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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应力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SOC=17.9%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。
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关键词:
- 锂离子电池 /
- 有限柱体电极 /
- 扩散诱导应力 /
- Boussinesq-Papkovich函数
A cylindrical electrode is approximated as a long cylinder in most existing models in which 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. Applying the superposition theorem, the Li-concentration is a sum of the concentration due to axial diffusion and the concentration due to lateral diffusion, and separation of variable method are used to solve diffusion equations separately. Employing Boussinesq-Papkovich function, the stress component distributions which are generalized for a linear combination products of the Fourier-Bessel series of exponential type are derived. The spatiotemporal of distribution of concentration and diffusion-induced stresses are calculated in a cylindrical electrode with traction-free condition. The results are compared with a simulation results calculated with a finite element software. For the concentration distribution, the numerical result and simulation result are almost identical. For the stress component, no significant difference exists between the two results, the largest relative difference for radial stress of ~4% is found at center and SOC=17.9%. The radial stress decreases with an increasing radial position, decrease to zero at the surface which is consistent with the boundary condition. The hoop stress is tensile around the center of electrode, turn to compressive near surface. Since the tensile hoop stress is responsible for crack initiation, this suggests cracks is first to found at the center when plastic deformation is negligible. The stress component with different length to radius ratios is calculated. It is found that the stress due to lateral diffusion increases with an increase of length to radius ratios, while the stress due to axial diffusion decreases. This is because that the lateral diffusion has a greater influences on Li-concentration distribution in a cylinder electrode with increasing length to radius ratio.-
Keywords:
- Lithium-ion batteries /
- Finite-length cylindrical electrode /
- Diffusion-induced stress /
- Boussinesq-Papkovich function
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