Stress Singularities and Discontinuities on the Free Surface of a Thermo-Elastoplastic Bimaterial Body

Abstract

Fracture mechanisms at the free surface of heterogeneous materials, polycristals, composites etc.., are investigated by consideration of a model of a bimaterial interface intersecting a free surface. The high stress level near the crossing point between the interface and the free surface can be related to discontinuous material properties : elastic moduli, thermal expansion coefficients, plastic behaviors. Analyses of interfaces between two elastic media, which results in logarithmic stress singularities, are widely reported in the literature. This paper is focused on thermal and plastic effects at interfaces. We find that the stress component parallel to the free surface is discontinuous at the crossing point, resulting in a very localized high stress, which we call the “Thorn Singularity”. The characteristics of the Thorn singularity are: boundedness of the stress, discontinuity on the free surface, singular gradient of stress. The jump relations between this stress component and the discontinuities of thermal strain and plastic strain are established. Analytical solutions and numerical ones confirm the analyses and show that the stress field can be splitted into a strong local discontinuous field and a global smooth stress field which can be modellized by a classical shell theory.