Finite element simulation of mode I dynamic, ductile fracture initiation

Effects of spatial random fluctuations in the yield condition of rigid-perfectly plastic continuous media are analysed in cases of Cauchy and characteristic boundary value problems. A weakly random plastic microstructure is modeled, on a continuum mesoscale, by an isotropic yield condition with the yield limit taken as a locally averaged random field. The solution method is based on a stochastic generalization of the method of slip-lines, whose significant feature is that the deterministic characteristics are replaced by the forward evolution cones containing random characteristics. Comparisons of response of this random medium and of a deterministic homogeneous medium, with a plastic limit equal to the average of the random one, are carried out numerically in several specific examples of the two boundary value problems under study. An application of the method is given to the limit analysis of a cylindrical tube under internal traction. The major conclusion is that weak material randomness always leads to a relatively stronger scatter in the position and field variables, as well as to a larger size of the domain of dependence--effects which are amplified by both presence of shear traction and inhomogeneity in the boundary data. Additionally, it is found that there is hardly any difference between stochastic slip-line fields due to either Gaussian or uniform noise in the plastic limit.