An Approach to Include the Effects of Plasticity in the Calculation of Crack Opening Areas for Through-Wall Cracks Subject to Combined Primary and Secondary Loading

Abstract The work presented within this paper looks at estimates of crack opening area (COA) under elastic-plastic material conditions. Developing leak before break (LbB) arguments with secondary (thermal or weld) stresses present is challenging. This potentially results from defect assessment methods like R6 not including guidance on the effect of plasticity on COA estimations in the presence of the secondary stresses, where the COA would be expected to increase compared to the elastic COA. The corresponding elastic-plastic stress intensity factor (KJ) could, conversely, reduce compared to handbook elastic solutions for stress intensity factor (KI). Current practise within an LbB assessment in the UK would be to assume a plasticity correction is applied to KI, calculated using the R6 failure assessment diagram (FAD) as a J estimation scheme, to provide KJ. COA’s are evaluated elastically to ensure that the assessment under-estimates real-plant scenarios and is therefore generally conservative. Including plasticity in COA evaluations will allow assessment of COA to be more accurate, and therefore provide a reduction in conservatism compared to current guidance when a defect is in the presence of a single load type or when different loading types are combined. This paper presents an approach which allows plasticity to be included in COA evaluations by calculating an additional crack opening as a result of plasticity, based on crack tip opening displacement and an enhancement calculated from the contributions of elastic and plastic reference strain (and is therefore consistent with the reference stress methods contained in R6 and elsewhere). This resulting crack opening area is then added to the elastic COA (COAe) calculated from the solutions published in a previous ASME PVP paper by France et al. The results of this approach are compared to elastic-plastic FEA results, where the primary membrane and secondary through-wall bending stresses were investigated when in isolation and combined with respect to K and COA. The method outlined herein provides an increase in crack opening and therefore a reduction in conservatism compared to the FEA results, whilst remaining conservative; i.e. elastic-plastic COA prediction (COAep) is less than the FEA results. Where a secondary through-wall bend has been applied in isolation, the restriction of crack overclosure (inclusion of crack face contact) in the FEA generates greater opening at the tensile surface. This is not replicated in the COAep method developed in this work and would need further development. Under combined loading, the inclusion of plasticity in COAep has a small effect as the primary and secondary stresses are low and the secondary stresses relax due to plasticity, ensuring the response remains nominally elastic and is therefore consistent with existing methodology.