D ec 2 01 3 Brittle fracture in a periodic structure with internal potential energy Gennady

We consider a brittle fracture taking account of self-equilibrated distributed microstresses. 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 is comprised of a discrete set of elastic bonds. In the initial state with no external forces, 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 the microstresses and under a combined action of the remote forces and the microstresses. Analytical solutions to the considered problems are presented based on the introduction of a selective discrete transform. We show that the microstresses can manifest themselves in a number of phenomena such as the crack bridging, occurrence of ‘porosity’ in front of the crack and crack growth irregularities. We demonstrate analytically and graphically that the microstresses can result in an increase as well as in a decrease of the crack resistance depending on the internal energy level. We also discuss different scenarios of the crack growth depending on the internal energy level. The results for the specified structure are presented with their dependence on anisotropy, whose role in the considered problem appears substantial. The corresponding dynamic problems, the spontaneous crack propagation under the internal energy and the crack dynamics under the combined action of the internal energy and remote forces will be submitted separately.