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We revisit the problem of describing creep in heterogeneous materials by an effective temperature by considering more realistic (and complex) non-mean-field elastic redistribution kernels. We show first, from theoretical considerations, that, if elastic stress redistribution and memory effects are neglected, the average creep failure time follows an Arrhenius expression with an effective temperature explicitly increasing with the quenched heterogeneity. Using a thermally activated progressive damage model of compressive failure, we show that this holds true when taking into account elastic interactions and memory effects, however with an effective temperature $T_{eff}$ depending as well on the nature of the (non-democratic) elastic interaction kernel. We observe that the variability of creep lifetimes, for given external conditions of load and temperature, is roughly proportional to the mean lifetime, therefore depends as well on $T$, on quenched heterogeneity, and the elastic kernel. Finally, we discuss the implications of this effective temperature effect on the interpretation of macroscopic creep tests to estimate an activation volume at the microscale.

We study the creep behavior of a disordered brittle material (concrete) under successive loading steps, using acoustic emission and ultrasonic sensing to track internal damage. The primary creep rate is observed to follow a (Omori-type) power-law decay in the strain rate, the number of acoustic emission events as well as the amplitudes of the ultrasonic beams, supporting a brittle-creep mechanism. The main outcome is however the discovery of unexpected history effects that make the material less prone to creep when it has been previously deformed and damaged under primary creep at a lower applied stress. With the help of a progressive damage model implementing thermal activation, we interpret this as an aging-under-stress phenomenon: during an initial creep step at relatively low applied stress, the easy-to-damage sites are exhausted first, depleting the excitation spectrum at low stress gap values. Consequently, upon reloading under a larger applied stress, although previously damaged, the material creeps (and damages) less than it would under the same stress but without pre-creeping. Besides shedding a new light on the fundamental physics of creep of disordered brittle materials, this has important practical consequences in the interpretation of some experimental procedures, such as stress-stepping experiments.

Creep is defined as time-dependent deformation and rupture processes taking place within a material subjected to a constant applied stress smaller than its athermal, time-independent strength. This time-dependence is classically attributed to thermal activation of local deformation events. The phenomenology of creep is characterized by several ubiquitous but empirical rheological and scaling laws. We focus here on primary creep following the onset of loading, for which a power law decay of the strain-rate is observed, with the exponent p varying between '0.4 and 1, this upper bound defining the so-called logarithmic creep. Although this phenomenology is known for more than a century, the physical origin of Andrade-like (p <1) creep remains unclear and debated. Here we show that p <1 values arise from the interplay between thermal activation and elastic stress redistribution. The latter stimulates creep dynamics from a shortening of waiting times between successive events, is associated to material damage and possibly, at high temperature and/or stresses, gives rise to avalanches of deformation events., Comment: to be published in Physical review Materials

Recently acoustic signature of dislocation avalanches in HCP materials was found to be long tailed in size and energy, suggesting critical dynamics. Even more recently, the intermittent plastic response was found to be generic for micro- and nano-sized systems independently of their crystallographic symmetry. These rather remarkable discoveries are reviewed in this paper in the perspective of the recent studies performed in our group. We discuss the physical origin and the scaling properties of plastic fluctuations and address the nature of their dependence on crystalline symmetry, system size, and disorder content. A particular emphasis is placed on the associated emergent behaviors, including the formation of dislocation structures, and on our ability to temper plastic fluctuations by alloying. We also discuss the "smaller is wilder" size effect that culminates in a paradoxical crack-free brittle behavior of very small, initially dislocation free crystals. We show that the implied transition between different rheological behaviors is regulated by the ratio of length scales $R=L/l$, where $L$ is the system size and $l$ is the internal length. We link this new size effect with other related phenomena like size dependence of strength ("smaller is stronger") and the size induced switch between different hardening mechanisms. One of the technological challenges in nanoscience is to tame the intermittency of plastic flow. We show that this task can be accomplished by generating tailored quenched disorder which allows one to control micro- and nano-scale forming and opens new perspectives in micro-metallurgy and structural engineering of ultra-small load-carrying elements. These results could not be achieved by conventional methods that do not explicitly consider the stochastic nature of collective dislocation dynamics.

