Stress concentration induced by an elastic spheroidal particle in a plastically deforming solid

摘要

The fracture of ductile solids occurs by the nucleation, growth and coalescence of microscopic voids. The nucleation stage usually involves the fracture of hard second-phase particles or their decohesion from the surrounding matrix materia1. In this study, the role of particle shape on the nucleation of microvoids is investigated by considering the axisymmetric deformation of a single isolated linearly elastic, prolate spheroidal particle embedded in a plastically deforming matrix. The local stress concentration factors at the particle matrix intertace and within the particle are evaluated using a Ritz procedure which combines an exact solution within the elastic spheroidal particle with a spectral representation for the plastically detbrn1ing matatrix. Accurate solutions for the stress concentration factors are provided for severa1 particle aspect ratios, for various sets of material properties and for several remote stress histories. It is shown that the particle shape has a strong effect upon the stress concentration tactors, with the degree of influence dependent upon the material properties and the triaxiality of the remote loading. In particular, as the particle aspect ratio is increased with other variables held fixed, the normal stress concentration within the particle rises at a greater rate than does that at the interface (despite the high curvature developed a[ the particle pole) and the distribution of normal traction on the boundary tends to become 'less tensile'. These findings suggest that there is a 'critical' aspect ratio at which the dominant mechanism of