Delayed fracture of a transversally isotropic viscoelastic material with a crack under monotonically increasing loading

The delayed fracture of a transversally isotropic viscoelastic material due to slow subcritical growth of a flat normal-fracture macrocrack with a circular cross-section under monotonically increasing load is examined. The calculations employ the modified δC of fracture, which is based on the concept of constancy of the prefailure region. The investigation is carried out within the framework of the Boltzmann-Volterra theory for difference-type bounded resolvent operators, which describe the transversal isotropy of the viscoelastic deformational properties of the material. To find the analytical form of the kernel of an irrational function of a linear combination of the above-mentioned integral operators, the method of operator continued fractions is used. Analytical and numerical calculations are carried out for difference-type bounded resolvent operators with the kernel in the form of Rabotnov's fractional-exponential function.