A cracked plate under transient thermal stresses due to surface heating

Abstract

The transient thermal stresses in a cracked plate due to sudden surface heating are investigated. The plate is assumed to be insulated on one face and heated on the other. A ramp heating function is assumed at the boundary, which is more realistic than a step function. It is shown that, in the case of an edge crack, the situation of a heated surface is very different to that of a cooled surface. When the surface of the plate is heated, compressive transient thermal stresses occur close to the surface, causing the crack surfaces to come into contact with each other over a certain contact length, but when the surface of the plate is cooled, high tensile stresses take place close to the surface which tend to open the crack. If the contact between the crack surfaces is not taken into account, the stress intensity factors will always yield negative values, but when the contact length is taken into account the resulting calculations produce positive stress intensity factors. So, the problem is reduced to a non-linear crack contact problem which is formulated in terms of a singular integral equation from the embedded crack problem with smooth closure conditions of the crack surfaces. The numerical results are obtained for stress intensity factors and the crack contact length is obtained as a function of Fourier number, crack length, and the duration of the heating rate.