Constitutive behavior and progressive mechanical failure of electrodes in lithium-ion batteries

Journal of Power Sources 357 (2017) 126e137

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Constitutive behavior and progressive mechanical failure of electrodes in lithium-ion batteries Chao Zhang a, b, Jun Xu c, d, Lei Cao a, Zenan Wu a, Shriram Santhanagopalan a, * a

Transportation and Hydrogen Systems Center, National Renewable Energy Laboratory, Golden, CO, 80401, USA Department of Aeronautical Structure Engineering, School of Aeronautics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710072, China c Department of Automotive Engineering, School of Transportation Science and Engineering, Beihang University, Beijing, 100191, China d Advanced Vehicle Research Center (AVRC), Beihang University, Beijing, 100191, China b

h i g h l i g h t s
Constitutive models under tensile and compressive mechanical loads were developed.
Failure criteria and damage models for cell components were built from test data.
Component models were used to study propagation of failure during a blunt rod test.
Model describes interplay of several failure modes when cell is subjected to crush.
Cell level data helps identify future directions in studying battery electrodes.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 March 2017 Received in revised form 25 April 2017 Accepted 28 April 2017

The electrodes of lithium-ion batteries (LIB) are known to be brittle and to fail earlier than the separators during an external crush event. Thus, the understanding of mechanical failure mechanism for LIB electrodes (anode and cathode) is critical for the safety design of LIB cells. In this paper, we present experimental and numerical studies on the constitutive behavior and progression of failure in LIB electrodes. Mechanical tests were designed and conducted to evaluate the constitutive properties of porous electrodes. Constitutive models were developed to describe the stress-strain response of electrodes under uniaxial tensile and compressive loads. The failure criterion and a damage model were introduced to model their unique tensile and compressive failure behavior. The failure mechanism of LIB electrodes was studied using the blunt rod test on dry electrodes, and numerical models were built to simulate progressive failure. The different failure processes were examined and analyzed in detail numerically, and correlated with experimentally observed failure phenomena. The test results and models improve our understanding of failure behavior in LIB electrodes, and provide constructive insights on future development of physics-based safety design tools for battery structures under mechanical abuse. © 2017 Published by Elsevier B.V.

Keywords: Lithium-ion battery Electrode Constitutive properties Progressive failure Fracture

1. Introduction The structural integrity and damage tolerance of lithium-ion battery (LIB) structures are an emerging concern of designers, with their increasing application in various industry fields, especially in electrical-vehicles [1e3]. One specific feature of lithiumion battery is its sensitivity to external or internal mechanical load, which can produce an internal short circuit resulting in

* Corresponding author. E-mail address: [email protected] (S. Santhanagopalan). http://dx.doi.org/10.1016/j.jpowsour.2017.04.103 0378-7753/© 2017 Published by Elsevier B.V.

thermal runaway, followed by cell venting and rapid dissipation of energy. Thus, understanding of the interactions between mechanical failure behavior and consequential evolution of the electrical/ thermal response is of great importance. Our recent numerical studies [4] revealed that a slight change of mechanical failure condition results in dramatic difference on the electrical and thermal response, for example, an increase of 0.06 mm penetration depth followed by an indentation-induced crush results in a 20 fold increase of short-circuit current. Similarly, the time it takes for the cell to completely discharge after the short-circuit under the two failure conditions changes from around 10 s to less than 1 s. Wang

