Yielding behaviour of glasses under shear deformation at constant pressure

Computer simulations of yielding of glasses under shear have typically been performed under constant volume, strain controlled protocols. However, volumetric effects, such as the dilatancy associated with plastic rearrangements, and the observed reduction of density in shear bands, make it interesting to consider constant pressure shear protocols. We present a computational investigation on the nature of yielding of glasses under constant-pressure conditions, for different pressures. For uniform shear, the stress-strain curves at different pressures differ only by the stress scale. We find stable shear bands under cyclic shear whose steady-state width increases with an increase in external pressure, with density within shear bands being lower compared to the average values reached. Cyclically sheared well annealed glasses yield with a discontinuous dilation at the yield point, whereas the poorly annealed glasses undergo compaction before yielding accompanied by dilation. The external pressure influences the quantitative mechanical response of the glasses, but the qualitative behaviour is similar at different pressures, and remains the same as that of yielding at the constant-volume strain-controlled conditions. We discuss directions along with further investigations may be pursued, based on the results presented.

💡 Research Summary

In this work the authors investigate the yielding transition of amorphous glasses under shear when the external pressure is held constant, a situation that has received little attention compared with the more common constant‑volume, strain‑controlled protocols. Using athermal quasistatic shear (AQS) simulations of the 80:20 Kob‑Andersen binary Lennard‑Jones mixture, they study both uniform (monotonic) and cyclic shear for two system sizes (N = 4 000 and N = 64 000) and three imposed pressures (P = 2, 10⁻³, −2 in reduced Lennard‑Jones units). Two preparation histories are considered: a poorly annealed glass with inherent structure energy e_IS ≈ −6.92 and a well‑annealed glass with e_IS ≈ −7.05.

For uniform shear the stress–strain curves at different pressures differ only by a multiplicative factor: the peak stress σ_P grows linearly with pressure, and when the stress is rescaled by σ_P all curves collapse onto a single master curve, identical to the constant‑volume case. This demonstrates that the shear modulus and the overall resistance to deformation scale directly with the applied pressure, while the underlying yielding mechanism remains unchanged.

Cyclic shear reveals the formation of stable shear bands. The number density inside the band is lower than the bulk, confirming dilatancy. Importantly, the steady‑state band width increases with external pressure. The width grows with the number of shear cycles n as a power law w ∝ n^α, with α≈0.2–0.3, before saturating at a pressure‑dependent value. Although the exponent is not exactly 1/3 as predicted by some coarsening theories, the systematic pressure dependence of both growth rate and saturation width is a robust observation.

Energy analysis shows that the energy density U/V decreases monotonically with increasing pressure, reflecting the tighter packing under higher pressure, whereas the per‑particle energy U/N exhibits a non‑monotonic pressure dependence because of competing effects of densification and structural rearrangements.

The annealing history strongly influences the dilation/compaction behavior at yielding. Well‑annealed glasses display a discontinuous dilation exactly at the yield strain (γ_Y ≈ 0.10) with virtually no change in density beforehand. Poorly annealed glasses first compact slightly as the strain amplitude approaches γ_Y, then undergo a sudden dilation at yielding. This difference is consistent with the deeper energy minima of well‑annealed samples, which require a larger stress to overcome the barrier.

Overall, the study concludes that imposing a constant pressure modifies quantitative aspects of the mechanical response—peak stress, shear‑band width, and density changes—but does not alter the qualitative nature of the yielding transition. The same scaling collapse of stress, the same shear‑band formation, and the same dependence on preparation history are observed as in constant‑volume simulations. These findings suggest that results obtained from traditional constant‑volume simulations can be transferred to experimental situations where the sample volume is free to change, such as high‑pressure extrusion or indentation of metallic glasses. The authors propose future work to explore temperature effects, anisotropic pressure states, and to validate the observations in realistic metallic‑glass models.