Constitutive Behavior and Mechanical Failure of Internal Configuration in Prismatic Lithium-Ion Batteries under Mechanical Loading

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Introduction
If an electric vehicle was involved in an accident or might run continuously on rough road surfaces, its lithium-ion batteries (LIBs) would be subjected to complex external mechanical loads, which could lead to some degree of deformation.A large deformation could damage the cell interior of the battery which induces short circuits or thermal runaway, while small deformations could cause small undetected internal cracks and fractures between the component material layers, which may potentially lead to micro-short circuits.According to the recent studies [1][2][3], different mechanical failure conditions of LIBs resulted in significantly different electrical-thermal responses, for example, Cannarella et al. [4,5] found that the LIBs manufactured with higher levels of stack pressure exhibited shorter cycle lives, because the higher levels of mechanical stress led to higher rates of chemical degradation, which affected the state of health (SOH) and state of charge (SOC) of the LIBs.Zhou et al. [6] established an electrochemi-cal-mechanical coupling model with the consideration of the influence of elastic stiffening on diffusion for graphite anode materials.The results showed that during the normal charging and discharging of LIBs (such as static without external mechanical loading), diffusion-induced stresses are generated which lead to deformation of electrode materials.Then, Zhou [7] developed a model for stresses generated during lithiation in the thin plate electrode considering the effects of external mechanical loading.The results showed that the external mechanical loading (negative stress gradient) enlarged stresses and deformation generated in the electrode materials, which led to the premature mechanical failure of LIBs after certain cycles.Wang [8] carried out uniaxial compression tests with different indentation depths on large format lithium-ion pouch cells.It was found that with the change of indentation depth, the internal short-circuit response of these cells shows different levels.The indented cells were disassembled and inspected for internal failure phenomenon, and observed multiple failure behaviors, including breaking of metallic current collectors (foils), shear slip of active coating materials, and rearrangement of fragments.Marcicki et al. [9] performed the impact experiments on cells with a rod which expressed a small drop (∆V = 200 mV) in open-circuit voltage occurs the instant of the impact.Although the cell could normally continue to discharge after the impact, the temperature at the impact site had increased significantly, which indicated that the cell had a short circuit.These results show that the mode of internal deformation failure could significantly affect the short-circuit responses.
Many published literatures have reported the related research.For example, Finegan et al. [10] utilized a conical nail to puncture a LIB horizontally, middle along the cell, in which severe thermal runaway occurred though the component materials above the punctured region were not significantly deformed.Sahraei and Wierzbicki et al. [11,12] conducted comprehensive studies on how deformations and failures in a LIB during mechanical abuse lead to short circuits and thermal runaway; particularly, they deployed indenters of varying size and shape to conduct mechanical abuse experiments on lithium-ion pouch cells and cylindrical cells.Greve et al. [13] performed radial crushing, local lateral indentation, and global three-point bending tests on cylindrical LIBs.It was found that local indentation resulted in deformation failures and internal short circuits in the component materials at the contact zone and three-point bending led to tensile fractures and internal short circuits at the opposite side of the jellyroll, while radial crushing, on the other hand, did not form internal short circuits.These series of experimental studies have revealed that the failure mode is a significant factor for the short-circuit response of a LIB.Wang et al. [14] performed dual spherical indentation experiments on lithium-ion prismatic cells and exploited optical microscopy to observe the mode of failure of the battery's component materials.They observed multilayered shear cracks, fractures in the current collectors, and shear offsets in the coatings of the electrodes.Chung et al. [15] dissected the lithium-ion pouch cells that failed after local indentation and found that shear faults had fully sliced through the cell's internal layers.The internal failure of LIB is an instantaneous propagation from local damage to overall fracture.The fracture failure of internal component materials cannot be directly identified from macroscopic response curves (force, voltage, and temperature), because this phenomenon will be formed in mesoscopic displacement increment.Therefore, it is necessary to fully understand the mechanical properties and failure behavior of internal component materials.
The cell interior consists of unique multilayered porous structures.The active coating materials are compressible and possess complex plastic flow properties, while the metallic current collectors are tough and ductile.Furthermore, the separator is strongly anisotropic [16,17].The tensile and compressive properties of the electrodes are significantly different, as their tensile strength depends on that of the current collector, while their compressive strength depends on the compaction and hardness of the active coating [17][18][19][20].The current collector is more likely to cause fracture failure than coating, because the toughness of the current collector is lower due to the damage applied by a rolling process, and the failure occurs earlier than the same thickness of the non-damage current collector.The mechanical properties of the separator depend on its material makeup as well as the manufacturing process, since different manufacturing processes can lead to significant differences in the separator's mechanical properties.Based on multidirectional mechanical tests on different types of separators, Zhang et al. [21] found that the dry-processed separators exhibit a greater degree of anisotropy than the wet-processed those.There are two distinct failure modes of dry-processed separators under different sizes of punches, which could explain the local micro-short characteristics of LIB.It was found that the tensile failure strain of the cathode/anode was far lower than that of the separator, thereby implying that internal short circuits within a LIB were primarily caused by the mechanical failure of the cathodes/anodes.A thoroughly understanding of the failure modes and sequences of component materials under mechanical loads is helpful to develop the finite element model of the layered structure.
A few researchers have studied the effects of mechanical abuse on LIBs using numerical and physical models.For example, Sahraei et al. [11,22] used a crushable foam material to model the homogenized behavior of small lithium-ion pouch cells aiming to predict the force-displacement relationship and moment of short-circuit formation under local indentation loading.Subsequently, a homogenized model for 18,650 cylindrical cells (whose mechanical properties were calibrated through a test) was developed to simulate the deformation and failure of these cells under various loads [12].Wierzbicki et al. [23] proposed a method for modeling 18,650 cylindrical lithium-ion cells based on representative volume elements (RVEs), which allows the stress-strain relationship of cells under local indentation to be obtained by analyzing the mechanical properties of the RVE.These model-based approaches are capable of predicting the mechanical behaviors of LIBs under mechanical loads, but unable to characterize their internal failure modes accurately.Zhu et al. [24] constructed a model of lithium-ion pouch cells including the cathode coating, cathode collector, anode coating, anode collector, and separator layers, which can be used to predict the macroscopic mechanical responses of these cells and characterize their mesoscopic fracture failure modes accurately.Therefore, the layered structure model can reasonably describe the failure modes of the internal cell through the deformation failure of component materials.This type of refined modeling is important for understanding the mechanisms of mechanical failure in LIBs.
As compared to the other two types of cells, the prismatic cell has the same internal microstructure but with same differences in mechanical structure.For instance, the mechanical properties and thickness of the shell of the prismatic cell are orders of magnitude different from the internal component materials, which means that the electrodes are in a rigid constraint.When the electrodes expand within a constrained environment, the evolution of diffusion-induced stresses in prismatic cell is more complicated.In addition, it is more difficult to observe the internal failure of the prismatic cell under such protection of the shell.In the aspect of modeling, in order to understand the mechanical behavior of the ultrathin layered structure model and the influence of different material models to characterize the separator, a layer element model (LEM) was proposed, which was composed of separator, cathode, separator, and anode stacked alternately.
In this work, a series of mechanical tests were carried out in order to understand the mechanical properties and failure behaviors on internal component materials within prismatic cells, including uniaxial and biaxial tests on the cathode, anode, and separator.To understand the failure mechanisms of the cell interior under local indentation, a microscale LEM was constructed.By the combination of experiment and simulation, the deformation failure of current collectors, coating materials, and separators in the LEM under spherical punches were analyzed in detail.The analysis with LEM was effective and accurate for predicting the force-displacement relationship and fracture mode.Furthermore, the layered structure model of the n-layer LEM stacked was constructed, and the progressive failure mechanisms of cathodes and anodes under spherical punch were studied.

