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

Transient mode I stress intensity factors (K-IT) distributions along semi-e lliptical 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 e llipticities of a/c = 0.5, 1.0 and 1.5 are evaluated for a cylindrical pres sure vessel of radii ratio of R-0/R-i = 2. As decoupling between the therma l and the elastic problems is assumed, the solution is performed in two ste ps 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 eva luated for various time steps in the interval 2 to 10 msec assuming convect ive 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 be en 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 d ecreases, as the crack ellipticity increases, and as time elapses from firi ng.