Crack singular field evaluation with characteristic tensor considering residual stress

ABSTRACT

To accurately evaluate the fracture behaviour and fatigue life of welded structures, it is necessary to consider welding residual stress in addition to the stress produced by the applied loads. Characteristic tensor, which has a proportional relationship to stress intensity factor (SIF), is one new approach to evaluate stress singularity caused by a crack. Characteristic tensor is the tensor that is easily calculated by integrating stresses in a simple sphere zone around a crack tip using coarse mesh without special limitation in the mesh division, even under general cases like mixed-mode loading conditions. In this study, the stress singularity in the welded plate is evaluated by characteristic tensor and its effectiveness with the residual stress field is verified. Firstly, the residual stress distribution in butt-welded plates is calculated by the finite element method. Secondly, the singular stress field is obtained by introducing a single straight crack in the welded plates. A crack with different lengths and the crack tip located at different residual stress states are considered in reproducing the stress singularity. In each case, SIF is estimated from the characteristic tensor calculated from stress distribution nearby a crack tip and compared to those from the Green’s function or virtual crack extension method. Additionally, the stress singularity caused by the external load is evaluated in the same manner. The estimated SIFs with coarse mesh are in good agreement with the conventional methods. The results suggest that characteristic tensor provides a practical approach to evaluating stress singularity in welding structures.

KEYWORDS:

• Characteristic tensor
• stress intensity factor
• stress singularity
• residual stress
• finite element method