Structural Dimensions and Component Materials of Prismatic Cells
The prismatic cell was used.Dimension of this cell is 130 mm (length) × 65 mm (width) × 16 mm (thickness), and voltage/capacity is 3.2 V/10 Ah, as shown in Figure 1a.This cell is composed of shell, interior, and electrolyte.The interior includes cathodes, anodes, and separators.The outside layer of the interior is wrapped by a layer of separator.The cathode and anode were prepared by coating both sides of the metallic current collector with active materials and rolling afterward.The cathode collector and the anode collector were made from aluminum foil and copper foil, respectively.The separators were ceramic-coated polymer films, as shown in Figure 1b.All the geometrical parameters of the prismatic cell are summarized in Table 1.Firstly, we performed uniaxial tests with the experimental specimens being prepared according to the ASTM D882 standard.Each specimen was cut into 100 × 10 mm strips using a scalpel, and the gauge length was 50 mm, as shown in Figure 2a.Because the separator is anisotropic, the separator specimens were cut in the machine direction (MD, 0°), diagonal direction (DD, 45°), and transverse direction (TD, 90°).An Instron uniaxial tensile tester with a maximum load of 2 kN was adopted as the tensile tester, the setup is shown in Figure 2b.To ensure that the ends of the specimen would be fully immobile and protected from clamping-induced damage during tensile testing, both ends of each specimen were protected with soft rubber, as shown in Figure 2c.The stretching speeds of the cathode/anode sheet and separator were 0.2 and 6 mm/min, respectively.The tensile tests were performed in triplicate for each set of specimens.
The stress-strain curves of the cathode, anode, and separator specimens to uniaxial tension are demonstrated in Figure 2d-f.These results indicate that the triplicate test curves of the cathode and anode specimens are highly consistent.The uniaxial stress intensity of the separator is much higher in the MD than in the DD and TD, with the stress intensity in the DD being similar to that in the TD, as shown in Figure 2f.The uniaxial tensile failure strains of the separator in the MD and TD were approximately 0.7 and 1.4 in the DD, respectively.It may be observed that the triplicate test curves are highly consistent in all the three directions.

