flow reversal and bauschinger effect in a glass forming liquid
TRANSCRIPT
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: [email protected]
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
z
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