PSI - Issue 25

Corrado Groth et al. / Procedia Structural Integrity 25 (2020) 136–148

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C. Groth et al. / Structural Integrity Procedia 00 (2019) 000–000

Fig. 2: Above: RBF setup for the crack morphing; bottom: baseline and morphed mesh.

In Figure 1 the round bar with notch radius ρ equal to 2 mm is shown. Other measures, complying with the already cited work by Carpinteri, are D 0 = 16 mm and D = 20 mm , maintaining a bar lenght of 80 mm in order to extinguish any boundary e ff ect, and a tensile load of 30 kN . The crack geometry was added to the bar by taking advantage of the fracture mechanics tool (FT) implemented in Workbench TM , that allows to insert a given crack geometry by locally modifying a pre-existing mesh. After a mesh convergence test with respect to the notch concentration factor ( K t computed equal to 2.214, com paring to a theoretical reference of 2.2 from Pilkey and Pilkey (2008)), a first benchmarking was executed on a predefined set of crack geometries to test the reliability of the numerical results obtained by RBF mesh morphing comparing them to a full remeshing. The employed computational grid, which mesh count is 29k elements and is composed of 10-nodes iso-parametric tetrahedrons, was modelled employing quarter-point wedges around the crack front in order to correctly capture the stress singularity for the SIF calculation. The RBF setup employed to morph the baseline crack is shown in fig. 2. Crack deformation was achieved by controlling three lines: one following the crack and two following the already mentioned set of quarter-point wedge elements around the defect on a perpendicular plane with respect to the notch. This strategy was followed in order to accurately deform the crack while maintaining a proper aspect ratio of the wedge elements around of it to guarantee a satisfactory SIF calculation. Several runs were carried changing the crack aspect ratio, defined as α = a / b , under a tensile static load of 30 kN . To compare results to literature data, the curvilinear abscissa and the resulting SIF were normalized by following these relations:

K I σ F √ π a

4 F π D 2 0

ζ h

ζ ∗ =

K ∗ I =

where σ F =

(11)

,

In fig. 3 left, the comparison of the SIF values along the normalized curvilinear abscissa is shown between the geometries obtained with a morphing action or by inserting cracks in the mesh using the FT tool. On the right image