Uniaxial Compressive Tests
Since the current collectors are isotropic materials, their tensile stress-strain curves could be used to characterize their compressive behaviors.However, the active coatings and separators are anisotropic materials and have distinctly different mechanical properties under tensile and compressive loads.The SUNS uniaxial compression tester with a maximum load of 100 kN was used to perform flat compression tests on the anode/cathode sheets and separator.The circular specimens of the 20-layer electrode stacked and 40-layer separator stacked were prepared using a Φ16 mm punching tool.This ensured that all the specimens had the same shape and initial orientation, as shown in Figure 3a.Prior to the compression tests, the specimens were preloaded with 0.05 MPa of prestress to eliminate inter-specimen gaps.The compression speeds of the cathode/anode sheets and separators were 0.1 and 0.12 mm/min, respectively.The same strain rate was used in the compression tests and tensile tests, and the tests on each set of specimens were performed in triplicate.The stress-strain curves of the cathode, anode, and separator under uniaxial compression are demonstrated in Figure 3b-d

Biaxial Tests
A punch tool was used to cut the anode/cathode sheets into circular specimens.Subsequently, the specimens were affixed to a fixture consisting of a base, cappers, washers, and locking bolts, as shown in Figure 4a.The internal diameter of the clamp was 32 mm, and the washers were made of soft rubber, which immobilized the specimens and prevented specimen damage during the clamping process.An Instron compression tester with a maximum load of 5 kN was used in these tests.The biaxial loading were performed with spherical punches made out of Teflon (PTFE) to reduce friction coefficient, which is helpful to minimize friction-induced damage on the specimens' surfaces.The dimensions of the punches ranged from Φ6.3 to Φ25 mm, as shown in Figure 4b.The loading speed was 0.1 mm/min.The specimens would be subjected to the in-plane tension and out-of-plane compression during biaxial test (see Figure 4c,d).Since the mesoscopic deformations and failures in the internal component materials of the prismatic cell have a direct influence on the LIB's macroscopic mechanical responses, an in-depth study of their failure characteristics can enhance the accurate understanding of the mechanisms by which internal short circuits occur in LIBs.By performing a comprehensive series of mechanical tests on the anode, cathode, and separator, we can gain the insight into the mechanical behaviors and failure mode of these materials under a variety of loads, which provides support for the construction of accurate finite element models for the prismatic cell.

Constitutive Properties of Component Materials and Modeling
The constitutive relationship of component materials in LIBs is the basis of constructing discrete layered structure model.The previous section gives a preliminary description of the uniaxial and biaxial tests of the electrodes and separators.In this section, the test results would be used to analyze the failure behaviors of component materials under different loads, and the corresponding constitutive relationship would be obtained.According to the constitutive properties, the finite element model of each component material is constructed.

