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Plastic flow vs. brittle fracture: role of solid friction in amorphous materials
- 1. 1
- 2. 2 OUTLINE + Background: flow of amorphous solids + Connection with “Geoscience”: a few old papers! + Eshelby-type events: “Mesoscopic” notion of plastic flow + Univesality of Eshelby picture (frictional systems)
- 3. 3 Amorphous Materials Metallic glasses, Vitreloy Silica glass Metallic glass Polymer glass Colloidal paste Foam Grains “Soft” amorphous materials “Hard” amorphous materials + Disordered elastic solids, far below/above any glass transition temperature + Extremely diverse in scales (nm-cm) and strength (100 Pa-100 GPa) + Still share universal features from granular media to metallic glasses μm cm nm cm
- 4. 4 + Low temperature, normal pressure, low driving rate + Bursty “quake”-like dynamics with a broad distribution of magnitudes + Many condensed matter systems with heterogeneities (polycrystals, metalic glass, earthquakes) Bursty Response Sheared granular material, Denisov et al. nature. Comm (2016) Force,N
- 5. 5 + Low temperature, normal pressure, low driving rate + Bursty “quake”-like dynamics with a broad distribution of magnitudes + Many condensed matter systems with heterogeneities (polycrystals, metalic glass, earthquakes) Bursty Response Scaled Magnitude Frequency Universal size distributions, Uhl et al. Sci. Rep (2015)
- 6. 6 OUTLINE + Background: flow of amorphous solids + Connection with “Geoscience”: a few old papers! + Eshelby-type events: “Mesoscopic” notion of plastic flow + Univesality of Eshelby picture (frictional systems)
- 7. 7 Simple cellular automaton on a square lattice with open boundaries (sandpile model) Slope -1 in 2d Driving: add grains randomly Diffusion-like Relaxation above threshold
- 8. 8 Spring network with threshold in force Slope -0.4 in 2D
- 9. 9 Papers published in Phys Rev Lett with “USSR” and “USA” in address
- 10. 10 236 citations but only 11 from the “Geoscience” fields
- 11. 11 OUTLINE + Background: flow of amorphous solids + Connection with “Geoscience”: a few old papers! + Eshelby-type events: “Mesoscopic” notion of plastic flow + Univesality of Eshelby picture (frictional systems)
- 12. 12 Statistical physics problem: + Correlation patterns best seen in experiments + Complex spatio-temporal fluctuations + Space-time interactions and correlations between events lead to avalanches and noise patterns Granular bi-axial test Le Bouil et al. Phys. Rev. Lett. (2014) ~10cm
- 13. 13 Statistical physics problem: + Correlation patterns best seen in experiments + Complex spatio-temporal fluctuations + Space-time interactions and correlations between events lead to avalanches and noise patterns Granular bi-axial test Le Bouil et al. Phys. Rev. Lett. (2014) ~10cm
- 14. 14 Quantify Events At Meso-scales Long-range non-local deformation patterns + Compared to grain size Characteristic angular symmetry + Close to four-fold symmetry Space-time interactions lead to noise patterns + Avalanche Process Le Bouil et al., Phy. Rev. Lett. (2014) Correlation Function
- 15. 15 Big Assumption: Mesoscopic patterns resemble response to Shear Transformations Of Eshelby Type Elastic Medium Shear Eshelby Inclusions Surroundings Respond Like A Homogeneous Elastic Continuum
- 16. 16 Shear s Non-local & Anisotropic Quadrupolar Symmetry In Shear Stress
- 18. 18 Shear s Shear p Regions With Positive Shear Negative Pressure Are More Prone To Instability
- 19. 19 Shear fy f Is The Friction Angle Coulomb Stress
- 20. 20 Close To The Angle Seen In The Experiment! Le Bouil et al., Phy. Rev. Lett. (2014)
- 21. 21 Close To The Angle Seen In The Experiment! Le Bouil et al., Phy. Rev. Lett. (2014) Take-home Message: Mesoscopic notion of flow + local flow induces flow elsewhere (triggering) + Non-local coupling described in the Eshelby framework
- 22. 22 OUTLINE + Background: flow of amorphous solids + Connection with “Geoscience”: a few old papers! + Eshelby-type events: “Mesoscopic” notion of plastic flow + Univesality of Eshelby picture (frictional systems)
- 23. 23 Finite Elements Method, Mohr-Coulomb Yield Criterion With Friction Angle f Local Damage Model With Damage Parameter D Strain FrictionalFrictionless Damage Field Diffuse vs. Localized
- 24. 24 Diffuse vs. Localized Different failure mechanism + Diffuse plastic flow + Localized brittle failure Common microscopic process? + Validity of “Eshelby” hypothesis (Friction?) Frictionless Frictional Strain
- 25. 25 Particle-based modeling Detailed micro-structural information but limited length and timescales
- 26. 26 Bi-axial Setup + Harmonic frictional disks in a bi-perodic box + Confining pressure regulated by a Barostat along x + Strain-controlled condition along y
- 27. 27 Normal Restoring Force Tangential Force Coulomb’s Friction Law Simulation & Protocol
- 28. 28 Simulation & Protocol Viscous Drag (Mean + Pair) Normal Restoring Force Tangential Force Coulomb’s Friction Law
- 29. 29 Simulation & Protocol Viscous Drag (Mean + Pair) Normal Restoring Force Tangential Force Coulomb’s Friction Law Solve Newton’s equation of motion Integrate in LAMMPS (open-source software)
- 33. 33 Scattered vs. Localized Modes: Transition Appears To Be Controlled By Friction and/or Cohesion Displacemnt Field
- 34. 34 Friction-less grains undergo localized Eshelby rearrangements. Frictional sliding involves a chain of grains that ride up on one another producing significant “dilatancy” during slip. Plastic Flow Frictional Flow Important Observation
- 35. 35 + The bulk response: monotonic toward flowing state with stress fluctuations + Volume fluctuations too but almost No net change + footprints of Eshelby process in microscopic deformation
- 36. 36 + A stress peak followed by a sheer reduction in strength + Substantial dilatancy prior to yielding + More extended than Eshelby features (like Mode II crack?)
