1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
On the Bauschinger effect in supercooled melts under shear: Results from mode coupling theory and molecular dynamics simulations
Rent:
Rent this article for
USD
10.1063/1.4770336
/content/aip/journal/jcp/138/12/10.1063/1.4770336
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4770336
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Linear plot of the stress–strain relation σ(γ) at fixed density and shear rate for various flow histories: start-up flow with constant shear rate (red), flow reversal in the steady state (s, purple), from the elastic regime (el, blue), and from the point of the stress overshoot (max, green). The linear increase with the quiescent elastic modulus G in start-up, and with G eff after shear-reversal are indicated by dotted lines. Characteristic stress–strain points, whose transient modulus is discussed in the text, are marked by symbols: The red square gives the stationary stress. It corresponds to an integration along the line from A to B in Fig. 7 . Triangles mark stresses after flow reversal in the linear regime and correspond to an integration along the line C' to E'. Discs mark stresses after flow reversal in the overshoot regime and are obtained via integrations along the line C to E in Fig. 7 .

Image of FIG. 2.
FIG. 2.

Plot of the stress–strain curves σ(γ) at fixed temperature for various shear rates. The dashed lines show the MCT results for Γ = 100, ε = −10−4, γ c = 0.75, , and γ*** = 1.33. γ* is 10−1, 7 × 10−2, 6 × 10−2, 4.5 × 10−2, 3.5 × 10−2, 1.5 × 10−2 for decreasing shear rates .

Image of FIG. 3.
FIG. 3.

Linear plot of the stress–strain relation |σ(|γ − γ0|)| at fixed temperature and shear rate for various flow histories: starting from equilibrium (EQ, red line), after flow reversal in the steady state (S, purple), from the elastic regime (el, blue), and from the point of the stress overshoot (max, green). Reversal at is in the steady state as seen from comparing with reversal at (black data). Smooth lines result from the schematic model.

Image of FIG. 4.
FIG. 4.

Velocity profiles v x (y) as a function of position along the gradient direction y for various times after application of a new flow direction. (a) Starting from a quiescent configuration (EQ), shear in +x direction. (b) Starting from the resulting steady state (S) at , shear in −x direction. Insets mark the points for which profiles are shown along the stress–strain curves. A total 100 independent configurations are averaged within a small time window to obtain the depicted graphics.

Image of FIG. 5.
FIG. 5.

Bauschinger effect as illustrated by a generalized Maxwell model (see text). Solid lines are σ(t) as a function of normalized time, , for the case γ w = 0.1 corresponding to and γ w = 0.8 corresponding to . Dashed lines display the contributions σI(t) (upper, red) and σII(t) (lower, blue).

Image of FIG. 6.
FIG. 6.

Linear stress responses from simulation, fits of the schematic model, and Maxwell model as labeled for various waiting strains γ w . The inset gives the strain γ w − γ0 required for the stress to reduce to zero after shear reversal. To include the simulation point for , this value has been divided by 200, using that the precise value of γ w is irrelevant in the steady state.

Image of FIG. 7.
FIG. 7.

View on the tt -plane, with the three different time regimes for the density correlator Φ. As the h-function depends only on the absolute value of , the one-time-solutions and are equal.

Image of FIG. 8.
FIG. 8.

(a) Shear moduli G(t, t ) after shear reversal at in the steady state, shown for three different fixed times t (respectively, strains γ), as functions of tt . Curves marked with violet triangle, disc, and diamond symbols correspond to points marked with the same symbol in Fig. 1 . For times , all curves collapse by construction onto the start-up result G(t, 0) shown in red (marked with a square). The inset shows the corresponding correlators Φ(t, t ) (they overlap on the resolution of the figure). (b) Corresponding stress integrands on a linear tt axis. Curves after shear reversal which would be negative for tt → 0 are mirrored to positive initial decay, where they overlap with the start-up curve.

Image of FIG. 9.
FIG. 9.

Similar to Fig. 8 , but now for shear reversal at in the elastic regime. The curves end at a time , where the memory has not decayed to zero yet. This is as expected, because the system still responds elastic like before the early reversal at ; see the blue curve in Fig. 1 .

Image of FIG. 10.
FIG. 10.

In Panel (a), linear stress response as function of waiting strain γ w in a fluid and a glass state; for the latter, two different shear rates are shown. The quiescent elastic shear constant G is observed in start-up flow. In Panel (b), the corresponding curves are given for the relative stress overshoots σ max s − 1.

Image of FIG. 11.
FIG. 11.

Simulation results of the self intermediate scattering functions F s (q, t) for the B-species in the two directions perpendicular to shear during start-up and after shear reversal in the stationary state, for wave vectors q = [π/σ AA , 2π/σ AA , 3π/σ AA , 4π/σ AA ] in descending order. A total 200 independent simulational runs are averaged to obtain these graphics. The corresponding equilibrium functions are included (dashed lines, label EQ), shifted to coincide at short times.

Image of FIG. 12.
FIG. 12.

(a) Mean-squared displacement of B particles in the vorticity direction. Shown are the equilibrium curve for T = 0.4 (label EQ), and transient MSDs δz 2(t, t ) as a function of , where t is the time of initial flow start-up from equilibrium (EQ), respectively, flow reversal according to the cases discussed in Fig. 2 (steady-state, s; elastic transient, el; strain corresponding to the overshoot, max). The equilibrium curve is shifted to coincide at short times. (b) Logarithmic derivative for the cases shown in (a).

Loading

Article metrics loading...

/content/aip/journal/jcp/138/12/10.1063/1.4770336
2013-01-03
2014-04-18
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the Bauschinger effect in supercooled melts under shear: Results from mode coupling theory and molecular dynamics simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4770336
10.1063/1.4770336
SEARCH_EXPAND_ITEM