TY - JOUR

T1 - Brittle fracture in a periodic structure with internal potential energy. Spontaneous crack propagation

AU - Ayzenberg-Stepanenko, Mark

AU - Mishuris, Gennady

AU - Slepyan, Leonid

PY - 2014/7/8

Y1 - 2014/7/8

N2 - Spontaneous brittle fracture is studied based on the model of a body, recently introduced by two of the authors, where only the prospective crack path is specified as a discrete set of alternating initially stretched and compressed bonds. In such a structure, 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 anisotropic chains and lattices considered earlier in quasi-statics, the dynamic problems are examined and discussed in detail. The crack speed is found to grow unboundedly as the energy approaches its upper limit. The steady-state sub- and supersonic regimes found analytically are confirmed by numerical simulations. In addition, irregular growth, clustering and crack speed oscillation modes are detected at a lower bound of the internal energy. It is observed, in numerical simulations, 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.

AB - Spontaneous brittle fracture is studied based on the model of a body, recently introduced by two of the authors, where only the prospective crack path is specified as a discrete set of alternating initially stretched and compressed bonds. In such a structure, 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 anisotropic chains and lattices considered earlier in quasi-statics, the dynamic problems are examined and discussed in detail. The crack speed is found to grow unboundedly as the energy approaches its upper limit. The steady-state sub- and supersonic regimes found analytically are confirmed by numerical simulations. In addition, irregular growth, clustering and crack speed oscillation modes are detected at a lower bound of the internal energy. It is observed, in numerical simulations, 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.

KW - Dynamic fracture

KW - Failure waves

KW - Periodic structure

UR - http://www.scopus.com/inward/record.url?scp=84901276769&partnerID=8YFLogxK

U2 - 10.1098/rspa.2014.0121

DO - 10.1098/rspa.2014.0121

M3 - מאמר

AN - SCOPUS:84901276769

VL - 470

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2167

M1 - 20140121

ER -