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et al. [5] examined the internal failure phenomena using an optical microscope, and observed a combination of multiple failure behaviors, including shear fault crossing multiple layers, breaking of current collectors, rearrangement of fragments and dislodging of electrode particles. Another recent study by Marcicki et al. [6] showed a soft internal-short (a decrease of voltage from 4.0 V to 3.5 V in 1500 s) following an impact-induced crush. These results suggest that the mode of internal failure behavior significantly affects the short-circuit responses. Thus, understanding the progression of failure across the layered structure system is very necessary for the design of safe lithium-ion batteries. Experimental work reported in the literature mainly considers the effective failure response of battery cells. Wierzbicki and Sahraei [7] and Sahraei et al. [8e10] evaluated the mechanical behavior of pouch format and cylindrical cells under different loading conditions. It was observed consistently that a sharp drop in cell voltage is instantaneously followed by a force drop. Lai et al. [11,12] studied the in-plane and out-of-plane compression, kink and shear band formation in representative volume element (RVE) specimens for prismatic graphite/LiFePO4 pouch cells. Xu et al. [2,13,14] studied extensively the static and dynamic mechanical properties of cylindrical 18650 cells and their dependency on strain rates and state of charge (SOC). The results show a linear relationship between the compression modulus and failure strain for various SOC values. The mechanical performance of a battery cell at the macroscale provides information on the load capacity of the structure, but cannot facilitate the understanding of failure mechanism or the interaction between mechanical failure and occurrence of a short circuit. To accomplish that, we need a comprehensive understanding on the constitutive and failure properties of the cell components (i.e., active material coating, separator, current collector), and the progressive failure behavior of the layered structure under an external crush load. Preliminary tests were conducted by Sahraei et al. [8] and Lai et al. [12] to evaluate the mechanical properties of cell components. The behavior of electrodes and separators in compression was found to be different from those under tension, and there is a gradual increase in stiffness during the compression tests due to the porous nature of the electrodes. The tensile results showed that the electrodes' mechanical responses were dominated by the properties of the current collectors. Based on these observations, the authors concluded the compressive response of cell components can be modeled as foam materials. It is also observed the tensile failure strain of the cathode and anode are lower than that of the cathode and anode current collectors (aluminum and copper). This is attributed to the damage induced by intrusion of active particles into the metal foil [15]. Separator properties were measured by Cannarella et al. [16] who reported strain-rate dependent tensile properties using an extensiometer. Properties of the dry versus wet membranes were compared by Sheidaei et al. [17] Xu et al. [18] studied the coupled effect of strain rate and solvent on mechanical behavior of commercial separators. Zhang et al. [19] measured and evaluated the mechanical properties of four types of lithium-ion battery separators using tensile, compression and biaxial punch tests. Luo et al. [20] examined the tensile properties of current collectors, electrodes and separators, and their rate sensitivities. It is noticed that the samples exhibit lower ductility under a higher loading rate. But so far, the failure behavior or the constitutive representation of electrode active material (the porous layered structure) has not been adequately characterized. On the modeling aspect, Sahraei et al. [9,10] and Avdeev and Mehdi [21] developed macro-scale models to represent the deformation and failure of single battery cell. Xu et al. [13,14] further improved the models taking into consideration strain-rate effects and incorporating a mechanical integrity criterion, and simulated

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the dynamic mechanical behavior of lithium-ion batteries. Zhang et al. [22] presented a representative-sandwich model that explicitly accounts for each cell component and predicted the electrical short-circuit and thermal ramp due to a mechanical crush. Saharei et al. [23] modeled the sequence of component failure under different loading scenarios using the representativesandwich model with periodic boundary conditions. In both experimental and numerical studies, we find that the initiation of structural failure is mainly driven by the breaking of electrodes due to the much lower tensile failure strains of cathode and anode compared to that of separator layer [4,20,23]. Thus, the understanding the failure behavior of electrodes is essential for investigating the progressive failure of lithium-ion batteries. In this work, we examine comprehensively the tensile and compressive properties, and indentation-failure behavior for electrodes. We summarize the constitutive properties of electrodes, and propose suitable constitutive models and their implementation in finite element simulations. Beyond these, we investigate in detail the failure behavior of cell electrodes and correlate the damage and failure process with the experimental observations. We introduce and discuss modeling approaches for implementing the component properties in battery crush simulation, explicitly simulate the deformation and damage behavior of electrodes, and study indepth the failure mechanism of indentation-crush tests. The experimental and numerical studies provide insights on improving the structural strength of lithium-ion battery and optimizing the design of safe battery structures. 2. Materials 2.1. Battery samples The lithium-ion battery cell we are studying in this work is a commercial graphite/NMC cell, with chemistry and thickness information summarized in Table 1. The cell has a capacity of 15Ah, and the length and width of the cell is 190 mm and 210 mm, respectively. Fig. 1(a) shows the images of the cell during a destructive physical analysis (DPA). After dissection, each layer of the battery cell is carefully isolated, cleaned in a glove box to remove deposits of the electrolyte. After cleaning, the test samples are taken out and cut into designated shapes for mechanical tests. Fig. 1(b) ~ (d) show the representative images of the samples before and after test under different loading conditions. 2.2. Experimental All the mechanical tests presented in this paper were conducted using an Instron machine with 5000 N load cell at National Renewable Energy Laboratory. The extension and force data were collected to interpret the constitutive and failure properties of the samples. Fig. 1 shows the specimen for tension, compression and indentation tests. For tensile tests, the cell components were cut into a rectangular shape of 101.6 mm (4 inch) by 10.16 mm (0.4 inch) using a specimen die. The specimen for the compression tests are circular pieces with diameter of 6.35 mm (0.25 inch), cut using a

Table 1 Chemistry and thickness information for the cell components used in this study. Thickness (mm)

