A unified model for the effective elastic response of inhomogeneities with finite sliding - Chowdhury, Shoieb Ahmed; Askari, Hesam (International journal of mechanical sciences, 2019)
•Sliding behavior of spherical inhomogeneity with linear sliding law is explored.•Non-dimensional study performed in FEM to develop model for average elastic field.•A unified model valid within full range of no- to free-sliding regime is presented.•Model captures relaxation over multiple orders of magnitudes of interface compliance.•The interplay between sliding energy and elastic energy controls the extent of sliding. A model for predicting mean elastic field over volume of a single spherical inhomogeneity encountering interfacial sliding along with elastic deformation is developed in this paper. Based on non-dimensional parametric study using finite element, our proposed semi-analytic model provides closed form solution for two non-linear coefficients necessary for computing average relaxation activity. Using such non-linear relationship for local relaxation law resulted in 7–18 times improvement in accuracy compared to existing models in estimating average strain for tensile and shear far-field loading respectively with only a few percentages of error. Besides being useful for a wide range of property mismatch between matrix and inclusion, it offers the uniqueness to be accurate over 5 to 6 orders of magnitude range of interfacial compliance factors spanning the spectrum from perfectly bonded to free-sliding interface. Additionally, we complement the study by an analysis of sliding energy distribution. Energy equivalency of the mechanics of sliding problem is found by showing closely similar trend between sliding energy and elastic field relaxation pattern. The interplay between sliding energy at interface and elastic energy is showed to provide significant insight on physical understanding of how sliding mechanism happens and what are its influencing parameters. This new approach can lead to further development for polycrystalline problems where grain boundary sliding is an active mechanism.