Uniaxial Tension Properties
The active coatings on either side of the electrodes are porous composite materials that consist of a solid powder and polymer binder.Owing to the discontinuous nature of the coatings' porous structure, the current collector carries most of the load when the electrode is subjected to uniaxial tension.In the experiments of Wang et al. [25], it was observed that the electrode coatings were still intact even after the current collectors cracked, which implies that the former is more resilient than the latter.Furthermore, Sahraei et al. [19] also observed that the current collectors are more susceptible to cracks than the coating since the current collectors were damaged by the rolling that occurred during electrode fabrication.As a result, the uniaxial tensile failure strains of the anode/cathode specimens are similar to those of the current collectors.Assuming that the uniaxial tensile strains of electrodes, active coatings, and current collectors are equal under uniaxial tensile load, the following results can be obtained: According to the tensile stress-strain curves, the electrodes characterized the elastic-plastic tensile behavior obviously, and the brittle fracture occurred.Therefore, the current collector was modeled using the isotropic linear-hardening model, and the expression was as follows: where σ and E are uniaxial tensile stress and elastic modulus of component materials respectively; Et and σs are tangent modulus and yield stress respectively.Equation ( 2) is used to describe the corresponding elastic-plastic stress and strain of materials in uniaxial tension.
In order to understand the uniaxial tensile mechanical properties of coatings and current collectors, a simple equation was introduced to describe the contribution of component materials to the uniaxial tensile properties of electrodes.According to Equation (1), the uniaxial tensile strains of electrodes, coatings, and current collectors are equal, and the tensile mechanical properties equations of electrode are as follows: ( ) where Fe, Fa, and Fc are the uniaxial tensile load of electrodes, coatings, and current collectors respectively; ξ is the contribution coefficient of coating to uniaxial tensile load.Since the linear response equation (Equation ( 3)), which describes the interactions between the coatings and the current collectors, is not entirely accurate, ξ is, in practice, a response function that correlates with strain.Since the coating is a porous structure that contributes little to the uniaxial tensile strength of the electrodes, it was assumed that ξ = 0.1.Figure 6a,b illustrates fitting curves for the uniaxial tensile stress-strain behaviors of the coating and current collector.The fitting curves for the coatings present that the uniaxial tensile strengths of the cathode and anode coatings are approximately 2.6 and 4 MPa, respectively.Based on peeling tests in a variety of loading directions, Zhu et al. [24] found that the adhesion strength between the coating and current collector varies between 3.0 and 4.5 MPa.They also observed that the effect of loading direction on adhesion strength is small.Therefore, the stress-strain curves of the coating and current collector that were obtained using Equations ( 1)-( 3) satisfy the requirements of this study.The mechanical properties of the separator include nonlinear viscoelastic plasticity and anisotropy.To ensure feasibility and convergence, the mechanical properties of the separator under uniaxial tension were simplified to an elastoplastic stress-strain model (see Equation ( 2)), as shown in Figure 6c.The MD and TD uniaxial tensile curves were thereupon simplified.We will address the DD uniaxial tensile stress-strain relationship of the separator in a follow-up study.The mechanical properties of the component materials under uniaxial tension are presented in Table 2.

Uniaxial Compression Properties
The stress-strain curves of current collector under uniaxial tension could be used to predict their properties to uniaxial compression.The coatings, on the other hand, have strikingly different mechanical properties under tensile and compressive loads.Generally, the compression curves exhibit two distinct stages: a nonlinear initial stage, where the effective modulus stiffens gradually due to decreasing porosity, and a linear compaction stage, where the coating material has compacted fully.The gradient of the cathode specimens' stress-strain curve did not decrease even when the compressive stress was 120 MPa, which indicates that the coating and current collector have yet to yield or be damaged at this level of stress, as shown in Figure 6d.The gradient of the anode specimens' stress-strain curves begins to decrease after 80 MPa, which is caused by damage or yielding of the coating, as shown in Figure 6e.The stress-strain curves of the separator specimens under uniaxial compression are similar to those of the cathode specimens.They are initially nonlinear and transit into the linear compaction stage afterward, as shown in Figure 6f.Since the effective modulus of these materials can be divided into two stages, we have assumed that the elastic modulus, E, is equal to E0 in the initial stage and Emax in the compaction stage when simulating the materials' compression response.During the stiffening process, E varies exponentially with strain, ε, as shown below: In this equation, εp is the plastic strain threshold for the compaction stage (i.e., the strain for the fully compacted material).If the compression strain of the material is less than εp, E varies exponentially with ε; if the strain exceeds εp, E varies linearly with ε.The averaged test curves of the cathode, anode, and separator indicate that their εp values are 0.14, 0.32, and 0.68, respectively.β fits the increase in the gradient of E in relation to ε during the stiffening stage.If β is large, the increase in E with increasing ε will be slow.The stress-strain relationship of the component materials under compression may be subsequently obtained from Equation ( 4 Under uniaxial compression, the coating and current collector have the same external load, and the compression displacement is the sum of the two displacements.It is assumed that the uniaxial compressive stresses of electrodes, coatings, and current collectors are equal: In Equation ( 6), β and Emax are unknown.Emax is derived from tests on the cathode and anode, while β must be determined by fitting the model against experimental data.Since the uniaxial compressive strain of the coating and current collector is equal to that of the electrode, the average strain of an electrode under uniaxial compression can be expressed as follows: where⎯εe,⎯εa, and⎯εc are the average compressive strains of electrodes, coatings, and current collectors under uniaxial compression load, respectively; νa and νc are the relative volume fraction of coatings and current collectors under uniaxial compression load.
Based on Equations ( 6)-( 8), the cathode specimen has an Emax of 920 MPa and β of 15.26, while the anode specimen has an Emax of 353 MPa and β of 8.99.The stress-strain curves of the electrode and coating under uniaxial compression were fitted by substituting these coefficients into Equation ( 6), as shown in Figure 6d,e.These results indicate that the fitting curve of the electrode is essentially identical to the average test curve.Therefore, the fitting curve of the coating is an accurate description of its mechanical properties under uniaxial compression.Figure 6f illustrates the fitted stress-strain curve of the separator under uniaxial compression, which reveals that its Emax and β coefficients are 220 MPa and 2.64, respectively.

