Abstract
The study is made of the delayed fracture of a viscoelastic orthotropic plate caused by subcritical advancement of a rectilinear microcrack, which is located along one of the orthotropic axes. The crack develops because of stretching of the plate by uniformly distributed increasing and cyclic external forces perpendicular to the crack line. The investigation is carried out within the framework of the Boltzmann-Volterra theory for resolvent integral operators of difference type, which describe the deformation of a material with time-dependent rheological properties. The analytical form of the kernel of an irrational function of a linear combination of the above integral operators is determined by the method of operator continued fractions. Numerical calculations are conducted for resolvent bounded integral operators with a kernel in the form of Rabotnov's fractional-exponential function. The kinetics of growth of a crack with tip regions commensurable with the crack length is studied. A comparison with the results obtained within the framework of the concept of the thin structure of the crack tip is given.
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Additional information
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 121–129, June, 2000.
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Kaminskii, A.A., Selivanov, M.F. Development of a crack with a considerable prefracture zone in a viscoelastic orthotropic plate under variable loads. Int Appl Mech 36, 811–820 (2000). https://doi.org/10.1007/BF02681989
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DOI: https://doi.org/10.1007/BF02681989