Approximate structures of thermoelastic fields induced by a penny-shaped thermal-medium crack in a transversely isotropic layer

Abstract

It is of practical significance to investigate thermoelastic fields at the front of a penny-shaped crack embedded in a material with finite thickness. The existing works always focus on numerical solutions of the derived integral equations and approximate solutions are seldom studied. In the present study, the problem of a penny-shaped crack in a transversely isotropic layer is addressed under uniform heat flow and mechanical loadings. The extended thermal-medium crack model with a nonlinear relation between heat flow of crack interior and crack opening displacement is used to capture the effect of heat conduction inside crack. The Hankel transform technique is applied to solve governing partial differential equations, then Fredholm integral equations of the second kind are derived. Applying integral kernel series expansion method, approximate solutions to the derived Fredholm integral equations are analyzed and determined. Approximate structures of thermoelastic fields around penny-shaped crack are further obtained. Theoretical analysis and numerical results are carried out to show the applicability of approximate solutions. The observations reveal that the determined approximate solutions have some significance to a practical engineering application. The advantages of the developed methods are to make approximate solutions visible, and some penny-shaped crack problems of thermo-piezoelectric and thermo-magnetoelectroelastic layers could be solved similarly.