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Investigation of mechanical property of cylindrical lithium-ion batteries under dynamic loadings
Journal of Power Sources 451 (2020) 227749
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Investigation of mechanical property of cylindrical lithium-ion batteries under dynamic loadings Wenwei Wang a, Sheng Yang a, b, *, Cheng Lin a, Weixiang Shen b, Guoxing Lu b, Yiding Li a, Jianjun Zhang b a b
National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing, 100081, China Faculty of Science, Engineering and Technology, Swinburne University of Technology, John Street, Hawthorn, Victoria, 3122, Australia
H I G H L I G H T S
� Two types of 18650 Li-ion batteries are performed dynamic compression tests. � Two types 18650 Li-ion batteries both exhibit strain rate hardening behaviors. � Establishing a finite element model of cylindrical Li-ion batteries suitable for dynamic loadings. A R T I C L E I N F O
A B S T R A C T
Keywords: Lithium-ion battery Mechanical abusive conditions Dynamic loading Constitutive model
Understanding of mechanical property of lithium-ion batteries is the key to unlock complicated and coupled behaviors of thermal runaway, which is triggered during electric vehicle collision. In this study, mechanical behaviors of cylindrical lithium-ion batteries under dynamic loadings are investigated. Two types of 18650 lithium-ion batteries, namely LiNiCoAlO2 and LiNiCoMnO2, are chosen to perform compression tests at various dynamic loadings. Experimental results indicate that these two types of 18650 lithium-ion batteries exhibit strain rate hardening behaviors, namely their resistances to deformation enhance as loading rate increases. LiNi CoMnO2 batteries show obvious strain rate hardening behaviors at low loading rates while LiNiCoAlO2 batteries can only show strain rate hardening behaviors until the loading rate increases to a certain value. The constitutive model of the jellyroll of lithium-ion batteries is proposed to describe these mechanical behaviors under dynamic loadings and it is validated by a finite element model of lithium-ion batteries. The proposed constitutive model can be utilized to evaluate the crashworthiness of lithium-ion batteries in the case of impact accidents and provide valuable guidance for the structure design of battery packs in electric vehicles.
1. Introduction The introduction of electric vehicles (EVs) can significantly reduce the dependence on oil fuel and the emission of greenhouse gas, which is beneficial to environmental improvement. Lithium-ion (Li-ion) batteries have been the primary energy storage for EVs due to its advantages over other energy storage, such as high energy/power density, long cycle life, high working voltage and low self-discharge rate [1–4]. As EVs need high capacity and energy density of Li-ion batteries to meet the demand for long driving mileage, the safety and reliability of Li-ion batteries have become more and more important. Many safety measures are taken in Li-ion batteries to avoid catastrophic failures including pressure relief vents, current interrupt devices, ceramic-coated separators, positive
temperature coefficient current-limiting switches as well as battery management systems (BMSs) [5,6]. However, in the case of EV collision, the poor thermal stability of Li-ion batteries may lead to fire and even explosion due to the existence of its flammable electrolyte. Many attentions are paid to deformation behaviors, voltage and thermal responses of Li-ion batteries under mechanical abusive condi tions in recent years. Yang et al. analyzed the stiffness of an 18650 Li-ion battery during compression tests and revealed that its deformation process could be divided into three stages [7,8]. Chung et al. revealed the deformation and failure mechanism of Li-ion batteries under trans verse loading [9]. They found that the angle between fault line and battery plane is consistently constant and approximately 62� . Li et al. recorded the voltage and temperature responses of Li-ion batteries
* Corresponding author. National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing, 100081, China. E-mail address: [email protected] (S. Yang). https://doi.org/10.1016/j.jpowsour.2020.227749 Received 19 October 2019; Received in revised form 24 December 2019; Accepted 12 January 2020 Available online 14 February 2020 0378-7753/© 2020 Elsevier B.V. All rights reserved.
