Deformation and failure of lithium-ion batteries treated as a discrete layered structure

doi:10.1016/j.ijplas.2019.06.011

International Journal of Plasticity

Volume 121, October 2019, Pages 293-311

https://doi.org/10.1016/j.ijplas.2019.06.011 Get rights and content

Highlights

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Deformation and failure of Li-ion batteries can be accurately described by a detailed FE model.
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The DPC plasticity model well characterizes the granular coatings of the anode and the cathode.
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Fracture of Li-ion batteries is preceded by strain localization, as indicated by simulation.
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Fracture initiates from aluminum foil and ends up with separator as the cause of short circuit.

Abstract

Safety of lithium-ion batteries under mechanical loadings is currently one of the most challenging and urgent issues facing in the Electric Vehicle (EV) industry. The architecture of all types of large-format automotive batteries is an assembly of alternating layers of anode, separator, and cathode. The anode is composed of a very thin copper foil double-side coated with graphite powders, while the cathode is an aluminum foil with the active material coating. Each of the five components may develop a large plastic deformation until fracture. This study focuses on the effect of the properties of the coated materials on the local and global responses of a battery cell. Both anode and cathode coatings are described by the Drucker-Prager/Cap plasticity model, which is carefully calibrated through axial and lateral compression tests and closed-die compaction test. A separate experimental effort is put on finding the strength of the interface between the foils and the granular materials with a binder.

The main new finding is that in the cases of plane-strain and axisymmetric loadings, the failure of cells proceeds in two stages. First, the shear bands localize along discrete lines. Then, fracture develops inside the shear bands due to large local strain gradient. The present model is applied to study the deformation and strength of large-format pouch cells subjected to local indentations by rigid punches. The prediction of the present model follows closely the measured load-displacement curve and captures with good accuracy the magnitude of the peak load and the corresponding critical displacement. In addition, an excellent correlation is achieved between the calculated profile of the through-thickness crack and the result of the micro CT scan.

The present detailed computational model should be useful in the battery design process and will serve as an important new computational tool for assessing the safety of lithium-ion batteries against mechanical loading.

Graphical abstract

Introduction

The lithium-ion batteries for Electric Vehicles (EV) are so different from other man-made structures that it is difficult to find anything of a similar design. Their primary function is to provide the energy (for extended range) and power (for accelerations). Batteries belong to the class of layered structures of alternating powders and metal foils, for which there is no easy analogy to any well-known materials or structures. Batteries subjected to compression develop a distinct pattern of folds and kinks (Wang, Simunovic, Maleki, Howard, & Hallmark, 2016) often observed in some granular materials, while on the other hand, the strength of the battery structure is significantly greater than that of natural granular media due to the existence of the current collectors. In other words, the mechanical behavior of the battery structure is a combination of the contributions of both the powders and the metal foils.

In the battery manufacturing community, the property of strength and resistance of lithium-ion cells to external loading has never been a design consideration. Yet, under local mechanical loading, the batteries are prone to developing a short circuit, which may lead to the generation of smoke, fire, and possible explosion. Safety of Li-ion cells is perhaps the main factor behind the efforts to develop suitable deformation and failure models. Batteries may also fail under thermal abuse (overheating) or electrical abuse (overcharging). This paper is concerned only with mechanical abuse, which is a relatively new topic. Sahraei et al. proposed in a series of publications (Sahraei et al., 2012a, 2012b; Xia et al., 2014) a homogenized computational model, in which properties of all components were smeared into a continuum mechanics model. The uncoupled crushable foam model (MAT 063 in LS-DYNA) was then used and calibrated through two simple punch indentation tests. Despite its simplicity, the model gave a rather good correlation with tests in terms of predicting the load-displacement response for a range of batteries with the different form factors, including cylindrical (Sahraei et al., 2012a), elliptical (Sahraei et al., 2016), prismatic (Sahraei et al., 2010) and pouch cells (Sahraei et al., 2014, 2012b). Several authors followed the same testing and calibration procedure, for example (Lai et al., 2014a, 2014b; Liu et al., 2018; Wang, Yang, & Lin, 2016; Zhang et al., 2015).

An alternative approach was taken by Xia et al. (2014) who used the Deshpande-Fleck model (crushable foam model in Abaqus) (Deshpande and Fleck, 2000) in the problem of the bottom ground impact on module consisting of cylindrical cells. The Deshpande-Fleck model is coupled but requires more tests for calibration. The same model was used for optimizing the bottom protective structure of EV with the help of the MMC (modified Mohr-Coulomb) ductile fracture model of the material (Bai and Wierzbicki, 2008; Zhu et al., 2018c). A comparison of the predictive capabilities of LS-DYNA and Abaqus crushable foam models was recently made by Lian et al. (2019).

