RPV Structural Integrity Assessment During a PTS Event: Application of an Extended Beremin Model Consistent With WPS Test Results

Abstract

Starting from the pioneering work of Beremin, the classical Beremin-Weibull fracture probability’s model was extended recently to tackle with non-monotonic thermomechanical loadings. As a result of temperature effect on mechanical fields’ heterogeneity, an apparent temperature dependence of tile cleavage stress was also introduced to fit correctly the fragile to ductile transition. Considering the classical expression of the fracture probability, this extension consists in substituting the instantaneous opening stress by the maximum of the instantaneous opening stress versus cleavage stress ratio, this maximum being searched for previous active plastic time. This extended Beremin model was successfully applied to WPS tests experienced on low alloy ferritic steel compact tension specimens. Through this work, we aim at applying this approach to assess RPV structural integrity, assumed to be affected by a subclad flaw, during a simulated PTS event. The pressurized vessel is submitted to a thermal transient applied on the inner cladded surface. Considering a circumferential flaw, a two-dimensional elastic-plastic Finite Element calculation is performed. Therefore, the time evolution of elastic-plastic stress intensity factor KJ at the crack tip in base metal is calculated. Then, the time evolution of the cumulative fracture probability, as predicted by the extended Beremin model, is derived to evaluate the vessel integrity.

Probabilistic definition of local criterion for brittle fracture under complex thermomechanical loading

“…It is evident that the relative scatter of fracture toughness values (which is assessed as a coefficient of variation D M, where D is the variance, M is the expectation function of K f or K c I ) upon TPL is smaller than that in standard tests. This conclusion reasonably agrees with the known experimental findings [4,15,27,28].…”

“…Stockl et al [15] put forward another modification of the Beremin approach which involved a more detailed description of the brittle fracture process in comparison to the classical [9] and modified [4,14] versions. Many of the physical concepts taken in [15] are essentially very close to those described earlier in [16,17].…”

“…In [10], the Beremin approach was used to predict the temperature dependence of fracture toughness K T c I ( ) for the case of isothermal monotonic loading. It was demonstrated in [4,[11][12][13]] that the following assumption should be made to ensure adequate prediction of K T c I ( ) by the Beremin approach: assume the brittle-fracture critical stress to be temperature-dependent.…”

“…This assumption is based on the analysis of stochastic nature of various critical parameters that govern brittle fracture in RPV steels [18]. 4. To describe the carbide strength distribution function, i.e., the function of distribution of the σ d parameter, a three-parameter Weibull distribution is used,…”

“…In case local approaches are used in a probabilistic statement, a brittle strength condition can be defined as follows [3,4]:…”