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Journal of Power Sources 451 (2020) 227749
during mechanical abusive tests [10]. They found that peak force is strongly related to open circuit voltage (OCV) drop and battery tem perature rise. Wang et al. developed a detailed finite element model (FEM) to study mechanical properties of cylindrical Li-ion batteries under four common loading conditions and proposed a short-circuit criteria based on separator failure [11]. Zhu et al. utilized scanning electron microscope (SEM) to investigate the deformation mechanisms of Li-ion batteries components under micro tests and found that defor mation mechanisms between cathode and anode coatings are different [12]. Zhang et al. revealed the degradation mechanism of trilayer separator of Li-ion battery during charge/discharge cycles and they found that failure stress and strain of a separator decreases when a number of cycles increase [13]. The mechanical properties of graphite anode and the adhesion strength of cathode in Li-ion batteries were studied in Refs. [14,15]. They found that shear strength of adhesion interface is nearly two times of its tensile strength. Zhang et al. inves tigated the mechanical failure behaviors of electrodes in Li-ion batteries and it was found that battery failure behaviors are complicated, which is a combination of tensile and compression failures [16]. The effect of porosity and thickness of electrodes in Li-ion batteries on internal short circuit was studied in Ref. [17]. It was found that both moderate porosity and appropriate increase in the thickness are beneficial to the stabilization of short-circuit voltage. Dixon et al. studied the effect of electrolyte of pouch Li-ion batteries on their mechanical behaviors [18]. It was found that the measured force and displacement of the pouch batteries with electrolyte is lower than those of the pouch batteries without electrolyte. The state of charge (SOC) hardening behaviors of Li-ion batteries were studied in Refs. [19,20] and the SOC-dependence mechanical behaviors of Li-ion batteries were found to be attributed to the internal stress caused by volume expansion [21]. Xu et al. investigated the effect of state of health (SOH) of Li-ion batteries on their mechanical behaviors [22]. They found that the SOH had a large effect on failure stress while its influences on failure strain were minimal. In real-world engineering scenarios, significant concern of EVs is safety performance at the time of vehicle collision, which belongs to dynamic loading conditions. However, the above studies on the mechanical properties of Li-ion batteries and its components were all carried out under quasi-static tests. Few publications focus on the investigation of the mechanical be haviors of Li-ion batteries under dynamic tests. Kisters et al. carried out dynamic impact tests on Li-ion batteries and they found that the peak force would change as the change of the loading rate [23]. Jia et al. reported the voltage response of Li-ion batteries during dynamic loading and they found that faster voltage drop would be induced by higher testing speed [24]. These two studies adopt experimental analysis. Xu et al. investigated the mechanical response of cylindrical Li-ion batteries under dynamic loadings by performing simulation [25]. Avdeev and Gilaki validated the established FEM under lateral impact loading [26], where the FEM was established based on the mechanical response of Li-ion batteries under quasi-static tests. In recent study, Xu et al. developed a FEM for 18650 Li-ion batteries considering strain rate [27]. They validated their model through drop tests. Kermani et al. carried out high speed compression tests on Li-ion batteries and established a FEM for Li-ion batteries based on Johnson-Cook model [28]. This paper is aimed to investigate the mechanical properties of cy lindrical Li-ion batteries under dynamic loadings and establish a FEM to predict their dynamic mechanical behaviors. The purpose to establish this FEM is to obtain the peak force of the Li-ion batteries under dynamic loadings because the peak force has a strong correlation with the trigger of thermal runaway under mechanical abusive conditions. Obtaining the peak force can guide the structure design of battery packs in EVs to ensure that thermal runaway will not be triggered under crash accidents. In this study, compression tests with various speeds are performed on two types of 18650 Li-ion batteries, namely LiNiCoAlO2 (NCA) and LiNiCoMnO2 (NCM) batteries, which have been the first choice of power battery for electrical passenger vehicles due to their advantages in the
