Doubly-periodic array and zig-zag array of cracks in solids under uniaxial tension

In 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 and a zig-zag array of cracks in a two-dimensional solid subjected to tension, as simplified models of randomly distributed cracks in materials. The analysis is based on the eigenfunction expansions of the complex stress potentials for properly chosen unit regions. Numerical results for the stress intensity factors, crack opening displacements and effects of cracks on the tensile stiffnesses of these solids are given for various combinations of the parameters. The results are then fitted to reliable polynomial formulae for convenience of engineering applications.