We study experimentally the fluctuations of deformation along a shear fault naturally emerging within a compressed frictional granular medium. Using laser interferometry, we show that the deformation inside this granular gouge occurs as a succession of localized micro-slips distributed along the fault. The associated distributions of released seismic moments, the memory effects in strain fluctuations, as well as the time correlations between successive events, follow exactly the empirical laws of natural earthquakes. Using a methodology initially developed in seismology and social science, we reveal, for the first time at the laboratory scale, the underlying causal structure. This demonstrates that the spatio-temporal correlations of the slip dynamics effectively emerge from more fundamental triggering kernels. This formal analogy between natural faults and our experimentally controllable granular shear band opens the way towards a better understanding of earthquake physics. In particular, comparing experiments performed under different imposed deformation rates, we show that strain, not time, is the right parameter controlling the memory effects in the dynamics of our fault analog. This raises the fundamental question of the relative roles of strain-dependent structural rearrangements within the fault gouge vs that of truly time-dependent, thermally activated processes, in the emergence of spatio-temporal correlations of natural seismicity.

Crackling dynamics is characterized by a release of incoming energy through intermittent avalanches. The shape, i.e. the internal temporal structure of these avalanches, gives insightful information about the physical processes involved. It was experimentally shown recently that progressive damage towards compressive failure of quasi-brittle materials can be mapped onto the universality class of interface depinning when considering scaling relationships between the global characteristics of the microcracking avalanches. Here we show, for three concrete materials and from a detailed analysis of the acoustic emission waveforms generated by microcracking events, that the shape of these damage avalanches is strongly asymmetric, characterized by a very slow decay. This remarkable asymmetry, at odds with mean-field depinning predictions, could be explained, in these quasi-brittle materials, by retardation effects induced by enhanced viscoelastic processes within a fracture process zone generated by the damage avalanche as it progresses. It is associated with clusters of sub-avalanches, or aftershocks, within the main avalanche.

In this paper, we study the effects of $\theta ^\prime$-Al$_2$Cu plate-like precipitates on the plasticity of Al-Cu micro-pillars, with a sample size allowing the precipitates to cross the entire micro-pillar. {100}-slip traces are identified for the first time in Al and Al alloys at room temperature. We investigate the underlying mechanisms of this unusual {100}-slip, and show that it operates along the coherent $\theta ^\prime$-Al$_2$Cu precipitate/$\alpha$-Al matrix interface. A combination of molecular dynamics simulations and stress analysis indicates that screw dislocations can cross-slip from the {111} plane onto the {100} $\theta ^\prime$-Al$_2$Cu/$\alpha$-Al interface, then move on it through a kink-pair mechanism, providing a reasonable explanation to the observed {100}-slips. The roles of the $\theta ^\prime$-Al$_2$Cu/$\alpha$-Al matrix interface on the properties of interfacial dislocations are studied within the Peierls-Nabarro framework, showing that the interface can stabilize the {100} screw dislocations from the spreading of the core, and increases the Peierls stress. These results improve our understanding of the mechanical behavior of Al-Cu micro-pillars at room temperature, and imply an enhanced role of interfacial slip in Al-Cu based alloys at elevated temperature in consideration of the underlying kink-pair mechanism., Comment: 24 pages, 10 figures

The continuous miniaturization of modern electromechanical systems calls for a comprehensive understanding of the mechanical properties of metallic materials specific to micrometer and sub-micrometer scales. At these scales, the nature of dislocation-mediated plasticity changes radically: sub-micrometer metallic samples exhibit high yield strengths, however accompanied by detrimental intermittent strain fluctuations compromising forming processes and endangering structural stability. In this paper, we studied the effects of plate-like $\theta^\prime$-Al$_2$Cu precipitates on the strength, plastic fluctuations and deformation mechanisms of Al-Cu alloys from micro-pillar compression testing. The plate-like precipitates have diameters commensurate with the external size of the Al-Cu micro-pillars. Our results show that these plate-like precipitates can strengthen the materials and suppress plastic fluctuations efficiently at large sample sizes ($\geq 3 \mu m$). However, the breakdown of the mean-field pinning landscape at smaller scales weakens its taming effect on intermittency. Over an intermediate range of sample sizes allowing the precipitates to cross the entire pillar, an enhanced apparent strain hardening and a sharp decrease of jerkiness are observed, in association with the presence of {100}-slip traces along the coherent $\theta^\prime$-Al$_2$Cu precipitate/$\alpha$-Al matrix interface and precipitate shearing. These complex effects of plate-like precipitates on plasticity are analyzed, experimentally and theoretically, in view of the interferences between external and internal sizes, and the related modifications of the underlying plastic mechanisms., Comment: 35 pages, 11 figures

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.

