Three-dimensional analysis of thermal shock effect on inner semi-elliptical surface cracks in a cylindrical pressure vessel

Abstract

Transient mode I stress intensity factors (K_IT) distributions along semi-elliptical crack fronts resulting from thermal shock typical to a firing gun are investigated. K_IT distributions for various crack arrays of n=2 to 48 cracks, bearing cracks of relative depths of a/W=0.1 to 0.4 and with ellipticities of a/c=0.5, 1.0 and 1.5 are evaluated for a cylindrical pressure vessel of radii ratio of R₀/R=2. As decoupling between the thermal and the elastic problems is assumed, the solution is performed in two steps via the finite element (FE) method using the standard ANSYS 5.0 code. In the first step temperature distributions through the vessel's wall are evaluated for various time steps in the interval 2 to 10 msec assuming convective boundary conditions. The temperature fields evaluated in the first step serve as input to the second step, the elastic analysis, in which K_IT is evaluated. The results show that K_IT is usually negative, as could have been anticipated, and reaches its largest negative value at the intersection of the crack plane with the inner surface of the cylinder. In general, the negative magnitude of K_IT increases as the number of cracks in the array decreases, as the crack ellipticity increases, and as time elapses from firing.