Component

Material

Anode active layers (2 sided) Anode current collector Cathode active layers (2 sided) Cathode current collector Separator

Graphite 123 Copper 14 LiNi0.33Mn0.33Co0.33O2 (NMC) 92 Aluminum 20 Trilayer PP/PE/PP 20

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Fig. 1. (a) Images of the battery cell before and after DPA; (b) Images of anode and cathode samples (0.2500 diameter) before and after compression test; (c) Images of anode and cathode samples (400 x 0.400 ) before and after tensile test; (d) Images of anode and cathode indentation samples (30 mm  30 mm).

specimen tube-punch. The indentation test specimens are square pieces with length/width of 30 mm. For tensile tests, we enforced a gage section of 50.8 mm by tabbing 25.4 mm on each end of the specimen. A constant displacement rate was applied to stretch the samples until fracture. The displacement rate of electrode specimens was set to 0.2 mm/ min considering their low failure strain. The displacement rate for the separator specimen was set to 2 mm/min. For compression, multiple layers of the specimen were stacked in the thickness direction and installed between two steel plates connected to the Instron© fixtures. Each electrode specimen comprised of a stack of 20 layers (Fig. 1), while the separator specimen contains a total of 96 layers. Considering the existence of air gaps between each layer of the specimens, a preload of 10 N was applied to eliminate any noise during the initial stage of the force-displacement responses. The compression tests were terminated either after the fracture of the sample or upon reaching the maximum load (5000 N). Three samples were tested under each tensile and compressive load. 3. Constitutive properties and modeling of electrodes As elaborated in our previous work [4], the prediction of mechanical abuse induced short circuit relies on the accurate modeling of progressive failure behavior, which requires explicit modeling of individual cell components. The development of representative constitutive models for the cell components is essential for the numerical modeling of mechanical crush of batteries. Our previous studies [4] provide some preliminary insights on the tensile and compression performance of electrodes and separators. In this paper, based on a comprehensive experimental examination, we analyzed the multi-stage deformation process and

conclude the constitutive behavior of each cell component. Taking into consideration the porous nature of active material layer, we propose methods to extract mechanical parameters from the experimental stress/strain data, develop analytical equations to describe the mechanical and failure properties for the porous electrode coatings.

3.1. Tensile tests Fig. 2 (a)e(e) show the stress-strain curves of the anode, cathode and separator, respectively. The three experimental results for each component show excellent repeatability on both the slope of the curves and the ultimate failure strain, especially for the cathode and separator specimens. The discrepancy in the anode tests is due to the poor performance of the anode binder. During the sample preparation phase, we noticed frequent breaking and peeling off of the anode active material. Overall, the test results characterize the elastic-plastic tensile behavior of cell components, and capture the brittle fracture of electrodes and compliance of polymer separators. The tensile test results are also consistent with the previous results reported by Sahraei et al. [8] and Lai et al. [11,12], who suggested that the copper and aluminum foils be modeled using an isotropic linear-hardening elastic-plastic model:

8 > <

Eε   s¼ sy > : sy þ Et ε  E

if s < sy if s  sy

(1)

where s, ε and E are the tensile stress, tensile strain and tensile modulus, respectively. Et and sy are the tangent modulus and yield

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Fig. 2. Experimental tensile stress-strain results for (a) anode and (c) cathode active-material/current collector/active-material composite samples; model curves for tensile responses of (b) anode and (d) cathode composites, current collectors and active material coatings regressed using equation (1). The ordinates for the curves corresponding to the current collectors in (b) and (d) are shown in the secondary axis on the right side of the plots.

stress: these parameters correspond to the stiffness of the material after transitioning to plastic deformation and the critical stress value at which the initiation of plastic deformation happens. Fig. 2(b) and (d) show the fits for the stress-strain curves of the anode and cathode respectively, using Eq. (1). As shown in Fig. 2, both the anode and cathode are layered composites of active material coatings and the current collector. The active material is a porous composite of active particles and polymer binders. Under uniaxial tension along the in-plane direction, due to the structural discontinuity of the porous active layer, the load is transferred mainly through the current collector and the active layer deforms due the shear stress transferred through the interface. To estimate the independent tensile stress-strain responses of the active layer and current layer, we introduce a simple equation to describe the contribution of each component to the effective response of the electrode as follows:

