![Probability distribution function of the nonaffine measure D2(t,T) after one cycle
tt
),(2
TttD
2
1
2
)]()([)()(
1
),(
iN
j
ijiij
i
ttJtttt
N
ttD rrrr
t
At small strain amplitudes,
0 0.05, width of PDF is more
narrow as the number of cycles
increases; the system dynamics
is nearly reversible after 600
cycles.
At large strain amplitudes,
0 0.06, PDFs become wider
as the number of cycles
increases; formation of shear
band; enhanced particle
diffusion.
Excellent diagnostic for identifying particle rearrangements
Falk and Langer, Phys. Rev. E 57, 7192 (1998).
Increasing
number of cycles](https://image.slidesharecdn.com/nvpaps18-200329003010/85/The-yielding-transition-in-periodically-sheared-binary-glasses-at-finite-temperature-7-320.jpg)
The yielding transition in periodically sheared binary glasses at finite temperature
- 1. The yielding transition in periodically sheared binary glasses at finite temperature N. V. Priezjev, The yielding transition in periodically sheared binary glasses at finite temperature, Comput. Mater. Sci. 150, 162 (2018). N. V. Priezjev, Molecular dynamics simulations of the mechanical annealing process in metallic glasses: Effects of strain amplitude and temperature, J. Non-Cryst. Solids 479, 42 (2018). 5 March, 2018 Nikolai V. Priezjev Department of Mechanical and Materials Engineering Wright State University Movies, preprints @ http://www.wright.edu/~nikolai.priezjev/
- 2. Structural relaxation and dynamical heterogeneities in deformed glasses Shear band due to accumulation of STZs at boundary Tension-compression cyclic loading of metallic glasses: Reversible avalanches in 2D amorphous solids: Regev, Weber, Reichhardt, Dahmen, Lookman, Nature (2015) Large particle displacements are completely reversed Metallic glasses: mechanical properties include high strength and low ductility Cyclic loading: yielding transition, fatigue lifetime, failure mechanism, nonaffine motion (??) Sun, Concustell, and Greer, Thermomechanical processing of metallic glasses: extending the range of the glassy state, Nature Reviews Materials 1, 16039 (2016). Candelier, Dauchot, and Biroli, Dynamical heterogeneity in the cyclic shear experiment on dense 2D granular media, Phys. Rev. Lett. 102, 088001 (2009). Knowlton, Pine, and Cipelletti, A microscopic view of the yielding transition in concentrated emulsions, Soft Matter 10, 6931 (2014). Sha, Qu, Liu, Wang, and Gao, Nano Lett. (2015)
- 3. Details of molecular dynamics simulations and parameter values Monomer density: = A + B = 1.20 3 Temperature: TLJ = 0.1 kB < Tg = 0.435 kB System size: L = 36.84σ, Np = 60,000 Lees-Edwards periodic boundary conditions LAMMPS, DPD thermostat, tMD= 0.005τ Instantaneous quenching to TLJ = 0.1 kB Binary Lennard-Jones Kob-Andersen mixture: 612 4)( rr rVLJ BABBABAA mm ,5.01.5,,0.1 88.00.8,,0.1 BBABAA Parameters for A and B particles: Oscillatory shear strain: )sin()( 0 tt Oscillation period: 5000/2 T 2080PNi
- 4. Potential energy per particle U/ during 600 oscillation cycles for different 0 Strain amplitudes: Quench,noshear T = 5000 = 1,000,000 MD steps At small strain amplitudes, 0 0.05, the potential energy acquires progressively lower minima with increasing strain amplitude. Minimum potential energy is at 0 = 0.05. Near the yield transition, 0 = 0.06, shallow minimum in potential energy during first 150 cycles. Potentialenergyseriesaredisplacedforclarity
- 5. Shear stress during 600 oscillation cycles for different strain amplitudes 0 At small strain amplitudes, 0 0.05: the amplitude of stress oscillations becomes larger with increasing strain amplitude; nearly reversible particle dynamics. Near the critical strain amplitude, 0 =0.06: shallow maximum in the amplitude of stress oscillations during first 150 cycles; then stress amplitude is reduced at t > 150T. (units) stressseriesaredisplacedforclarity