Plasticity in soft amorphous materials typically involves collective deformation patterns that emerge upon intense shearing. The microscopic basis of amorphous plasticity has been commonly established through the notion of "Eshelby"-type events, localized abrupt rearrangements that induce flow in the surrounding material via non-local elastic-type interactions. This universal mechanism in flowing disordered solids has been proposed despite their diversity in terms of scales, microscopic constituents, or interactions. However, we argue that the presence of frictional interactions in granular solids alters the dynamics of flow by nucleating micro shear cracks that continually coalesce to build up system-spanning fracture-like formations on approach to failure. The plastic-to-brittle failure transition is uniquely controlled by the degree of frictional resistance which is in essence similar to the role of heterogeneities that separate the abrupt and smooth yielding regimes in glassy structures.

Acoustic emission (AE) measurements performed during the compressive loading of concrete samples with three different microstructures (aggregate sizes and porosity) and four sample sizes revealed that failure is preceded by an acceleration of the rate of fracturing events, power law distributions of AE energies and durations near failure, and a divergence of the fracturing correlation length and time towards failure. This argues for an interpretation of compressive failure of disordered materials as a critical transition between an intact and a failed state. The associated critical exponents were found to be independent of sample size and microstructural disorder and close to mean-field depinning values. Although compressive failure differs from classical depinning in several respects, including the nature of the elastic redistribution kernel, an analogy between the two processes allows deriving (finite)-sizing effects on strength that match our extensive dataset. This critical interpretation of failure may have also important consequences in terms of natural hazards forecasting, such as volcanic eruptions, landslides, or cliff collapses., Comment: Supplementary Material included

The failure of brittle solids involves, before macroscopic rupture, power-law distributed avalanches of local rupture events whereby microcracks nucleate and grow, which are also observed in for an elastic interface evolving in a non-homogeneous medium. For this reason, it is tempting to relate failure to the depinning of an elastic interface. Here we compute the elastic kernel of the interface representing the damage field of a brittle solid. In the case of a damage model of rupture under compression, which implements the Mohr-Coulomb criterion at the local scale, we show that the elastic kernel is unstable, and hence is very different from the kernels of usual interfaces. We show that the unstable modes are responsible for the localization of damage along a macroscopic fault observed in numerical simulations. At low disorder, the most unstable mode gives the orientation of the macroscopic fault that we measure in numerical simulations. The orientation of the fault changes when the level of disorder is increased, suggesting a complex interplay of the unstable modes and the disorder.

The Mohr-Coulomb criterion is widely used in geosciences to relate the state of stress at failure to the observed orientation of the resulting faults. This relation is based on the assumption that the fault occurs along a plane that maximizes the Coulomb stress. Here, we test this hypothesis using an elastic, progressive damage model that implements the Mohr-Coulomb criterion at the local scale. We find that the orientation of the fault is not given by the Mohr-Coulomb criterion. Instead, for minimal disorder, it corresponds to the most unstable mode of damage in the model, which we determine through a linear stability analysis of the homogeneously damaged state. Our simulations show that microstructural disorder significantly affects the orientation of the fault, which, however, remains always far from the Mohr-Coulomb prediction.

The extreme miniaturization in modern technology calls for deeper insights into the non-conventional, fluctuation dominated mechanics of materials at micro- to nano-scales. Both experiments and simulations show that sub-micron face-centered-cubic (FCC) crystals exhibit high yield strength, which is, however, compromised by intermittent, power law distributed strain fluctuations, typical of wild plasticity. At macro-scales, the same bulk materials show mild plasticity characterized by bounded, uncorrelated fluctuations. Both anomalous strength and intermittency appear therefore as size effects. While the former is highly desirable, the latter is detrimental because stochastic dislocation avalanches interfere with forming processes and endanger structural stability. In this paper we show that defectiveness, which is used in classical metallurgy to harden materials, can be used at sub-micron scales to suppress intermittent fluctuations. We quantify the coexistence of wild and mild fluctuations in compressed Al alloys micro-pillars, demonstrate that the statistical nature of fluctuations is determined by sample size, and propose quantitative strategies allowing one to temper plastic intermittency by artificially tailored disorder. Our experimental results are rationalized using a theoretical framework which quantifies the competition between external (size related) and internal (disorder related) length scales., Comment: 36 pages, 15 figues

We investigate the evolution of multi-scale mechanical properties towards the macroscopic mechanical instability in frictional granular media under multiaxial compressive loading. Spatial correlations of shear stress redistribution following nucleating contact sliding events and shear strain localization are investigated. We report growing correlation lengths associated to both shear stress and shear strain fields that diverge simultaneously as approaching the transition to a dense flow regime. This shows that the transition from quasi static to dense flow regime can be interpreted as a critical phase transition. Our results suggest that no shear band with a characteristic thickness has formed at the onset of instability.

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments.

