An assessment of mechanism-based plasticity models for polycrystalline magnesium alloys

TL;DR

This work compares two coarse-grained, mechanism-based plasticity frameworks (2S and 3S) for magnesium polycrystals against high-fidelity crystal plasticity data across textures and grain sizes to assess their ability to reproduce evolving anisotropy and tension–compression asymmetry. The 2S model aggregates all slip into a single glide surface while the 3S model splits slip into soft/basal and hard/non-basal surfaces plus twinning, with Norton-type flow rules and nonquadratic yield criteria for slip and twinning. Calibrated against a large CP dataset, both models show generally low global errors, with 2S excelling at macroscopic stress–strain predictions and 3S better capturing deformation anisotropy and micromechanics, especially for strongly textured or off-axis loading. The results guide practical model choice: use 2S for efficient, orientation- and texture-spanning analyses, and rely on 3S when detailed account of basal vs non-basal slip and twinning interactions is essential for damage and failure predictions in Mg alloys.

Abstract

The objective of this work is to assess computationally efficient coarse-grained plasticity models against high-fidelity crystal plasticity simulations for magnesium polycrystals over a wide range of textures and grain sizes. A basic requirement is that such models are able to capture {\it evolving} plastic anisotropy and tension-compression asymmetry. To this end, two-surface and three-surface plasticity models are considered. The two-surface constitutive formulation separately accounts for slip and twinning, while the three-surface model further apportions the contributions of basal and nonbasal slip. Model identification is based on stress-strain responses for loading along six orientations under both tension and compression. The evolution of overall plastic anisotropy, as well as microscale relative activities of slip and twin systems, is analyzed in detail. The prospects of using coarse-grained plasticity models in guiding the development of physically sound damage models for magnesium alloys are discussed.

Figures (87)

• Figure 1: Initial $[0001]$ and $[10\bar{1}0]$ pole figures projected on the LT plane for textures A-K. For a particular texture, the angles in the brackets indicate the maximum standard deviations in the Euler angles. Adapted from Baweja23.
• Figure 2: (a) Polycrystal setup with illustrative case of a material principal direction (S) aligned with the loading (y) axis is shown. Panel (b) shows the grain size distribution. Adapted from Baweja23.
• Figure 3: Calibrated stress-strain responses for material B with $\bar{d} = 10^4 \mu$m under uniaxial loading along principal material (left column) and off-axis (right column) directions. Symbols: CP data Baweja23, Dashed lines: 2S model, Solid lines: 3S model. Red: Compressive responses, Blue: Tensile responses.
• Figure 4: Predicted lateral strain, $E_{xx}$, for material B with $\bar{d} = 10^4 \mu$m under uniaxial loading along principal material (left column) and off-axis (right column) directions. Symbols: CP data Baweja23, Dashed lines: 2S model, Solid lines: 3S model. Red: Compressive responses, Blue: Tensile responses
• Figure 5: Predicted lateral strain, $E_{zz}$, for material B with $\bar{d} = 10^4 \mu$m under uniaxial loading along principal material (left column) and off-axis (right column) directions. Symbols: CP data Baweja23, Dashed lines: 2S model, Solid lines: 3S model. Red: Compressive responses, Blue: Tensile responses