Fe ¼ aFa þ ð1  aÞFc

(2)

where Fe, Fa and Fc are the tensile force experienced by the electrode, active material and current collector layers, respectively. The parameter a represents the fractional contribution of the active material coating to the tensile resistance. Equation (2) approximates the response of the composite electrode as a linear combination of the properties of the active material and the current collector. More complex interactions can be simulated as a series of locally linearized responses, where a is a function of the strain. In this work, considering the negligible contribution of active layer to the tensile strength of electrode, we assume a ¼ 0.1 for both anode and cathode. Subsequently, we obtain the force against tensile strain curves for active layer and current collector separately. Knowing the cross-section areas (product of the width and

thickness), we can then derive the stress-strain curves of active layers and current collectors for anode and cathode, as shown in Fig. 2(b) and (d). Tensile failure in electrodes is consistent with the tensile failure of current collectors, while the active material layer exhibits better toughness (higher tensile failure strain) than the current collectors, based on the observations reported in the literature [5] and our inhouse experiments (Appendix Fig. A1). In-situ tensile test of a cathode sample was conducted while monitoring the initiation of failure simultaneously using a microscope, with set-up shown in Fig. A1 (a). Fig. A1 (b) and (c) show the fracture of sample and its localized view at the instant of tensile failure, where we can see the remaining connections between the fractured pieces on the active layer and its relatively rough fracture surface. This indicates that the active layer is tougher than the current collector. Further evidence was shown by Wang et al. [5] who experimentally observed the integrity of the active material layers while current collectors of the same electrode layers were fractured. The greater compliance of active layer is attributed to its porous structure and good ductility of the polymeric binder. On the other hand, the current collector thin films are known to be relatively brittle (with failure strain less than 10%) as characterized by Sahraei et al. [8] and Luo et al. [20]. Also during the calendaring process, the current collector is further damaged. Damage induced during the manufacturing process (e.g., calendaring of the electrodes) reduce the toughness of current collectors significantly and result in earlier failure of current collectors within the cell, than plain metal foils of comparable thickness. With the information above, we estimate the tensile properties of the active layer, current collector of electrodes and their effective tensile properties for a lithium-ion battery cell as summarized Table 2. These parameters can then be used for building

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constitutive models for numerical simulation, as discussed in a later section below. We note that within a working lithium-ion cell, there are gradients due to diffusion induced stresses within the electrodes. We have explicitly modeled diffusion induced stresses in the past [24] and formulated criteria for when such intercalation stresses contribute to the failure behavior of the electrode. However, in this work, we focus mainly on the constitutive description of the components in response to an external mechanical load. The modeling methodology presented in here focuses beyond the particle scale, on the electrode-level response to impact and crush, where we treat the active-material layer as a homogenous material while ignoring stress gradient inside the material. A more rigorous formulation should incorporate the intercalation stresses within the particle domain (e.g., as a form of residual stress) and will consequently have stress gradients within the material. However, based on our previous results [22,24], the diffusion induced stresses for typical cell designs are below the failure metrics observed under external mechanical loads.

and the separator, we use a two-stage model we presented before [22], assuming that the Young's modulus E of the stiffening stage varies exponentially with the strain ε from initial modulus E0 to a fully compacted value Emax.

 E¼

(3)

E0 ¼ Emax ebεp

(4)

In Eqs. (3) and (4), εp is the strain for the fully compacted material. The value of εp is approximately equal to the initial porosity of the specimen. The fitting parameter b captures the increase in gradient of the Young's modulus against the strain during the stiffening stage (See region between 0 < ε < 0.36 for the anode and 0 < ε < 0.29 for the cathode on Fig. 3(a) and c respectively). A higher value of b indicates a slower increase of modulus with strain. We then calculate the corresponding stress-strain relationship (See equation (1)):

3.2. Compression The active material coating is porous in nature and computing its mechanical properties is complicated. One feature of these porous layers is their completely different mechanical behavior under tension and compression. The current collector foils are treated as isotropic under tension and compression, which means the tensile stress-strain curves of Fig. 2 can be used to describe their compression response as well. Fig. 3 (a) and (c) show the compressive stress-strain curves of the anode, cathode and separator layers, respectively. Measurement of the in-plane compressive response for the electrodes is not practical. Since the compressive properties of the active-material are generally considered to be isotropic [4,22], we assume that the throughthickness compressive response can adequately represent the compressive response in other directions. Both the anode and cathode layers show a two-step deformation, including a gradual stiffening of the effective modulus at the initial stage due to a reduction in the porosity and a linear stage after compacting, which are consistent with our previous observations [22]. Beyond that, we are able to characterize the compression failure of anode samples under the compressive strain in the range of 0.54e0.56 or compressive stress of 162e177 MPa. The damage at the anode is initiated by the shear failure of the current collector, but a more detailed experimental study is needed to explore the detailed failure mechanism. For the cathode, the compressive stress-strain curves show a discontinuous slope at stress levels around 12 MPa, which is likely due to the yielding of the polymeric binder in the active layer. Another change of slope occurs at the stress level around 105 MPa, which is consistent with the yield stress value for the aluminum foil (the cathode current collector). This suggests that the latter change in slope is most likely due to the yielding of the current collector under compression. To model the compression response of the active material layers