aspects of cost, energy density and etc. Experimental results indicate that cylindrical Li-ion batteries with different cathode materials show similar mechanical, electrical and thermal response under the compression tests. General trend of mechanical responses at different loading rates are similar for NCA or NCM Li-ion batteries. They both exhibit strain rate hardening behaviors, namely their deformation re sistances increase as the loading rate increases. However, the strain rate hardening behaviors of NCA Li-ion batteries can’t be obviously observed until the loading rate increases to a certain value. These experimental results have enriched the knowledge of mechanical properties for Li-ion batteries. Besides, the established FEM can also be utilized to evaluate the crashworthiness of Li-ion batteries in the case of impact accidents and provide valuable guidance for the structure design of battery packs in EVs. The remaining part of this paper is organized as follows. Section 2 analyzes the mechanical responses of NCA and NCM Li-ion batteries under compression tests at different loading rates. Section 3 proposes a constitutive model of cylindrical Li-ion batteries suitable for dynamic loadings. Section 4 establishes a FEM to validate the proposed model. Finally, the conclusions are summarized in Section 5. 2. Experiments and analysis Two types of cylindrical Li-ion batteries with different cathode ma terials, namely NCA and NCM, are chosen to perform compression tests, their specifications are listed in Table 1. We bought these two types of the batteries, where the manufacturers of NCM and NCA Li-ion batteries are Sony and Samsung, respectively. To avoid fire or even explosion under compression tests, all the Li-ion batteries are discharged at constant current (2 A) to their cut-off voltage. INSTRON VHS 8800 as shown in Fig. 1(a) is used to perform compres sion tests at high speed while MTS EXCEED E45 100 KN as shown in Fig. 1(b) is used to perform compression tests at low speed. The indenter of MTS EXCEED E45 100 KN is installed at the top plate while that of INSTRON VHS 8800 is installed at the bottom plate. It should be noted that safety equipment is placed around INSTRON VHS 8800 to provide necessary protection. Besides, Phantom V2512 as shown in Fig. 1(a) is placed in front of INSTRON VHS 8800 to record the compression tests at high speed. Load and displacement are measured over time during all compression tests and then load-time relation is converted into loaddisplacement relation for easy comparison of mechanical responses at different loading rates. NCM Li-ion batteries are compressed at 0.5 mm/min, 5 mm/min, 25 mm/min and 3 m/s, respectively. NCA Li-ion batteries are compressed at 0.5 mm/min, 5 mm/min, 25 mm/min, 60 mm/min and 3 m/s, respec tively. All the batteries are compressed between two plates and these compression tests are repeated at least three times to make sure the credibility of experimental data. Their experimental results are shown in Fig. 1 (c) and (d), respectively. The videos of NCM and NCA Li-ion batteries compression tests performed at 3 m/s can be downloaded from the supplementary material (S1–S2). The strain rate for cylindrical Li-ion batteries can be calculated as:
Table 1 Specifications of two types of 18650 Li-ion batteries. Items Normal Capacity Normal Voltage Full Charge Voltage Discharge cut-off Voltage Maximum Discharge Current Size Cathode Material Anode Material
2
Specifications NCM Li-ion battery
NCA Li-ion battery
2100 mAh 3.6 V 4.2 V 2.5 V 30 A 65 x 18 x 18 (mm) LiNiCoMnO2 LixC6
2500 mAh 3.7 V 4.2 V 2.5 V 20 A 65 x 18 x 18 (mm) LiNiCoAlO2 LixC6
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Journal of Power Sources 451 (2020) 227749
exhibit strain rate hardening behaviors, namely their abilities to resist deformation increase as the loading rate rises. On the other hand, we also see the differences between the mechanical responses of NCM and NCA Li-ion batteries. Firstly, the measured maximum force of NCA Liion batteries is different from that of NCM Li-ion batteries at the fully discharged state. It indicates that the structure design of battery packs in EVs should be designed differently for the safety of different Li-ion batteries, even for 18650 Li-ion batteries with different cathode mate rials. Secondly, For NCM Li-ion batteries, their strain rate hardening behaviors can be obviously observed from their mechanical responses at low loading rates, namely 0.5 mm/min, 5 mm/min and 25 mm/min. For NCA Li-ion batteries, their mechanical responses at 0.5 mm/min, 5 mm/ min and 25 mm/min are almost the same. Their strain rate hardening behaviors can’t be obviously observed until the loading rate increases to 60 mm/min. Thirdly, there are still some differences before the displacement of 4 mm. This is due to the difference in those gaps inside NCM and NCA Li-ion batteries. The appearance of an NCM and an NCA Li-ion battery after the compression at 3 m/s is showed in Fig. 1 (c) and (d), respectively. It can be found that many layers of electrodes