Modelling Intercalation Induced Stresses in All Solid State Batteries Using Discrete Element Method
Authors: So Magnus , Hirate Ryusei , Nunoshita Keita , Ishikawa Shota , Inoue Gen , Tsuge Yoshifumi 
Published: December 2020

Recently, all-solid-state lithium-ion batteries (ASSLiB) has emerged as one of the most promising candidates for next-generation power sources for electric vehicles (EVs) and energy storage. The main reason is the introduction of non-flammable solid electrolyte (SE) which substantially reduces the risk of battery fires. However, more research is needed in order to improve the durability and the overall performance.
High charge capacity active material (AM) such as Si have been developed but their high expansion during charging and discharging reduces the durability. 1 During charge, AM in the cathode will absorb Lithium by intercalation and expand. A reverse contraction process occurs in the anode. This is known as Vegards expansion/contraction and cause buildup of high stresses, so called intercalation induced stresses. Although materials with less expansion/contraction have been developed, it is unclear how much expansion/contraction the materials in AM and SE can tolerate.
Previous studies that model intercalation induced stress can be found in the literature. Most of the research is focused on the intercalation induced stresses either inside the AM or inside SE material. In the study of Bucci et al., 2 the stress in the SE due to Vegards expansion of AM was modelled by the finite element method (FEM) and the location of cracks could be predicted. However, according to Sun et al., 3 the critical region of failure is not within AM and SE but at the interface. Moreover, in FEM it is difficult to resolve the grained boundaries at the interfaces and the continuity assumption may not be valid as there are often void spaces between SE particles. These issues can be solved by modelling AM and SE as particles as in the Discrete Element Methods (DEM).
In this study we perform DEM simulations and utilize the multisphere method for the AM particles. In the multisphere method, non-spherical particles are represented as a cluster of spherical sub-particles as illustrated in Figure 1 (a). We assume elliptical shapes which is in agreement with TEM image of graphite AM. In the DEM solver, the particle motion is determined from the forces acting on each particle. The elastic contact force between two particles with radii Ri
and Rj
is calculated by the Herzian contact law:

F
elastic = 4/3∙E
eff
δ
3/2
R
eff
1/2 (1)
where R
eff = RiRj
/(Ri
+ Rj
) is the effective radius and E
eff is the effective elastic modulus given by
1/E
eff = (1-ν

i

2)/E
i
+(1-ν

j

2)/E
j
(2)

where E
i
and E
j
are the Young modulus of elasticity of the particles. In the DEM solver, collision damping force and the tangential forces due to static and kinetic friction are also calculated. The motion and rotation of each particle was calculated from the sum of forces and torques acting on the particles.
A series of DEM simulations were conducted. Different aspect ratios of the elliptical shapes were generated and the relationship between the aspect ratio and circularity agreed well with the experimental results. A gravity driven packing simulation was conducted followed by a press simulation at 500 MPa and a release simulation to stack pressure at 25 MPa. In order to solve for the intercalation induced stresses, expansion of AM particle was calculated by gradually increasing the particle radius. The results of the spatial distribution of the stresses of the SE material is shown in Figure 2 in the case of a volume expansion of 10%.
During cold pressing of ASSLiB electrode, the contact force is not perfectly elastic but plasticity effects of SE plays a role large role and is an important design parameter 4. In cold pressing applications the normal force is often modeled as follows 5

F
normal = min(F
elastic , F
plastic ) (3)
where F
plastic is the plastic force. A model is currently under development that can simulate the effect of plasticity on stress and damage during cold pressing and intercalation. The model can aid in the development and selection of favorable of materials for ASSLiB electrode.
This research was supported by Grants-in-Aid for Scientific Research on Innovative Areas, “Science on Interfacial Ion Dynamics for Solid State Ionics Devices” MEXT, Japan FY2019-2023.

References

M. N. Obrovac, L. Christensen, D. B. Le, and J. R. Dahn, J. Electrochem. Soc., 154, A849 (2007).

G. Bucci, T. Swamy, Y.-M. Chiang, and W. C. Carter, ArXiv170300113 Cond-Mat (2017) http://arxiv.org/abs/1703.00113.

C. Sun, J. Liu, Y. Gong, D. P. Wilkinson, and J. Zhang, Nano Energy, 33, 363–386 (2017).

K. Nagao et al., Solid State Ion., 308, 68–76 (2017).

C. L. Martin, D. Bouvard, and S. Shima, J. Mech. Phys. Solids, 51, 667–693 (2003).

Figure 1