Based on approaches of the linearized theory of elasticity, we consider an axisymmetric problem of stress-strain state of a composite with initial (residual) stresses containing a periodic system of parallel coaxial radial-shear 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 “resonance-like” 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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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 54, No. 4, pp. 59–70, October–December, 2011.
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Bogdanov, V.L. On the interaction of a periodic system of parallel coaxial radial-shear cracks in a prestressed composite. J Math Sci 187, 606–619 (2012). https://doi.org/10.1007/s10958-012-1087-6
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DOI: https://doi.org/10.1007/s10958-012-1087-6