Emax ebðεεp Þ ε < εp ε  εp Emax

s¼

  Emax ebε  1

8 > > > > > <

bebεp

ε < εp  ε  εp >  b ε > > Emax 1  e p >   > : þ Emax ε  εp 

(5)

b

We use 0.29 and 0.37 for porosity of the positive and negative active material as reported by the supplier. The porosity of the separator and the values for the fitting parameter b for all components are determined by fitting the model against data from the average of the experimental curves for each component as shown in Fig. 3(b) and d). For the electrodes, which are three layer laminates of active material layers and the current collector, we assume that seff across each layer within the electrode is the same: [22]

seff ¼ sactive ¼ scollector

(6)

Then, the parameters b and Emax are the only two unknowns to resolve, before we can simulate the mechanical response of the active materials. These parameters can be estimated using the procedure outlined below. The effective through-thickness strain (εeff) equals the volume (thickness) averaged strain for the components:

εeff ¼ nactive εactive þ vcollector εcollector

(7)

where nactive and ncollector represent the ratio of the initial volume of the individual component to the total electrode volume. Using known values for the properties of the current collectors (See Table 2) and the compressive response of the electrodes (Fig. 3(b) and d) together with equations (6) and (7), the values of unknown parameters are regressed and summarized in Table 3. As shown in Fig. 3(b, d) and f, the model curves capture the experimentally measured compressive response well.

Table 2 Tensile parameters of lithium-ion battery cell components. Anode

Elastic Modulus (MPa) Yield Stress (MPa) Tangential Modulus (MPa) Failure Strain a

Cathode

Separator

Active Layer

Current Collector

Electrode

Active Layer

Current Collector

Electrode

674 2.43 6.9 0.3a

49708 174 680 0.077

6000 21.7 60 0.0807

609 2.56 4.9 0.5a

25200 105.8 202 0.0306

5000 21 40 0.0306

Regressed from test data collected during a blunt-rod test.

1206 12 512 0.731

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Fig. 3. Compression stress-strain results of (a) anode and (c) cathode samples; Model curves for compression responses of (b) anode and (d) cathode.

3.3. Damage model To predict the failure response of a battery cell, failure criteria and a damage model are necessary. For compression, we assume there is no compressive failure occurring in the current collectors and separator layers due to the relatively higher value of their mechanical strength (as measured by the maximum stress) than active materials. Based on the compressive stress-strain curve of the anode specimen (Fig. 3(a)), a strain based failure criterion and damage model are used to describe the compressive stress-strain behavior of active materials assuming that the active material in either electrode has the same damage behavior. We specify a strain for failure initiation within the active material (ε0f ), and the damage starts accumulating once the strain exceeds ε0f . The damage evolution follows the damage equation below:

D¼

ε εf

!4 (8)

where εf is the strain at complete failure and 4 is a non-dimensional parameter that defines the rate of damage evolution. D is the

Table 3 Parameters for simulating the compression behavior of active materials in a lithiumion battery cell. Parameter

Anode Active

Cathode Active

Emax (MPa)

480 8.1 0.36 0.56

460 12 0.29 0.6

0.68 2 4.2

0.75 2 4.2

b

εp ε0f εf

f

4

damage variable, where a value 0 indicates no damage and a value 1 corresponds to complete failure. The accumulation of damage will result in softening of the material followed by a decrease in the stress. The mechanical response of the active material layer damaged under compression can then be expressed as follows:

s* ¼ s 1 



D  Dc 1  Dc

f !

c

D > Dc

(9)

where s* is the effective stress correcting s, the stress calculated using the constitutive equation (Eq. (5)) using a damage factor, Dc is the critical damage variable that equals (ε0f /εf)f and 4 is constant used to capture the slope of the stress-strain curves on Fig. 3. The failure initiation strain is determined as the onset strain of yielding for the compressive stress-strain curve, for example, ε0f ¼ 0:56 for anode active layer. The other parameters, εf, f and 4, are regressed from the experimental curve. As shown in Fig. 3(b), model equation (3) through (9) capture the experimental data reasonably well. These equations are used in a subsequent section to simulate a deformation of the electrodes during a blunt rod test. For the cathode, the load cell reached the maximum value before reaching the compression failure point. For the sake of completion, we used data from an indentation test (See Fig. 8) to determine the damage parameters for the cathode active material. 3.4. Implementing constitutive models for cell components in LSDYNA The numerical simulations in this paper were conducted using the commercial explicit finite element code LS-DYNA. As reported in our previous work [4] the active materials and the porous separator are modeled as homogeneous solids using LS_DYNA material model MAT26 (MAT_HONEYCOMB). The elasto-plastic

