CESS Seminar: Fundamentals of brittle failure at the atomic scale
Event details
| Date | 22.03.2019 |
| Hour | 12:15 › 13:00 |
| Speaker | Dr. Laurent Brochard, researcher in Civil Engineering at Laboratoire Navier (ENPC, CNRS, IFSTTAR) |
| Location | |
| Category | Conferences - Seminars |
Abstract
Brittle failure is ubiquitous in civil engineering materials from concrete to rocks and faults. And yet, how brittle failure initiates is still debated. While the failure of pre-cracked bodies is predicted by an energy criterion (fracture mechanics), that of flawless materials is usually given by a stress criterion, and no clear scientific consensus exists about intermediate cases (e.g., notch). In this work, we use atomistic simulation techniques to investigate the elementary mechanisms behind brittle failure. A difficulty, though, is that the process zone size of the studied material must be nanometric to comply with the computational limits of molecular simulations. Very few materials exhibit such a small process zone (e.g., the process zone of rocks is typically 10-100 mm) and the candidate material we study is graphene. We also investigate a fictitious material (2D triangular lattice with harmonic interactions between closest neighbours).
Investigating the failure behaviour of graphene in various configurations, we characterize the transition from the energy criterion of fracture mechanics to the stress criterion. Interestingly, one particular situation exhibits an unexpected result: when the distance between two crack tips approaches the process zone size, the average stress in-between the tips exceeds the strength. While most macroscopic theories of initiation would not expect this behaviour, Leguillon’s criterion does [1]. Leguillon’s criterion is a finite fracture mechanics approach requiring both energy and stress criteria to be fulfilled over an initiation length. The peculiarity of our situation is that energy is the limiting factor since stress is highly concentrated between the tip while only little mechanical energy is available in the material [2].
To further investigate the atomic processes of failure, we consider the athermal limit (0K). Since atomic interactions are conservatives, failure can be viewed as an instability arising when one of the eigenvalues of the hessian matrix becomes negative. And the associated eigenvectors provides a description of the elementary mechanism of failure. Interestingly, failure of flawless materials exhibits infinite failure bands the width of which recalls the process zone size, i.e., a property that one usually gets from a cracked material. The corresponding eigenvalue are highly degenerated, whereas for flawed materials, the eigenvalues have little or no degeneracy and failure involves localized atom moves only.
At non-zero temperature, failure is no more deterministic because of thermal agitation. We conduct an extensive study over many time and length scales and identify a temperature-time-size equivalence that can be formalized by a universal scaling law of strength and toughness which extends Zhurkov’s theory [3] to size effects [4]. Interestingly, the scaling of strength and toughness differ only regarding the scaling in size, and therefore was not previously identified in Zhurkov’s work. One can formally relate this difference to the degeneracy of the negative eigenvalues in the athermal limit. Such scaling law is also of very practical interest to relate failure properties at different length and time scales.
[1] Leguillon, D. (2002). Strength or toughness? A criterion for crack onset at a notch. European Journal of Mechanics, A/Solids, 21(1), 61–72.
[2] Brochard, L., Tejada, I. G., & Sab, K. (2016). From yield to fracture, failure initiation captured by molecular simulation. Journal of the Mechanics and Physics of Solids, 95, 632–646.
[3] Zhurkov, S. N. (1984). Kinetic concept of the strength of solids. International Journal of Fracture, 26(4), 295–307.
[4] Brochard, L., Souguir, S., & Sab, K. (2018). Scaling of brittle failure: strength versus toughness. International Journal of Fracture, 210(1-2), 153–166.
Bio
Laurent Brochard is a researcher in Civil Engineering at Laboratoire Navier (ENPC, CNRS, IFSTTAR) since 2012. He received his M.S. and Ph.D. from Ecole des Ponts ParisTech in 2008 and 2011. He is also engineer from Ecole Polytechnique (France) and from École des Ponts ParisTech (France). His research focuses on multi scale approaches for the study of the physics and mechanics of materials with emphasis on phenomena that have their origin at the molecular scale: adsorption and poromechanics, fracture mechanics and failure initiation, thermo-mechanical couplings. Targeted applications are mostly in geomechanics (CO2 sequestration, nuclear waste storage, unconventional oil and gas, cementitious materials).
