An opening mode crack in a nonhomogeneous elastic material

Abstract

In this thesis, an opening mode crack in a nonhomogeneous material is studied by assuming a continuously varying shear modulus which characterizes a decreasing rigidity near the crack tip. Explicit expressions for the stress and displacement fields are derived and numerical results are presented which illustrate the effects of material softening upon these quantities. It is shown that the crack tip stresses are either bounded, asymptotic to r^a, 0 < a < ½, or exhibit a logarithmic singularity at the crack tip. In all cases the components of stress are less than those for the corresponding problem in a homogeneous medium and the crack surface displacements are increased as a result of the reduced rigidity.