Analysis of a crack with a non-flat surface in an elsatic solid

Abstract

A crack with a non-flat surface in an elastic solid is analyzed. Three problems of a non-planar crack are considered. First one is a problem of a three-dimensional axisymmetric crack with a slightly non-flat surface in an isotropic linear solid under axisymmetric loading. The problem is formulated by using the Hankel transform and a perturbation solution is obtained, which is accurate to the first order of the parameter representing the non-flatness. The stress intensity factor for the problem is evaluated. In particular, the stress intensity factor at the onset of axisymmertric kinking from a penny-shaped crack is obtained. It is also shown that the two-dimensional Cotterell-Rice theory for the effect of tensile stress acting parallel to the crack surface on the stability of the crack path is valid for the axisymmetric crack. Second one is a problem of a two-dimensional interfacial crack with a curved interface of dissimilar elastic solids. A new conservation integral, which consists of path and area integrals, for the interfacial crack is proposed. The conservation integral is shown to have the physical meaning of the energy release rate. The relation of the integral to the energy release rate is also examined for the interfacial crack with a small frictionless contact or no-slip zone on the surfaces near the crack tip. With the help of a weighting function the domain representation associated with the energy release rate is obtained, which is amenable to the finite element computation. Some numerical computations are carried out to verify the usefulness of the domain integral form for the energy release rate. Third one is a problem of a three-dimensional interfacial crack with a non-flat interface of dissimilar elastic solids. A domain integral associated with the crack tip integral, which has the meaning of the pointwise energy release rate, along the front of the interfacial is obtained. Application of the domain integral to a thermal stress problem is als...