Brittle fracture in a periodic structure with internal potential energy. Spontaneous crack propagation

Abstract: Spontaneous brittle fracture is studied based on the recently introduced model (Mishuris and Slepyan, Brittle fracture in a periodic structure with internal potential energy. Proc. Roy. Soc. A, in press). A periodic structure is considered, where only the prospective crack-path layer is specified as a discrete set of alternating initially stretched and compressed bonds. A bridged crack destroying initially stretched bonds may propagate under a certain level of the internal energy without external sources. The general analytical solution with the crack speed $-$ energy relation is presented in terms of the crack-related dynamic Green's function. For the anisotropic two-line chain and lattice considered earlier in quasi-statics, the dynamic problem is examined in detail. The crack speed is found to grow unboundedly as the energy approaches its upper limit. It is revealed that the spontaneous fracture can occur in the form of a pure bridged, partially bridged or fully open crack depending on the internal energy level. Generally, the steady-state mode of the crack propagation is found to be realised, whereas an irregular growth, clustering and the crack speed oscillations are detected in a vicinity of the lower bound of the energy.