TY - JOUR

T1 - Brittle fracture in a periodic structure with internal potential energy

AU - Mishuris, Gennady S.

AU - Slepyan, Leonid I.

PY - 2014/5/8

Y1 - 2014/5/8

N2 - We consider a brittle fracture taking account of selfequilibrated 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.

AB - We consider a brittle fracture taking account of selfequilibrated 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.

KW - Fracture mechanics

KW - Integral transforms

KW - Lattices

KW - Microlevel stresses

UR - http://www.scopus.com/inward/record.url?scp=84896929909&partnerID=8YFLogxK

U2 - 10.1098/rspa.2013.0821

DO - 10.1098/rspa.2013.0821

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AN - SCOPUS:84896929909

SN - 1364-5021

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

IS - 2165

M1 - 20130821

ER -