PSI - Issue 42

1596 Lucas Mangas Araújo et al. / Procedia Structural Integrity 42 (2022) 1591–1599 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 It is noted from Fig.3 that the SAE 1045 steel is not a von Mises type material, since the 2 -formulation cannot describe its behavior in shear conditions. Therefore, this material Ductile Fracture response has 3 -dependence. Moreover, the blue square-dashed curve furnished by the simulation with = 0 and = −60.0 shows better agreement with the experimental curve, which demonstrates that more accurate predictions are indeed achieved by considering 3 . The shaded region on t he left portion of Fig.3 depicts the differences between von Mises and Gao’s approaches due to 3 . Interestingly, Fig.3 shows that the activation of b lowers the numerical reaction curve towards the experimental one. The higher b (limited by the model convexity), higher it is the downward movement produced. With = −60.0 , a similar analysis is used to compute a by the experimental reaction curve from the vertical tensile test (” Butterfly +90◦” in Table 1). Thus, the Mises numerical response ( = = 0) is registered to analyze whether 1 influences the material behavior. The red star-dashed lines in Fig.4 represents the referred numerical reaction curve. 6

Fig. 4. Comparison between the numerical responses of Mises and Gao based formulations with the experimental reaction curve for the vertical tension test (+90◦ loadin g direction). On the left, only is activated, while on the left both and are considered. Several simulations were conducted with different and keeping = −60.0 fixed. The search interval was defined as [0.0001, 1.0] , also based on works in the literature. The best result was reached with = 0.0005 , and the numerical reaction curve (green triangle-dashed line) is shown on the right plot on Fig.4. The correction obtained by the incorporation of 1 is substantial and demonstrates the strong influence of this parameter in tensile (or compressive) conditions. The shaded region on the right plot in Fig.4 highlights the difference between von Mises and Gao’s reaction curves due to 3 and 1 . 3.3. Ultra-Low Cycle results. The Ultra-Low Cycles tests were simulated using the a and b values calibrated with the monotonic data. Figures 5 and 6 display the numeric reaction curves obtained from the Finite Element simulations of the compression-tension tests (−90◦ to + 90◦ ). As observed in Fig.4, in both cases 1 is the key factor controlling SAE 1045 ULCF behavior in compression- tension. This latter confirms the remarks pointed out previously in Fig.4. Nevertheless, the Gao’s based simulations were not satisfactorily close the experimental versus data, as in the monotonic case. This suggests that perhaps a recalibration of and for ULCF applications is required. The shaded regions on the left plots of Fig.5 and 6 represent the effect of 3 , while on the left express the effect of both 1 and 3 .