inside the Li-ion batteries have broken after the compression test. To further investigate the safety performance of NCM and NCA Li-ion batteries under dynamic loadings, compression tests are performed on the NCM and NCA Li-ion batteries at the SOC of 0.4. INSTRON 5985 is used to conduct these compression tests with the loading rate of 60 mm/ min, as shown in Fig. 2 (a). The battery voltage and temperature are recorded simultaneously by HIOKI MR 8880 and FLUKE TI 400 (i.e. an infrared camera) during the compression tests. Fig. 2 shows the exper imental results for the NCM Li-ion battery while Fig. 3 shows the experimental results for NCA Li-ion battery. For the NCM Li-ion battery, the maximum force is 92.47 kN at 7.83 s, as shown in Fig. 2 (a), the voltage rapidly decreases from 3.64 V at 8 s to 2.12 V at 8.5 s and then decreases to 0.01 V at 10.5 s, as shown in Fig. 2 (b) and the temperature slowly increases from 17:03 � C at 8.88 s to its maximum value of 102:78 � C at 86.58 s and then starts to slowly decrease, as shown in Fig. 2 (c). For the NCA Li-ion battery, the maximum force is 90.817 kN at 7.83 s, as shown in Fig. 3 (a), the voltage rapidly decreases from 3.64 V at 8.3 s to 1.65 V at 8.85 s and then decreases to 0.07 V at 8.9 s, as shown in Fig. 3 (b), and the temperature slowly increases from 20:38 � C at 9.99 s to its maximum value of 112:51 � C at 74.37 s and then starts to slowly decrease, as shown in Fig. 3 (c). It can also be observed from Figs. 2 and 3 that the general trends of the voltage and temperature responses of the NCM Li-ion battery are almost the same as those of the NCA Li-ion battery but the maximum temperature for the NCA Li-ion battery after the trigger of internal short circuit is slightly higher than that of the NCM Li-ion battery.
Fig. 1. (a) INSTRON VHS 8800; (b) MTS EXCEED E45; (c) Measured me chanical responses for NCM Li-ion batteries at different loading rates; (d) Measured mechanical responses for NCA Li-ion batteries at different loading rates.
dε = dt ¼ v=ð2RÞ
(1)
where v is the loading rate and R is the radius of Li-ion batteries. The strain rate for 60 mm/min and 3 m/s is 5:5 � 10 2 s 1 and 1:67 � 102 s 1 , respectively. The strain rate for 60 mm/min belongs to quasistatic compression. But it should be noted that the radius of 18650 Li-ion batteries is small, so the whole process of compression test at 60 mm/ min takes around 8 s. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.jpowsour.2020.227749 As observed in Fig. 1(c) and (d), we see the similarities between the mechanical responses of NCM and NCA Li-ion batteries. Firstly, the experimental data at the loading rate of 3 m/s for both NCM and NCA Liion batteries have good repeatability. Secondly, NCM and NCA Li-ion batteries have similar mechanical behaviors at the same loading rate. The general trend of mechanical responses at different loading rates is almost same for NCM and NCA Li-ion batteries. Thirdly, the measured load for NCM and NCA Li-ion batteries both slowly increases in the early stage and then increases exponentially. The reasons are: 1). The coating materials of cathode/anode are porous. 2). There are some gaps among each layer of the jellyroll, between metal casing and the jellyroll and within the hollow metal core. They account for slow increase in load response in the early stage. The jellyroll becomes densified as the compression continues. This accounts for significant increase in load response subsequently. Moreover, NCM and NCA Li-ion batteries both
3. Mechanical characteristics for jellyroll under dynamic conditions The deformation process of NCM and NCA Li-ion batteries at different loading rates are similar. Regardless of the indenter installed at the top or bottom plate, it will result in the same deformation. Hence, we choose the top plate as a moveable indenter to describe the deformation process under dynamic compression tests as shown in Fig. 4. It should be mentioned that a rectangular coordinate system (x, y, z) is used to describe the geometry of a Li-ion battery due to the flat contact area between the battery and two plates. H is the compression load and w is the vertical displacement of the top plate. Besides, experimental results indicate that the mechanical responses of both NCM and NCA Li-ion batteries at high speed are similar with those at low speed in the aspect of general trend, as depicted in Fig. 1(c) and (d). In our previous study, it was found that the whole deformation process of Li-ion batteries under quasi-static loading cases can be divided into three distinct stages [7,8]. Hence, Gaussian functions are 3
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Journal of Power Sources 451 (2020) 227749
Fig. 3. (a) Measured Load-time curve for NCA Li-ion battery at the SOC of 0.4; (b) Measured voltage response; (c) Measured temperature response.
