Emergence of Cooperativity in Plasticity of Soft Glassy Materials

Abstract

The elastic coupling between plastic events is generally invoked to interpret plastic properties and failure of amorphous soft glassy materials. We report an experiment where the emergence of a self-organized plastic flow is observed well before the failure. For this we impose an homogeneous stress on a granular material, and measure local deformations for very small strain increments using a light scattering setup. We observe a non-homogeneous strain that appears as transient bands of mesoscopic size and well defined orientation, different from the angle of the macroscopic frictional shear band that appears at failure. The presence and the orientation of those micro-bands may be understood by considering how localized plastic reorganizations redistribute stresses in a surrounding continuous elastic medium. We characterize the lengthscale and persistence of the structure. The presence of plastic events and the mesostructure of the plastic flow are compared to numerical simulations. [5,6], suggest that such materials may be described using a common framework [1,7,8]. At the center of those descriptions is the hypothesis of localized reorganizations. Such events have been observed in many different studies [3,4,9,10]. Each event modifies locally the mechanical equilibrium, causing the surrounding material to deform, and creating internal stresses. These stresses may then provoke other events, leading to a succession or avalanche of events [11,12]. The coupling between events, and its relevance to an avalanche-like cascade scenario for the description of the final persistent shear-band is still an open question [12,13].Several experimental works show isolated reorganizations followed by localized flow structures, suggesting the existence of such coupling. Conclusions remain elusive in direct observation of colloidal glasses due to the dominance of thermal activity over the triggered events [9]. In athermal systems such as granular materials [10] or foams [3], the steps between accumulation of individual events and appearance of shear bands remain unclear. Very recent numerical and theoretical results suggest that reorganization events may indeed couple in order to produce bands [12,[14][15][16][17]25]. However, the bands observed numerically resulting from the interacting local events are transient and correspond to self-healing micro-cracks, of a different nature than the final persistent shear-bands. To our knowledge such transient micro-bands forming a clear intermittent structure have never been reported experimentally.We present in this letter the first direct experimental evidence showing the progressive emergence of cooperative effects during plastic deformations of an amorphous material. For this, we use a very sensitive light scattering setup to monitor the homogeneous biaxial compression of a granular material. We then show that the plastic flow at the early stage of the loading of a granular material is concentrated along self-healing micro-bands. The orientation of those transient micro-bands are clear...

Experimental study of shear band formation: Bifurcation and localization

“…-A movie of the successive correlation maps during the loading is in supplemental material. The general phenomelogy observed during the loading has been already described elsewhere [11,12]. Strain repartition in the sample is inhomogeneous.…”

“…Intermittent micro-bands are observed from the beginning of the loading until the final shear bands are established. This microstructure has been studied before and the orientation of the micro-bands differ from the orientation of the final shear bands [12]. The former corresponds to the orientation predicted by elasticity for stress released by local plastic rearrangements (Eshelby's quadrupolar redistribution [23]) and does not depend of the frictional properties of the material.…”

Response to a localized stress perturbation during a biaxial test

“…2) are visualized in an analogous way, the same features appear, with the bands being more prominent [2].…”

Experimental study of shear bands formation in a granular material

“…Intermittent heterogeneities of the strain are observed from the very beginning of the loading [12][13][14]. This behavior corresponds to correlated plastic events in the amorphous material and have been analyzed and interpreted in references [13,18].…”

“…Theoretically the phenomenon is described as a bifurcation [2, 8,9]. Experimental works using full-field measurements have studied the distribution of the deformation in a granular materials showing that strain heterogeneities are observed before failure [3,[10][11][12][13][14] but, to the best of our knowledge, the bifurcation initiating the localization process has never been reported in a quantitative study. Here, we report an experimental study where we are able to characterize objectively the distribution of plastic strain in the sample.…”