Brittle Fracture Prediction Using Code_Aster: Review of Available Models and Focus on the GP Energy Approach

Abstract

With the life extension of NPPs world-wide, new challenges have emerged in engineering calculations. These challenges often stem from the difficulty to demonstrate an adequate margin for some key components, which have gradually been ageing during the operation of the plant. In particular, the Reactor Pressure Vessel (RPV) is impacted by the irradiation, and the risk of brittle fracture under severe cold shocks must be assessed. Over the past decades, the RSE-M code [1], which is used in France and internationally for in-service inspection, has been developing methods using a conventional approach to brittle fracture. Analyses are typically performed either using tabulated indices to evaluate analytically the stress intensity factor, or using more advanced approaches which require more complex and time-consuming FEA calculations. Recently, the ongoing trend has been to rely on the latter to demonstrate an adequate margin on the RPV for potential operation beyond 40 years: the question today is whether these existing methods will still provide adequate margins after 50 or 60 years of operation. In parallel to the conventional approach, a significant amount work has been performed over the past 20 years in France to adapt the historic Griffith energy release-rate approach [2] to engineering space. The work was initiated by Francfort and Marigo [3] who set up a new elastic fracture theory, extended from the Griffith approach. Within EDF R&D, Lorentz et al. [4] and Wadier et al. [5] have then relied on some of their ideas and applied them to the easier case of the propagation onset of a preexisting crack along a given crack path. Several ingredients are involved in this reduced formulation: the application of an energy minimization principle, the definition of a specific damage model and the use of a notch to represent the crack. Among other advantages, the Gp method has been developed as a true engineering approach, i.e. not relying on difficult and time-consuming models to set up. It is hence easy to implement in a FE software as a postprocessing of a mechanical calculation. The method has also been applied to various test cases and has shown the potential to increase margins. The drawbacks are that the method is likely restricted to 2D cases for practical reasons. The paper also provides an overview of the methods implemented in the EDF open source tool code_aster with a specific focus on the Gp approach.