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Research Papers

Effects of Hydrostatic Stress and Concentration-Dependent Elastic Modulus on Diffusion-Induced Stresses in Cylindrical Li-Ion Batteries

[+] Author and Article Information
Zhansheng Guo

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China;
Shanghai Key Laboratory of Mechanics
in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: davidzsguo@shu.edu.cn

Tao Zhang

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China

Hongjiu Hu

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China;
Shanghai Key Laboratory of Mechanics
in Energy Engineering,
Shanghai University,
Shanghai 200072, China

Junqian Zhang

Department of Mechanics,
Shanghai University,
Shanghai 200444, China;
Shanghai Key Laboratory of Mechanics
in Energy Engineering,
Shanghai University,
Shanghai 200072, China

1Corresponding author.

Manuscript received May 11, 2013; final manuscript received July 31, 2013; accepted manuscript posted August 22, 2013; published online October 16, 2013. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 81(3), 031013 (Oct 16, 2013) (10 pages) Paper No: JAM-13-1191; doi: 10.1115/1.4025271 History: Received May 11, 2013; Revised July 31, 2013; Accepted August 22, 2013

The effects of hydrostatic stress and concentration-dependent elastic modulus on diffusion-induced stress (DIS) in a cylindrical Li-ion battery are studied. It is found that the hydrostatic stress has little effect on the distribution of stresses but the change of elastic modulus has a significant effect on the distribution of stresses. The hydrostatic stress has little effect on the location of maximum hoop stress in active layer. The change of elastic modulus can slow down the trend with closing to the inner surface for the location of the maximum hoop stress in active layer with the thicker current collector or larger modulus of current collector and speed up the trend with closing to the outer surface with the smaller ratio of electrode radius to thickness. The current collector should be as thin and soft as possible when its premise strength is satisfied. The ratio of electrode radius to thickness should be preferably larger than 15.

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Figures

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Fig. 1

Coiled-layered structure of cylindrical Li-ion battery

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Fig. 2

Vertical view of a single hollow cylindrical anode

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Fig. 3

Cross-sectional view of a single hollow cylindrical anode

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Fig. 4

DIS during galvanostatic charging under 11 condition, where Ω = 4.17×10-6 m3mol-1, k = 82.234× 109/cs: (a) dimensionless concentration; (b) dimensionless hoop stress; and (c) dimensionless radial stress. The concentration is normalized by C¯ = CFD/inb, stress by σ¯ = 3σFD/EΩinb, and time by t¯ = Dt/b2.

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Fig. 5

The Li-ion concentration during galvanostatic charging with different conditions

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Fig. 6

The hoop stresses during galvanostatic charging with different conditions

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Fig. 7

The radial stresses during galvanostatic charging operation with different conditions

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Fig. 8

The maximum hoop stress location and its value of active layer with different thickness ratios of current collector to active layer during galvanostatic charging

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Fig. 9

The hoop stresses during galvanostatic charging with different current collector thicknesses: (a) hc/h1 = 0.1; (b) hc/h1 = 0.2; (c) hc/h1 = 0.33

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Fig. 10

The maximum hoop stress location and its value of active layer with different modulus ratio of current collector to active layer during galvanostatic charging

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Fig. 11

The hoop stresses during galvanostatic charging with different modulus ratios: (a) Ec/E = 5; (b) Ec/E = 10; (c) Ec/E = 20

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Fig. 12

The maximum hoop stress location and its value of active layer with different ratios of electrode radius to thickness during galvanostatic charging

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Fig. 13

The maximum and minimum stresses of active layers with different ratios of electrode radius to thickness under 11 condition, where Ω = 4.17×10-6 m3 mol-1, k = 82.234×109/cs

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Fig. 14

The hoop stresses during galvanostatic charging with different electrode radius ratios: (a) a/helectrode = 4.09; (b) a/helectrode = 15.45; (c) a/helectrode = 22.27; (d) a/helectrode = 45

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