Constitutive Modeling and Simulating
The finite element models were constructed with the LS-DYNA.In the electrodes, the current collector was described with *MAT_003 elastoplastic material, which is suitable for isotropic hardening elements.The coatings were described with *MAT_026 honeycomb material, which is suitable for truly anisotropic honeycomb and foam elements.Since the separator is extremely thin and occupies a slight proportion of the electrode, it does not affect the electrodes' mechanical properties significantly.Therefore, the separator may be described using either *MAT_126 modified honeycomb material or *MAT_063 crushable foam material.Since the former is an orthogonally anisotropic honeycomb material, it is necessary to input the stress-strain curves of each of the principal directions (tension, compression, and shear).The latter is an isotropic foam material, which solely requires the input of a compressive stress-strain curve.In this study, the results obtained with both materials were compared and analyzed.
The failure modes of the cathode and anode are completely different under uniaxial tension and compression.The in-plane tensile resistance provided by the coatings is less during the tensile test, and the current collector is prone to tensile fracture.During the compression test, the contribution of the current collector to the compression load is less, and the coatings would experience a damage accumulation.Figure 2 indicates that tensile failure occurs in the following order: the cathode collector, cathode coating, anode collector, anode coating, and lastly, the separator.The coating is expected to induce a significant degree of strain localization, which will lead to deformation failure or fracture of the current collector under local indentation.The failure and crack in the current collector may directly lead to the separator failure, thereby causing short circuits in the LIB.Therefore, accurate failure criteria and failure parameters are significant for the prediction of short circuit formation in LIBs subjected to local indentation loading.The tensile failure of each component occurs at their maximum tensile strains, and the maximum tensile strains of *MAT_003, *MAT_026, and *MAT_126 materials are presented in Table 2.As for the failure under compression, the damage behaviors of *MAT_026 and *MAT_063 materials were implemented by inputting their stress-strain curves under uniaxial compression.*MAT_126 material not only requires MD-and TD-uniaxial tension stress-strain curves (see Figure 6c), a uniaxial compression curve (see Figure 6f), but also requires to use the stress transformation equations of composite materials to obtain the stress-strain curve for DD shear.Figure 7a illustrates the relationship between two coordinate systems in the separator plane, where θ represents the anticlockwise angle between the 12-coordinate system and XY-coordinate system.The stress equilibrium equation can be derived from the inter-element equilibrium conditions of the oblique plane (see Figure 7b): where, σ1 and σ2 are the MD-and TD-uniaxial tensile stresses of the separators, respectively; σx and σy are the stress components of θ angle in the MD and TD counter clockwise rotation respectively; τ12 is the shear stress in the 12-coordinate system; τxy is the shear stress in the XY-coordinate system.
(a) (b) Assuming that θ = 45° and σ1, σ2 and σx are the MD-, TD-, and DD-uniaxial average tensile stresses of the separator in Figure 2f, respectively; According to Equation ( 10), the shear stress expression of separator in the DD can be obtained: ( ) *MAT_063 material requires solely the input of a compressive stress-strain curve, and the tension cut-off stress was defined as the average flow stress for tension in the MD, 108 MPa.Finite element models for the cathode, anode, and separator were constructed.The spherical punches were represented as rigid spheres with diameters of Φ12.5 and Φ6.3 mm.The contact between the spherical punch and component material model was defined as an automatic surface-to-surface contact with a friction coefficient of 0.4.The size of the smallest element was 0.1 mm in the contact zone and 0.8 mm in the noncontact zone.All of the component material models consisted of solid elements, whereas the spherical punches were made of shell elements.The coatings were connected to the current collector via common nodes.The coating and separator had a minimum two solid elements through their thickness.The maximum tensile strain criterion was varied for each component material model, and *MAT_ADD_EROSION was used to delete the elements that reached their corresponding maximum tensile strain value.This ensured that the numerical simulation would not diverge on account of excessively large deformations.
Figure 8a-d reveals that the experimental curves of the spherical indentation tests on the anode/cathode were accurately predicted by our numerical simulations.However, the simulation of the anode being indented by a Φ6.3 mm spherical punch exhibited slightly higher load intensities than the experiment.Figure 8e,f, on the other hand, indicates that the simulated curves for spherical indentation tests on the separator are significantly different from the experimental curves.This could be attributed to the use of simplified material models to describe the separator.It is found that the strength of the *MAT_126 model is significantly higher than the *MAT_063 model, and provides a more accurate approximation of the separator's mechanical behaviors, but the calculation time is also longer.The elements that failed during the simulated spherical indentation test with a Φ12.5-mm spherical punch were deleted from the cathode, anode, and separator models, as shown in Figure 9.The simulated cracks in the cathode and anode models are similar to the experimentally observed cracks.In the *MAT_126 separator model, the cracks are slightly different from the experiment, but the crack initiation position and primary shear band are similar to those of the experiment.However, the cracks in *MAT_063 separator model are essentially different from those in the experiment (not shown).By comparing the simulated and experimental results of the local indentation tests, we have proved that the abovementioned models are capable of predicting the macroscopic force-displacement curves and mesoscopic failure modes of a prismatic LIB's component materials.

