An analysis of an antiplane shear crack in a nonhomogeneous elastic medium

In this thesis, a rigorous derivation of the energy release rate based on the change in potential energy of a body is given for a nonhomogeneous linear elastic medium. The energy release rate is calculated for an antiplane shear crack whose shear modulus corresponds to a reduced rigidity about the crack tip. Plastic zones about the crack tip are calculated based upon the yielding condition of von Mises, and the effect of decreasing rigidity upon these zones is displayed. In addition, the crack problem is analyzed within the framework of the strain energy density theory and the maximum cleavage stress theory.