Development and validation of a high constraint modified boundary layer finite element model

When a notched structure is loaded, its behaviour is not only affected by the material properties but also by the geometry (of both the structure and the defect) and loading condition, alternatively termed as constraint condition. Therefore, the relation between the failure behaviour of a small scale fracture mechanics test and a full scale structure needs to be elucidated. In an attempt to understand and describe such relationships, the crack tip stress fields are analysed by means of finite element simulations and compared for several test specimen geometries. A reference for comparison is the crack tip stress field obtained from a high constraint reference geometry, further called a modified boundary layer model. First, this article provides some theoretical background on the modified boundary layer model. Second, the development of a 2D model is outlined in detail, focussing on the mesh design in the vicinity of the crack tip and the applied boundary conditions. Afterwards, an analytical and numerical validation is provided, based on the level of the applied load and, on the other hand, on the magnitude of the crack tip stress fields. Finally, this validated model is used for the comparison of several constraint parameters. This comparison indicates a weak influence of the T-stress on the Q-parameter for positive T-stresses. In contrast, negative T-stresses result in more pronounced negative Q-values