Solution of Bonded Dissimilar Planes under Couples

A solution is derived for the elastic problem of two bonded dissimilar planes. The bonded planes 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. Elastic constants of the solution is expressed by Dundur’s parameters. The first derivative of the loading term is obtained as a closed form, which does not include an integral term. Therefore, there is no need of a numerical integration to obtain components of stress. As an example, the analysis is carried out for bonded half-planes subjected to concentrated couples at infinities and with cracks at an end of the finite interface. Stress distributions before and after initiation of the crack are investigated. Stress-intensity factors are investigated for some elastic constants. In particularly stress-intensity factors for short cracks are obtained, and it is also investigated that a crack initiates at either material.

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