Thermally stressed multiple systems in steady state

Abstract

This work is concerned with formulating the steady state linear thermoelastic problem for bodies with finite dimensions and multiple cracks. A superposition scheme is used such that the finite body problem is divided into three component problems involving the infinite region. The first and second component problem are concerned, respectively, with prescribing displacements/tractions and thermal disturbance in an infinite region at the site that conforms to the boundary of the finite body. The third component problem corresponds to an infinite region with cracks subjected to the negative of the tractions obtained from the mechanical and thermal loadings. Upon adding all three component problems the mechanical and thermal boundary conditions of the original problem with multiple free surface cracks are recovered. Numerical results are obtained for edge crack, three parallel cracks and three inclined cracks along the sides of an equilateral triangle. In all cases, a steady state temperature difference is maintained either uniformly over or across the specimen with fixed edges. Constant contours of shear stress are calculated and they compared well with the corresponding isochromatics observed in experiments.