The homogenized model of cells is an effective tool for predicting the global load-displacement response and in some instance the first failure of cells. However, the model parameters for failure are loading case dependent property, which limits to a certain extent its widespread applicability. In addition, no information is given on the sequence of deformation and fracture pattern inside the cells, which are important for understanding limits on safe battery operation under accidental loading. Sahraei and Bosco (Sahraei et al., 2016) developed the Representative Volume Element (RVE), consisting of a basic repeatable unit and run FE simulations of some loading cases. The coating in their model was treated as the crushable foam. It was found that a combination of two compressive strains applied to the boundary of the RVE makes the separator to fracture, thus opening the way for creating the short circuit and battery thermal runaway. Finegan et al. (Finegan, 2016; Finegan et al., 2017) performed the in-situ tests of the nail penetration and produced high-resolution images of formation of the global shear crack from the tip of the nail. A full computational model, where all five components of the cell are describes separately and then combine into a system, removes this restriction. Despite differences in size, shape, and specific properties, all lithium-ion cells have the same architecture, consisting of alternating layers, which are wound (cylindrical and prismatic) or stacked (pouch) on one another. For a short description of the architecture of cells, the reader must jump ahead to Section 2. While the mechanical properties of the individual layers were studied with varying success in a number of recent publication (Chung et al., 2018; Wang et al., 2018; Zhang et al., 2017; Zhu et al., 2016), none succeeded in putting together a detailed model, applicable to all loading situations.

Two major challenges have been encountered. One is the very small thickness (10–25 μm) of the aluminum and copper foils. The determination of the hardening curve requires a sub-size tensile specimen with less than 1 mm gauge length. Even the best cutting technique leaves edge imperfection that combined with difficulties in mounting and alignment of specimens makes the stress-strain curve unreliable. Several earlier papers suffer from this deficiency (Lai et al., 2014a, 2014b; Liu et al., 2018; Sahraei et al., 2015; Zhang et al., 2017). The construction of the miniature loading device removed finally this deficiency (Bonatti and Mohr, 2016; Gorji and Mohr, 2017; Zhu et al., 2018b). The second shortcoming of the existing detailed models is the description of the coating of the electrodes. The previously discussed coupled and uncoupled crushable foam models do not distinguish between two fundamental deformation modes of the granular materials, which are sliding and consolidation. In the search for a most suitable constitutive model, it must be understood the batteries are subjected only to predominantly compressive in-plane and out-of-plane loading. From this perspective, the Drucker-Prager/Cap (DPC) model emerges as the model of choice for numerical simulation of industrial die compaction operations and therefore is adopted to the present battery research. For an excellent review of the state of art in this field, the reader is referred to (Atrian et al., 2018; Han et al., 2008a; Shang et al., 2012). The present paper uses the generally accepted notation of (Shang et al., 2012).

The main focus of the paper is put into testing and calibration of the coating of the negative (anode) and positive (cathode) electrodes and formulating interface conditions between various layers. The properties of the anode and cathode coatings are different. Separate tests and calibration are performed for both types of coatings of the commercial pouch cells and then the finite element model is assembled for the entire cells subjected to several typical loading cases. The shear band localization is predicted under out-of-plane punch loading while buckles, folds, and kinks and zones of delamination are visible in the case of the in-plane compression. A separate effort is devoted to establishing a fracture criterion for each of the five components. The calculated local deformation and failure patterns are compared with the CT scan images, showing very close agreement. Likewise, the numerically obtained global load-displacement curve and the peak load and displacement corresponding to the onset of short circuit and the thermal runaway matches the experimental results. The present detailed computational model is ready to be used in the battery design process and will serve as an important new computational tool for assessing the safety of lithium-ion batteries against mechanical loading.

Section snippets

The architecture of lithium-ion battery cells

The basic structure of the commercial lithium-ion pouch cells is a wounded roll or laminated stack of battery components enclosed by an aluminum/polymer pouch or casing (Zhu et al., 2018a), as shown in Fig. 1. The jellyroll/stack is the core of the battery cell structure because it is where the electrochemical reactions happen. It consists of alternating electrodes and separator. All the layers are immersed in a liquid electrolyte, which is lithium salts (e.g. LiPF₆) in an organic solvent (e.g.

Constitutive relations

The plastic behavior of granular materials has been proven by vast experimental evidence since the 1950s to be pressure dependent. The yield function and plastic flow should, therefore, be analyzed in the space of $(p, q)$ , where $p$ is the hydrostatic pressure (first invariant of the stress tensor) $p = - \frac{1}{3} σ_{i i},$ and $q$ is the equivalent stress (second invariant of the stress deviator tensor) $q = \sqrt{\frac{3}{2} S_{i j} S_{i j}} .$ Here, $S_{i j} = σ_{i j} + p δ_{i j}$ is the deviatoric stress.