- 37. 37 Correlation Function Eshelby process + Four-fold angular symmetry with ductile shearing which occurs on planes of maximum shear stress Correlation Patterns
- 38. 38 Correlation Function Frictional flow + the quadro-polar shape is distorted with maximal correlation angles tilted toward planes with lower normal stresses Correlation Patterns
- 39. 39 Failure Transition: Sharp vs. Smooth Fluctuations grow exponentially Algebraic divergence StressDropS
- 40. 40 Take-home Messages & Open Questions Relaxation Mechanism Macroscopic Response Prefailure Dynamics Frictionless Dynamics Frictional Dynamics Relax stress via localized Eshelby modes Plastic flow Non-critical associated with mechanical healing Abrupt shear faulting like Mode II fracture Brittle fracture Critical dynamics attributed to progressive damage What are the implications in the Geophyics/Geoscience contexts?
- 41. 41 Take-home Messages & Open Questions Relaxation Mechanism Macroscopic Response Prefailure Dynamics Frictionless Dynamics Frictional Dynamics Relax stress via localized Eshelby modes Plastic flow Non-critical associated with mechanical healing Abrupt shear faulting like Mode II fracture Brittle fracture Critical dynamics attributed to progressive damage What are the implications in the Geophyics/Geoscience contexts? Thank You!
Editor's Notes
- dark regions show activity (before failure) that ultimately localizes into well-defined bands; what was surprising is that structure correlations different; correlations anisotropic form (similar to quadropolar) means sit at damaged site next event likely to occur close at 53 degrees which surprisingly lead to a band with different angle.
- dark regions show activity (before failure) that ultimately localizes into well-defined bands; what was surprising is that structure correlations different; correlations anisotropic form (similar to quadropolar) means sit at damaged site next event likely to occur close at 53 degrees which surprisingly lead to a band with different angle.
- the picture is that eshelby-like events perturbes stress field in some particular way
- perturbation in stress negative positive lobes: it’s very likely to see next event because shear is big at 45 degrees
- why i’m showing pressure
- be more quantitative about this angle, we should look at fy (coulomb) \phi=35 perturbation in coulomb stress still has quadropolar symmetry positive lobes slightly tilting upwards depending on internal friction \phi
- you might have noticed by now … reminder about the message: mesoscopic notion of flow -> eshelby-like picture show that picture with signal and noise thing (use the hidden bottom slide)
- you might have noticed by now … reminder about the message: mesoscopic notion of flow -> eshelby-like picture show that picture with signal and noise thing (use the hidden bottom slide)
- +the paper discusses two types of failure: first homogeneous damage in frictionless systems shear-band (strain localization) in frictional system + explain what this figure is initial defect that is nucleatad because its stress has reached its columb its elastic constant is reduced by a factor threshold D elastic consequence of this softening in the form of these polar features +depending upon friction trigger in a very localized way or diffuse way
- + explain what this figure is +depending upon friction trigger in a very localized way or diffuse way continuum fem model you’re gonna see my model is almost the same but the damage part
- + bi-disperse disks that can interact + normal spring -> have overlap do work + friction modeled by slide overcome friction plus cohesion too + viscous force proportional to velocity + two rigid plates: moving at constant rate contant pressure applied by a barostat + rather standard dem model for granular medium: prepare the sample load the system and see how it evolves
- + bi-disperse disks that can interact + normal spring -> have overlap do work + friction modeled by slide overcome friction plus cohesion too + viscous force proportional to velocity + two rigid plates: moving at constant rate contant pressure applied by a barostat + rather standard dem model for granular medium: prepare the sample load the system and see how it evolves
- + normal spring -> have overlap do work + friction modeled by slide overcome friction plus cohesion too + viscous force proportional to velocity + two rigid plates: moving at constant rate contant pressure applied by a barostat + rather standard dem model for granular medium: prepare the sample load the system and see how it evolves
- + bi-disperse disks that can interact + normal spring -> have overlap do work + friction modeled by slide overcome friction plus cohesion too + viscous force proportional to velocity + two rigid plates: moving at constant rate contant pressure applied by a barostat + rather standard dem model for granular medium: prepare the sample load the system and see how it evolves
- + bi-disperse disks that can interact + normal spring -> have overlap do work + friction modeled by slide overcome friction plus cohesion too + viscous force proportional to velocity + two rigid plates: moving at constant rate contant pressure applied by a barostat rather standard dem model for granular medium: prepare the sample load the system and see how it evolves lammps
- more quantative look localized but long-range compared to size
- picture (mode II crack)