Abstract
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 halfplanes) 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 selfequilibrated stresses may also exist. A twoline chain and a lattice are examined as the specified structure. We consider the states of the bodywithacrack 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.
Original language  English 

Article number  20130821 
Pages (fromto)  125 
Number of pages  25 
Journal  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 
Volume  470 
Issue number  2165 
Early online date  19 Feb 2014 
DOIs  
Publication status  Published  08 May 2014 
Keywords
 fracture mechanics
 microlevel stresses
 lattices
 integral transforms
 RESPONSE SENSITIVITY
 LATTICE
 INTERFACE
 COMPOSITE
 DYNAMICS
 CRACK
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Gennady Mishuris
 Faculty of Business and Physcial Sciences, Department of Mathematics  Professor of Mathematical Modelling, Royal Society Wolfson Research Merit Award Holder
Person: Teaching And Research, Other