Interfacial crack analysis in layered media using couple-stress elasticity and the displacement discontinuity method
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Interfacial cracks between dissimilar materials represent a critical failure mechanism in layered structural systems such as coatings, composite laminates, and micro-structured materials. However, classical elasticity theory cannot adequately capture the size-dependent behavior observed at micro- and nano-scales. This study investigates a pre-existing interfacial crack in a multilayered elastic medium using couple-stress elasticity and the displacement discontinuity method. The crack is modeled as a prescribed normal opening displacement discontinuity along the interface between two bonded layers resting on an elastic half-plane. The corresponding reaction tractions, stress fields, and couple-stress components are determined using Fourier transform techniques and Gauss-Legendre quadrature. The numerical results indicate that the material length-scale parameter and stiffness mismatch significantly influence the near-tip reaction stress field. For a prescribed crack opening, couple-stress effects enhance the microstructural resistance near the crack tip, highlighting the importance of size-dependent modeling in the analysis of layered interfacial fracture problems.
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