恒流充电有限柱体电极浓度分布及扩散诱导应力解析分析

Analytical analysis of concentration distribution and diffusion-induced stress of finite-length cylindrical electrode under galvanostatic operation

常见的柱状电极模型中,在轴向方向一般采用无限长假设广义平面应变分析方法,本文考虑恒流充电下有限柱形电极模型,基于力-化耦合一般方程,推导出位移与扩散诱导应力解析解.有限柱体电极中浓度分布由仅考虑径向扩散和仅考虑轴向扩散两部分叠加求解.将浓度函数代入力学方程,使用Boussinesq-Papkovich函数得到应力分量解析解.计算了表面自由柱状电极中浓度和应力场,并将其结果与有限元软件计算的结果进行对比计算.结果表明,理论解和数值解中浓度分布一致,应力分量趋势一致数值相差较小,在荷电状态为17.9%时径向应力在中心处相对误差最大约为4%.本文分析了不同长径比柱状电极中径向和轴向单向扩散对应力场的影响,结果表明,随着长径比的增大,轴向扩散对浓度分布影响下降,径向扩散对应力场影响上升.

A cylindrical electrode is approximated as a long cylinder in most of existing models in which a generalized plane strain condition/plane strain is used.Based on the theory of elasticity,analytical expressions are derived for concentration distribution and stress component in a finite-length cylindrical electrode under galvanostatic operation.Using the superposition theorem,the Li-concentration is a sum of the concentration due to axial diffusion and the concentration due to lateral diffusion,and the separation of variable method is used to solve diffusion equations.By using the Boussinesq-Papkovich function,the generalized stress component distribution of a linearly combined product of the exponential-type Fourier-Bessel series is derived.The spatiotemporal distribution of concentration and diffusion-induced stresses are calculated in a cylindrical electrode with traction-free condition.The results are compared with the simulation results from a finite element software.For the concentration distribution,the numerical result and simulation result are almost the same.For the stress component,no significant difference exists between the two results,the largest relative difference for radial stress in the center is found to be about 4%and state of charge(SOC)=17.9%.The radial stress decreases with radial position increasing,and decreases to zero at the surface,which is consistent with the results under the boundary condition.The hoop stress is tensile stress around the center of electrode,and becomes a compressive stress near the surface.Owing to the fact that the tensile hoop stress is attributed to the crack initiation,this implies that when plastic deformation is negligible,cracks first form in the center.The stress components with different length-to-radius ratios are calculated.It is found that the stress caused by lateral diffusion increases with length-to-radius ratio increasing,while the stress induced by axial diffusion decreases with length-to-radius ratio increasing.This is because the lateral diffusion has a greater influence on Liconcentration distribution in a cylinder electrode with length-to-radius ratio increasing.