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.

Automated summary

The couple-stress elasticity theory is used to analyze an anti-plane shear crack at the interface between two dissimilar elastic materials. The deviatoric couple stress tensor, governing equation, and boundary conditions are derived. The singularity index is determined using the eigenfunction expansion method, and then the Fourier transform is employed to convert the crack problem to a hypersingular integral equation. The resulting equation is numerically solved using the Chebyshev series method to evaluate various factors and reveal the influence of different parameters.