Fig. 2. (a) Measured load-time curve for NCM Li-ion battery at the SOC of 0.4; (b) Measured voltage response; (c) Measured temperature response.
chosen to fit these curves measured at different loading rates as follows HðwÞ ¼ a0 *expð ððw
b0 Þ=c0 Þ2 Þ
(2)
where a0 , b0 and c0 are the fitting parameters corresponding to different loading rates which are listed in Table 2. The curve fitting function in MATLAB is used to fit the experimental data and obtain the values of these fitting parameters. Fig. 5 shows the analytical fitting curves for NCM Li-ion batteries while Fig. 6 shows those for NCA Li-ion batteries. It should be noted that the mechanical response for the NCA Li-ion battery at 0.5 mm/min is almost same as that at 5 mm/min. Hence, for NCA Li-ion batteries, the measured data for the 0.5 mm/min compression test isn’t analyzed and processed in this paper. The measured load-displacement data of a Li-ion battery can be used to establish its corresponding stress-strain relationship and the detailed process to develop this relationship can be found in Ref. [8]. Fig. 7 shows the calculated equivalent stress and strain of NCM Li-ion battery at different loading rates while those calculated results for NCA Li-ion batteries are shown in Fig. 8. Several conclusions can be obtained from these calculated stress-strain curves as follows. Firstly, NCM Li-ion batteries have the similar constitutive model with NCA Li-ion batteries. The reasons are shown as follows. The deformation is mainly attributed from the porous coating materials of the electrodes during the compression of a Li-ion battery [29,30]. The coating materials of
Fig. 4. Schematic description of Li-ion battery deformation compressed be tween two plates.
cathodes of NCM and NCA Li-ion batteries are both porous although their material compositions are different. Secondly, for both NCA and NCM Li-ion batteries, the stress starts to increase exponentially when the strain exceeds 0.2. This is due to the porous coating materials of elec trodes, the gaps among each layer of the jellyroll, between the jellyroll and the steel casing and within the metal core. The densification of the jellyroll accounts for significant increase in load response subsequently. Thirdly, NCM Li-ion batteries and NCA Li-ion batteries both have the similar constitutive model at different loading rates. The reason is that 4
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Table 2 Fitting parameters a0 , b0 and c0 for NCM and NCA L-ion batteries at various loading rates. Loading rete
NCM Li-ion batteries
NCA Li-ion batteries
0.5 mm/min
5 mm/min
25 mm/min
3 m/s
5 mm/min
25 mm/min
60 mm/min
3 m/s
Coefficient a0
74.99
75.96
87.11
61.67
102.8
95.43
90.95
72.18
Coefficient b0
10.26
9.927
10.19
6.835
9.981
9.766
9.566
7.014
3.771
3.56
3.836
2.377
3.028
3.019
3.105
2.087
Coefficient c0
Fig. 5. Measured force-displacement relations at various loading rates when a NCM Li-ion battery is compressed between two rigid flat plates and their analytical fittings: (a) v ¼ 0.5 mm/min; (b) v ¼ 5 mm/min; (c) v ¼ 25 mm/min; (d) v ¼ 3 m/s.
