Plasticity-Twinning Interactions in Magnesium
Owing to its hcp crystallography, deformation mechanisms of magnesium involve both deformation twinning and plastic slip. To describe and understand, and ultimately to predict the mechanical response of Mg and Mg alloys, we develop a theoretical-computational framework that captures the intricate interaction mechanisms of twinning and dislocation activity and thus provides a basis for
- understanding microstructural deformation mechanisms,
- describing the resulting effective macroscopic mechanical response,
- predicting effective mechanical behavior,
Figure: the effective response of polycrystalline Mg (resulting from slip and twinning) is modeled by (i) an effective crystal-plasticity model based on plastic slips and twin volume fractions as internal variables, and (ii) a combined phase field/continuum dislocation model based on a twinning phase field parameter and the plastic slip distribution.
On the one hand, we have combined a phase field model that describes the deformation twinning process with a gradient plasticity description (or, continuum dislocation theory) which models dislocation activity based on a continuum dislocation density tensor that can be uniquely linked to the plastic slips on all active systems. Due to its nonlocal formulation, this model is size-aware; that is it is well suited to describe intrinsic size effects such as those arising from dislocation pile-ups within grains as well as between twin boundaries. The graphics below illustrate an example of a microtwin nucleating out of an untwinned crystal, showing the distribution of both the dislocation density and the twin phase. The twin boundary accumulates dislocations as the twin phase expands.
Figure: simulated results for a twin nucleating homogeneously from a seed in the untwinned phase. The left image shows the plastic slip distribution, the center image illustrates the twin phase distribution (in terms of the order parameter), and the right image highlights the corresponding dislocation density distribution.
On the other had, we have developed and implemented a new model for Mg of extended crystal-plasticity type to account for the disparate scales involved: twinning is commonly observed at a much smaller length scales (typical twin spacings in Mg can be as low as several nanometers) than dislocations (which live on the polycrystals' scale of many microns). The crystal plasticity model decouples the length scales by finding an effective description for twinning in terms of twin volume fractions. The model has been calibrated and validated by comparison with experimental data for single- and polycrystalline Mg, and it has given reasonable predictions not only of the resultant stress-strain response but also of the microstructure evolution in polycrystals, the dominant slip/twin modes, and the underlying texture development.
Figure: simulated stress-strain responses for two differently-oriented Mg single crystals (activating slip and twinning, respectively) as well as the texture evolution in a Mg polycrystal during cold rolling.
The crystal plasticity model has been used to predict the texture evolution in polycrystalline Mg samples produced by Equal Channel Angular Pressing (ECAP), which admits comparison to experimental data. The below animations illustrate the increase in basal, prismatic and pyramidal slip as well as in tensile twin activity during compression of a cylindrical sample at high rate.
Figures (from left to right): basal slip, prismatic slip, pyramidal slip, and tensile twin activity.
- Y. Chang, J. T. Lloyd, R. Becker, D. M. Kochmann. Modeling microstructure evolution in magnesium: comparison of detailed and reduced-order kinematic models, Mechanics of Materials 108 (2017), 40-57.
- Y. Chang, D. M. Kochmann. A variational constitutive model for slip-twinning interactions in single- and polycrystalline magnesium, Int. J. Plasticity 73 (2015), 39-61.