Abstract The plastic flow in a silicon electrode during lithiation can alter the stress state in the silicon electrode and retard the fracture of the silicon electrode. In this work, we develop a rate-dependent model to investigate the plastic flow and phase transformation, which concurrently occur during the lithiation of a cylindrical silicon electrode. Using a power law for the plastic-flow potential and neglecting elastic deformation, we obtain analytical solutions of the stresses in the silicon electrode, which are dependent on the temporal evolution of the interface between lithiated phase and un-lithiated phase. A simplified diffusion model, which captures the temporal evolution of the interface, is proposed in the framework of the Cahn-Hilliard phase-field theory. The numerical results are in good accord with the results from the phase-field model with finite deformation. Under galvanostatic operation, the stresses are dependent on the lithiation rate, and the stresses on the surface of the silicon electrode are independent of initial radius and lithiation time. Under potentiostatic operation, the stresses in a silicon electrode of a smaller radius is larger than that in a silicon electrode of a larger radius. The magnitudes of the stresses on the surface decrease with the increase of both initial radius and the lithiation time.

中文翻译：

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圆柱形硅电极中锂化诱导的同时塑性流动和相变的分析模型

摘要 锂化过程中硅电极中的塑性流动可以改变硅电极的应力状态，延缓硅电极的断裂。在这项工作中，我们开发了一个速率相关模型来研究在圆柱形硅电极锂化过程中同时发生的塑性流动和相变。使用塑性流动势的幂律并忽略弹性变形，我们获得了硅电极中应力的解析解，这取决于锂化相和非锂化相之间界面的时间演变。在 Cahn-Hilliard 相场理论的框架中，提出了一种捕捉界面时间演变的简化扩散模型。数值结果与有限变形相场模型的结果吻合良好。在恒电流操作下，应力取决于锂化速率，硅电极表面的应力与初始半径和锂化时间无关。在恒电位操作下，半径较小的硅电极中的应力大于半径较大的硅电极中的应力。表面应力的大小随着初始半径和锂化时间的增加而减小。半径较小的硅电极中的应力大于半径较大的硅电极中的应力。表面应力的大小随着初始半径和锂化时间的增加而减小。半径较小的硅电极中的应力大于半径较大的硅电极中的应力。表面应力的大小随着初始半径和锂化时间的增加而减小。