Tension of an infinite solid containing a doubly-periodic array of slant cracks

In the fatigue of materials, it is often observed that a number of cracks initiate from preexisting defects and propagate to form major cracks causing the final failure. In this paper, we consider a doubly-periodic array of slant cracks in an infinite solid subjected to tension as two-dimensional models of randomly distributed cracks in materials. In the analysis, we choose a suitable unit region and express the complex stress potentials in eigenfunction expansions satisfying the traction-free conditions of the crack edges. The unknown coefficients are determined from the boundary conditions of the unit region. At this stage, we use a new procedure based on element-wise resultant forces and displacements in order to get highly accurate results. Numerical calculations are performed for various combinations of the parameters. The results of the stress intensity factors and the tensile stiffnesses of the solids with the slant cracks are summarized as forms ready for practical use. The accuracy of the numerical results confirms the utility of this approach.