Plasticity and Avalanches: Connections Between Systems Ranging from Metals to Granular Materials

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TECHNICAL SUMMARYThis award supports theoretical research and education to combine concepts from statistical physics, materials science, solid mechanics, engineering, granular mechanics, and metallurgy to advance and unify understanding of the response of materials to external stresses. Recent experiments on the shear response of small metal or ice crystals reveal that the deformation is not smooth, but rather jerky, through a sequence of dislocation-slip events that span a broad range of sizes. Similarly, densely packed granular materials respond to shear with a sequence of slip avalanches. In both cases, the distribution of slip event sizes is described by a power law over several decades. The associated power law exponents are the same for a large class of different materials; they are "universal". Simulations of these systems are useful, but connections between different systems can often more easily be recognized using analytic approaches. Building on recent analyses, the size of the class of systems having avalanches and showing the same behavior on long length scales, can be assessed. In this project, the PI will analytically compute predictions for the dependence of the slip-avalanche statistics on a series of important experimental tuning parameters, such as strain rate, stress rate, disorder, and temperature. The approach will also be used to investigate the connection between driven dynamics at low temperature and relaxation dynamics at higher temperature in the absence of driving. A main goal is to expand and test recent analytical approaches in order to unify the understanding of non-equilibrium phenomena that were previously thought to be unrelated. The methods include techniques from the theory of phase transitions, the renormalization group, disordered-systems theory, Monte Carlo simulations and molecular dynamics simulations. Predictions from these studies are compared with experiments on plastic deformation, granular materials, magnets, and results from large-scale simulations. The highly interdisciplinary nature of this research promotes an ideal learning environment for the diverse group of graduate and undergraduate students working on this project. Collaborations with a network of national and international theorists, experimentalists, materials scientists, engineers, and seismologists will be fostered. Simulation codes will be shared with the research community. Potential applications of this work include: materials-failure prediction and control on a broad range of scales, from nanodevices to bulk materials, nondestructive materials testing, improved understanding of the often undesirable Portevin-Le Chatelier effect in metallurgy, increased materials stability during processing, improved understanding of jamming and avalanches of granular materials such as powders and grains in silos, and long-term security of magnetic information storage.NONTECHNICAL SUMMARYThis award supports theoretical research and education to combine concepts from statistical physics, materials science, solid mechanics, engineering, granular mechanics, and metallurgy to advance and unify understanding of how materials respond to external stresses. Many systems crackle when they are pushed slowly: Wood can crackle when it is slowly bent. Similarly, small metal or ice crystals deform in a rather jerky way, through a sequence of local slip events that span a broad range of size. In these slip events, weak spots fail in response to the slowly increasing applied shear stress. On a much larger scale roughly the same phenomenon gives rise to earthquakes, when the slow tectonic motion triggers slips of weak spots in the earth's crust. Many other systems exhibit similar failure avalanches, ranging from granular materials to magnets. This project develops a quantitative understanding of the similarities of the avalanche statistics of these systems, many of which were previously studied separately. The goal is to predict to what extent the results and understanding can be transferred from one system to another. Recently, powerful mathematical tools have been developed to answer these questions. These methods will be coupled with computational simulations and comparisons with experiments on plastic deformation of metals, alloys, granular materials, and magnets. The results are relevant for a number of applications, including: materials failure predictions and control from nanodevices to bulk materials, nondestructive materials testing, increased materials stability during processing, improved understanding of jamming and avalanches of granular materials, and long-term security of magnetic information storage. The diverse group of graduate and undergraduate students involved in this project will receive broad interdisciplinary training, and will learn to use modern tools from statistical physics, materials science, mechanical engineering, and mathematics. Collaborations with a network of national and international theorists, experimentalists, materials scientists, engineers, and seismologists will be fostered. Simulation codes will be shared with the broader research community.