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

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 To∗−a/b space, where To∗ is the tensile strength of the interface, normalized to ηγ̇, where η and γ̇ are 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 To∗ 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.