Athermal creep deformation of ultrastable amorphous solids

TL;DR

We address how preparation history and stability control athermal creep and fluidization in amorphous solids under constant stress. Using swap-Monte-Carlo prepared glasses spanning poorly annealed to ultrastable states and a stress-controlled MD protocol, we map macroscopic creep, diverging fluidization times, and microscopic precursors to failure. The findings reveal monotonic creep in poorly annealed samples versus abrupt, S-shaped transients with sharp shear-band formation in ultrastable glasses, with a stability-dependent threshold $\sigma_c$ and exponents $\beta$ and $\nu$ that test scaling theories. Seed-induced nucleation of shear bands demonstrates how rare soft zones can depress the yield stress, highlighting the need for stability-aware theoretical frameworks relevant to metallic and oxide glasses.

Abstract

We numerically investigate the athermal creep deformation of amorphous materials having a wide range of stability. The imposed shear stress serves as the control parameter, allowing us to examine the time-dependent transient response through both the macroscopic strain and microscopic observables. Least stable samples exhibit monotonicity in the transient strain rate versus time, while more stable samples display a pronounced non-monotonic S-shaped curve, corresponding to failure by sharp shear band formation. We identify a diverging timescale associated with the fluidization process and extract the corresponding critical exponents. Our results are compared with predictions from existing scaling theories relevant to soft matter systems. The numerical findings for stable, brittle-like materials represent a challenge for theoretical descriptions. We monitor the microscopic initiation of shear bands during creep responses. Our study encompasses creep deformation across a variety of materials ranging from ductile soft matter to brittle metallic and oxide glasses, all within the same numerical framework.

Figures (6)

• Figure 1: (a, b, c): Time evolution of ensemble-averaged shear-rate in response to imposed stresses $\sigma$ (as marked) for three-dimensional initial amorphous states prepared via quench from $T_{\rm ini}=0.200$ (a), $T_{\rm ini}=0.120$ (b), and $T_{\rm ini}=0.062$ (c). Filled symbols correspond to cases where steady-state flow is observed in all samples, whereas open symbols are used for cases where the system remains solid in all samples. Dashed lines correspond to $\dot \gamma (t) \sim t^{-\nu}$ with $\nu=$ 0.62 (a), 1.25 (b), and 1.75 (c). (d): Steady-state flow curve, viz. the evolution of the imposed stress with the steady-state ensemble-averaged shear-rate obtained by gathering data for $t \to \infty$ in (a, b, c), for flowing states. The dashed curve corresponds to the Herschel-Bulkley law, with $\sigma_d=0.144$ and $n=0.41$.
• Figure 2: (a): Fluidization timescale, $\tau_{ss}$, as a function of applied shear stress, $\sigma$, for states having different $T_{\rm ini}$. Dashed curves correspond to a power law fitting, $\tau_{ss} \sim 1/(\sigma - \sigma_c)^{\beta}$ with $\sigma_c$ and $\beta$ are listed in Table \ref{['tab1']}. (b): Same data shown as a function of $(\sigma/\sigma_c-1)$, compared to theoretical predictions $\beta=1/n-1/2$ in Ref. popovic2022scaling (dashed line) and $\beta=9/(4n)$ in Ref. benzi2019unified (dotted-dashed line), using our numerical estimate of $n$ in Fig. \ref{['fig1']}(d). Open symbols show estimates for the timescale $\tau_m$, defined via the minimum of $\dot{\gamma}(t)$, for $T_{\rm ini}=0.062$.
• Figure 3: (a): Time evolution of the strain rate for a 3D ultrastable glass sample ($T_{\rm ini}=0.062$) under constant imposed stress $\sigma=0.42$, i.e. just above $\sigma_c$ corresponding to this initial state. (b-e): Maps of accumulated plastic events measured via non-affine displacements $D^2_{\rm min}$, at $t=$459.35 (b), 950 (c), 1050 (d), and 1150 (e), marked as square points in (a).
• Figure 4: (a): Time evolution of the strain rate for a 2D ultrastable glass sample ($T_{\rm ini}=0.035$) under constant imposed stress $\sigma=0.43880$, i.e., just above $\sigma_c$ corresponding to this initial state. (b-h): Maps of accumulated plastic events measured via non-affine displacements $D^2_{\rm min}$ at $t=$ 800 (b), 160000 (c), 169000 (d), 169650 (e), 169800 (f), 169900 (g), and 169950 (h), marked as points in (a). These maps demonstrates how yielding proceeds via the relevant precursors.
• Figure 5: Comparative response of the same initial state, analyzed in Fig. \ref{['fig4']}, to imposed stresses of $\sigma=0.43879$ and $0.43880$, i.e., a difference of ${10^{-5}}$. (a, b): Time evolution of observed strain (a) and strain-rate (b) responses. (c-f): Sequence of maps of non-affine displacements $D^2_{\rm min}$, at the points marked in (a, b), viz. $t=$800 (c), 34280 (d), 160000 (e), and 169800 (f), for $\sigma=0.43879$ (top) and $\sigma=0.43880$ (bottom).