Brittle fracture in a periodic structure with internal potential energy.

Abstract

We consider a brittle fracture taking account of self-equilibrated distributed stresses existing at microlevel in the absence of external forces. To determine how the latter can affect the crack equilibrium and growth, a model of a structured linearly elastic body is introduced, consisting of two equal symmetrically arranged layers (or half-planes) connected by an interface as a prospective crack path. The interface comprises a discrete set of elastic bonds. In the initial state, the bonds are assumed to be stressed in such a way that tensile and compressive forces of the same value alternate. In the general considerations, the layers are assumed to be of an unspecified periodic structure, where such self-equilibrated stresses may also exist. A two-line chain and a lattice are examined as the specified structure. We consider the states of the body-with-a-crack under such microlevel stresses (MS) and under a combined action of the remote forces and MS. Analytical solutions to the considered problems are presented based on the introduction of a selective discrete transform. We demonstrate that MS can increase as well as decrease the crack resistance depending on the internal energy level. We also discuss different scenarios of the crack growth.