A Complex-Variable Method for Two-Dimensional Internal Stress Problems and Its Applications to Crack Growth in Nonelastic Materials: Part II—Applications

In Part I of this work the internal stress due to a field of nonelastic strain in an infinite uncracked or cracked elastic body is derived for the case of antiplane shear, plane strain and plane stress. We will apply these results to solve a variety of self-stress problems in this paper. Exact solutions are obtained for a homogeneous distribution of nonelastic strain in a circular or polygonal region for an uncracked body. For a cracked body, closed form solutions are found for homogeneous nonelastic strain in two circular or polygonal regions symmetrically located with respect to the crack line. These results can also be applied to study internal stresses due to a homogeneous stress-free strain transformation or a uniform temperature distribution in the regions considered. Integral equations of stress are derived for stationary cracks and quasi-static growing cracks imbedded in nonelastic materials under small scale yielding condition. An integral equation for steady state dynamic Mode III crack growth is also given. It is shown that for steady-state crack growth problem, the presence of the trailing deformation wake introduces a residual stress that invalidates the dominance of the K field in the wake. Numerical implementation of the proposed method for inelasticity problems is discussed.