Mode-III interface crack in a bi-material with initial stress and couple stress

The couple-stress elasticity is applied to study an anti-plane shear crack at the interface between two bonded dissimilar elastic media with initial stresses. First, the deviatoric couple stress tensor is proven. The governing equation alongside associated boundary conditions is derived. Using the eigenfunction expansion method, the singularity index is determined. Then, the Fourier transform is employed to convert the mode-III interface crack problem to a hypersingular integral equation. Using the Chebyshev series method, the resulting hypersingular integral equation is numerically solved. The crack-tearing-displacement, couple-/force-stress intensity factors, and energy release rate are evaluated to reveal the influence of the intrinsic characteristic lengths, couple-stress material constants, and initial stresses. •Mode-III interface crack in a bi-material with couple stress and initial stress is studied.•Antiplane shear stresses near the crack tips have an r−3/2 singularity.•Couple stresses near the crack tips have an r−1/2 singularity.•The strains at the crack tips vanish and are no longer singular.•Effects of characteristic lengths and initial stresses on fracture parameters are analyzed.