Size effect on the fracture resistance of rough and frictional cracks

Abstract

Elastic fracture mechanics commonly defines the fracture resistance of brittle materials within an idealized picture of planar and traction-free cracks. An efficient approach to describe the interface conditions in real cracks, such as those occurring in concrete, ceramics or stones, is to include the effect of both roughness and friction by means of a constitutive relationship between opposite points on the interface. In the present paper, we use a numerical technique, based on the solution of singular integral equations, to derive the near-tip stress field with various interface conditions. Then, the technique is applied to investigate the size effect of the interface roughness, where such an effect is related to the ratio between the characteristic length of the roughness and the nominal length of the crack. It is found that the resulting near-tip stresses can be profoundly influenced by the crack path, particularly for short cracks.