Yield stress discontinuity in a simple glass

Large-scale molecular-dynamics simulations are performed to study the steady-state yielding dynamics of a well-established simple glass. In contrast to the supercooled state, where the shear stress, $\sigma$, tends to zero at vanishing shear rate, $\dot{\gamma }$, a stress plateau forms in the glass which extends over about two decades in shear rate. This strongly suggests the existence of a finite dynamic yield stress in the glass, ${\sigma }^{+}\left(T\right)\equiv \sigma (T;\dot{\gamma }\to 0)>0$. Furthermore, the temperature dependence of ${\sigma }^{+}$ suggests a yield stress discontinuity at a critical temperature of $T_{\mathrm{c}}=0.4$ in agreement with recent mode coupling theory predictions. The corresponding qualitative change of the flow curves enables us to bracket the critical temperature $T_{\mathrm{c}}$ of the theory from above and from below. We scrutinize and support this observation by testing explicitly for the assumptions (affine flow, absence of flow-induced ordering) inherent in the theory. Furthermore, while qualitative similarity is found between the viscosity and the final relaxation time of stress fluctuations, significant quantitative differences are observed in the nonlinear regime.

Figure 1

(Color online) A-A pair correlation functions along $x$ (flow), and $y$ and $z$ (shear gradient) directions, for three characteristic temperatures: $T=0.2$ (glass), $T=0.42$ (close to $T_{\mathrm{c}}$), and $T=0.6$ (supercooled state). The shear rate is $\dot{\gamma }={10}^{-4}$. For clarity, data at $T=0.42$ $(T=0.2)$ are shifted upwards by 1 (2).

Figure 2

(Color online) Simulated shear stress (symbols) compared to theoretical model calculations (solid lines) for various temperatures (from top to bottom: $T=0.01$, 0.2, 0.3, 0.34, 0.36, 0.38, 0.4, 0.42, 0.43, 0.44, 0.45, 0.47, 0.5, 0.525, 0.55, 0.6). The inset shows the fitted separation parameter $ϵ$ vs $T$.

Figure 3

(Color online) Determination of dynamic yield stress and its temperature dependence (see text).

Figure 4

(Color online) $\widehat{\sigma }\equiv \dot{\gamma }V∕\left(k_{\mathrm{B}}T\right){\int }_0^{\infty }dt⟨{\sigma }_{xy}\left(t\right){\sigma }_{xy}\left(0\right)⟩$ vs shear rate for various temperatures ranging from the glassy phase to the supercooled state (from top to bottom: $T=0.1$, 0.2, 0.3, 0.34, 0.4, 0.42, 0.45, 0.47, 0.5, 0.55, 0.6). The inset shows the ratio of this stress to the real shear stress.