PSI - Issue 28

F. Conrad et al. / Procedia Structural Integrity 28 (2020) 2195–2205 F. Conrad, A. Blug et al. / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 5. Full-field analysis of a biaxial measurement. (a) Displacement in x-direction (y-direction is similar). (b) Divergence of the displacement field. (c) Rotation of the displacement field. The crack contour (green line) is a 7 th degree polynomial fitted to the divergence. The green arrows mark the rotation gradients perpendicular to the crack contour for crack tip detection. As a reference for the biaxial crack growth experiment a FEM simulation was performed to compare the DIC measured displacement field. Due to the low thickness in the center of the specimen, plane-strain-conditions are assumed to be prevalent over the whole cross section. With this adaptation, a suitable two-dimensional model was established which requires less meshing effort and calculation resources than a three-dimensional model. Furthermore, the model forms a basis to implement an incremental crack-path detection routine for two dimensional cases that will be used for experimental design and theoretical review of experiments, Conrad et al. (2018). The modelling strategy will be outlined in the following starting with Fig.6.

Fig. 6: (a) Cross section of cruciform geometry through the center (left) indicating the approach of discretization. (b) Two-dimensional FEM model with crack-contour from experiment modelled as a seam. The left side of Fig. 6 shows the cross section along axis A through the center of the specimen geometry. Within the two-dimensional reduction the concave taperings leading to the center of the specimen are discretised as areas with constant thicknesses in a first step. The right side of the cross section shows the explained approximation with overlaid rectangles and their respective thickness. In a second step a 2D-planar-shell-model in the FEM-Software Abaqus TM Fig. 6. is generated. The discretised areas of tapering are modelled as two dimensional sections with the respective thickness lodged for plane stress/strain calculations. The sections appear as rings on the top view of the model and lead to an approximate relationship between the external forces and the prevalent stresses and strains in the center.