A theoretical approach of strain localization within thin planar bands in porous ductile. materials

Propagation of cracks in ductile materials is well known to occur through two possible mechanisms: coalescence of cavities and formation of shear bands ('void sheet mechanism'). The classical Gurson-Tvergaard-Needleman (GTN) homogenized model for such materials incorporates some phenomenological modelling of coalescence, but not of formation of shear bands assisted by the presence of microvoids, and this generates a number of shortcomings. In order to solve these difficulties, this paper presents a unified model of both coalescence and formation of shear bands in porous plastic solids, including the possible couplings between the two. Both phenomena are viewed as expressions of the same basic effect, namely strain localization within thin planar bands, the only difference being the mode of deformation. The model is first developed assuming a periodic distribution of cavities, then critically assessed through comparison with some micromechanical numerical simulations based on the same assumption, and finally extended to the case of a random distribution of voids.