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The materials used in lithium ion insertion electrodes experience large changes in volume as the battery is charged or discharged and they absorb or emit lithium. For example, a graphitic electrode increases in volume by 10% when lithiated; while high-capacity materials such as Si expand by up to 300%. The stress generated by this volume expansion can lead to plastic flow and fracture, which cause batteries to lose their capacity. There is consequently great interest in designing failure resistant composite battery microstructures. Modeling deformation and failure in candidate battery materials, together with careful experimental measurements of the behavior of battery materials during lithiation will be important steps in this process. To this end, we formulate the continuum field equations and constitutive equations that govern deformation, stress, and electric current flow in a Li-ion half-cell. The model considers mass transport through the system, deformation and stress in the anode and cathode, electrostatic fields, as well as the electrochemical reactions at the electrode/electrolyte interfaces. It extends existing analyses by accounting for the effects of finite strains and plastic flow in the electrodes, and by exploring in detail the role of stress in the electrochemical reactions at the electrode-electrolyte interfaces. In particular, calculations show that that stress directly influences the rest potential at the interface, so that a term involving stress must be added to the Nernst equation if the stress in the solid is significant. The model is used to predict the variation of stress and electric potential in a model 1-D half-cell, consisting of a thin film of Si on a rigid substrate, a fluid electrolyte layer, and a solid Li cathode. The predicted cycles of stress and potential are shown to be in good agreement with experimental observations. In addition, a simple finite element method for modeling deformation and fracture in more complex microstructures will be described, together with some preliminary models of fracture and plastic flow in thin films and particles during lithiation.
About the Speaker
Allan Bower is Royce Family Professor of Teaching Excellence and Professor of Engineering at Brown University. He received undergraduate and graduate degrees from the University of Cambridge. He has served as co-director of the GM-Brown collaborative research laboratory in computational materials research for the past 8 years. His research interests have included contact mechanics, fracture mechanics, thin films, electromigration failures in interconnects, multiscale modeling of formability in high strength steels and lightweight Aluminum and Magnesium alloys, and mechanics of energy storage materials.
*Times, dates and titles are subject to change. Check mechanical.illinois.edu for updated information. These seminars count toward the requirements for ME 590 and TAM 500.