How amorphous materials respond to applied stress
How amorphous materials respond to applied stress
Matthieu Wyart
Contributors • A large research effort involving many PIs, affiliates, and collaborators. L. Berthier G. Biroli S. Franz L. Manning S. Nagel A. Liu G. Parisi M. Wyart F. Zamponi
A. Ikeda E. Lerner S. Sastry G. Tarjus H. Yoshino
Workshops: Yielding (ENS Paris 2017, Agoritsas, Urbani, Zamponi) Royaumont ( 2017, Berthier, Biroli)
E. Agoritsas H.H. Boltz E. DeGiuli T. DeGeus D. Hexner Y. Jin C. Lupo P. Morse M. Ozawa M. Popovic S. Ridout S. Spigler P. Urbani G. Zhang
Amorphous Materials
Granular materials Andreotti et al.
Structural glasses
Emulsions, Foams Brujic
Colloidal Suspensions
Solid phase is “glassy”: out-of-equilibrium, history-dependence
“Tilting” the landscape E
⇒ Increase stress
1/ How do they flow?
Strongly driven. Rheology of complex fluids. 2/ How do they yield? Preparation dependence. 3/ Elementary excitations? Local rearrangements, Two-level-systems? Preparation dependence. TODAY: 2/
⇒
⇒
Importance of the yielding in amorphous solids • Material science, soft matter, geophysics (landslides, earthquakes) rock 1cm
Granular matter Zooming in a fault • How granular materials yield? Precursors to yielding?
The different natures of Yielding
Strain g
• Stress-strain curves
foam
colloids
Brittle glasses
Yang and Liu, 2012
What controls brittleness? • Brittle bulk metallic glasses display shear bands Mechanisms causing shear Localization?
Shear band
Homogeneous plasticity
Plastic deformation, precursor to yielding? • Plastic strain accumulates before macroscopic yielding
Accumulated strain in granular matter Amon et al., PRL 2012 Le Bouil et al., 2013, 2014
• Strain accumulates via “avalanches” of plasticity. When? Statistics?
Elementary rearrangements: Shear transformations • Crystal: dislocation • Amorphous material?
U=
X
U
V (~ri
~rj )
ij
stress
è
g
strain Quasistatic: elastic loading with Sudden energy release
Local rearrangement: Shear transformation Maloney, Lemaitre Argon, Falk, Langer
Density of shear transformations??
Rearrangements organize into avalanches Maloney, Robbins
1/ New computational methods for brittle glasses • Knowledge gap: glasses on the computer yield as soft caramel (colloids, foam). Never brittle.
Hinders ability to understand brittleness and shear bands. • Hypothesis: cooling rate up to 0.1 K/s in experiments, 1010 K/s in numerical studies. Real glasses much more stable. ⇒ Use swap to generate glasses with realistic stability!
1/ Brittle numerical glasses • -
Protocol: Equilibrate at varying Temperature T with swap (Tg=0.72) Quench to T=0 Overdamped quasi-static (i.e. very slow) shear
Result: From a simple crossover to a smooth overshoot to a discontinuous yielding, separated by a critical point! Glass stability key factor on glass brittleness
1/ New handle to study “brittle” shear bands
T=1.2
T=0.062
• Proves thermal feedback not necessary for brittle shear bands • Future: inertia, temperature, etc….
2/ Exact calculations d=∞ • One equilibrated master replica {Ri}, One slaved replica {Xi}. • Fix the distance • Franz-Parisi potential in d=∞
Liquid T>Tc
can be computed exactly
Glass T
Matthieu Wyart
Contributors • A large research effort involving many PIs, affiliates, and collaborators. L. Berthier G. Biroli S. Franz L. Manning S. Nagel A. Liu G. Parisi M. Wyart F. Zamponi
A. Ikeda E. Lerner S. Sastry G. Tarjus H. Yoshino
Workshops: Yielding (ENS Paris 2017, Agoritsas, Urbani, Zamponi) Royaumont ( 2017, Berthier, Biroli)
E. Agoritsas H.H. Boltz E. DeGiuli T. DeGeus D. Hexner Y. Jin C. Lupo P. Morse M. Ozawa M. Popovic S. Ridout S. Spigler P. Urbani G. Zhang
Amorphous Materials
Granular materials Andreotti et al.
Structural glasses
Emulsions, Foams Brujic
Colloidal Suspensions
Solid phase is “glassy”: out-of-equilibrium, history-dependence
“Tilting” the landscape E
⇒ Increase stress
1/ How do they flow?
Strongly driven. Rheology of complex fluids. 2/ How do they yield? Preparation dependence. 3/ Elementary excitations? Local rearrangements, Two-level-systems? Preparation dependence. TODAY: 2/
⇒
⇒
Importance of the yielding in amorphous solids • Material science, soft matter, geophysics (landslides, earthquakes) rock 1cm
Granular matter Zooming in a fault • How granular materials yield? Precursors to yielding?
The different natures of Yielding
Strain g
• Stress-strain curves
foam
colloids
Brittle glasses
Yang and Liu, 2012
What controls brittleness? • Brittle bulk metallic glasses display shear bands Mechanisms causing shear Localization?
Shear band
Homogeneous plasticity
Plastic deformation, precursor to yielding? • Plastic strain accumulates before macroscopic yielding
Accumulated strain in granular matter Amon et al., PRL 2012 Le Bouil et al., 2013, 2014
• Strain accumulates via “avalanches” of plasticity. When? Statistics?
Elementary rearrangements: Shear transformations • Crystal: dislocation • Amorphous material?
U=
X
U
V (~ri
~rj )
ij
stress
è
g
strain Quasistatic: elastic loading with Sudden energy release
Local rearrangement: Shear transformation Maloney, Lemaitre Argon, Falk, Langer
Density of shear transformations??
Rearrangements organize into avalanches Maloney, Robbins
1/ New computational methods for brittle glasses • Knowledge gap: glasses on the computer yield as soft caramel (colloids, foam). Never brittle.
Hinders ability to understand brittleness and shear bands. • Hypothesis: cooling rate up to 0.1 K/s in experiments, 1010 K/s in numerical studies. Real glasses much more stable. ⇒ Use swap to generate glasses with realistic stability!
1/ Brittle numerical glasses • -
Protocol: Equilibrate at varying Temperature T with swap (Tg=0.72) Quench to T=0 Overdamped quasi-static (i.e. very slow) shear
Result: From a simple crossover to a smooth overshoot to a discontinuous yielding, separated by a critical point! Glass stability key factor on glass brittleness
1/ New handle to study “brittle” shear bands
T=1.2
T=0.062
• Proves thermal feedback not necessary for brittle shear bands • Future: inertia, temperature, etc….
2/ Exact calculations d=∞ • One equilibrated master replica {Ri}, One slaved replica {Xi}. • Fix the distance • Franz-Parisi potential in d=∞
Liquid T>Tc
can be computed exactly
Glass T
