Calculating hot spot stress and remaining fatigue life using the finite element method
Detailed finite element analysis of structures may make it difficult to evaluate the “nominal stress” to use together with the S-N curves, as some of the local stress due to detail is accounted for in the S-N curve. In many cases, it may be more convenient to use an alternative approach to calculate fatigue damage when local stresses are obtained from finite element analysis. In developing the finite element model, the mesh size needs to be fine enough to properly predict the hot spots in the element subject to fatigue. It is also important to have a continuous, and not too steep, change in the density of the element mesh in the areas where the hot spot stresses are to be calculated. In addition, the size of the model should be so large that the calculated results are not significantly affected by assumptions made for boundary conditions and the application of loads.
After calculating the hot spots, stress points within a distance of 0.5 t and 1.5 t away from the hot spot need to be evaluated, where “t” is the plate thickness (plate thickness at the weld toe where the hot spot at the connection point is evaluated). These locations are also denoted as stress read-out points. These hot spot stress values need to be compared with the specified fatigue upper limit in a linear analysis (Fig. 5).
In another approach, and in case the need arises to model stationary discontinuities, such as a crack, the conventional finite element method requires the mesh to conform to the geometric discontinuities. Therefore, considerable mesh refinement is needed in the crack tip area to capture the singular asymptotic fields adequately.
Modelling a growing crack is even more cumbersome because the mesh must be updated continuously to match the geometry of the discontinuity as the crack progresses. The extended finite element method (XFEM) alleviates the shortcomings associated with meshing crack surfaces. It is an extension of the conventional finite element method, which allows local enrichment functions to be easily incorporated into a finite element approximation. The presence of discontinuities is ensured by the special enriched functions in conjunction with additional degrees of freedom (Fig. 6). However, the finite element framework and its properties, such as sparsity and symmetry, are retained.