Leak-before-Break assessments require a reliable method to obtain leakage rates from narrow cracks. The ability to predict leakage accurately is crucial to the overall success of Leak-before-Break arguments as the detection capability and limiting crack size are often very small. This can make it difficult to achieve the desired margin between limiting defect size and the crack size required for detectable leakage. The resulting narrow flow paths (< 0.1mm) relative to the wall thickness (> 10mm) necessitates the use of complex thermodynamic and friction models in the leak rate calculation.
A method to calculate leakage rates through complex paths was presented in PVP2015-45468 using an ordinary differential equation (ODE) for Mach number. This model was developed to account for crack opening displacements that vary non-linearly through the wall of a pipe. This situation typically arises when there is a through wall crack at a weld, where significant residual stresses are present. This paper considers an FEA model of a plate with a weld residual stress (WRS) profile applied. The WRS is prescribed with nodal displacements, and the COD is calculated from post processing of the elastic stress analysis solution. This results in a COD function in terms of the distance through the wall, which can then be used in the leak rate calculation. Comparisons are made with the R6 methodology recommended software DAFTCAT and the benefits of using the ODE method are discussed.
In collaboration with Framatome, Germany, a test case based on the previous European project STYLE was considered. The test case involves a Type 316L Stainless Steel pipe with a girth weld, and the FEA model includes postulated through wall defects at the weld interface to assess crack opening displacements. This model will be used to extract crack opening displacements and calculate leak rates using various methods. Two phase flow will be considered for this test case as the pipe geometry is very relevant to PWRs.