Dynamic stress intensity factors for a longitudinal semi-elliptical crack in a thick-walled cylinder
The dynamic stress intensity factors are derived for an internal longitudinal semi-elliptical crack in a thick-walled cylinder subjected to transient dynamic stresses. First, the problem of dynamic elasticity in a thick-walled cylinder is solved analytically using the finite Hankel transform. Transient pressure is assumed to act on the inner and outer surfaces of the cylinder. Then, a three-dimensional finite element method is used to calculate accurate weight functions for semi-elliptical surface crack in the cylinder. Finally, the dynamic stress intensity factors are extracted for both the deepest and surface points of the semi-elliptical crack using the weight function method. An effective and accurate process of computing closed-form stress intensity factors is employed which can be used for any kind of boundary conditions. It is shown that for narrow cracks, the deepest point is always the starting point of any problem crack propagation. However, for cracks with high aspect ratios, the critical point of the crack front displaces between the deepest to the surface point in different instants of time.
Keywords: Semi-Elliptical Crack – Weight Function – Thick-Walled Cylinder – Dynamic stress intensity factor – Hankel Transform.