Progressive Failure of Cathodes and Anodes
In order to further understand the failure mechanisms of lithium-ion prismatic cell under spherical indentation, it is necessary to understand the progressive deformation failure of the cell interior.Considering that the interior is composed of component materials stacked alternately, a layer element model (LEM) composed of separator, cathode, separator, and anode is established.The mechanical behavior and failure response of LEM were studied under spherical indentation.The simulation results were compared and verified with the experimental results.Based on the LEM, a discrete layered structure model was constructed to analyze the progressive failure mechanisms of cathodes and anodes under spherical punch.

Modeling of Mesostructural Layer Element
The specimen dimensions and experimental apparatus are the same as those in Figure 4.The Φ6.3 mm and Φ25 mm spherical punches were used to perform quasistatic local indentation at a loading speed of 1 mm/min (see Figure 10a).We chose to use a Φ25 mm spherical punch because of the universal applicability of this loading condition.The finite element models for the cathode, anode, and separator were already constructed in the previous section.The surfaces were modeled using CON-TACT_AUTOMATIC_SURFACE_TO_SURFACE protocol to prevent the elements of the cathode, anode, and separator from penetrating each other.The kinetic friction coefficient was set to 0.4.Figure 10b illustrates the stacked separator-cathode-separator-cathode model; this is the repeating element that makes up the internal configuration of a prismatic LIB, the LEM.The finite element model of a Φ6.3-mm spherical punch acting on the LEM is depicted in Figure 10c.The sizes of the elements in the contact zone and noncontact zone were 0.1 and 0.6 mm, respectively, and there were 202,268 nodes and 160,758 elements in the LEM.The separator was represented either by *MAT_126 material or by *MAT_063 material.
The simulated and experimental results for spherical indentation with Φ6.3 mm and Φ25 mm spherical punches are illustrated in Figure 11.Although the simulated and experimental peak forces and failure displacements are slightly different, the simulated and experimental curves are essentially the same from the initial stage (initial stiffening) up to the failure-induced load drop-offs.Furthermore, there were no significant differences between the results obtained with *MAT_126 or *MAT_063 to represent the separators.This indicates that the separator influences a prismatic LIB's mechanical properties minimally.Since the use of the *MAT_126 material is computationally expansive and the failure modes of the separator are not important for this study, *MAT_063 material was used for the separator in all subsequent simulations to improve computational efficiency.Spherical indentation leads to complex mechanical behaviors in the layer elements since this includes tensile failures in the current collector, compressive damage in the coatings, and the formation of holes owing to debonding between the coatings and current collectors.There are two distinct force drop in the force-displacement curve of a layer element.The first force drop is caused by the tensile failure of the cathode current collector; further increase in load will eventually lead to the second force drop, which is caused by the tensile failure of the anode current collector.By analyzing the results, it was found that the cathode current collector would fail first, followed by the anode current collector and, finally, the separators.Therefore, strain localization in the coating does not lead directly to short circuits in a prismatic LIB since short circuits are primarily caused by separator damage owing to fractures and slips in the current collectors.According to Figure 11a, the cathode current collector cracked when the strain reached 0.31 (displacement = 0.87 mm) during the indentation by a Φ6.3 mm spherical punch.This failure manifested itself as a cross-shaped crack in the contact zone, and the force drops off when the crack propagates to the coating on the current collector.When the strain increases to 0.86 (displacement = 1.83 mm), the anode current collector begins to exhibit tensile fractures, which appear as cross-shaped cracks in the contact zone.Afterward, the force drops off again when these fractures extend to the coating.After the cathode and anode in the layer element have cracked and failed, the separator will continue to bear loads until it fails.To simulate a universally applicable loading condition, a layer element was indented by a Φ25 mm spherical punch, as shown in Figure 11b.The simulated curve agrees well with the experimental curve, and the stiffening response was essentially identical in both curves.However, the simulated peak force and failure displacement are slightly higher than those of the experimental curve.During the simulation, crack initiation occurred just off the center of the spherical punch, and the fracture eventually propagates to form a petal-shaped crack, similar to that in the experiment.