the constitutive model is established based on the measured load-displacement curves which are similar at different loading rates. Finally, the internal stress of an NCA or NCM Li-ion battery increases as the loading rate increases when the same deformation occurs inside it.
improved the computational efficiency while maintaining good simu lation accuracy. High computational efficiency is especially important when an EV crash simulation is carried out which contains thousands of batteries. Hyperworks/Ls-dyna software utilizes explicit time integration and has powerful abilities to perform nonlinear dynamic analysis. It is suit able for crash or large deformation simulation. Therefore, it is used to perform simulation analysis in this paper. To simulate compression test, the models of the jellyroll and two plates are established, respectively, where the solid elements are used to model the jellyroll and the shell elements are used to model the two plates. The grid size for the jellyroll is 0.8 mm and that for two plates is 1 mm. The material property of the jellyroll is set as isotropic, crushable foam (Material type 63) is utilized to model mechanical characteristics of the jellyroll. The rigid material is chosen to model the mechanical characteristics of two plates, which is consistent with the experimental setup. The stress-strain curves depicted in Figs. 7 and 8 are used as the input to the crushable foam to simulate the mechanical behaviors of two types of Li-ion batteries at different loading rates. The other simulation parameters are listed in Table 3. The FEM of the jellyroll is placed on the bottom plate whose six degrees of freedom are fully constrained. The top plate compresses the FEM of the jellyroll at a constant speed which is respectively corresponding to various loading rates used in the experimental program. Surface-tosurface is utilized to define the contact between top or bottom plate and the FEM of the jellyroll. The friction coefficient between the jellyroll and the top or bottom plate are both set as 0.3.
4. Simulation analysis 4.1. Establishment of the FEM This paper selects 18650 cylindrical Li-ion batteries with different cathode materials for investigation. They have almost the same me chanical structure which mainly consists of four parts, namely a steel casing, a positive end-cap, a jellyroll and a metal core. The contributions of the steel casing to the overall strain and stress is small which can be neglected due to its thin thickness (around 0.2 mm), so does the metal core. The positive end-cap has a complicated mechanical structure which is composed of several small parts, but its contribution to the overall stress is also small. Neglecting the above-mentioned three parts in modeling this type of a battery, we establish a FEM of the jellyroll to simulate the mechanical response of a battery for effectively improving computational efficiency. The jellyroll is tightly rolled by five layers, namely two layers of metal foils, one layer of separator and two layers of electrodes. The thickness of each layer is less than 0.5 mm. A detailed FEM of the jellyroll establishing for each layer will generate lots of el ements which will take a long time to compute. In our previous studies [8,19,29], we established a FEM of the jellyroll by integrating five layers into one homogenized representative element (RVE) and significantly 5
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Journal of Power Sources 451 (2020) 227749
Fig. 6. Measured force-displacement relations at various loading rates when a NCA Li-ion battery is compressed between two rigid flat plates and their analytical fittings: (a) v ¼ 5 mm/min; (b) v ¼ 25 mm/min; (c) v ¼ 60 mm/min; (d) v ¼ 3 m/s. Table 3 Simulation parameters. Component
Young’s modulus
Poisson ratio
Density
Jellyroll
Ejellyroll ¼ 1:5 Gpa
0:15
νjellyroll ¼
2:8 g cm
Tensile cut-off value 3
σf ¼ 10 Mpa
