Benchmark of Finite Elements and Extended-Finite Elements Methods for Stress Intensity Factors and Crack Propagation

Abstract

Stress intensity factors (SIFs) are a major feature in regulatory analyses of Nuclear Power Plants (NPP) components, as they allow to rule on the acceptability of defects when compared to a critical experimental value (K1c). Simplified and robust evaluations of SIFs have been provided in major regulations standards for cracks having usual geometries and locations in major components. However, their evaluations still require a significant effort in the case of important deviations of the geometry of cracks regarding the usual semi-elliptical shape, or in the case of specific geometries of components, and specific locations of cracks in components. In these cases, time-consuming Finite Element meshes must be constructed, either manually or using semi-automatical tools, to represent the components and its defect(s). This method can become particularly costly, especially in the case of fatigue crack propagation. The eXtended-Finite Elements Method (X-FEM) has been proposed to overcome this issue. The representation of the defect is carried out by the level-set method, and specific enrichment functions are used to represent the solution near the crack surface and the crack front. This paper proposes a benchmark of numerical predictions of stress intensity factors using SYSTUS software [5]. It will be based on: a) Available analytical solutions; b) Classical Finite Element method; c) EXtended-Finite Elements Method. The classical case of a circular and elliptical crack in a semiinfinite body is first presented. Then the case of a circumferential crack in a valve under a thermo-mechanical loading is analyzed. The accuracy of the different methods is then compared and discussed.