Progressive Failure of Cathodes and Anodes on Multilayered LEMs
The results above revealed that a layer element would fail in a progressive manner under local indentation.As the basic element of the interior, the layer element determines the mechanical behavior and deformation failure of the cell interior.Considering that the layer element number of the lithium-ion prismatic cell is up to 45 layers, it needs to be simplified.Figure 12a illustrates a local indentation test on a stack of layer elements.Based on this, to ensure that the model would be computationally feasible, we constructed a 1/4 finite element model of an eight-layer layer element stack to simulate their inter-component interactions and failure propagation mechanisms.An axially symmetrical model of a Φ6.3 mm spherical punch acting on a multilayered stack of layer elements is depicted in Figure 12b.The spherical punch was a rigid sphere moving in the through-thickness direction of the LEM, and the base was a completely constrained rigid plane.To prevent the elements of the spherical punch, cathode, anode, separator, and rigid plane from penetrating each other, the surfaces were modeled with the CONTACT_ AUTOMATIC_SURFACE_TO_SURFACE protocol, with a kinetic friction coefficient of 0.4.The sizes of the smallest elements in the contact zone and noncontact zone were 0.1 and 0.6 mm, respectively, and the model contained 502,418 nodes and 380,800 elements (see Figure 12c).This simulation required 23 h to complete with 44 CPUs.deleted elements formed ring-shaped cracks.As damage continued to accumulate during the indentation test, a rough ring-shaped section was formed by the failure cracks of the first anode layer.In addition, the ruptured areas on the top and bottom side of the coating were almost identical.Figure 14 compares the experimental and simulated failure modes of the eight-layer model's anode layers.Here, it is obvious that failures in the first, second, and third anode layers led to a variety of failure modes via the propagation of failure cracks from one layer to another.The failure mode of the first layer was a distinct ring-shaped crack, which had a significantly larger ruptured area and smoother crack edges than the failure mode in the second layer.In the third anode layer, element deletion was not observed.This is close to the experimental test of the third anode layer, which exhibited solely fine cracks at the center of the contact zone.The tensile failure strain of the cathode current collector was relatively low, as shown in Figure 15.When the strain due to indentation loading increased to 0.21 (displacement = 0.36 mm), the cathode current collector failed at the center of the contact zone and the cracks propagated along its symmetric edges.The damage of the cathode coating began when the strain increased to 0.26 (displacement = 0.43 mm); this damage manifested itself as compression fractures in the contact zone and tensile fractures that propagated along the symmetric edges.The strain's increase to 0.33 (displacement = 0.54 mm) caused the compression fracture in the first cathode layer to propagate in the annular direction from the center of the contact zone while tensile cracks continued to propagate along the symmetric edges, thereby forming a petal-like crack.The tensile strain-induced changes of the first, second, and third cathode layers as well as their top and bottom coatings are shown in Figure 16a.It is clear that the tensile strain on the bottom coating is much higher than that on the top coating, which implies that the bottom coating will fail first.By comparing the simulated and experimental results, it becomes clear that the failure behaviors of the cathode and anode under spherical indentation are radically different.In the first cathode layer, the number of elements that were deleted from the bottom coating is significantly higher than that from the top coating, and the failure modes of the bottom coating are somewhat reminiscent of the anode's failure modes.In the second cathode layer, the outer elements around the center of the contact zone were deleted; this resembles the ring-shaped cracks that were experimentally observed in the contact zone, as shown in Figure 16b.The analysis above indicates that the failure responses of the cathode and anode to spherical indentation are somewhat different.These differences may be due to differences in strength between the current collectors and coatings, or to differences in the constitutive properties of the cathode and anode coatings materials.According to the local indentation results in the eight-layer LEM, the electrode materials of the lithium-ion prismatic cell produce progressive failure, that is to say, the failure of the cell interior is a propagation from the local fracture to the overall failure.The fracture of current collectors and strain localization of coating materials cannot be distinguished by macroscopic force-displacement response curve, because the whole failure process is instantaneous.The multilayered LEMs can reasonably predict the failure modes and understand the progressive failure mechanisms of component materials.In addition, during the local indentation, the strain localization of the coating materials of the electrodes lead to the rapid increase in the current collectors' equivalent strain, which ultimately causes the current collectors to crack.Therefore, internal short circuits are primarily caused by separator damage owing to fractures and slips in the current collectors.

