PSI - Issue 34

Sigfrid-Laurin Sindinger et al. / Procedia Structural Integrity 34 (2021) 78–86 S.-L. Sindinger et al. / Structural Integrity Procedia 00 (2019) 000–000

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intersection. Initial failure of the bottom skin is not unexpected for the given loadcase and was observed in a similar location for all tested samples (see Fig. 4b). Rib fracture occurred in a brittle manner without considerable plastic deformation and typically led to abrupt collapse of the entire structure. Solely the third sample from the top in Fig. 4b did not break into two separate pieces immediately after initial rib failure due to arrest of crack propagation.

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Fig. 4: ( a ) First captured rib failures during bending test and ( b ) samples with fracture locations indicated via red lines .

Load-displacement D curves of the bending experiments are shown in Fig. 5a, including individual measured curves as well as mean failure and standard deviation indicated as × -marker, dashed lines and shaded area, respectively. Moreover, load-displacement results obtained from the FE analysis are displayed as markers, color-coded with the highest Hill failure index H occurring in each simulation increment. Three model versions were investigated that were identical in terms of mesh and boundary conditions but varied regarding the elastic material parameters and the approach of strength assessment. The sti ff ness of the first model, FE HH , was defined by a single homogeneous material for the entire beam. Also, for the failure prediction, no thickness e ff ect was considered. As would be conventional practice, the experimentally determined material parameters using the standard ISO 527 type 1A tensile coupons, which are 4 mm thick, were utilized. Both other versions were modeled using the property mapping strategy, making the elastic parameters vary according to local element thickness and orientation. The di ff erence between FE MH and FE MM was the implementation of the homogeneous (4 mm) and the thickness dependent failure criterion, respectively. When the load-displacement curves between experiment and simulations are compared, it becomes obvious that map ping the thickness dependent orthotropy leads to a considerable improved prediction of the sti ff ness response, as is elaborated in-depth by Sindinger et al. (2021b). Considering the prescribed enforced displacement and the absence of reduced elastic parameters in the FE HH model, resulting stresses predicted failure at a displacement almost 35 % lower than it actually occurred in the experiment. While the mapped variants were over 15 % closer to the measured failure displacement, a substantial underestimation of approximately 18 % remained. Thereby, the consideration of H ( t ) (see Eq. 4) in FE MM , wherein the structure is assessed based on deteriorated strength of thin ribs, led to failure prediction one simulation increment earlier than FE MH . Di ff erences in tested and predicted reaction force at failure were similar between simulation variants and leveled around 10%˙ below the actual measured value. In Fig. 5b- 5d, contour plots of the failure index are depicted for the first displacement increment D ∗ at which an element scored a value larger than one (i.e. element failure), which corresponds to the vertical red dotted line s in Fig. 5a. The predicted failure locations are similar between models, however, in the sti ff er homogeneous FE HH , two elements are estimated to fail, opposing a single element in the inhomogeneous variants. On a first glance, these locations coincide exactly with the ones captured in the physical experiment (see Fig. 4a). Among closer inspection, however, it is disclosed that on the bottom skin not the region inside the junction of three ribs fails but rather the adjacent one to the outside. Further, it can be stated that for the mapped models the central section of the bottom skin does not surpass a failure index of 0.75 suggesting reserves in the load bearing capacity.