4.2. Validation and discussion Fig. 9 depicts the simulated displacement-load curves for NCM Li-ion batteries at different loading rates and Fig. 10 shows those for NCA Liion batteries at different loading rates. Overall, the simulation results for both NCM and NCA Li-ion batteries have a good agreement with their corresponding experimental results. For the NCM Li-ion battery com pressed at 0.5 mm/min, the measured force at 8 mm is 52.08 kN and the corresponding simulation force is 55.05 kN, as shown in Fig. 9 (a). For that at 5 mm/min loading rate, the measured and simulated force at 8 mm is 56.928 kN and 59.57 kN, respectively, as depicted in Fig. 9 (b). The measured and simulated force at 8 mm for an NCM Li-ion battery compressed at 25 mm/min is 63.557 kN and 67.69 kN, see Fig. 9 (c). For a compression test at 3 m/s, the experimental result at 6.08 mm and 6.318 mm is 57.919 kN and 58.2 kN, respectively. The simulated result at 6.0866 mm and 6.286 mm is 59.893 kN and 67.193 kN, respectively, see Fig. 9 (d). When it comes to the NCA Li-ion battery, the measured and simulated value at 8 mm is 66.489 kN and 68.324 kN, respectively, at 5 mm/min loading rate, as shown in Fig. 10 (a). For that at 25 mm/ min loading rate, the measured force at 8 mm is 67.105 kN and the corresponding simulation force is 69.944 kN, as depicted in Fig. 10 (b). The measured and simulated force at 8 mm for the NCM Li-ion battery compressed at 60 mm/min is 70.819 kN and 74.541 kN, respectively, as shown in Fig. 10 (c). For a compression test at 3 m/s, the experimental result at 6.7 mm is 71.398 kN and the simulated result at 6.714 mm is 74.904 kN, see Fig. 10 (d). For a real 18650 Li-ion battery, there are the porous coating mate rials of electrodes and the gaps among each layer of the jellyroll,
Fig. 7. Calculated stress-strain curves for NCM Li-ion batteries at different loading rates.
Fig. 8. Calculated stress-strain curves for NCA Li-ion batteries at different loading rates.
6
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Journal of Power Sources 451 (2020) 227749
Fig. 9. Simulated and measured force-displacement curves for NCM Li-ion batteries at different loading rates: (a) v ¼ 0.5 mm/min; (b) v ¼ 5 mm/min; (c) v ¼ 25 mm/min; (d) v ¼ 3 m/s.
Fig. 10. Simulated and measured force-displacement curves for NCA Li-ion batteries at different loading rates: (a) v ¼ 5 mm/min; (b) v ¼ 25 mm/min; (c) v ¼ 60 mm/min; (d) v ¼ 3 m/s.
between the jellyroll and the steel casing and within the metal core. However, the material property of each layer of the jellyroll is integrated into one homogenized representative element in the establishment of
the FEM, which is modeled by solid elements. This simplification ac counts for the relative errors in all simulation results especially in the part from 0 mm to 4 mm. The gaps inside the jellyroll are filled with 7
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electrolyte. The mechanical property of the Li-ion batteries at radial direction is different from that at axial direction. Even the tensile and compression mechanical property of the Li-ion batteries at radial di rection is also different. The material property of the jellyroll is set as isotropic and the electrolyte isn’t considered in the FEM of the jellyroll. This simplification is responsible for the relative errors in the part after 4 mm. For the NCM Li-ion battery compressed at 3 m/s, the relative error at 6.3 mm is large, which is around 20%. For the NCA Li-ion battery compressed at 3 m/s, the relative error between 4.5 mm and 6.5 mm is also large. The reasons for this large error are shown as follows. Under compression tests at 3 m/s, the top and bottom plates are covered by aluminum foil in case that they are corroded by the leak of the elec trolyte. This aluminum foil may cause a Li-ion battery slightly to slip during the compression tests. Furthermore, the compression process of the Li-ion battery can be divided into three steps as shown in the videos. Firstly, the Li-ion battery moves with the bottom plate. Secondly, the Liion battery shoots to the top plate due to its inertia before it is com pressed by the bottom plate. Thirdly, the Li-ion battery is compressed by the bottom plate. Some measurement errors may be caused under this process. Further investigation is needed to reveal the reasons to induce such a large relative error at high loading rate. The mechanical property of each component of an 18650 Li-ion battery at high loading rate is the focus of our future studies. Nonetheless, the overall accuracy of this established constitutive model is sufficiently high to be used to predict mechanical behaviors of 18650 Li-ion batteries under dynamic loadings.
