PSI - Issue 13

Moritz Lessmann et al. / Procedia Structural Integrity 13 (2018) 1232–1237 Author name / Structural Integrity Procedia 00 (2018) 000–000

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2.1. Mixed Element Type Meshing By adopting a mixed element type meshing strategy of hexahedral elements in the near-defect region and second order tetrahedral elements in the remaining structure, it is possible to achieve a highly refined and structured radial mesh along the defect front, whilst permitting sufficient resolution of other features. Tied constraints are adopted to connect the two element type regions. Contours for calculation of J-Integral/SIFs should lie fully within hexahedrally meshed region, such that the size of this region is driven by the adopted mesh density and contour convergence. Experience of the authors in austenitic stainless steel has shown that a size of 0.5 – 1 mm in all directions from the crack tip is generally sufficient, within which 10-30 radial rings of planar elements are defined. However, this is dependent on the size of the assessed component, the adopted mesh density and the convergence of the J-Integral / SIFs, since the region must contain the complete contour region. As for any tied interfaces in finite element models, care should be taken to ensure that there isn’t a mismatch in the element size across the interface. Convergence checks on the mesh density within both regions is highly recommended. Examples of tied mixed element type regions are illustrated in Figure 2.

Figure 2 – Illustration of mixed element type meshing strategy on the surface (a) and along a defect front (b)

Figure 3 – Hexahedral (a) and mixed element type (b) meshing approaches to a semi-elliptical internal surface breaking defect in a cylinder. Comparable and smooth stress contours are observed across the transition in all cases

The effect of the mixed element type meshing strategy and tied constraint in proximity to a crack front has been assessed for a semi-elliptical internal surface breaking defect in a cylinder under axial, bending and pressure loading. Two different tetrahedral meshes with intentionally coarse elements in either direction of the transition are chosen and compared to a fully hexahedral mesh. In both cases smooth stress and strain contours are observed across the transition, see Figure 3. Differences in the computed J-Integral values between the three meshes and relative to the analytical solution are below 0.1% when considering elastic material properties. When an elasto-plastic material response is considered, additional attention to the mesh refinement must be paid. This is a general requirement and should always be addressed in the form of a mesh refinement sensitivity study. However, even for the extremely coarse tetrahedral meshing in proximity to the tied constraint in Figure 3 (c), a solution deviating by less than 0.3% is found. The use of a tetrahedral mesh, even with poor-quality elements, is therefore shown to not have a significant effect on the CBFEA results provided the mesh is sufficiently refined. This conclusion extends to more complex geometries