Stress Singularities Applied to Crack Initiation by Damage of Multimaterial Joints

We consider a multimaterial consisting of dissimilar layers submitted to plane deformations. The elastic stress field at any corner of this kind of joint often exhibits a stress singularity expressed as a function of the r-θ polar coordinates by σ_=hrδ−1F_(θ) where h is the intensity factor and δ the singuarity exponent. The resolution of the local singularity problem leads to the closed-form expression of F when δ is obtained as a root of a 2 × 2 determinant. The exponent δ, always larger than 0 and smaller than 1, leads to a finite strain energy which is used as an input in a damage law. The damage rate D˙, where D represents the surface density of microcracks or microvoids, is a function of the strain energy density release rate Y. Some examples of crack initiation conditions are pointed out for brittle or quasi-brittle materials for joints loaded in monotonic loading or in fatigue.