Cleavage Fracture Modelling for RPV Steels: Discrete Model for Collective Behaviour of Micro-Cracks

Abstract

The ability to predict variations in cleavage fracture toughness behaviour of ferritic RPV steels, accounting for the effects of irradiation and defect geometry, is vital to safety assessment and life extension decisions. Local approaches to cleavage fracture offer a promising methodology to accomplish such calculations. However, the limited progress achieved by improving the local failure probability expression suggests that the methodology for calculating global cleavage might not be adequately representing real material. The basis for the existing methodology is the weakest-link assumption that all individual failure events are independent and non-interacting. Here an approach is considered which utilises a microstructure-informed model incorporating the experimental knowledge needed to postulate deterministic criteria for particle rupture and micro-crack propagation, whilst accounting for the probabilistic distribution of particle sizes. This is then used in a lattice model that can help detail the evolution of the formation of micro-cracks on global failure, therefore inferring the suitability of the weakest-link assumption. Predicting the probability of cleavage fracture requires such models, as the macroscopic cleavage phenomenon is governed by a number of micro-structural features.The material microstructure is represented by a regular lattice of truncated octahedral cells forming a computational sitebond model, with sites located at the cell centres and connected by two distinct sets of bonds. These bonds are modelled with structural beam elements, which represent all the possible relative deformations between coordinated sites. Particles of various sizes are distributed in the bonds, based on an experimentally determined distribution of cleavage initiating particles in RPV steel (Euro Material A). Although only elastic deformations are considered here, the results demonstrate that the interactions between individual failure events could potentially have a strong effect on the way global failure is reached.Nucleation of micro-cracks by rupturing second-phase particles affects their subsequent formation. In particular, it was found that once formed there is a reduced probability of further development of micro-cracks at particles outside the crack planes and an enhanced probability of formation at particles along the crack planes. This will therefore influence the distribution of micro-crack sizes that could in principle be used to calculate the global probability of failure, and could lead to substantially different distributions of particle sizes, then used in the current local approach methods.

Evaluation of CTOD resistance curves in clamped SE(T) specimens with weld centerline cracks

“…The value of the T-stress depends on crack size, geometry, and the traction parallel to the crack plane; also, it has an effect on plastic zone size and crack tip opening displacement [36]. Further studies showed that compressive T-stress can reduce the crack tip constraint which is followed by an increase in fracture toughness [37][38][39]. Very close to the crack tip (𝑟 → 0), the first term on the right hand of equation 2.1 exhibits a singularity and the equation's value tend to infinity, which means the rest of the terms can be ignored and simplify the equation 2.1 as:…”