Penny-shaped Dugdale crack in a transversely isotropic medium and under axisymmetric loading

The present work is concerned with a penny-shaped crack embedded in a transversely isotropic medium and oriented in parallel with the isotropic plane of the latter. Three axisymmetric crack problems are investigated. In the first one, the upper and lower lips of the crack are subjected to a pair of annular opposite pressures. In the second and third problems, two opposite concentrated forces of the same magnitude are applied successively at the upper and lower crack lip centres and at any two points outside the crack and on the axis perpendicular to the crack. Using the basic idea underlying Dugdale's crack model, the extent of the plastic zone is analytically estimated in each of the three cases. In addition, the corresponding crack surface displacement is determined explicitly. Numerical examples are provided to discuss the effects of some geometrical and material parameters involved. Apart from their own usefulness in carrying out some simplified crack analyses, the results obtained in this work can in particular serve as benchmarks for computational fracture mechanics.