On the interaction of a periodic system of parallel coaxial radialshear cracks in a prestressed composite
 V. L. Bogdanov
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Get AccessBased on approaches of the linearized theory of elasticity, we consider an axisymmetric problem of stressstrain state of a composite with initial (residual) stresses containing a periodic system of parallel coaxial radialshear cracks. Using representations of general solutions of the linearized equilibrium equations in terms of harmonic potential functions and the apparatus of integral Hankel transformations, we reduce the problem to a system of dual integral equations and then to a Fredholm integral equation of the second kind. We obtain expressions for the stress intensity factors near the crack edges and, for a laminated composite with isotropic layers, analyze dependences of these factors on the initial stresses, mechanical characteristics of components, and geometric parameters of the problem. On the basis of analysis of the sharp “resonancelike” behavior of the stress intensity factors, for certain values of the initial compressive stresses, we determine critical parameters of compression along the periodic system of parallel coaxial cracks.
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 Title
 On the interaction of a periodic system of parallel coaxial radialshear cracks in a prestressed composite
 Journal

Journal of Mathematical Sciences
Volume 187, Issue 5 , pp 606619
 Cover Date
 20121201
 DOI
 10.1007/s1095801210876
 Print ISSN
 10723374
 Online ISSN
 15738795
 Publisher
 Springer US
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 Authors

 V. L. Bogdanov ^{(1)}
 Author Affiliations

 1. Timoshenko Institute of Mechanics, Ukrainian National Academy of Sciences, Kyiv, Ukraine