Flow reversal and Bauschinger effect in a glass forming liquid

Flow reversal and Bauschinger effect in a glass-forming liquidAmit Kumar Bhattacharjee1, Jürgen Horbach2, Thomas Voigtmann3,4

1Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany2Institut für Theoretische Physik II, Soft Matter, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany3Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany4Zukunftskolleg, Universität Konstanz, 78457 Konstanz, Germany

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Contact: Amit.Bhattacharjee@dlr.de

Effect of shear

- Overshoot in stress, leading to super-

diffusive behaviour in mean squared

displacement [1].

Effect of shear reversal

- A lesser yield strength in the reversed

direction than the forward: known as the

Bauschinger effect [3].

Quantification through measurement of stress response after reversal of shear

flow at three different times, corresponding to elastic transient (tw

ET ), at overshoot

top (tw

OT ) and at plastic steady state (tw

SS ).

Interaction potential

- Soft spheres, purely repulsive (truncated and shifted Lennard-Jones)

Dissipative particle dynamics [2]

Planar Couette flow

- Lees-Edwards boundary condition.

The stress tensor

- Flow reversal at time tw

ET is symmetric without much history dependence.

- Flow reversal at time tw

OT diminishes the overshoot peak.

- Flow reversal at time tw

SS yields into complete absence of stress overshoot.

- The elastic constant is fixed at tw=0 and at t

wET, t

wOT and t

wSS.

However, the slope diminishes for inflection of shear at higher waiting times.

- Glass forming colloidal mixture exhibits “Bauschinger effect” for a bidirected

shear flow.

- Flow reversal at plastically deformed steady state yields in a vanishing stress

overshoot and superdiffusive particle motion with essentially a higher fluctuation

of local stress at all times.

- Flow reversal at any other time at transient regime shows Bauschinger effect

only when the local stress fluctuation is significantly higher than the threshold.

MSD in the vorticity direction

- No shear: glassy dynamics.

- Positive shear at tw=0 : stress overshoot with a decrement of the

plateau.

- Positive shear at tw

SS : absence of stress overshoot with an early

initiation of a diffusive scaling.

- Shear reversal at tw

SS depicts of a similar behaviour that of the previous.

- Shear reversal at earlier stages, corresponding to tw

ET and

tw

OT still exhibits superdiffusion (less pronounced).

Effective exponent

- Ballistic ( ) to diffusive ( ) with sub and super diffusive scales for

different flow behaviour.

Local stress element

- Increase in around corresponding to stress overshoot

with a crossover from elastic to plastic flow regime for positive shear.

- Shear reversal at time tw

SS : remains constant at the higher level

with a small dip at .

- Shear reversal at tw

ET and tw

OT reflects of a stress overshoot only when

the initial variance is sufficiently below than that in the steady-state flow.

REFERENCES

[1] Zausch, Horbach, Laurati, Egelhaaf, Brader, Voigtmann, Fuchs, J. Phys.: Condens. Matter 20, 404210 (2008). [2] Zausch, Horbach, Europhys. Lett. 88, 60001 (2009).[3] Karmakar, Lerner, Procaccia, Phys. Rev. E 82, 026104 (2010).

ACKNOWLEDGEMENTSFunded by German Academic Exchange Service, DLR-DAAD program &Helmholtz-Gemeinschaft, HGF VH-NG 406.

x

y

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We study the nonlinear rheology of a glass-forming binary 50:50 colloidal mixture under the reversal of shear f low. A strong history dependence is observed depending on the t ime of reversal after init ial startup of the f low, most pronounced in the modif ication of the stress overshoot. The init ial distr ibution of local stresses at the point of f low reversal is shown to be a signature of the subsequent response. We link the history-dependent stress-strain curves to a history dependence in the single-part icle dynamics measured in the transient mean-squared displacement, showing regions of superdiffusion.

xy=⟨ xy⟩=−1/V ⟨∑i=1

N

[mi vi , x vi , y∑ j≠ir ij , x F ij , y ]⟩ .

z2=3⟨[ z tt w−ztw]

2⟩ .

t =d log z2t /d log t

xy=−1 /V∑ j≠irij , x F ij , y .

var xy ≈0.1

≈0.1

var xy

=75

=0

=2 =1

m r= p ; p=−∑i≠ j∇V ij r −∑i≠ j

2 rij r ij⋅v ij r ij2k BT rijN ij rij .

(conservative) (dissipative) (stochastic)

Elastic Plastic

tw

ET

tw

OT

tw

SS

Over-shoot

=0.035

=0.086t

w=0

Equlibrium

G=d ⟨ xy⟩/d