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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and loading scenarios, with smooth stress and strain contours across the transition observed by the authors for a range of industrial components assessed with elastic and elasto-plastic material models. 2.2. Node Transformation Techniques For simple geometries and straight defect fronts, it is generally possible to obtain adequately structured hexahedral mesh qualities with commercially available software. The desired mesh structure is defined on the outer surfaces and then extruded along the defect front, as shown in Figure 2 (b). Challenges can arise for curved defects and straight defects positioned in proximity to geometrical features or transitions. In such cases, commercial mesh algorithms can struggle to produce a suitable mesh, often not achieving the required planes of nodes forming the contour integrals aligned normal to the defect front. For such cases, a multi staged approach to generating a suitable mesh has been developed, consisting of the transformation of a regular mesh into the required defect shape. The steps for this approach are outlined below: 1. The main model is meshed with a commercial software. A region surrounding the defect front, which would otherwise be meshed with hexahedral elements, is excluded from the model, such that a cut-out exists in the resulting mesh. Since this mesh is excluded from the contour integral calculation, tetrahedral elements may be used for this global mesh. The mesh seeding in proximity to the cut-out should be chosen to be compatible with the seed density adopted in step (2). 2. A mesh for a rectangular box is generated with a commercial meshing algorithm. The width and depth of this model should correspond to the size of the cut-out in (1), its length to the approximate length of the defect front. Focussed hexahedral elements as detailed in section 2.1 are extruded along the length of the box. Since this model is not curved, meshing algorithms will generate contour planes which remain normal along the length. 3. The mesh generated in (2) is exported. The nodal coordinates can then be modified via a transformation into the required defect shape (i.e. a semi-ellipse). Geometrical transformation functions for a range of geometries are readily available and may be implemented in an automated script. 4. For components with non-planar surfaces (e.g. pipes) at the extremities of the defect front, a further transformation is required of the end nodes. 5. A final modification of coordinates is required for mid-side nodes to ensure these lie mid-way between their respective corner nodes. Combining the modified nodal coordinates with the original element definition provides a local hexahedral mesh, its size and geometry corresponding to the cut-out in the global mesh. The above steps are illustrated in Figure 4. The local and global mesh are combined, with tied constraints defined on the mating surfaces. Since the position of the nodes is defined through the geometrical transformation, contour planes are guaranteed to lie normal to the defect front. An example of a mesh generated for a surface-breaking semi elliptical defect in a toroidal pipe is illustrated in Figure 5.

Figure 4 – Illustration of the nodal transformation technique for obtaining the near-defect front mesh region