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Phase field models have gained growing popularity in fracture analysis. However, phase field modelling still remains lacking for complex real-life applications such as structural crushing analyses to date. The novelty of this study is to propose an explicit phase field modelling framework considering complex loading history to predict the crushing behaviour of additively manufactured metallic structures. Firstly, the explicit phase field model is formulated by considering stress state dependent fracture initiations with non-proportional loading. Second, five types of material specimens with a wide range of stress states were experimentally tested to calibrate material parameters for additively manufactured 316L steel and Ti-6Al-4V titanium. Third, the square tubes were 3D-printed and tested under three-point bending and axial compression to demonstrate the capacity of the proposed model. The modelling results unveil that the crushing behaviour of both the materials could be properly reproduced in terms of force-displacement curves and crack paths. Finally, the fracture mechanism of crushing deformation is analysed. For the three-point bending of Ti-6Al-4V tubes, cracks were mainly induced by the medium stress triaxiality tension and shear loading. For the axial compression of 316L tubes, the stress states of critical elements were relatively diverse yet slightly concentrated at the shear, compression-shear, and high stress triaxiality tension regions. Remarkably, non-proportional loading is significant in crushing deformation as a material point may experience a significant change in stress state with loading. By considering a non-proportional loading dependent threshold, the proposed phase field model can predict the crushing behaviour of structures even when the fracture initiations do not locate on the fracture locus. This study provides an effective explicit phase field framework featured with an insightful fracture mechanism for quasi-static crushing of additively manufactured metallic materials.
Li et al. (Tue,) studied this question.