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response is represented using experimentally measured stressstrain curves. These nonlinear orthotropic curves are defined separately for each of the normal and shear components of the stress values. The stress-strain curves (Fig. 2(b), d and 2f, Fig. 3(b), d and 3f) are then implemented in LS-DYNA as the normal loading curves. Additional details on the implementation can be found in our earlier work [22]. Any anisotropic behavior can be readily accommodated by using separate normal loading curves for each direction. The associated properties to be specified in LS-DYNA are listed in Table 2. Proper specification of failure criteria and failure parameters is of great importance for the accurate prediction of short circuit within a cell, as a result of mechanical crush. This work intends to study the mechanism of progressive mechanical failure in LIB. For illustrative purposes, the maximum tensile strain criterion is applied for tensile failure of each component, which is implemented using the default functions in the MAT_HONEYCOMB and MAT_PLASTIC KINEMATIC models. The elements in the corresponding component that reach the predefined maximum tensile strain values listed in Table 2 are deleted. For failure under compression, the damage behavior is implemented using the tabulated stress-strain curves for the MAT_HONEYCOMB model in LS-DYNA, as an extension of the constitutive curves. The complete failure strain εf is defined via the MAT_EROSION model to active element deletion. 4. Progression of failure in battery electrodes during a blunt rod test We intend to study the progressive failure of the different cell components when the cell is being subjected to mechanical abuse. In this work, we conducted a comprehensive set of blunt-rod tests and implemented finite element simulations to calibrate the complete failure process and explore the mechanism for the propagation of damage across the different layers within the cell. Understanding failure response of individual electrodes can further promote our interpretation of the progression of failure in battery cells. So, in addition to alternating plate pairs comprised of anode/ separator/cathode units, we also studied multiple layers of electrodes of each kind stacked on top of one another, to investigate interactions between the current collector and active materials and to identify the differences in failure behavior between anode and cathode samples. 4.1. Blunt rod test on dry electrodes The fundamental tensile and compression tests provide information of the constitutive properties of the cell components under ideal deformation conditions. When a battery undergoes mechanical crush, a combination of multiple failure modes contribute to the initiation of electrical short circuit and subsequent propagation of failure. Several studies [20e23,25] report the cell level response; but it is difficult to probe step-by-step, the mechanical failure of the individual layers, when the cell is electrically active. In this study, we conducted blunt rod tests on electrode layers using a hemisphere punch of diameter 4 mm as shown in the test setup in Fig. 4(a). The indentation specimens are square pieces with length and width of 30 mm (see Fig. 1(d)). The punch was positioned over the center of the cell. The indentation tests started with a preload of 2 N and then continued at a constant displacement rate of 0.2 mm/ min. Each test sample had ten representative sandwiches (RSs) where each RS comprised of a separator layer on top, followed by a cathode layer, another separator layer and an anode layer at the bottom. The indentation tests were stopped with the fracture of the sample, as observed by a continuous drop in the force. The failure

