Extensional detachment at the inclusion-matrix interface in a multiple inclusion system

Abstract

This paper deals with a theoretical analysis of extensional fissures around spherical rigid inclusions hosted in a ductile matrix undergoing bulk shear. The analysis shows that the mechanical interaction of inclusions is a function of the inclusion concentration a/b (2a and 2b are the inclusion diameter and mean inter-inclusion distance, respectively), and intensifies the tensile stress imparted by the flowing matrix on the inclusion-matrix interface. Inclusion concentration a/b thus appears to be a crucial parameter in perturbing the inclusion-matrix coherence and leading to formation of extensional fissures around an inclusion. We performed numerical simulations to delineate the fields for coherent and incoherent interfaces in the T_o^∗-a/b space, where T_o^∗ is the tensile strength of the interface, normalized to ηϒ, where η and ϒare the viscosity of matrix and bulk shear rate, respectively. For a given a/b, the interface cannot remain coherent unless the tensile strength is greater than a critical value. The critical T_o^∗ increases almost linearly at a gentle gradient with increasing a/b. However, for a/b>0.7, this increases nonlinearly, assuming a large value when the concentration is high (a/b>0.8). It is also revealed that under the same deformation conditions, the instantaneous opening in fissures may vary depending upon the a/b values.