Scale effects in the initiation of cracking of a scarf joint

The singular stress field at the interface-corner of a bi-material scarf jo int is analysed for a strip of finite width, w, under remote tension and be nding. The two substrates are taken as linear elastic and isotopic. The int ensity of the singular stress field is calculated using a domain integral m ethod, and is plotted as a function of joint geometry and material mismatch parameters. It is envisaged that the intensity of singularity can serve as a valid fracture criterion provided the zone of nonlinearity is fully embe dded within the singular elastic field. It is assumed that fracture initiat es when the magnitude of the corner singularity attains a critical value; c onsequently, the fracture strength of the joint depends upon the size of th e structure. In addition, the interfacial stress intensity factor and the a ssociated T-stress are determined for an edge interfacial crack. When the c rack is short with respect to the width of the strip, the stress intensity factor is dominated by the presence of the corner singularity; a boundary l ayer formulation is used to determine the coupling between the crack tip fi eld and the interface-corner field. The solution suggests that an interfaci al crack grows unstably with a rapidly increasing energy release rate, but with only a small change in mode mix.