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 delta(c)-model 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.