Conclusions
The mechanical failure behavior of prismatic LIB component materials were expressed experimentally and numerically.The mechanical properties of the anode, cathode and separator under uniaxial tension, compression, and biaxial indentation were tested, and the results of these tests were used to derive the stress-strain constitutive models of the metallic current collectors, active coatings, and separator.The maximum tensile strain failure criterion was proposed to describe the indentation failure of component materials, and an ultrathin LEM was constructed by the experimental stress-strain curves to simulate the mechanical behaviors and failure modes under the spherical punches.Through the combination of experiments and numerical simulations, we identified the progressive failure mechanisms of the n-layer LEM stacked structure model, including the tensile and compressive failure of cathodes and anodes, and compared the failure modes of experimental tests and simulations.
Based on the numerical simulations of the LEM, it was determined that failure cracks in the current collectors could rupture their adjacent separators, which ultimately led to internal short circuit.By constructing an accurate layered structure model, we were able to accurately predict the force-displacement relationships, failure modes, and the moment of short circuit initiation in a prismatic LIB.These predictions will provide a profound insight into the progressive failure mechanisms of prismatic LIBs subjected to mechanical load.Furthermore, we demonstrated that the macroscopic force-displacement curve of a LEM had no significant relationship with the use of different types of material models to represent the separators.The anisotropic material model could characterize the mechanical behaviors and failure modes of the separator more accurately, but it would consume more calculation time.In the layered structure model, if the failure modes of the separator are not important, the isotropic material model could be used to represent the separator to reduce the calculation time.

Figure 1 .
Figure 1.The photos of lithium-ion prismatic cells and internal component materials: (a) Prismatic shell and interior; (b) Internal component materials.
. It can be observed that the compressive test curves of the component materials are consistent.

Figure 3 .
Figure 3. Compressive test of component materials for prismatic cell: (a) Test setup and specimens of tested component materials; (b) Compressive stress-strain curves for cathode specimen; (c) Compressive stress-strain curves for anode specimen; (d) Compressive stress-strain curves for separator specimen.
Figure 5 shows the force-displacement curves of the component materials under the Φ12.5 and Φ6.3 mm spherical punches.The fluctuation of the triplicate test curves of the cathode is more obvious than that of the anode and separator, which is caused by the slight shedding of the coatings during indention.

Figure 7 .
Figure 7. Diagram of separator plane coordinate system: (a) Rotating coordinate system in the separator plane; (b) Equilibrium coordinate system in oblique plane.

Figure 8 .
Figure 8. Force-displacement curves of lithium-ion prismatic cell components under different sizes of spherical punches: (a) Cathode tests and simulation under Φ12.5 mm; (b) Cathode tests and simulation under Φ6.3 mm; (c) Anode tests and

Figure 10 .
Figure 10.Test and simulation of an layer element model (LEM) under spherical punch: (a) Experimental setup; (b) A layer element structure model; (c) Finite element model of a layer element.

Figure 11 .
Figure 11.Force-displacement curves of a layer element under spherical punch: (a) Comparison of test and simulation curves under Φ6.3-mm spherical punch; (b) Comparison of test and simulation curves under Φ25 mm spherical punch.

Figure 12 .
Figure 12.Local indentation test of multilayered LEMs under 6.3 mm spherical punch: (a) Experimental setup; (b) Finite element model of multilayered LEMs; (c) Enlarged view of layered structure of finite element model.

Figure 13 compares
Figure13compares the simulated and experimental force-displacement curves of the anodes in the eight-layer LEM.The force-displacement curve of the anodes indicates that ring-shaped cracks formed in the first anode current collector layer when the strain due to spherical indentation reached 0.57 (displacement = 0.94 mm).The crack in the anode current collector led to local stress concentrations, which caused the damage to propagate to its coating rapidly.The damage on the coating manifested itself as elements being deleted in the contact zone around the indenter, and it could be observed that the

Figure 13 .
Figure 13.Comparison of experimental and simulated force-displacement curve and numerically prediction failure evolution of anode in multilayered LEMs during local indentation.

Figure 14 .
Figure 14.Comparison between experimental tests and simulation of fracture modes of anodes across different layers under local indentation.

Figure 15 .Figure 16 .
Figure 15.Comparison of experimental and simulated force-displacement curve and numerically prediction failure evolution of cathode in multilayered LEMs during local indentation.

Table 1 .
Specifications of the prismatic cells and internal components.

Table 2 .
Tensile properties of lithium-ion prismatic cell components.