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

Abstract

When a notched structure is loaded, its behaviour is not only affected by the material propertiesbut also by the geometry (of both the structure and the defect) and loading condition, alternatively termedas constraint condition. Therefore, the relation between the failure behaviour of a small scale fracturemechanics 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 bymeans of finite element simulations and compared for several test specimen geometries. A reference forcomparison is the crack tip stress field obtained from a high constraint reference geometry, further called amodified boundary layer model.First, this article provides some theoretical background on the modified boundary layer model. Second, thedevelopment of a 2D model is outlined in detail, focussing on the mesh design in the vicinity of the crack tipand the applied boundary conditions. Afterwards, an analytical and numerical validation is provided, basedon 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 comparisonindicates a weak influence of the T-stress on the Q-parameter for positive T-stresses. In contrast, negativeT-stresses result in more pronounced negative Q-values.

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“…A modified boundary layer model describes a two-dimensional disc containing a crack, loaded under plane strain conditions. More details regarding this type of geometry can be found in [61]. In this study, a displacement field u i is applied at the disc boundary corresponding to the theoretical displacement field associated with a stress intensity factor of K I = 89.2 MPa √ m.…”