenomenon of mesoscopic strain localization, the model is indeed able to reproduce the results of these numerical experiments, in contrast to Gurson's model disregarding void shape effects

Out-of-plane deviation of a mode I+III crack encountering a tougher obstacle

AbstractOne possible explanation of out-of-plane deviations of cracks loaded in mode I+III was suggested by Gao and Rice in 1986. These authors noted that small in-plane undulations of the crack front, arising from fluctuations of the fracture toughness, should generate a small local mode-II component, causing the crack to depart from planarity. Their analysis is completed here by explicitly calculating the evolution in time of the out-of-plane deviation of a mode-I+III crack encountering a tougher obstacle. The calculation is based on (i) first-order formulae for the stress intensity factors of a crack slightly perturbed within and out of its plane; and (ii) a “double” propagation criterion combining a Griffith condition on the local energy-release rate and a Goldstein–Salganik condition on the local stress intensity factor of mode II. It is predicted that the crack must evolve toward a stationary state, wherein the orthogonal distance from the average fracture plane to the perturbed crack front is constant outside the obstacle and varies linearly across it. We hope that this theoretical prediction will encourage comparison with experiments, and propose a fracture test involving propagation of a mode-I+III crack through a 3D-printed specimen containing some designed obstacle

Un modèle de type Gurson pour les matériaux ductiles poreux contenant des cavités ellipsoïdales arbitraires

Le modèle de rupture ductile de Gurson en 1977 est basé sur l'analyse limite d'une sphère creuse. Leblond et Gologanu en 1997 ont ensuite développé des modèles pour des cavités sphéroïdales allongées ou aplaties. On étend ici ces modèles à des cavités ellipsoïdales générales en s'appuyant sur la famille de champs de vitesse proposée par Leblond en 2008. Le modèle analytique qui en résulte est entièrement validé à l'aide des calculs par éléments finis sur cellule