On the Quantification of the Constraint Effect Along a Three-Dimensional Crack Front

Elbows with a shallow surface cracks in nuclear pressure pipes have been recognized as a major origin of potential catastrophic failures. Crack assessment is normally performed by using the J-integral approach. Although this one-parameter-based approach is useful to predict the ductile crack onset, it depends strongly on specimen geometry or constraint level. When a shallow crack exists (depth crack-to-thickness wall ratio less than 0.2) and/or a fully plastic condition develops around the crack, the J-integral alone does not describe completely the crack tip stress field. In this paper, we report on the use of a three-term asymptotic expansion, referred to as the J-A 2 methodology, for modeling the elastic-plastic stress field around a three-dimensional shallow surface crack in an elbow subject to internal pressure and out-of-plane bending. The material, an A 516 Gr. 70 steel, used in the nuclear industry, was modeled with a Ramberg-Osgood power law and flow theory of plasticity. A finite deformation theory was included to account for the highly nonlinear behavior around the crack tip. Numerical finite element results were used to calculate a second fracture parameter A 2 for the J-A 2 methodology. We found that the used three-term asymptotic expansion accurately describes the stress field around the considered three-dimensional shallow surface crack.