The Drucker-Prager/Cap model is used to characterize the

Interfaces and boundary conditions

Two types of interfaces exist in the battery structure – the cohesive interface between the granular coatings and the metal foils and the frictional interface between the coatings and the separator. The cohesive interface was studied using a series of peeling tests in different directions (see Fig. 8a and b) by the authors’ team (Luo et al., 2018). The thin double-side-coated electrode (coating/foil/coating) was glued to two substrate plates to be stretched. The substrate plates were designed

Indentation tests of battery cells

The commercial large-format secondary automotive batteries are too large to be fitted inside the chamber of the micro CT device. It is important to get images from the CT scan in order to validate the detailed FE model. Therefore, it was decided to manufacture much smaller pouch batteries from the same component from which large-format commercial batteries were made. The manufacturing procedure including cutting, stacking, and sealing is standard for making prototype cells. The overall

Numerical model

A detailed finite element model of the lithium-ion pouch battery cell is established in Abaqus/Explicit and is shown in Fig. 10. All the solid components are modeled at their realistic thicknesses, as listed in Table 1. Each of these six materials, discussed in the previous sub-sections, is assumed to be isotropic. This is clearly an approximation. In reality, the only isotropic component in the battery is the granular coating of the anode and the cathode before calendering. The aluminum and

Closed-form solution for the battery failure

The present Section follows closely the general procedures of the so-called kinematic method in plasticity. The upper bound theorem for rigid-plastic material, proved by Drucker and Prager (1952) was extended to dynamic loading by Martin and Symonds (1965). The extension to moderately large deflection of structures was done by Jones (2011), while Wierzbicki proposed a rigorous extension to the axis-symmetric shells (Wierzbicki and Abramowicz, 1983).

The method starts with a selection of the

Discussion and conclusions

The present paper develops the fully calibrated and assembled constitutive and computational model of the lithium-ion batteries. The model offers a new insight into the response of pouch batteries under quasi-static loading. The numerical simulation of a few typical loading cases provides information on the sequence of deformation and failure of various components that is impossible to obtain through any other available experimental techniques. One of the main new findings is that failure of

Acknowledgment

The financial support from the MIT Battery Modeling Consortium (Altair, AVL, Boston-Power, Dassault Systèmes Simulia, Jaguar-Land Rover, LG Chem, Mercedes-Benz, Murata, and PSA Groupe), the International Science and Technology Cooperation Program of China (Grant No. 2016YFE0102200), and the National Natural Science Foundation of China (Grant No. 51675294) is gratefully acknowledged. Thanks are also due to Ford Motor Company for supporting. Also, the partial support from the USAID SHERA Program

References (55)

L. Anand et al.
Granular materials: constitutive equations and strain localization
J. Mech. Phys. Solids
(2000)
A. Anandarajah
Multi-mechanism anisotropic model for granular materials
Int. J. Plast.
(2008)
Y. Bai et al.
A new model of metal plasticity and fracture with pressure and Lode dependence
Int. J. Plast.
(2008)
Y. Bao et al.
On fracture locus in the equivalent strain and stress triaxiality space
Int. J. Mech. Sci.
(2004)
M.W. Barsoum et al.
Kink bands, nonlinear elasticity and nanoindentations in graphite
Carbon N. Y.
(2004)
C. Bonatti et al.
Anisotropic viscoplasticity and fracture of fine grained metallic aluminum foil used in Li-ion batteries
Mater. Sci. Eng. A
(2016)
S.H. Chung et al.
Failure in lithium-ion batteries under transverse indentation loading
J. Power Sources
(2018)
V.S. Deshpande et al.
Isotropic constitutive models for metallic foams
J. Mech. Phys. Solids
(2000)
M.B. Gorji et al.
Micro-tension and micro-shear experiments to characterize stress-state dependent ductile fracture
Acta Mater.
(2017)
C. Gu et al.
Constitutive equations for metal powders: application to powder forming processes
Int. J. Plast.
(2001)

L. Wang et al.

Mechanical characterization and modeling for anodes and cathodes in lithium-ion batteries

J. Power Sources

(2018)

W. Wang et al.

Clay-like mechanical properties of components for the jellyroll of cylindrical lithium-ion cells

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¹: These authors contributed equally to this paper.

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Deformation and failure of lithium-ion batteries treated as a discrete layered structure

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

The architecture of lithium-ion battery cells

Constitutive relations

Interfaces and boundary conditions

Indentation tests of battery cells

Numerical model

Closed-form solution for the battery failure

Discussion and conclusions

Acknowledgment

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Int. J. Plast.

Int. J. Solids Struct.

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Int. J. Impact Eng.

J. Power Sources

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J. Power Sources

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J. Power Sources

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