Effect Of Local Velocity Research Articles

Influence of local velocity on diffusion-induced stress and axial reaction force in a hollow cylindrical electrode of lithium-ion batteries with cosidering expasion rate of medium

Silicon, as the next-generation cathode material in lithium-ion batteries, exhibits excellent electrochemical performances compared with traditional cathode material, such as high capacity and cheap price. However, its cycling performances are greatly affected by the volume change of silicon due to the insertion of Li atoms. Lots of work focuses on the analysis of diffusion-induced stresses in electrode, but the convection term is seldom considered in analyzing the diffusion-induced stress in an electrode. In this paper, a mathematical model is established, where the convection term is taken into consideration in the diffusion process. The mechanics equations and diffusion equation are derived based on continuum mechanics and the diffusion theory. Diffusion-induced stress, axial reaction force and the critical buckling time in a hollow cylindrical electrode under galvanostatic charging are calculated. The effects of local velocity, ratio of the outer radius to inner radius, charging rate, material parameters and lithiation induced softening factors on stress field and the critical buckling time are studied. According to the results, it is found that the influence of local velocity on stress distribution increases with the increasing of Li concentration, and the contribution of local velocity to axial reaction force is insignificant. Compared with the results without local velocity, the tensile hoop stress of inner surface is large, and compressive stress at the outer surface is small. The axial reaction force and the critical buckling time are calculated with different ratios of outer radius to inner radius. As the radius ratio increases, the axial reaction force and critical buckling time decrease. The effects of three main material parameters (elastic modulus, diffusion coefficient, partial molar volume) on axial reaction force are discussed. The dimensionless force is independent of elastic modulus due to stress varying linearly with Young's modulus. The critical time is inversely proportional to diffusion coefficient. As the partial molar volume increases, which indicates larger volume change induced by the intercalation of the same quantity of Li-ions, the critical buckling time drops and the effect of local velocity on stress field increases. It takes less time for axial reaction force to reach the critical buckling force at a higher charging rate. The elastic properties of silicon in the lithiation process should be a function of Li concentration due to the formation of Li-Si alloy. The elastic modulus is assumed to be a linear function of Li concentration. The hollow cylindrical electrodes with increasing absolute value of lithiation induced softening factor have lower maximum axial reaction force. However, the lithiation induced softening factor has a limited effect on the critical buckling time due to the fact that the Li concentration at critical buckling time is relatively small.

Effect of local velocity on diffusion-induced stress in large-deformation electrodes of lithium-ion batteries

In this work, the contribution of local velocity to the resultant flux of lithium in lithium-ion battery is introduced into the diffusion equation to describe the migration of lithium in the active material of electrodes. The effect of the local velocity on the stress evolution in a spherical electrode made of silicon is analyzed, using the derived diffusion equation and nonlinear theory of elasticity. Two boundary conditions at the surface of the electrode, which represent two extreme conditions of real electrode materials, are used in the stress analysis: one is stress-free, and the other is immobile. The numerical results with the stress-free boundary condition suggest that the effect of the local velocity on the distribution of radial stress and hoop stress increases with the increase of time and the effect of the local velocity on the distribution of lithium is relatively small. In comparison with the results without the effect of the local velocity, the effect of the local velocity is negligible for the immobile boundary condition. The numerical result shows that the use of the immobile boundary condition leads to the decrease of von-Mises stress, which likely will retard the mechanical degradation of electrode and improve the electrochemical performance of lithium-ion battery.

Effect of local deformation on the coupling between diffusion and stress in lithium-ion battery

It is known that the local deformation in electrode plays an important role in controlling the migration rate of lithium in lithium-ion battery, which can alter the stress state in electrode. This work derives a new diffusion equation, which takes account of the effect of the local velocity in an electrode, to describe the migration of lithium in the electrode. The effects of the local velocity on the lithium migration and stress evolution are analyzed, using the derived diffusion equation and the theory of linear elasticity. Numerical analysis of diffusion-induced stress in an isotropic, spherical electrode is performed. The numerical results show that there is a larger concentration gradient in the spherical electrode with the effect of local velocity than that without the effect of local velocity, which results in larger magnitudes of radial stress, hoop stress, and von-Mises stress than the corresponding magnitudes without the effect of local velocity. The effects of the current density on the distributions of the lithium concentration and stresses are also analyzed. For a small lithiation rate, the concentration gradient is relatively small, and the stresses in the spherical electrode are small. The results suggest that using small lithiation rates can retard the electrode from fast capacity fading and mechanical degradation.