Schmidt method to study the disturbance of steady-state heat flows by an arbitrary oriented crack in bonded functionally graded strips

Abstract

This article aims to investigate the impact of a partially insulated crack on vertical and horizontal components of heat flow. The crack is arbitrary oriented and its center is located at the interface of bonded finitely thick functionally graded strips. Employing the integral transformation, the thermoelastic equations are reduced to a set of singular integral equations. The unknown variables of these equations are the jump in temperature and displacements across the crack surfaces. Representing the unknowns as a series of Jacobi polynomials, the solutions of the singular integral equations are obtained by employing the Schmidt method which further helps to determine the analytical forms of crack tip heat flux intensity factors (HFIFs) and thermal stress intensity factors (TSIFs). The results of the present study are also validated for a particular case.To quantify the strength of heat flow components, the crack tip HFIFs and TSIFs as a function of crack angle, crack insulation parameter, strips’ width, and non-homogeneity parameters’ ratio are demonstrated pictorially. © 2022 Elsevier Ltd