Graphite-based anode materials undergo electrochemical reactions, coupling with mechanical degradation during battery operation, can affect or deteriorate the performance of Li-ion batteries dramatically, and even lead to the battery failure in electric vehicle. First, a single particle model (SPM) based on kinetics of electrochemical reactions was built in this paper. Then the Li-ion concentration and evolution of diffusion induced stresses (DISs) within the SPM under galvanostatic operating conditions were analyzed by utilizing a mathematical method. Next, evolution of stresses or strains in the SPM, together with mechanical degradation of anode materials, was elaborated in detail. Finally, in order to verify the hypothesis aforementioned surface and morphology of the graphite-based anode dismantled from fresh and degraded cells after galvanostatic charge/discharge cycling were analyzed by X-ray diffraction (XRD), field-emission scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The results show that large volume changes of anode materials caused DISs during Li-ion insertion and extraction within the active particles. The continuous accumulations of DISs brought about mechanical failure of the anode eventually.
Li-ion cells are very compelling candidates for power supplies with their high-power and energy density and low self-discharge rate. They have been widely used in new-energy vehicles such as battery electric vehicles (BEV), hybrid electrical vehicles (HEV), and plug-in hybrid electric vehicles (PHEV) in the past few decades [
Unfortunately, the mechanical degradation under some special working conditions is one of the critical challenges in improving performance and prolonging life span of the cells at present. The difficulties existing in measurement of the critical properties and phenomena in electrode materials instigated extensive research activities on numerical modeling of Li-ion batteries worldwide in the last few years [
The literature on modeling of stress and crack formation within active electrode particles is quite extensive. Stresses and fracture in electrodes undergoing volume changes were predicted in a one-dimensional model by Huggins and Nix in [
Despite significant advances in the theoretical investigation of stress and strain evolution within electrode active materials of Li-ion batteries, some innovative researches are still needed to explore the mechanisms of mechanical failure. In this paper, the SPM was established in Section
The single particle model (SPM) was first proposed by Haran et al. [
Schematic illustration of a Li-ion battery during discharge/charge.
For a spherical particle, several groups provided evidence for lithium ion diffusion and phase transformations in mechanical properties. Qi et al. [
The stresses induced by Li-ion diffusion are considered in a SPM of radius
For infinitely small formulation of deformation, the radial and tangential strains of the spherically symmetric particle are given by the following:
The boundary condition
One principal shear stress equals zero and the other two are both
Thus, the stresses distributed at any given time and location can be obtained under the conditions that the concentration distribution is known [
The stress evolution within the spherical particles under galvanostatic condition is studied in this paper since Li-ion batteries applied in EVs are mostly charged with a typical constant current constant voltage (CC-CV) charging strategy. A simple relevant equation of Li-ion diffusion within a spherical SP of radius
Considering that the particle parameters of different batteries will be different, (
This condition denotes that the current is a constant and the ionic flux is invariant at electrode surface. The initial and boundary conditions subjected to galvanostatic control in dimensionless form are given by
The analytic solution to address the diffusion equation (
By utilizing (
Equation (
Figure
Characteristic profile of SPM in the insertion process under galvanostatic control.
Li-ion concentration
Radial stress
Tangential stress
Shear stress
The current sign in (
The tangential stress appears as tensile stress near the sphere center and compressive close to the surface. The maximum of tensile tangential stress appears at the center before the Li-ions reach there and decreases monotonically towards the surface; then, it reverses and appears as compression stress. Afterwards, it increases along the direction of sphere surface. Moreover, the tangential stress increases in magnitude with time at any location and finally tends to a steady-state (see Figure
To demonstrate the complex causality between electrochemistry and mechanical degradation of anode in lithium ion batteries, we opted to study mesophase-carbon-microbead (MCMB) anode as a representative material that undergoes interactions and subsequent DISs during electrochemical cycling. The investigated commercial batteries used in this work have a normal capacity rating of 87 Ah and contain carbon material in anodes. The fresh battery was first charged at 1 C rate to 4.2 V and discharged to 3.0 V subsequently. 1 C rate means the current is 87 A. During each cycle, the battery was operated in a constant current (CC) charge mode and then underwent a CC discharge until its voltage reaches 3.0 V. The rest time between charge and discharge is two hours. The stop criterion for the cycling tests is SOH = 80% at 25°C. The surface and structure morphology of anode materials dismantled from fresh and cycled cells were investigated by XRD, SEM, and TEM.
The graphitic MCMB is spherical and contains somewhat randomly oriented graphitic domains. It consists of graphene sheets staggered in either an AB (hexagonal, the most common form) or ABC (rhombohedral) stacking arrangement. Upon insertion of lithium ions during charge, the graphite was lithiated, and every fourth layer was filled before the next layers begin to take up lithium. However, lithiation may be initiated at several different sites on the surface of a graphite grain, and the lithiated layers did not need to correspond to one another at different nucleation sites. Hence, the expansion of each grain may represent a large fraction of the expansion of a fully lithiated grain [
XRD spectra of graphite-based anode from fresh and degraded cell.
SEM images of (a) fresh graphite-based anode before cycling tests and (b) degraded graphite-based anode after 500 cycles.
Fresh graphite-based anode
Degraded graphite-based anode
This paper studied the evolution of stresses in a graphite-based anode of Li-ion batteries for EVs considering solid mechanics, diffusion theory, and electrochemical interfacial kinetics under galvanostatic condition. The profiles of Li-ion concentration and radial, tangential, and shear stresses in the SPM were analyzed and presented in the insertion and deinsertion process of the lithium ions in the particles. Furthermore, the evolution of phase structure and morphology for materials with anode demonstrates that a combination of XRD, SEM, and TEM can track the cause and effect of electrochemical and mechanical failure processes in a Li-ion battery for EVs. The experimental and analytical results show that large volume changes of anode materials occur during Li-ion insertion and extraction within the active particles. The accumulated changes lead to stresses within the active particles as the battery cycles, and they further lead to mechanical failure of the anode.
The authors declare no competing interests regarding the publication of this article.
This work was supported by the National Natural Science Foundation of China (51575044) and Sichuan Provincial Key Lab of Process Equipment and Control Foundation (GK201603).