Three-dimensional thermal analysis of an infinite solid containing an elliptical surface crack

Abstract

This paper deals with the thermal problem of an infinite solid with an elliptical insulated surface crack subjected to a uniform heat flow. Using conformal mapping technique, the elliptical crack region is first mapped conformally onto a penny-shaped crack for which the solution on the crack surface is available. The complete solution of the temperature field of the entire solid studied is then obtained by the inverse Fourier transform technique and the singularity of temperature gradient on the crack surface near the crack front can be found. To explore the temperature gradient along and around the crack front further, a three-dimensional finite element model with collapsed quarterpoint singular elements around the crack front is employed. Several examples with various crack aspect ratios are solved analytically and numerically. The influence of the elliptical insulated surface crack on the local intensification of temperature gradient and heat flow is also illustrated.