Study of strain and electric field gradients effects on two unequal oriented semi-permeable mode-III cracks in piezoelectric media

This study investigates size-dependent fracture behavior of two unequal, arbitrarily oriented semi-permeable Mode-III cracks in a polarized piezoelectric strip using coupled strain gradient (SG) and electric field gradient (EFG) theories. Closed-form expressions for crack sliding displacement (CSD), crack opening potential drop (COPD), stress intensity factor (SIF), and electric displacement intensity factor (EDIF) are derived through a hyper-singular integral formulation. Results reveal that intrinsic length-scale parameters significantly reduce CSD and SIF, indicating gradient-induced mechanical stiffening, while enhancing electric field localization near crack tips. Crack–crack interaction strongly depends on relative orientation: nearly collinear cracks amplify fracture intensity, whereas increasing angular difference produces shielding effects. The semi-permeable crack model notably alters near-tip electromechanical fields compared to ideal permeable/impermeable assumptions. In the limit of vanishing length-scale parameters, the model recovers classical piezoelectric fracture solutions. These findings provide insight into microscale fracture mechanisms in piezoelectric materials relevant to miniaturized electromechanical devices.