Strain gradient fracture in an anti-plane cracked material layer

Fracture mechanics analysis in terms of evaluating stress intensity factors of an anti-plane isotropic cracked layer is carried out using strain gradient elasticity theory. The crack plane is assumed parallel to the layer edges. Both volumetric and surface strain gradient material characteristic lengths are considered in formulations and numerical solutions. Two boundary value problems corresponding to "stress-free" and "clamped" boundaries are considered in which each solution is reduced to the dual integral equations. The Fredholm integral equation, proceeding from the dual integral equations, is numerically solved to evaluate crack tip stress intensity factor. Stress intensity factors for stress-free boundary conditions are higher with smaller height (or with a longer crack) and vice versa for clamped boundaries. Volumetric strain gradient effect reduces stress intensity factor and demonstrates strong size effect on a smaller scale. Crack stiffness becomes more pronounced with positive surface strain gradient, while negative surface gradient leads to a more complaint crack. In general, the contribution of volumetric strain gradient is shown to be more dominant than that of surface strain gradient.