Issue 41

M. Vormwald et alii, Frattura ed Integrità Strutturale, 41 (2017) 314-322; DOI: 10.3221/IGF-ESIS.41.42 320 Figure 8: Crack tip parameters measured and calculated for specimen R-033, phase shift 45° between tension 33kN and torsion 382Nm loads. The second simulation was done with the R-031 specimen (axial and torsional non-proportional mixed load). The crack path was modeled by defining a surface where two parts of the geometry-model are connected. The surfaces (future crack faces) were initially connected with normal surface-to-surface contact, whose properties were changed when a contact surface was being opened. No penetration was allowed in the normal direction and friction was neglected between the crack surfaces. The growth of the crack was achieved by switching these tie constraints along the crack surface to normal contact properties. Due to the complicated geometry of the 3D crack surfaces, linear tetrahedral elements were used to mesh the model. In the simulation, crack growth steps of 1 mm were applied. This step size is not actually recommended. However, achieving convergence was a bigger challenge in this simulation and this large step size was mandatory to achieve any result at all. After several iterations, convergence was achieved up to a crack size of 5 mm. It was not possible to attain convergence after this point, due to the many sources of nonlinearity such as the contact conditions and the complex plasticity model, see [14] for details. Note that, this simulation includes plasticity induced crack closure. The crack closure from the simulation and the experiment for a crack length of 4 mm is given in Fig. 9. In the experiments, the criterion for crack closure was whether the COD was negative or positive. In the simulations, the contact at one of the nodes on the crack surface was considered to be enough for the crack to be closed. The observed crack opening and closing times differ slightly between the simulation and the experiments. Therefore, it can be concluded that the crack closure ranges from simulations can be seen as an acceptable source of information regarding crack closure ranges. More simulations have to be done in the future with other phase angles, or other types of non-proportional loadings to derive an overall conclusion. However, this comparison can be seen as promising and is expected to be a good foundation for future studies. A second result from the simulations was the crack tip parameters calculated from these simulations. As indicated before, the effective cyclic  J eff -integral was used as a crack tip parameter. For the crack lengths of 3mm and 4mm and the given loading pattern nearly identical values of  J eff  5 N/mm were obtained. Transformed to an equivalent, plasticity-corrected stress intensity factor gives  K J,eff  32 MPa  m. This value can be compared to the corresponding values derived from the DIC-investigation and by applying Eq. (5), Fig. 7. Although the DIC-based values are in the order of magnitude, they appear to be larger, possibly due to the capturing of the mode III contribution. Comparing fatigue crack growth rates for pure mode I (R-028) and non-proportional mixed mode (R-031) it can be concluded that a valid mixed mode hypothesis 0 25 50 75 100 125 150 175 200 225 1 2 3 4 5 6 7 8 9 10 [MPa√m] a*[mm] ΔK vs a*. R-033 ΔKI ΔKII ΔKIII ΔK S3D ΔK ES -50 -40 -30 -20 -10 0 1 2 3 4 5 6 7 8 9 10 θo [deg] a*[mm] θo vs a*. R-033 θo θo S3D θo ES -90 -80 -70 -60 -50 -40 -30 -20 -10 0 0,0 0,5 1,0 1,5 2,0 2,5 1 2 3 4 5 6 7 8 9 10 θo[deg] ΔKi/ΔK I a*[mm] ΔKi/ΔK I vs a* R-033 ΔKII/ΔKI ΔKIII/ΔKI θo -20 0 20 40 60 -20 0 20 40 60 K II K I K I vs K II [MPa√m]. R-033 15000 14500 14000 13000 12000 11000 10000