广义平面应变锂离子电池柱形梯度材料颗粒电极中扩散诱导应力分析

柱形梯度材料是最有潜力的锂离子电池电极之一. 为了研究恒压充电过程中柱形梯度材料颗粒电极下力学机理, 以Li_1.2(Mn_0.62Ni_0.38)_0.8O₂为例, 讨论弹性模量、扩散系数和偏摩尔体积三个重要材料参数对应力场影响. 并推导出非均匀柱形颗粒电极的扩散方程和力学方程. 结果表明, 柱形梯度材料纳米电极, 沿着半径方向Mn 的材料组分升高Ni 的材料组分降低, 其材料结构有利于降低最大径向应力和环向拉应力, 有效地避免电极的力学失效现象. 并根据计算结果, 对梯度材料电极提出材料结构优化建议.

Stress analysis of a cylindrical composition-gradient electrode of lithium-ion battery in generalized plane strain condition

A novel cylindrical composition-gradient electrode is considered to be one of most potential structures in lithium-ion battery. To investigate the mechanism of a cylindrical composition-gradient electrode under potentiostatic operation, we take Li_1.2(Mn_0.62Ni_0.38)_0.8O₂ for example. The effects of the three main factors, i.e., diffusion coefficient, Young’s modulus, partial molar volume of solute, on the stress field in the cylindrical electrode are discussed. Each of the three material parameters is assumed to be a linear function of the distance from the center to surface. The small deformation theory and thermodynamic theory are employed to establish the mathematical model of composition-gradient cylindrical electrode. The mechanics equations and diffusion equation of cylindrical electrode are derived for an inhomogeneous material in plane strain condition. By comparing with single-phase electrode, it is found that Young’s modulus increasing from the center to the surface greatly reduces the max tensile radial stress and tensile hoop stress and changes the location of max radial stress since the radial displacement of the center is restricted. The time for the lithium-ions to reach the center is longer and the tensile stress near the center decreases at dimensionless time τ=0.0574 when diffusion coefficient decreases along the radial direction. Owing to the smaller diffusion coefficient at the surface, there is a reduction in the number of lithium-ions through the unit area in unit time when their corresponding concentration gradients are the same. The variation of partial molar volume means that the volume expansion caused by the intercalation of lithium-ions decreases along the radial direction. Therefore the partial molar volume decreasing along the radial direction considerably reduces the radial stress and the distribution of tangential stress becomes flat. The center point is picked, showing the development of hoop stress. The results show that the hoop stress increases and reaches a maximal value close to the dimensionless time τ=0.0574. Maximal tensile hoop stress at the center is reduced in an inhomogeneous material. The tensile hoop stress turns into compressive stress over time when elastic modulus and partial molar volume are denoted with E(r) and Ω(r) respectively. The results indicate that the cylindrical composition-gradient electrode with core enriched Ni and edge enriched Mn reduces the max tensile radial stress and tensile hoop stress. It is an efficient way to avoid mechanical fracture in electrode since evidence has accumulated that tensile stress is the lead cause of crack in electrode. The result also provides useful guidance for mitigating the stresses in a cylindrical electrode.