The iIteractions between Shear Bands and Rigid Lamellar Inclusions in a Ductile Metal Matrix

A ductile metal matrix (modelled as a nonlinear elastic material) containing a dilute suspension of an iso-oriented lamellar stiff phase (modelled as stiffeners, i.e. zero thickness, rigid inclusions) is subject to a simple shear of finite amount, parallel to the inclusion orientation, and subsequently perturbed through an incremental Mode I loading, uniform at infinity. Solution to this problem permits analytical investigations of the emergence of shear bands and their interaction with a rigid inclusion (involving a stress square-root singularity at its tip) and discloses the mechanisms of ductile failure in reinforced materials (explaining for instance the experimental evidence that shear bands tend to nucleate and grow parallel to thin hard inclusions). Finally, investigated beyond the elliptic range, the obtained solution becomes non-unique and reveals non-decay and singularity of the fields, facts that provide analytical justification for the difficulties associated with numerical treatment of shear bands.