THE R-1/2(IN R) SINGULARITY AT INTERFACE CRACKS IN ANISOTROPIC BIMATERIALS DUE TO HEAT-FLOW

The Stroh formalism for two-dimensional deformations of anisotropic elastic solids has been extended to include the effects of heat conduction. The formalism is employed here to study stress singularities in anisotropic elastic bimaterials with the presence of interface cracks. It is known that, without the effects of heat conduction, there are three singularities of the form r-1/2, r-1/2+i-gamma and r-1/2-i-gamma, where r is the radial distance from the crack tip and gamma is a positive constant that depends on the mismatch of elasticity constants of the two materials. With the inclusion of heat effects, there is a r(delta-kappa) singularity in which -1 < delta(kappa) < 0 depends on the heat conduction coefficients kappa(ij). The special case delta(kappa) = 1/2, which occurs in particular when kappa(ij) in the two materials are identical or when the Onsager reciprocal relations are invoked so that kappa(ij) = kappa(ji), is studied here. We show that the r(delta-kappa) singularity may convert into a r-1/2(ln r) singularity. The conditions for the existence of r-1/2(ln r) singularity are presented explicitly.