Leakage Rates Through Non-Linear Through Wall Cracks Obtained From Finite Element Analysis

This paper presents work that has been carried out to extract leakage rates from finite element models. The benefit of using a more sophisticated leak rate model in combination with finite elements is the increased accuracy in leakage rate calculation for more complex crack shapes and loading conditions. The methodology involves extracting the crack opening displacement (COD) from the Extended Finite Element Method (XFEM) and standard finite elements, then outputting the data to an Excel spreadsheet. A polynomial is then fitted to the data and this is inputted into a MATHCAD code which calculates leakage rate using the Ordinary Differential Equation (ODE) model developed in a previous paper. Test cases were considered which were based on a thick plate with a central crack under various loading conditions. These included primary membrane loading, through-wall bending, and a residual-stress field. The through wall bending and residual stress fields were induced from a temperature field imposed on the plate. A difference of 20% in leak rate is observed between results from the DAFTCAT (Reference 1) code and the ODE method for the residual stress field considered. The paper concludes with recommendations for improved guidance in R6 Section III.11 (Reference 2) for cases when complex crack shapes and loading are present.