Mixed‐mode I/II stress intensity factors of a biaxially loaded plate with a central slant frictional crack: An analytical comprehensive solution

Abstract

This work presents a comprehensive analytical solution for the mixed‐mode I/II stress intensity factor of a biaxially loaded plate that has a centrally straight inclined crack with frictional surfaces. The solution addresses every possible combination of coefficient of friction, biaxial ratio, crack length, and angle. The present results agree with the available corresponding finite element solutions. For the tension‐compression and compression‐tension biaxial loading, crack angles are recognized to achieve pure mode I, pure mode II, and mixed‐mode crack tip deformation in terms of stress biaxiality and friction coefficient. In the compression‐compression biaxial loading, only mode II crack tip deformation is operative. The ranges of crack angles necessary to produce dormant cracks are determined for the biaxial loading patterns, where a compressive stress is involved, as a function of the biaxial ratio and friction coefficient. It is possible to apply the present solution to cracked plates with two‐dimensional stresses that include a shear stress.