The essential role of long range elastic interactions in recrystallization is demonstrated using a simple analytical model: pileup rearrangements following absorption of leading dislocations by a dislocation-free embryo provides an additional driving force that results in a drastic decrease of both the nucleation critical radius and the saddle point energy. A very sharp transition is evidenced, at which the saddle point totally disappears and nucleation becomes spontaneous. This transition occurs for a well defined critical stress corresponding to both a critical density of geometrically necessary dislocations and a critical strain, without invoking any critical nucleus size that may be reached with the help of some dislocation microstructure instability. The present model is illustrated here by the case of polycrystalline ice, but may apply to other crystalline material with significant plastic anisotropy, as Zircaloy for instance., Comment: 7 pages, 3 figures

Previous acoustic emission (AE) experiments on ice single crystals, as well as numerical simulations, called for the possible occurrence of self-organized criticality (SOC) in collective dislocation dynamics during plastic deformation. Here, we report AE experiments on hcp metallic single crystals. Dislocation avalanches in relation with slip and twinning are identified with the only sources of AE. Both types of processes exhibit a strong intermittent character. The AE waveforms of slip and twinning events seem to be different, but from the point of view of the AE event energy distributions, no distinction is possible. The distributions always follow a power law, even when multi-slip and forest hardening occur. The power law exponent is in perfect agreement with those previously found in ice single crystals. Along with observed time clustering and interactions between avalanches, these results are new and strong arguments in favour of a general, SOC-type, framework for crystalline plasticity., Comment: 12 pages, 10 figures

Recently, mechanical tests on ice as well as dislocation dynamics simulations have revealed that plastic flow displays a scale-free intermittent dynamics characterized by dislocation avalanches with a power law distribution of amplitudes. To further explore the complexity of dislocation dynamics during plastic flow, we present a statistical analysis of dislocation avalanche correlations and avalanche triggering. It is shown that the rate of avalanche triggering immediately after any avalanche is larger than the background activity due to uncorrelated events. This self-induced triggering increases in intensity, and remains over the background rate for longer times, as the amplitude of the mainshock increases. This analysis suggests that stress redistributions and the associated collective dislocation rearrangements may be responsible for aftershock triggering in the complex process of plastic deformation., Comment: 8 pages, 3 figures, presented at ICSMA-13, August 2003, Budapest

The ice microstructure (grain boundaries) is a key feature used to study ice evolution and to investigate past climatic changes. We studied a deep ice core, in Dome Concordia, Antarctica, which records past mechanical deformations. We measured a "texture tensor" which characterizes the pattern geometry and reveals local heterogeneities of deformation along the core. These results question key assumptions of the current models used for dating.

We present a statistical analysis of the acoustic emissions induced by dislocation motion during the creep of ice single crystals. The recorded acoustic waves provide an indirect measure of the inelastic energy dissipated during dislocation motion. Compression and torsion creep experiments indicate that viscoplastic deformation, even in the steady-state (secondary creep), is a complex and inhomogeneous process characterized by avalanches in the motion of dislocations. The distribution of avalanche sizes, identified with the acoustic wave amplitude (or the acoustic wave energy), is found to follow a power law with a cutoff at large amplitudes which depends on the creep stage (primary, secondary, tertiary). These results suggest that viscoplastic deformation in ice and possibly in other materials could be described in the framework of non-equilibrium critical phenomena.

The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated `dislocation-dynamics' simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that dislocations move in a scale-free intermittent fashion. This result is confirmed by numerical simulations of a model of interacting dislocations that successfully reproduces the main features of the experiment. We find that dislocations generate a slowly evolving configuration landscape which coexists with rapid collective rearrangements. These rearrangements involve a comparatively small fraction of the dislocations and lead to an intermittent behavior of the net plastic response. This basic dynamical picture appears to be a generic feature in the deformation of many other materials. Moreover, it should provide a framework for discussing fundamental aspects of plasticity, that goes beyond standard mean-field approaches that see plastic deformation as a smooth laminar flow.

We propose a numerical model to study the viscoplastic deformation of ice single crystals. We consider long-range elastic interactions among dislocations, the possibility of mutual annihilation, and a multiplication mechanism representing the activation of Frank-Read sources due to dislocation pinning. The overdamped equations of motion for a collection of dislocations are integrated numerically using different externally applied stresses. Using this approach we analyze the avalanche-like rearrangements of dislocations during the dynamic evolution. We observe a power law distribution of avalanche sizes which we compare with acoustic emission experiments in ice single crystals under creep deformation. We emphasize the connections of our model with non-equilibrium phase transitions and critical phenomena.