shapes and crack patterns were subsequently imaged using an optical microscope. The results are discussed in detail in the sections below. The force on the load cell is recorded as the reactive force on the indenter and the strain is calculated as the ratio of indentation depth against total thickness of the test samples (1.38 mm and 1.12 mm for anode and cathode, respectively). 4.2. Finite element model of the blunt rod test Fig. 4 (b) shows the geometry used in the finite element model for the blunt rod test. Only one quarter of the surface is simulated due to symmetry. The bottom surface is constrained using a fixed rigid plane. A rigid solid sphere with a constant velocity moving down through the thickness direction of the sample was used to represent the indenter. The surface between any two adjacent layers of the test article were modeled using a standard contact protocol (CONTACT_AUTOMATIC_SINGLE_SURFACE) defined for the interfaces in LS-DYNA to prevent penetration of elements in the through-plane direction between adjacent layers. The interface between current collector and the active-material elements was treated as a perfectly bonded interface, since no delamination between active-material layer from current collector was observed in our experiments. Inside the electrodes, the nodes between current collector and the active material elements were merged assuming a perfectly bonded interface. We used an element size of 0.15 mm for the elements directly under the loading area and 0.8 mm for other elements Sensitivity of model convergence to the element size was verified. Each layer has three elements through the thickness direction, resulting in a total of 217890 elements for the whole model (10 layers of electrodes). The numerical model was solved on our High Performance Computer system equipped with a total of 31,104 Intel Xeon processors providing a total of about 608 TeraFLOPS. The computational time for the indentation simulation was about 8 h using 100 CPUs. 4.3. Progressive failure of anode under indentation Fig. 5 compares the experimental and numerical simulation results. Despite minor differences in the initial shape and the ultimate force, the experimental curves and the simulation results are consistent on the gradually stiffening response at the initial stage, damage initiation induced softening and force drop due to the accumulation of damage zone. The experimentally observed fracture pattern for the sample is also shown in Fig. 5, where we can see a complex failure behavior including a hole induced by compression failure, tensile cracking of the electrode and delamination of the active layer from the current collector. Examination of the mechanical response of the individual layers in the model shows that the initial onset of damage is observed in the anode current collector layer in the form of circular tensile cracking at a strain level of 0.36 due to the relatively low tensile failure strain of the current collector. The tensile crack results in a localized stress concentration, due to which the crack then propagates to the active-material layers adjacent to the current collector. At a strain level of 0.53, damage of active-material layer is observed, in the form of compressive failure in the region directly under the area in contact with the indenter and tensile failure along the twosymmetrical boundaries. The compression failure causes a reduction in mechanical resistance of the structure corresponding to the softening of the force-strain curve. As damage further accumulates, the compressive failure zone expands and forms a circular erosion zone in the center of 1st layer of electrode, while the tensile crack propagates further from the origin, forming a flower-shaped crack pattern similar to the experimental results. To further investigate

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Fig. 4. (a) Set-up for the indentation test; (b) FEM model of the indentation test with each layer of the cell components simulated explicitly.

Fig. 5. Comparison of experimental and numerical force-strain responses, experimental fracture pattern and numerically predicted failure evolution in the anode during a blunt rod test: the simulation results capture various kinds of failure modes experimentally observed for the individual cell components across the thickness of the test article.

progressive failure in the anode, each layer of the test sample was examined under an optical microscope. Fig. 6(a) shows the fracture pattern for the 1st, 4th and 7th layers of the 10-layer sample, from which we can have a clear view on the propagation of damage through the different layers. As expected, the layer on the top presents a larger damage zone: for example, the number of elements eroded in the first layer is larger than that of the fourth layer. It is also found that the delamination of the active material is more significant on the backside of the electrode than that on the front side. This is due to the fact that the in-plane tensile strain is generally larger on the lower surface of the sample than that on the upper surface, as numerically illustrated in Fig. 6(b). Across the thickness direction, the stress pattern changes due to the preferential accumulation of in-plane tensile strains in the active material layer on the lower side of the current collector compared to those in the layer immediately above the current collector (See Fig. 6(b)). For

the 7th layer, we observe a tensile crack along a single direction, which is also captured well in the numerical simulation as shown in Fig. 6(c). 4.4. Progressive failure of cathode under indentation Cathode shows a different failure behavior under indentation compared to that of anode. Fig. 7 shows the facture and damage images across the different layers of cathode in a test sample. As seen from the fracture pattern for the 1st layer of the cathode, both compression and tension failure modes are observed similar to that of anode specimens. Compared to the fracture image in Fig. 5, the compression failure zone (penetrated area) is larger, and tensile cracking contributes to a small fraction of the surface area damaged due to the load. Another obvious difference is that the adhesion of the active-material layer with the current collector is excellent, as

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Fig. 6. (a) Cracking behavior of the anode across different layers after a blunt rod test (b) Numerically predicted in-plane strain (X-strain) contour of active-material layers show that the active material layer on the lower side of the current collector incurs higher in-plane tensile strains compared to the layer immediately above the current collector; (c) Numerically predicted cracking pattern for the 7th layer in a test sample comprised of ten layers of the anode.

Fig. 7. Failure images of the cathode across different layers in the through-plane direction in an indentation test sample.

no interfacial failure is observed in any of the samples we tested. The interfacial strength plays an important role on the mechanical strength of composites in general, and this is especially true for

porous electrodes where the interfacial strength between binder and active material particles affects the tensile strength of the electrode. The variability in interfacial strength for cathodes and

