About the stress state of a piecewise homogeneous elastic rectangle with two symmetric central cracks in antiplane deformations.

This paper presents a boundary value problem and formulation for the analysis of linear elastic fracture mechanics problems involving piecewise homogeneous bimaterials. Investigation and mathematical works in this paper is focused on the stress- strain state of plates with two symmetric central cracks that are made of two bonded dissimilar materials which behave as a piecewise homogeneous elastic plate. Two cracks are on the bondness line of the two segments of plate that have two different shear modulus G1 and G2, and equal length and height. The antiplane distributed shear loading act on the edges of plate. Using sinusoidal Fourier transformation the equation governing this boundary value problem converts to a singular integral equation (S.I.E) of the Cauchy form, which can be solved with the aid of Gaussian numerical-analytical solution for singular integral equations. Consequently the dislocation field around the cracks boundaries and the tearing stresses of plate and the Stress Intensity Factor (S.I.F) equations at the tips of cracks are derived.