PSI - Issue 61

Necdet Ali Özdür et al. / Procedia Structural Integrity 61 (2024) 277–284 N.A. O¨ zdu¨r et al. / Structural Integrity Procedia 00 (2024) 000–000

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Fig. 5. The evolution of Taylor-Quinney coe ffi cient as (a) measured experimentally; (b) obtained from simulation; (c) rolling texture used in the polycrystal simulation.

it can be seen that not only it is not constant, but also for Magnesium it is found to be considerably low; indicating majority of the plastic work applied is stored in the material ( W b , magenta curve in Fig. 4). The median value (0.4), indicated by the red line on β plot is in agreement with the value given in the Kingstedt and Lloyd (2019), which is about 0.35 for twin dominated deformation. The advantage of variational formulation, which is briefly introduced earlier, is that it ensures thermodynamic consistency when hardening and rate dependency relations are defined as derivations from potential functions W and ∆ ∗ , respectively. Since the value of the Taylor-Quinney coe ffi cient only depends on the form of these potentials, this framework allows an a priori calculation of β as well. Now that its evolution under deformation is experimentally found, this information will be used in validation of thermomechanical fidelity of an established crystal plasticity model. The overall dissipation characteristic predicted by the polycrystal simulation is given in the Taylor-Quinney coe ffi cient evolution graph on Fig. 5(b). Similarly indicated by a red line, the median β value of the simulation is about 0.2, which is lower than both the experimentally measured value and the value reported in the literature. This indicates that the overall hardening behavior generated by this model and set of model parameters under-predicts the dissipation characteristic (rate dependency) and puts more weight on energy storage mechanisms. In this work, a novel thermomechanical investigation method is detailed, which aims to verify thermodynamic consistency in crystal plasticity models. The methodology is applied on a Magnesium AZ31 sample with rolling texture by loading it in a way that mainly activates tensile twins and simultaneously recording its surface temperature using an IR camera. The combined stress, strain, and temperature measurements obtained from the experiment is used to compute energetic contributions of di ff erent thermomechanical processes and ultimately the dissipated portion of the applied plastic work, β . The experimental value for β is found to be close to the value presented in the literature. The additional information on dissipative behavior is then used to check the thermomechanical validity of a simple crystal plasticity model. This is achieved by comparing the median β value from the experiment to the crystal plasticity simulation. The model used in the simulation is formulated in variational framework, so it is inherently thermodynam ically consistent. However, the simulation results hints at that the currently used model parameters cannot accurately capture the dissipative characteristic of Magnesium. 4. Conclusion

Acknowledgements

This work was partially supported by the “PHC Bosphore” programme (project number: 46626ZM), funded by the French Ministry for Europe and Foreign A ff airs, the French Ministry for Higher Education and Research and the Scientific and Technological Research Council of Turkey (TU¨ B˙ITAK), Grant No: 120N722.