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anodes results in the difference in their failure response. Across the layers, we can see the domination of compressive failure. On the 3rd layer of the 10-layer sample, we observed a complete failure of active-material layer in a circular area directly below the contact surface and a few tensile cracks in a limited area. For the 7th layer, mild compressive failure of active-material layer was observed under the microscope across the area directly below the indenter due to the concentration of local stresses in that area. Fig. 8 shows the experimental and numerically predicted forcestrain curves. Compared to the indentation response of the anode shown in Fig. 5, the initial stiffening stage in the experimental curves for the cathode is negligible, following which there is slight yielding (around ε ¼ 0.3) and a moderate stiffening process thereafter. For strain values beyond 0.5, the slope becomes linear followed by softening past ε ¼ 0.9 and an ultimate drop in the force. The different indentation responses for the anode and cathode can be attributed to the differences in constitutive behavior of the active-material layers. The cathode active-material tends to be tougher and stiffer (see failure strain values in Table 3). The differences can be explained based on the formulation of the two electrode coatings: the anode coating uses a water-based process to make the slurry whereas the cathode coating employs an organic solvent. The properties and composition of the binders are accordingly very different. The numerically predicted force-strain

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curve on Fig. 8 does not match well with the experimental result. This is because we used the same the same set of constitutive equations to represent the mechanical behavior of the cathode and the anode, which results in similar force-strain responses for the anode and thee cathode in our numerical simulations. This assumption then limits the accuracy of the model. The discrepancy is caused by the insufficient knowledge of the constitutive properties and the use of certain assumptions in the model. In-situ mechanical characterization of the multi-layered porous structures will further enhance our understanding of the constitutive behavior of the electrodes. The progression of failure in the cathode sample under indentation was also studied numerically, as shown in Fig. 8. A tensile crack is observed at a strain level of 0.49 and propagates along a circular direction. The size of the crack is relatively smaller compared to that in the anode current collector on Fig. 7, due to the good binding strength between the active material and the current collector, and a relatively higher toughness of the cathode active material which provides additional resistance to crack propagation. Compression failure initiates in the active-material layer at a strain level of 0.57. As shown in Fig. 8, the compression failure zone is in a circular region directly under the indenter. Unlike what we noted in the simulation of the anode specimen (Fig. 5), we observe no tensile failure. This is attributed to the high tensile failure strain

Fig. 8. Comparison of experimental and numerical force-strain responses, and numerical prediction of failure propagation for the cathode under indentation tests.

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of cathode active-material layer. The ultimate failure shape is also well predicted using the current model which captures the center compression failure zone and the presence of tensile cracks. It is also obvious comparing Figs. 5 and 8 that compression failure dominates the indentation failure of the cathode while tensile failure contributes more towards that of the anode. The experimental and numerical results presented in Sections 4.3 and 4.4 highlight the complexity of the failure behavior for anode and cathode films. Both the anode and cathode show a similar force-strain response, including the initial stiffening of the curve, softening due to damage propagation and gradual force drop after structure fracture. During the indention tests, the tensile failure of current collector is identified to be the first damage event for both anode and cathode specimens. After that, the failure sequence varies due to the difference in toughness for the activematerial layer of anode and cathode. We note that although our model is able to simulate experimental observations during a blunt rod test on dry electrodes, there are still gaps between the model and experiments that need further improvements. For example, the quantitative agreement between the force-strain curves can be improved with a better knowledge of the interactions among the different failure modes for the activematerial layers and the current collectors. The modeling method presented here uses independent failure criteria for tension and compression failure of the anode and the cathode, and thus cannot accurately describe the multi-axial aspects of failure during the blunt rod test. 5. Conclusions In this paper, we present experimental and numerical studies on the progressive failure behavior of electrodes for lithium-ion batteries. The tensile and compression properties of anode and cathode were tested and utilized to extract constitutive properties of active materials and current collectors. We proposed a strain-based damage model to describe compression failure of active-material layer and obtained parameter values by correlating experimental stress-strain curves. The constitutive models developed were then implemented into finite element models for failure simulation of dry electrodes during a blunt rod test. Using a combination of experiments and numerical simulations, we identified the mechanism of complex failure behavior that involves both tensile and compression failure and shows sensitivities to the tensile strength of active materials. We also observed that the yielding of the current collector results in a slope change for the global compressive stress-strain response and the global force-strain curve for the indentation tests. These suggest that it is essential to take into consideration the tensile properties of the active-material layer and plastic deformation of the current collectors. When simulating the crush response of a battery cell, the failure mode of the electrodes will affect the consequential failure of adjacent layers such as the separator, and the ultimate electrical response. The results of this work serve as input for the development of multi-physics simulation tools, and enable a more accurate prediction of the sequence of events between the onset of damage/ failure leading to the moment of short which will then further enhance our understanding on the internal failure mechanism of battery cells under mechanical abuse. Acknowledgements This study was supported by Computer Aided Engineering for Batteries (CAEBAT) project of the Vehicle Technologies Office, Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy under contact number WBS1.1.2.406. The research was

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