40 V. Arra` et al. correlation between triaxiality and fracture behavior. Dremeier specimen revealed a strain to failure slightly lower than P1 and P2. Consequently, the comparison between the results obtained with empirical ductile damage models showed that the Bao-Wierzbicki model better represents the material’s behavior compared to the Rice-Tracey or Cockcroft-Latham models. Figure 6a shows the trend of strain to failure as a function of stress triaxiality T in quasi-static conditions. The extension to strain rate as a third axis leads to the bi-cubic surface given in Figure 6b. a) b) Fig. 6 Calibrated Bao-Wierzbicki: a) application to quasi-static data; b) extension to strain rate effect by polynomial surface The results demonstrate the validity of the chosen approach to describe the behavior of 550W steel under dynamic loads. The FEM methodology enabled the investigation of phenomena that are not directly measurable in the laboratory, such as the evolution of strain and stress tensors and the fracture surface. The Bao-Wierzbicki damage model showed high predictive capability for fracture in complex loading states. Nevertheless, Figures 7 show that the trend of the material ductility with strain rate is not very smooth; as a result, the simple quadratic law appears to be not well representative, whereas the cubic law is affected by a certain overfitting effect; further investigation is needed, especially at an intermediate strain rate. a) b) c) Fig. 7 Trend of strain to failure at different strain rates and triaxiality values according to quadratic or cubic surface fitting: a) T=0.14 (Driemeier samples), b) T=0.34 (P1 and P2 samples), c) T=0.54 (P3 notched samples) Conclusion The research confirms the reliability of the adopted approach in predicting the behavior of 550W steel under operational conditions and provides a significant contribution to the modeling of ductile damage in structural materials. The methodology adopted allowed for an accurate description of the material’s behavior and successful calibration of the Bao-Wierzbicki damage model. The results can be applied to the railway industry to improve the performance of crash absorbers.
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