Thermo-elastic dislocation with application to crack problems

The notion of Volterra dislocation is generalized to define a quasi-static uncoupled thermo-elastic dislocation. The solution to dislocation is obtained in a layer with a fixed and a free boundary. A layer containing multiple cracks with specified temperature at the boundary and aforementioned mechanical boundary conditions is considered. By means of the distributed dislocation technique, the dislocation solution is introduced into the layer to derive integral equations for dislocation density functions on the surfaces of cracks. These equations are Cauchy singular and are solved numerically. The solutions are employed to determine stress intensity factors (SIFs) for cracks in both cases of the impermeable and partially permeable heat flux.