Delayed fracture of a transversally isotropic viscoelastic material with a crack under a cyclic load

The delayed fracture of a transversally isotropic viscoelastic material due to slow subcritical growth of a flat circular macrocrack of normal separation under a cyclic load is investigated. The analysis is based on the modified δC of fracture and the hypothesis of the constancy of the prefracture zone. The study is made within the framework of the Boltzmann-Volterra theory for bounded resolvent operators of difference type, which describe the transversal isotropy of the strain properties of the material. To determine the analytic form of the kernel for the irrational function of a linear combination of the above-mentioned integral operators, the method of continued fractions is used. Analytical and numerical calculations are carried out for the bounded resolvent operators of difference type with the kernel in the form of Rabotnov's fractional exponential function.