Tensor Representation Method Applied to Magnesium Alloys

• Published in: Crystals (Basel) 2023-04, Vol.13 (5), p.719
• Main Author: Zubelewicz, Aleksander
• Format: Article
• Language: English
• Subjects: Aluminum; Analysis; Constitutive models; crystallographic reorientations; Crystallography; Deformation; Deformation mechanisms; Magnesium alloys; Magnesium base alloys; Manganese; Mathematical analysis; Mathematical models; Metals; Methods; Physics; Plastic flow; plasticity; Representations; Specialty metals industry; Streamlining; Temperature; tensor representation method; Tensors; Yield stress
• ISSN: 2073-4352; 2073-4352
• DOI: 10.3390/cryst13050719

The tensor representation method (TRM) offers tensorial tools suitable for streamlining the development of constitutive models. The TRM reduces the empiricism of phenomenological descriptions and provides physics-based justifications for the tensorial construction of material models. The method is presented in a stepwise manner, thus giving the reader an opportunity to appreciate the details of the concept. The selected material is magnesium alloy AZ31B (wt% composition: Mg 95.8, Al 3.0, Zn 1.0, and Mn 0.2), and the choice is not coincidental. The hexagonal close-packed (hcp) structure of rolled sheets exhibits highly directional plastic flow, while the crystallographic reorientations add to the complexity of the material’s behavior. A generic structure of the deformation mechanisms is determined first. In the next step, the TRM tools enable the coupling of the mechanisms with proper stimuli. Lastly, the thermo-mechanical flow rules for plasticity and twinning complete the constitutive description. The model predictions for Mg AZ31B have been compared with experimental data, demonstrating a desirable level of predictability.