Stable growth of penny-shaped crack in viscoelastic composite material under time-dependent loading

Considered is the long-term cracking of the three-dimensional fiber-reinforced viscoelastic composite with a plane penny-shaped crack under time-dependent loading. The composite has a hexagonal structure and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled by transversally isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. The crack propagation planecoincides with the plane of isotropy. A ring-shaped yield zone in front of the moving crack is modeled as a Dugdale's zone with time-dependent stresses. Crack growth under deformation of the composite occurs by application of a slowly increasing tensile load; it is normal to the plane of crack propagation. A convolution-type time operator describes the viscoelastic properties of the matrix material. Use is made of the Volterra principle and the theory of long-term cracking of viscoelastic bodies. The irrational function of integral operator associated with the viscoelastic crack opening expression is expanded into a continued fraction of operators. The solution is reduced to the nonlinear integral equations of crack growth. Numerical results are obtained for a specific material. Crack growth kinetics is discussed in connection with the onset of stable crack growth and crack border stress intensity factor.