![Flow reversal and Bauschinger effect in a glass-forming liquid
Amit Kumar Bhattacharjee1
, Jürgen Horbach2
, Thomas Voigtmann3,4
1
Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
2
Institut für Theoretische Physik II, Soft Matter, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
3
Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
4
Zukunftskolleg, Universität Konstanz, 78457 Konstanz, Germany
Question,methodandresultsAbstractConclusion
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 tw
ET
, tw
OT
and tw
SS
.
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).
ACKNOWLEDGEMENTS
Funded 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 flow. A strong history dependence is observed depending on the time of reversal after initial
startup of the flow, most pronounced in the modification of the stress overshoot. The initial
distribution of local stresses at the point of flow 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-
particle 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≠i
rij , x Fij , y]〉.
˙
˙
z
2
=3〈[ z ttw−ztw]2
〉.
t=d log z
2
t/d logt
xy=−1/V ∑j≠i
rij , x Fij , 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 rij⋅vij rij2kB T rij Nij rij .
(conservative) (dissipative) (stochastic)
Elastic Plastic
tw
ET
tw
OT
tw
SS
Over-
shoot
=0.035
=0.086
tw
=0
Equlibrium
G=d 〈xy 〉/d ](https://image.slidesharecdn.com/poster-lmc-wien2011-180325080500/85/Poster-LMC-Wien-2011-on-Colloidal-Glassy-Rheology-1-320.jpg)
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Flow Reversal and Stress Response in Sheared Glass
- 1. Flow reversal and Bauschinger effect in a glass-forming liquid Amit Kumar Bhattacharjee1 , Jürgen Horbach2 , Thomas Voigtmann3,4 1 Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany 2 Institut für Theoretische Physik II, Soft Matter, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany 3 Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany 4 Zukunftskolleg, Universität Konstanz, 78457 Konstanz, Germany Question,methodandresultsAbstractConclusion 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 tw ET , tw OT and tw SS . 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). ACKNOWLEDGEMENTS Funded 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 flow. A strong history dependence is observed depending on the time of reversal after initial startup of the flow, most pronounced in the modification of the stress overshoot. The initial distribution of local stresses at the point of flow 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- particle 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≠i rij , x Fij , y]〉. ˙ ˙ z 2 =3〈[ z ttw−ztw]2 〉. t=d log z 2 t/d logt xy=−1/V ∑j≠i rij , x Fij , 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 rij⋅vij rij2kB T rij Nij rij . (conservative) (dissipative) (stochastic) Elastic Plastic tw ET tw OT tw SS Over- shoot =0.035 =0.086 tw =0 Equlibrium G=d 〈xy 〉/d