PSI - Issue 33

Umberto De Maio et al. / Procedia Structural Integrity 33 (2021) 954–965 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Table 2. Material parameters for the traction-separation law used in the L-shaped plate test. max  [MPa] max  [MPa] Ic G [N/m] IIc G [N/m] 0 n K [N/mm 3 ] 0 s K [N/mm 3 ] DIM 2.7 3.81 95 475 2.0018E14 1.0659E14 ECM 2.7 - 95 - - -

Similar to the computational discretization adopted for the mode-I analyses, reported in Section 3.1, the cohesive interface and the breakable solid elements, used in the DIM and ECM, respectively, are placed only in the damage zone (see Fig. 6a), whose location and size are predetermined from the experiments. Here, a Delaunay tessellation with three-node bulk elements four-node zero thickness elements has been considered for the DIM simulation (Fig. 6b), whereas a mapped discretization with eight-node constant-stress user-defined solid elements is adopted for the ECM simulation (Fig. 6c). A free quadrilateral tessellation is performed for both models in the remaining part of the specimen. The numerical analysis associated with the DIM model has been conducted under quasi-static loading condition by means of a displacement-controlled path following scheme. On the other hand, an explicit solver, with a suitable loading rate to avoid inertial effects, has been used for the ECM simulations.

Fig. 7. Comparison between DIM and ECM approaches in terms of load versus displacement  curve.

Fig. 7 shows the load versus displacement  curves predicted by the DIM and ECM models, together with experimental results taken for comparisons purposes from (Winkler, 2001). The DIM model, as expected, provides a slightly stronger structural response respect to the ECM model, especially at the peak load and in the first part of the softening stage, due to the artificial toughening effect induced by the discretization. However, the numerically predicted curves are very close to each other showing only a little deviation from the experiment envelope in the second part of the softening branch, probably due to the fact that the friction behavior is not implemented in the adopted numerical models. Moreover, some numerical convergence problems associated with crack locking occur in the final part of the loading curve predicted by ECM model. In Fig. 8 are reported the crack patterns predicted by the adopted models at simulation steps A and B highlighted in the loading curve of Fig. 7. In particular, in this case, the DIM approach appears to be closer to the lower limit curve of the experimental envelope, thus showing a more realistic overall fracture pattern. On the other hand, the ECM crack prediction, results to be slightly outside the experimental envelope. Such a result highlights little estimation