Evaluation of axisymmetric steady thermal stress and thermal stress intensity factor in Kassir's nonhomogeneous infinite body with a penny-shaped crack

Abstract

In this work, a theoretical analysis of the axisymmetric thermal stress problem and the associated thermal stress intensity factor K 1 is developed for Kassir's nonhomogeneous body with a penny-shaped crack with radius a subjected to a uniform heat supply from the crack surfaces. Assuming that the thermal conductivity λ, shear modulus of elasticity G and coefficient of linear thermal expansion a vary with the axial coordinate z according to the relations λ(z)=λ 0 (|z/a|+1) β , G(z)=G 0 (|z/a|+1) m and a(z)=a 0 (|z/a|+1) n , the axisymmetrical steady temperature solution is obtained. Then, the associated thermal stress distribution and the thermal stress intensity factor at the crack tip are evaluated theoretically using the method of superposition. Numerical calculations are carried out for three different cases taking into account the nonhomogeneity of the above-mentioned material properties, and the numerical results obtained are shown in graphical form. The influences of the nonhomogeneous material properties on the temperature distribution, the corresponding thermal stress distribution and the stress intensity factor are examined.