Solution of a bonded bimaterial problem of two interfaces subjected to different temperatures

A closed-form solution is derived for the bonded bimaterial planes at two interfaces subjected to different temperatures. The bonded planes with two interfaces are symmetric with respect to the interface, which is straight. A rational mapping function and complex stress functions are used for the analysis. The problem is reduced to a Riemann–Hilbert problem. The solution includes an integral term. This integral cannot be carried out. However, the first derivative of complex stress functions which does not include integral terms with regard to the variables of the mapping plane is achieved. Therefore, there is no need for numerical integration to calculate stress components and to determine unknown coefficients in a complex stress function. This is very beneficial. It is more difficult to derive the solution to the two-interface problem compared to the general solution. As a demonstration of geometry, semi-strips bonded in two places at the ends of strips are considered. Unbonded parts are a model of debonding. The solution for different geometrical shapes can be obtained by changing the mapping function. Some stress distributions are shown for different lengths of the interface. The stress intensity of debonding (SID) (corresponding to the root of strain energy release rate) is investigated for the debonding extension. SID is the same as the root of strain energy release rate for the evaluation of the strength at the debonding tip.