The alloy in question, Mg-8wt.%Li, sits in a sweet spot of composition. Above roughly 8 percent lithium by weight, the material becomes dual-phase, containing both the hexagonal close-packed alpha phase typical of magnesium and the body-centered cubic beta phase that lithium stabilizes. That b.c.c. beta phase is the secret ingredient: it deforms far more readily than the hexagonal phase, endowing the alloy with ductility that no other magnesium alloy system can match. The Mg–Li family holds the record for elongation among all magnesium alloys, although its absolute strength remains modest, which is precisely why understanding and controlling its deformation mechanisms matters so much for lightweight structural applications.

To push the alloy into its most deformable state, the team turned to high-pressure torsion, a severe plastic deformation technique in which a disk of material is squeezed under a nominal pressure of 4 gigapascals while being twisted through five full turns. The process shears the microstructure into an ultrafine grain structure. Electron microscopy and transmission Kikuchi diffraction revealed that the extruded material, which started with grains of about 2.2 micrometers, was refined to an average spatial grain size of roughly 0.4 micrometers, with individual subgrains resolved in the range of 0.15 to 0.40 micrometers. The two phases became elongated and aligned with the torsion direction, a signature of the intense shear the disk experienced.

Miniature tensile specimens, cut from the disk mid-radius by electric discharge machining with a gauge cross-section of just 0.8 by 0.8 millimeters, were then pulled at room temperature across strain rates spanning from 10^-5 to 10^-3 per second. The results were striking. The peak stress varied dramatically with strain rate, a hallmark of high strain rate sensitivity, and the alloy exhibited large elongations at the slowest rates of 10^-4 and 10^-5 per second. This unusual increase in ductility at low strain rates, previously reported for similar alloys, is exactly the behavior that makes dual-phase Mg–Li alloys candidates for room-temperature superplasticity, a property normally reserved for ceramics and exotic superalloys at soaring temperatures.

Creep tests added another layer of intrigue. Under constant loads between 10 and 100 megapascals at room temperature, and at 373 kelvin under 10 and 25 megapascals, the creep rates steadily decreased as strain accumulated. Such decelerating creep is normally seen in coarse-grained metals at high temperature, where dislocation substructures build up during the initial stage of deformation, but that explanation should not apply to an ultrafine-grained material whose grains are already smaller than any stable subgrain size. The authors point to a recent study on ultrafine-grained aluminum that attributed similar behavior to strengthening by dynamic recovery, and they adopted the strain rate at 2 percent strain as representative of the as-processed state for further analysis.

The most consequential number to emerge from the creep experiments was the activation energy. Using the temperature dependence of the creep rate between room temperature and 373 kelvin, the team estimated activation energies of 64 kilojoules per mole at 25 megapascals and 77 kilojoules per mole at 10 megapascals. Both values fall well below the 135 kilojoules per mole for self-diffusion and the 92 kilojoules per mole for grain boundary diffusion in pure magnesium. The authors attribute this reduction to the large fraction of the b.c.c. beta phase, which has a lower melting temperature and correspondingly lower diffusion barriers. Reported grain boundary diffusion energies for related alloys, 65 kilojoules per mole for Mg-9%Li and 61 kilojoules per mole for Mg-8%Li-1%Zn, bracket the measurements, and the team settled on 75 kilojoules per mole for their modeling. The low activation energy is a clear signal that thermally activated mechanisms are at work even at room temperature.

To interpret these observations, the researchers deployed a two-pronged computational strategy. First, they applied a recently updated model for grain boundary sliding, the mechanism in which grains slide past one another along their boundaries, which is the canonical explanation for superplastic flow. The model treats the total flow stress as the sum of a threshold stress, capturing other strengthening contributions such as solid solutions, and a grain boundary sliding contribution that depends on shear modulus, temperature, grain size, Burgers vector and the grain boundary diffusion coefficient. A rectified linear function is used as a mathematical constraint to prevent the model from predicting negative stresses when thermal activation is strong. Second, they trained machine learning algorithms on 67 carefully curated data points from the literature, restricted to dual-phase Mg–Li alloys containing no alloying elements other than lithium, with lithium contents between 8 and 12 weight percent, to keep composition effects from contaminating the analysis.

The machine learning lineup included two black-box models, support vector regression and random forest, and two white-box symbolic regression models, one unconstrained and one constrained by dimensional consistency. The black-box models, evaluated with Shapley Additive Explanations, agreed that temperature is the dominant control on flow stress, that strain rate plays an intermediate role, and that grain size matters only marginally. On the training data the algorithms performed well, with mean absolute percentage errors ranging from 11.5 percent for the random forest to 35.3 percent for support vector regression. But when the models were asked to predict the new experimental data generated in this study, the black-box approaches collapsed, producing errors exceeding 250 percent, while the grain boundary sliding model and the dimension-constrained symbolic regression held their ground at roughly 35 percent error.

The deeper story emerged when the team plotted predicted flow stress against grain size, strain rate and temperature and compared the trends with experiment. The experiments revealed a fascinating crossover: for grains larger than about half a micrometer, refining the grains strengthens the alloy in classic Hall–Petch fashion, but below that threshold, further refinement actually softens it, the inverse Hall–Petch regime. Only the grain boundary sliding model captured this transition cleanly. The black-box models failed to reproduce the steep strain rate dependence of the flow stress, with support vector regression even predicting a physically implausible negative strain rate sensitivity at high rates. The dimension-constrained symbolic regression, guided by physically meaningful features such as the Zener–Holomon parameter and dimensionless groups derived from the grain boundary sliding equations, performed far better than its unconstrained counterpart, demonstrating that embedding physical knowledge into machine learning pays real dividends.

The take-home message resonates well beyond magnesium. Machine learning models are only as trustworthy as the data behind them, and with a sparse training set of 67 points, the black-box algorithms interpolated plausibly but extrapolated badly, especially outside the temperature and strain rate ranges they had seen. The century-old physics-based model, by contrast, reproduced every experimental trend once its activation energy was adapted to the dual-phase alloy. For engineers dreaming of lightweight magnesium–lithium components that can be superplastically formed at room temperature, the study offers both a validated design tool and a cautionary tale: in materials science, the white box and the physics still matter, and the smartest models are those that know the laws they are trying to learn.

Subject of Research: Deformation mechanisms and grain boundary sliding in ultrafine-grained dual-phase Mg–Li alloys processed by high-pressure torsion

Article Title: Analysis of deformation mechanism of dual-phase Mg–Li alloy, processed by high-pressure torsion, using experiments and machine learning

Article References: Carvalho, A. P., Edalati, K., & Figueiredo, R. B. (2026). Analysis of deformation mechanism of dual-phase Mg–Li alloy, processed by high-pressure torsion, using experiments and machine learning. Journal of Materials Science. https://doi.org/10.1007/s10853-026-13355-x

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13355-x

Keywords: magnesium-lithium alloy, high-pressure torsion, grain boundary sliding, severe plastic deformation, machine learning, superplasticity, creep, activation energy, Hall-Petch, symbolic regression, ultrafine grains, flow stress