- 6. Storage and loss moduli and mean-square displacements for different 0 0 0.06 0 0.05 1 At small strain amplitudes, 0 0.05, the storage modulus G’ dominates the response; nearly reversible particle dynamics. N. V. Priezjev, The yielding transition in periodically sheared binary glasses at finite temperature, Comput. Mater. Sci. 150, 162 (2018). At large strain amplitudes, 0 0.06, the loss modulus G” increases; irreversible particle diffusion; formation of shear band. The critical strain amplitude, G’=G”, > c , onset of diffusion. Kawasaki & Berthier, PRE (2016). Steady state: last 40 cycles
- 7. Probability distribution function of the nonaffine measure D2(t,T) after one cycle tt ),(2 TttD 2 1 2 )]()([)()( 1 ),( iN j ijiij i ttJtttt N ttD rrrr t At small strain amplitudes, 0 0.05, width of PDF is more narrow as the number of cycles increases; the system dynamics is nearly reversible after 600 cycles. At large strain amplitudes, 0 0.06, PDFs become wider as the number of cycles increases; formation of shear band; enhanced particle diffusion. Excellent diagnostic for identifying particle rearrangements Falk and Langer, Phys. Rev. E 57, 7192 (1998). Increasing number of cycles
- 8. Spatial configurations of atoms with large nonaffine displacements at 0=0.03 Department of Mechanical and Materials Engineering Wright State University After 20-th cycle After 80-th cycle After 200-th cycle After 600-th cycle Disconnected sparse clusters Nearly reversible particle dynamics B
- 9. Spatial configurations of atoms with large nonaffine displacements at 0=0.05 Department of Mechanical and Materials Engineering Wright State University After 20-th cycle After 80-th cycle After 200-th cycle After 600-th cycle Large clusters of nonaffine displacements Nearly reversible particle dynamics Small clusters of nonaffine displacements
- 10. Spatial configurations of atoms with large nonaffine displacements at 0=0.06 Department of Mechanical and Materials Engineering Wright State University After 20-th cycle After 80-th cycle After 200-th cycle After 600-th cycle Reduced shear stress amplitude Shear band formation Finite width of shear band Enhanced diffusion Large shear stress amplitude
- 11. Spatial configurations of atoms with large nonaffine displacements at 0=0.07 After 20-th cycle After 80-th cycle After 200-th cycle After 600-th cycle Reduced shear stress amplitude Shear band formation Finite width of shear band The width of shear band increases with 0
- 12. Conclusions: http://www.wright.edu/~nikolai.priezjev Wright State University • MD simulations of binary 3D Lennard-Jones glasses under periodic shear at finite TLJ. • At small strain amplitudes, 0 0.05: the potential energy acquires progressively lower minima; stress amplitude increases with 0; sparse transient clusters of atoms with large nonaffine displacements; nearly reversible particle dynamics. • Near the critical strain amplitude, 0 = 0.06: the dynamic transition from disconnected clusters to a shear band of large nonaffine displacements: leads to drop in shear stress amplitude. • At large strain amplitudes, 0 0.07: diffusive particle dynamics; quick formation and growth of shear bands; irreversible particle displacements lead to hysteresis & increase in the potential energy. The width of shear band increases with 0 LAMMPS, DPD thermostat 600 cycles N. V. Priezjev, The yielding transition in periodically sheared binary glasses at finite temperature, Comput. Mater. Sci. 150, 162 (2018). N. V. Priezjev, Molecular dynamics simulations of the mechanical annealing process in metallic glasses: Effects of strain amplitude and temperature, J. Non-Cryst. Solids 479, 42 (2018).