We present results of an investigation of the development of a transverse shear crack in a composite material with linearly viscoelastic components under external shear load. The solution is divided into the following two main stages: determination of the time dependence of the crack tip opening displacement and determination of the crack-growth kinetics as a result of the solution of integral equations. In the first stage, we use the solution of the corresponding elastic problem of determination of the crack opening displacement and the problem of determination of the effective moduli of the composite reinforced with unidirectional discrete fibers. Using the theoretically proved principle of elasto-viscoelastic analogy and the method of Laplace inverse transformation, we obtain a solution in a time domain. In the second stage, using the criterion of critical crack opening displacement for a transverse shear crack and an equation for the viscoelastic crack opening displacement of this crack, we construct an equation of crack growth. We present results of the numerical solution, which illustrate the influence of relations between the relaxation parameters of the materials of the components on the durability of the body with a crack.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 1, pp. 98–108, January–March, 2010.
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Kamins’kyi, A.O., Selivanov, M.F. & Chornoivan, Y.O. On subcritical development of a shear crack in a composite with viscoelastic components. J Math Sci 176, 616–630 (2011). https://doi.org/10.1007/s10958-011-0426-3
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DOI: https://doi.org/10.1007/s10958-011-0426-3