Numerical studies on crack problems in three-layered elastic media using an image method

Two-dimensional crack problems in a three-layered material are analyzed numerically under the conditions of plane strain. An image method is adopted to obtain fundamental solutions for dislocation dipoles in trilayered media. The governing equations for equilibrium cracks can be constructed by distributed dislocation technique and their solutions are sought in terms of the displacement discontinuity method (DDM). Comparisons are made with available analytical or reference solutions for several examples at various contrasts of material constants, and good agreements are found. A crack within a brittle adhesive layer joining two semi-infinite blocks can propagate in a variety of ways. In particular, crack paths in the form of sigmoidal waves within the adhesive layer are revisited to reveal the sensitivities of cracking paths to initial crack locations and directions and residual stresses. In addition, Z-shape and H-shape cracks alternating from interface to interface are re-examined to highlight the transition of failure modes and the role of the interlayer thickness.