Path-independent H-integral for interface corners under thermal loadings

It is well known that the path-independent H-integral is an appropriate tool for calculating the mixed mode stress intensity factors for the interface corners between dissimilar elastic materials.To extend the applicability of the H-integral from the mechanical loading condition to the thermal loading condition, a modified H-integral is proposed in this paper.This modified H-integral possesses an extra domain integral which needs the input of temperature field.Moreover, this domain integral contains singular functions that come from the strain components of the auxiliary system, and a special treatment should be made for the accurate computation of stress intensity factors.The near-tip solutions and auxiliary solutions of displacements, stresses, and temperature required in the calculation of H-integral are all provided in this paper.The validity and versatility of the proposed approach are then shown by carrying out several numerical examples such as cracks under mixed-mode thermal loadings, interface cracks/corners under uniform heat flow or uniform temperature change, and an electronic package, in which the chip has a heat generation rate, placed at a constant temperature ambiance.