Ice: the paradigm of wild plasticity

Abstract

Ice plasticity has been thoroughly studied, owing to its importance in glaciers and ice sheets dynamics.In particular, its anisotropy (easy basal slip) has been suspected for a long time, then fully characterized 40 years ago. More recently emerged the interest of ice as a model material to study some fundamental aspects of crystalline plasticity. An example is the nature of plastic fluctuations and collective dislocation dynamics. 20 years ago, acoustic emission measurements performed during the deformation of ice single crystals revealed that plastic "flow" proceeds through intermittent dislocation avalanches, power law distributed in size and energy. This means that most of ice plasticity takes place through few, very large avalanches, thus qualifying associated plastic fluctuations as "wild". This launched an intense research activity on plastic intermittency in the Material Science community. The interest of ice in this debate is reviewed, from a comparison with other crystalline materials. In this context, ice appears as an extreme case of plastic intermittency, characterized by scale-free fluctuations, complex space and time correlations as well as avalanche triggering. In other words, ice can be considered as the paradigm of wild plasticity.*Author for correspondence (jerome.weiss@univ-grenoble-alpes.fr). Phil. Trans. R. Soc. A.crystal/sample scale) dynamics of plastic deformation. We show that ice plastic "flow" actually occurs in a strongly spatially heterogeneous and intermittent way, through dislocation avalanches spanning a huge range of size. We relate this with the plastic anisotropy mentioned above that maximizes the role of long-range elastic interactions in collective dislocation dynamics, and discuss the link with the absence of significant isotropic hardening in ice or of development of an internal characteristic microstructural length scale.This "wild" dynamics, characterized by power law distributions of plastic fluctuations (with infinite variance) [17], strongly contrasts with the plasticity of FCC and BCC metals characterized, for sample sizes larger than few μm, by "mild" (finite variance, Gaussian-like) fluctuations, the development of dislocation sub-structures (e.g. dislocation cells) and isotropic hardening. In this context, ice appears as the paradigm for wild plasticity, including at bulk (>mm) scales. 2.Some specificities of ice plasticityThe fundamentals of ice plasticity have been extensively detailed elsewhere [16,18,19]. Here, the goal is not to give such overview, but instead to focus on some specificities of ice plasticity that are playing a key role in collective dislocation dynamics. Plastic anisotropyAs already stressed above, plastic anisotropy is the most prominent characteristic of ice plasticity. This has been exemplified by the creep tests reported by Duval and others [6] showing, for a given resolved shear stress, basal slip creep rates orders of magnitude larger than non-basal slip creep rates. It is related to the hexagonal structure of ice Ih, shared with

Variety of scaling behaviors in nanocrystalline plasticity

“…For single-slip pure nanocrystals with weak disorder dislocation immobilization can be neglected, so c/D 1, and the stochastic evolution of ρ governed by (20) reduces in this case to a geometric Brownian motion with α ∼ 1. In the automaton model we observe in the low-disorder limit dislocation self-organization, governed exclusively by elastic long-range elastic interactions [32,56], and recover the same value of the exponent τ ∼ 1. With increasing disorder, the immobilization rate c should increase leading to a higher value of τ , which is in qualitative agreement with our numerical experiments.…”

“…It has to be mentioned, however, that our association of the variance of disorder with crystal size is exclusively targeting systems without bulk criticality, as in the case of Mo crystals. One can, in principle, manufacture small crystals with strong (dense) quenched disorder [18] or grow almost pure large crystals with very weak (sparse) quenched disorder [56]. In general, both quenched disorder and the crystal size would affect brittleness, even though to grow almost defect free crystals (without solutes, precipitates and dislocations), is almost impossible except in case of extremely small sizes (nanoparticles).…”

The duration-energy-size enigma for acoustic emission

“…Experimentally, the power law exponents ε and τ′ are typically measured over many decades and our knowledge of any systematics of the dynamic properties of energies and amplitudes is rather good. The same is not true for the duration D. There are very few AE measurements available to determine α with reasonable accuracy 17,42,43 . The PDF of the duration D often follows a power law in some approximation for long durations, while it shows either constant or exponential distributions for short durations.…”

Fluctuations in crystalline plasticity

“…With all this said, the determination of l p , as well as the check of the correctness of the similitude relation, remain fully empirical. Moreover, in crystalline structures characterized by a strong plastic anisotropy, such as HCP crystals, the implied dislocation patterns with a well-defined characteristic size do not form at all [33], which leaves the question of the averaging scale completely open.…”