The characterization of the response of crystalline materials upon the application of external stress is important since it gives rise to material yielding. Above this threshold, the formability of materials at small scales can be challenged by the development of plastic avalanches. Avalanches, as individual plastic events, have been observed experimentally under stress control conditions at various scales. Although such plastic fluctuations may be hard to detect at macroscopic scales, they dramatically affect mechanical properties at smaller scales. Several nanoindentation techniques have been developed to measure material resistance to irreversible deformation and plastic flow. Nevertheless, the experimental observation of plasticity at the nanoscale still represents a formidable challenge, and very valuable help to this growing field comes from the mechanical testing of several model crystals.
We study the collective behavior of dislocation assemblies in a simplified Discrete Dislocation Dynamics (DDD) model of plastic deformation in two dimensions, including long range dislocation interactions and dislocation motion constraints. These ingredients typically give rise to a yielding transition separating stationary and moving dislocation phases. Intermittent relaxation of the plastic strain-rate is also observed around this transition at mesoscopic scales, and this intermittent
behavior gives rise to an average slow power law relaxation in time known in the literature as Andrade’s creep. In the steady regime, plastic deformation proceeds in the form of plastic avalanches whose size and duration are broadly distributed and statistically characterized.
Jamming of dislocations
Crystalline solids such as metals and ice deform and flow if loaded above the yield stress. Should the external loading be smaller, the plastic deformation – or the movement of the dislocations – comes eventually to a stop. The dislocations resist collectively the applied stress, and as a result the material “hardens” or deforms more slowly. This kind of jamming arises from the complex mutual long-range interactions. A closer look, using simulations of a dislocation dynamics model, reveals that the phase transition between the flowing and jammed states is a dynamical one.
It is similar to jamming transitions observed in many other systems, from granular materials and foams to cars on a highway during the morning rush hour. The collective dislocation dynamics is characterized by a growing dynamical correlation length, diverging at the critical point. Static dislocation structures and patterns however look the same on both sides of that point, regardless of whether the external stress is large enough to make the material flow or not. The existence of a non-equilibrium phase transition should be important for the rheology and deformation of many materials.
In collaboration with
- Mikko Alava
- Lasse Laurson
- Alessandro Vespignani
- Jérôme Weiss
- Michael Zaiser
- Stefano Zapperi