Negative Strain-Rate Sensitivity in Metallic Glasses Driven by Rejuvenation-Relaxation Competition: Kinetic Monte Carlo Simulations and a Minimal Effective Model

Abstract

When strain-rate sensitivity (SRS) is negative in metallic glasses, the material becomes weaker as the deformation rate increases, leading to accelerated plastic deformation and, eventually, catastrophic fracture. In this study, we elucidate the mechanism underlying the negative SRS using micromechanics-based kinetic Monte Carlo simulations that couple heterogeneous randomized shear transformation zone (STZ) models for metallic glasses. The model accounted for both the thermomechanical structural rejuvenation and relaxation of the energy barrier for thermal activation of STZs, incorporating a Kohlrausch-Williams-Watts (KWW)-type relaxation function. The present simulations systematically reproduce the dependence of flow stresses on strain rate, temperature, and the form of the relaxation function. The SRS tends to decrease at high strain rates and low temperatures in the simulations, and negative SRS appears when a compressed-exponential relaxation function is employed. Shear localization also appears; however, the conditions under which the observed localization emerges do not fully coincide with those leading to the negative SRS, leaving the dominant factor unclear. To clarify the dominant factor, we introduce a simplified theoretical model that reproduces flow stresses consistent with the simulation results. An analytical expression derived from the theoretical model reveals that negative SRS originates primarily from the temporal evolution of the activation barrier. Specifically, negative SRS arises when the timescale of external loading exceeds that of STZ relaxation.

Figures (13)

• Figure 1: Schematic of the heterogeneously randomized STZ model. (a) Each STZ possesses multiple plastic deformation modes with randomized shear strains. (b) Potential energy surface and changes in the energy barrier during STZ deformation (plastic deformation) and structural relaxation.
• Figure 2: Typical examples of the activation barrier $Q(t)$ at $T=400K$, where blue, orange, and green curves correspond to the cases with $\beta = 0.6, 1.0$, and $1.3$, respectively. The dashed lines describe the approximated shape of $Q(t)$ [Eqs. (\ref{['eq:Q_approx-before']}), (\ref{['eq:Q_approx-trans']}), and (\ref{['eq:Q_approx-after']})]. The circles and triangles represent the barrier heights at $t_R$ and $t_s$, respectively.
• Figure 3: Stress-strain curves at $400$ K and strain rates from $10^{-5}$ to $e+3s^{-1}$. (a) Time-independent STZ model. (b) $\beta=0.6$. (c) $\beta = 1.0$. (d) $\beta = 1.3$.
• Figure 4: Flow stress $\sigma_\mathrm{f}$ as a function of the strain rate $\dot{\varepsilon}$ at $T=300$, $340$, $400$, $440$, and $500$ K. (a) Time-independent STZ model. (b) $\beta=0.6$. (c) $\beta = 1.0$. (d) $\beta = 1.3$.
• Figure 5: Strain-rate sensitivity index, $m^\dagger(T, \dot{\varepsilon})$, obtained from the kMC simulations with (a) the time-independent STZ model, (b) $\beta = 0.6$, (c) $\beta = 1.0$, and (d) $\beta = 1.3$. The dashed and dotted lines represent the strain rates corresponding to $t_R$ and $t_s$, respectively [see details in Sec. \ref{['sec:discussion']}].