Hypersingular Integral Equations for the Solution of Penny-shaped Interface Crack Problems

Based on the theory of elasticity, previous analytical solutions concerning a penny-shaped interface crack employ the derivative of the crack surface opening displacements as the primary unknowns, thus leading to singular integral equations with Cauchy-type singularity. The solutions to the resulting integral equations permit only the determination of stress intensity factors and energy release rate, and do not directly provide crack opening and sliding displacements. However, the crack opening and sliding displacements are physically more meaningful and readily validated against the finite element analysis predictions and experimental measurements. Therefore, the present study employs crack opening and sliding as primary unknowns, rather than their derivatives, and the resulting integral equations include logarithmic-, Cauchy-, and Hadamard-type singularities. The solution to these singular integral equations permits the determination of not only the complex stress intensity factors but also the crack opening displacements.