Effect of couple-stresses on the stress intensity factors for a crack in an infinite elastic strip under tension

Abstract

Stresses around a crack in an infinite elastic strip are evaluated based on linearized couple-stress theory under uniform tension. The crack is perpendicular to the stress-free edges of the strip. Solutions are constructed both for a half-plane and for a strip. First, the boundary conditions at the stress-free surfaces are satisfied using a Fourier transform. Next, the mixed boundary value conditions with respect to the crack are reduced to dual integral equations. To solve these equations, differences in the displacement and the rotation at the crack are expanded through a series of functions that are zero -valued outside the crack. The unknown coefficients in each series are solved in order to satisfy the boundary conditions inside the crack using the Schmidt method. The stresses are expressed in terms of infinite integrals, and the stress intensity factors are determined using the integrand characteristics for an infinite value of the variable of integration. Numerical calculations are conducted for selected crack configurations, and the effect of the couple-stresses on the stress intensity factors is revealed.