PSI - Issue 28

R. Moreira et al. / Procedia Structural Integrity 28 (2020) 943–949 R.Moreira et al. / Structural Integrity Procedia 00 (2019) 000–000

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the magnesium hardening in compression is lower than in tension. Also cannot capture accurately the plastic strains and back stresses. This incapability is more evident for higher strains levels. For the shear component, the Armstrong Frederick model estimate much lower maximum stress limits than the experimental tests. Regarding the non-proportional loadings, the Armstrong-Frederick model also fails to follow the experimental results. For the strain level of 0.83% the HYPS model results are close to the experiments. However for 1.14% of strain level, the model cannot follow with acceptable accuracy the shear mechanical behaviour, despite estimating the plastic strains, the back stresses and the stresses at maximum total shear strain for both loading directions with very good accuracy. Due to the fact that the HYPS model is based on a polynomial function it has difficulties to accurately follow the shape of the axial and especially of shear stress-strain curves of the non-proportional loading. This becomes more evident for higher strain levels. The main advantage of the HYPS model comparatively with Armstrong-Frederick model is the possibility to simulate the strain amplitude ratio effect in the elastic-plastic behaviour, in other words, the HYPS model takes into account the loading type and strain level, so it can accurately capture the plastic deformation mechanisms (twinning and de-twinning), that occur in the cyclic response of magnesium alloys during multiaxial proportional loadings. 5. Conclusion The experimental results were correlated with the well-known Armstrong-Frederick model and the phenomenological HYPS elastic-plastic approach that was successful implemented in a commercial finite element program Abaqus/standard 6.14 through an external subroutine (UMAT). The HYPS model implemented in the subroutine strictly follows the HYPS analytical model, for all loading paths and strain amplitudes. The Armstrong Frederick model showed poor estimations especially for high strain amplitudes, these results are explained by its inability to follow the asymmetric mechanical behaviour of magnesium behaviour. In multiaxial proportional loadings with strain amplitude ratio for the condition of 30 ° the HYPS model followed with very good accuracy the stress strain curves however a slight deviation was observed for strain levels of 1%. For 90 ° out-of-phase loading with strain level of 1.14% the HYPS model fails to capture the shear behaviour, despite the model estimate very well the stress for the maximum total strain amplitude, the plastic strain and back stress, for both loading directions. Acknowledgements The authors gratefully acknowledge financial support from FCT - Fundação para Ciência e Tecnologia (Portuguese Foundation for Science and Technology) through the project PTDC/EME-PME/104404/2008 and LAETA/IDMEC, project UIDB/50022/2020. References Yu Q., Zhang J., Jiang Y., Li Q., 2011. Multiaxial fatigue of extruded AZ61A magnesium alloy. International Journal of Fatigue 33(3):437–447. Xiong Y., Yu Q., Jiang Y., 2012. Multiaxial fatigue of extruded AZ31B magnesium alloy. Materials Science and Engineering: A 546:119–128. Reis L., Anes V., Li B., Freitas M., 2013. Characterizing the Cyclic Behaviour of Extruded AZ31 Magnesium Alloy. Materials Science Forum, Trans Tech Publ. pp. 727–732. Albinmousa J., Jahed H., 2014. Multiaxial effects on LCF behaviour and fatigue failure of AZ31B magnesium extrusion. International Journal of Fatigue 67:103–116. Anes V., Freitas M., Reis L., 2015. Evaluation of a new Phenomenological Cyclic Elastic-Plastic Approach for Magnesium Alloys. Congresso de Métodos Numéricos em Engenharia. Anes V., Moreira R., Freitas M., Reis L., 2018. Magnesium alloy elastoplastic behavior under multiaxial loading conditions. 18th International Conference on New trends in fatigue and fracture. Anes V., Reis L., Freitas M., 2019. Evaluation of a phenomenological elastic-plastic approach for magnesium alloys under multiaxial loading conditions. Fatigue & Fracture of Engineering Materials & Structures 42: 2411-2608.