PSI - Issue 19

Marc J.W. Kanters et al. / Procedia Structural Integrity 19 (2019) 698–710 Marc Kanters et al. / Structural Integrity Procedia 00 (2019) 000–000 magnitude of experimental � value by decreasing the notch radius. Furthermore, it appears that although the gradient might vary with sample orientation, there seems little angle dependence of � for a given . This indicates that for the theory of critical distances using a single value for characteristic length for all orientations suffices. Fitting ∗ on this dataset results in the gray lines in Figure 10a, showing that this single value yields an overall proper description within ±15% accuracy. Although this seems a proper accuracy, please be aware that, in consequence, the scaling of the local stress can easily introduce ± factor 5 error in lifetime. 707 10

Figure 10: � versus for different notch radii and sample orientations (a). Comparison of the Digimat material model and experiments for the notched specimens at , where different markers represent different notch radii, different colours the different sample orientations (b). Note that when also the test geometry used for the characterization of the material card comprises a minor gradient in stress, the material model requires recalibration using the corrected input curves. Like calibrating for the localization factor as illustrated in Figure 6, this requires an iterative loop with rescaling of the input curves using the � for that specific geometry, which could involve a different fitting compromise for the failure indicators, and re-computation of the experimental � and corresponding characteristic length. The consistency between model and experiments are displayed in Figure 10b. This shows that for the higher number of cycles there is a very good match between model and experiments. At shorter number of cycles, however, there appears to be a systematic underestimation by the model. This is related to the use of the linear elastic material model, which for high loads and small notch radii results in an overestimation of the local stress, hence underestimation of the lifetime. This can be solved by using an elastoplastic material model, but a computationally more favorable option is to correct via a plasticity correction according to e.g. Neuber or Glinka’s approach [Neuber1961, Molski1981]. The latter is currently being implemented within the Digimat software. 4.2.1. Local stress- and load ratio To validate the material model calibrated as discussed in section 4.1, a demonstrator part was developed, moulded, tested and modelled. The geometry is shown in Figure 12a. One can notice that the geometry is asymmetric, hence also the stiffness of the part is asymmetric and, consequently, the local stresses as function of the applied load differ when loaded in tension or compression. For example, as illustrated in Figure 11, when loading the demonstrator part with 1500N, the local maximum principal stress at the failure location is 94.3MPa. When applying the same load, but in opposite direction, the minimum principal stress at the failure location is -34.3MPa. In other words, although the force ratio, � , is -1, the local stress ratio, � , is only -0.36. 4.2. Validation on a demonstrator part