Solution of two-parameter cohesive law using Chebyshev polynomials for singular integral equation

Complex stress and displacement potentials are used to examine the effect of cohesive stress on crack opening and stress around a two-dimensional slit-like crack in an isotropic material. A two-parameter right-angled triangular relationship between the cohesive stress and crack opening is assumed to hold. Following an earlier work, the problem is reduced to a singular integral equation (SIE), which is solved numerically using Chebyshev polynomials. The results quantify the effect that the cohesive stress has on the crack opening, and on the stress field around the crack. Finally, it is also shown that the region of action of cohesive stress (“cohesive zone”) comes out as a part of the solution based on the choice of the two parameters. The presented method is more direct than the commonly used variational methods.