Axially symmetric thermal stress of a penny-shaped crack subjected to general surface temperature

Abstract

Axially symmetric stress distribution in the neighbourhood of a penny-shaped crack stituated in an infinite isotropic elastic solid under general surface loadings and general surface temperature is considered. Surface loadings and surface temperature applied on the crack surfaces are axisymmetric but they are unsymmetrical about the crack planez=0. The equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel integral operator of the second kind. The stresses, displacements, temperature and flux functions at a general point in the solid are derived in terms of stress, displacement, temperature and heat flux discontinuities at the plane of the crack. Using the boundary conditions and the continuity conditions problem is reduced to that of solving Abel integral equations of the first and the second kind. Explicit expressions are obtained for stress components, crack opening displacement and stress intensity factors in terms of the prescribed surface temperature functions. For some special cases of thermal loading these quantities are compared with those available in the literature. Stress at a general point of the medium is obtained in the special case, when the one face of the crack is subjected to constant temperature while the other face is kept at the reference temperature.