A few surprising consequences of crystallographic anisotropy in magnesium and its alloys

Kaushik Bhattacharya

Magnesium has a hexagonal close packed crystal structure, and the resulting crystallographic anisotropy has important consequence on its mechanical properties.  This talk will provide a few examples where this anisotropy manifests itself in unexpected ways and causes a reexamination of “common” knowledge.   First, we examine the growth of nano voids, and show that basal dislocations and prismatic loops result in void growth with no secondary hardening.  This has important consequences for spall strength.  Second, we will show that there is a proliferation of twinning modes, and this has an important consequence on yield and flow behavior.  The talk will end with a speculative discussion of how this uncommon knowledge can lead to new strategies for alloy design.



Exact theory of vacancy-mediated solute transport in magnesium

Dallas Trinkle

Mass transport controls crucial materials processing, such as segregation and precipitation, and properties, such as ionic conductivity, in a wide variety of materials. First-principles methods can determine the activated state energies at the atomic level involved in mass-transport such as vacancies moving in a crystal. Upscaling from activation barriers to mesoscale mobilities requires the solution of the master equation for diffusivity. For all but the simplest cases of interstitial diffusivity, and particular approximations with vacancy-mediated diffusion on simple lattices, calculating diffusivity directly is a challenge. This leaves two choices: uncontrolled approximations to map the problem onto a simpler (solved) problem, or a stochastic method like kinetic Monte Carlo, which can be difficult to converge for cases of strong correlations. Moreover, without analytic or semi-analytic solutions, evaluating derivatives of transport coefficients is also difficult. We describe and demonstrate the development of direct and automated Green function solutions for transport that take full advantage of crystal symmetry. To showcase the new functionality, we focus on magnesium alloys containing Al, Zn, and rare earth elements (Gd, Y, Nd, Ce and La), where current theoretical models to predict diffusivity from atomic jump frequencies make uncontrolled approximations that affect their accuracy. Density-functional theory identifies nine different solute-vacancy configurations from which symmetry analysis determine 17 transitions states corresponding to a 27-frequency model. Our Green function approach computes diffusivity for 14 solutes using the density-functional theory data. We find significant differences for solute drag of Al, Zn, and rare earth solutes, and improved predictions of activation energies for diffusion. The differences with prior predictions can be directly attributed to missing jumps in the 8- and 13-frequency models. The underlying automation also makes the extension of first-principles transport databases significantly more practical and eliminate uncontrolled approximations in the transport model.


Grain neighbor effects on twin transmission in Mg and its alloys

Mechanical Engineering Department, Materials Department, University of California Santa Barbara, Santa Barbara, CA 93106-5070, USA

The interaction between grain boundaries and twins has an important influence on the deformation behavior of hexagonal close packed (hcp) materials.  In this presentation, we closely examine experimentally and numerically the interaction between deformation twins and internal microstructural boundaries.  The analysis involves a combination of automated electron backscatter diffraction (EBSD) and full-field 3D spatially resolved, Fast-Fourier-Transform (FFT) mechanics modelling to study the influence of the localized shear effects of twin lamellae and other material and boundary characteristics (crystallography, active slip modes, etc.) on the stress distributions at twin/grain boundary intersections. Results from a large-data-set statistical analysis for both Mg and Zr suggest that whether or not twins transmit across grain boundaries depends not only on grain boundary crystallography but also strongly on the anisotropy of crystallographic slip. The modeling investigation further reveals that enhancing material plastic anisotropy or the spread in the CRSS values among the prismatic, pryamidal <c+a>, and basal slip systems increases the driving forces for twin transmission and the cut-off misorientation grain boundary angle above which twin transmission is not likely. We apply the insight gained to understand the effects of alloying on the likelihood of twin transmission within deformed polycrystalline Mg alloys.


Efforts to Strategize Mesoscale Modeling of Twinning beginning with the Atomistic Scale

Haitham El Kadiri

Magnesium has been a very challenging material for mechanical metallurgists, modelers, and experimentalists alike.  Though of so much interest to scientists, magnesium has put materials designers to a daunting test, as none of the traditional design approaches have enabled affordable wrought alloys in critical safety transportation components. Despite many remarkable attempts, lack of ductility, further exacerbated at high rates, has persistently plagued the future of magnesium in industry. However, magnesium has consequently become the fortress of recent paradigm waves that claim an understanding based-design is possible: specifically including ICME methods and its multiscale modeling cornerstone.

This talk provides insights on some of the most essential bricks of understanding, which may need to be incorporated in any consummated ICME approach that seeks to provide a ground-breaking improvement of magnesium ductility. We hypothesize that the lack of desired ductility in magnesium originates essentially from the extreme disparities of the active deformation modes as compared to those in ductile FCC metals. Deformation modes clash rather than simply interact, as in the case in twinning-induced plasticity steels. The most notorious clash involves the inevitable need of both moving interfaces (twins) and remarkably hard-to-move dislocations (c+a). Moving interfaces have an atomic structure that admits mobile disconnections, and facile formation of interfacial disclination dipoles. Depending on the moving interface in question, whether compression/contraction or tension/extension twins, the outcome could lead to products that exacerbate hardening and thus lead to the formation of hot spots.

We begin building these bricks of understanding by studying twin nucleation at the atomic level, and attempt to elect the most important feature relevant for a mesoscale level. This allows us to develop a micromechanical model for twin nucleation that may be implemented into a full-field crystal plasticity model. We then follow through with an atomistic study aiming to understand how slip dislocations interact with twin interfaces, by building different admissible kinematic scenarios. From there, we try again to extract the most important mechanism for the mesoscale level, and suggest an implementable formulation for crystal plasticity.

Most of this talk will focus on the different results and tools built to decipher the aforementioned mechanisms at the atomistics level, including interfacial defect theory. This talk will also cover plasticity as well as dynamic recrystallization in an effort to set the stage for understanding of magnesium and the issues associated with ductility limits.