Brittle failure is ubiquitous in civil engineering materials from concrete to rocks and faults. And yet, how brittle failure initiates is still debated. While the failure of pre-cracked bodies is predicted by an energy criterion (fracture mechanics), that of flawless materials is usually given by a stress criterion, and no clear scientific consensus exists about intermediate cases (e.g., notch). In this work, we use atomistic simulation techniques to investigate the elementary mechanisms behind brittle failure. A difficulty, though, is that the process zone size of the studied material must be nanometric to comply with the computational limits of molecular simulations. Very few materials exhibit such a small process zone (e.g., the process zone of rocks is typically 10-100 mm) and the candidate material we study is graphene. We also investigate a fictitious material (2D triangular lattice with harmonic interactions between closest neighbours).
Investigating the failure behaviour of graphene in various configurations, we characterize the transition from the energy criterion of fracture mechanics to the stress criterion. Interestingly, one particular situation exhibits an unexpected result: when the distance between two crack tips approaches the process zone size, the average stress in-between the tips exceeds the strength. While most macroscopic theories of initiation would not expect this behaviour, Leguillon’s criterion does [1]. Leguillon’s criterion is a finite fracture mechanics approach requiring both energy and stress criteria to be fulfilled over an initiation length. The peculiarity of our situation is that energy is the limiting factor since stress is highly concentrated between the tip while only little mechanical energy is available in the material [2].
To further investigate the atomic processes of failure, we consider the athermal limit (0K). Since atomic interactions are conservatives, failure can be viewed as an instability arising when one of the eigenvalues of the hessian matrix becomes negative. And the associated eigenvectors provides a description of the elementary mechanism of failure. Interestingly, failure of flawless materials exhibits infinite failure bands the width of which recalls the process zone size, i.e., a property that one usually gets from a cracked material. The corresponding eigenvalue are highly degenerated, whereas for flawed materials, the eigenvalues have little or no degeneracy and failure involves localized atom moves only.
At non-zero temperature, failure is no more deterministic because of thermal agitation. We conduct an extensive study over many time and length scales and identify a temperature-time-size equivalence that can be formalized by a universal scaling law of strength and toughness which extends Zhurkov’s theory [3] to size effects [4]. Interestingly, the scaling of strength and toughness differ only regarding the scaling in size, and therefore was not previously identified in Zhurkov’s work. One can formally relate this difference to the degeneracy of the negative eigenvalues in the athermal limit. Such scaling law is also of very practical interest to relate failure properties at different length and time scales.
[1] Leguillon, D. (2002). Strength or toughness? A criterion for crack onset at a notch. European Journal of Mechanics, A/Solids, 21(1), 61–72.
[2] Brochard, L., Tejada, I. G., & Sab, K. (2016). From yield to fracture, failure initiation captured by molecular simulation. Journal of the Mechanics and Physics of Solids, 95, 632–646.
[3] Zhurkov, S. N. (1984). Kinetic concept of the strength of solids. International Journal of Fracture, 26(4), 295–307.
[4] Brochard, L., Souguir, S., & Sab, K. (2018). Scaling of brittle failure: strength versus toughness. International Journal of Fracture, 210(1-2), 153–166.
Bio
Laurent Brochard is a researcher in Civil Engineering at Laboratoire Navier (ENPC, CNRS, IFSTTAR) since 2012. He received his M.S. and Ph.D. from Ecole des Ponts ParisTech in 2008 and 2011. He is also engineer from Ecole Polytechnique (France) and from École des Ponts ParisTech (France). His research focuses on multi scale approaches for the study of the physics and mechanics of materials with emphasis on phenomena that have their origin at the molecular scale: adsorption and poromechanics, fracture mechanics and failure initiation, thermo-mechanical couplings. Targeted applications are mostly in geomechanics (CO2 sequestration, nuclear waste storage, unconventional oil and gas, cementitious materials).
Practical information
- Informed public
- Free
- This event is internal
Organizer
- Profs. Brice Lecampion & Alexandre Alahi
Contact
- Prof. Brice Lecampion