Declaration of competing interest There are no conflicts of interest. Acknowledgements This research was funded by Beijing Science and Technology Pro gram (grant number Z181100004518005). The authors would also like to acknowledge the financial support of China Scholarship Council. References [1] J.P. Tian, R. Xiong, W.X. Shen, J. Wang, Frequency and time domain modelling and online state of charge monitoring for ultracapacitors, Energy 176 (2019) 874–887. [2] R.X. Yang, R. Xiong, H.W. He, Z.Y. Chen, A fractional-order model-based battery external short circuit fault diagnosis approach for all-climate electric vehicles application, J. Clean. Prod. 187 (2018) 950–959. [3] Z.D. Zhang, X.D. Kong, Y.J. Zheng, L. Zhou, X. Lai, Real-time diagnosis of microshort circuit for Li-ion batteries utilizing low-pass filters, Energy 166 (2019) 1013–1024. [4] R.X. Yang, R. Xiong, H.W. He, H. Mu, C. Wang, A novel method on estimating the degradation and state of charge of lithium-ion batteries used for electrical vehicles, Appl. Energy 207 (2017) 336–345. [5] Q.S. Wang, B.B. Mao, S.I. Stoliarov, J.H. Sun, A review of lithium ion battery failure mechanisms and fire prevention strategies, Prog. Energy Combust. Sci. 73 (2019) 95–131. [6] D.P. Finegan, E. Darcy, M. Keyser, B. Tjaden, T.M.M. Heenan, R. Jervis, et al., Characterising thermal runaway within lithium-ion cells by inducing and monitoring internal short circuits, Energy Environ. Sci. 10 (2017) 1377–1388. [7] S. Yang, W.W. Wang, C. Lin, W.X. Shen, Y.D. Li, Investigation of internal short circuits of lithium-ion batteries under mechanical abusive conditions, Energies 12 (2019) 1885. [8] S. Yang, W.W. Wang, C. Lin, W.X. Shen, Y.D. Li, Improved constitutive model of the jellyroll for cylindrical lithium ion batteries considering microscopic damage, Energy 185 (2019) 202–212. [9] S.H. Chung, T.T. Dejean, J.E. Zhu, H.L. Luo, T. Wierzbicki, Failure in lithium-ion batteries under transverse indentation loading, J Power Sources 389 (2018) 148–159. [10] W. Li, Y. Xia, G.H. Chen, E. Sahraei, Comparative study of mechanical-electricalthermal responses of pouch, cylindrical, and prismatic lithium-ion cells under mechanical abuse, Sci. China Technol. Sci. 61 (2018) 1472–1482. [11] L.B. Wang, S. Yin, J. Xu, A detailed computational model for cylindrical lithium-ion batteries under mechanical loading: from cell deformation to short-circuit onset, J Power Sources 413 (2019) 284–292. [12] J.E. Zhu, X.W. Zhang, H.L. Luo, E. Sahraei, Investigation of the deformation mechanisms of lithium-ion battery components using in-situ micro tests, Appl. Energy 224 (2018) 251–266. [13] X. Zhang, J.E. Zhu, E. Sahraei, Degradation of battery separators under chargedischarge cycles, RSC Adv. 7 (2017) 56099–56107. [14] J.E. Zhu, W. Li, Y. Xia, E. Sahraei, Testing and modeling the mechanical properties of the granular materials of graphite anode, J. Electrochem. Soc. 165 (2018) 1160–1168. [15] H.L. Luo, J.E. Zhu, E. Sahraei, Y. Xia, Adhesion strength of the cathode in lithiumion batteries under combined tension/shear loadings, RSC Adv. 8 (2018) 3996–4005. [16] C. Zhang, J. Xu, L. Cao, Z.N. Wu, S. Santhanagopalan, Constitutive behavior and progressive mechanical failure of electrodes in lithium-ion batteries, J Power Sources 357 (2017) 126–137. [17] J. Xu, Y.J. Wu, S. Yin, Investigation of effects of design parameters on the internal short-circuit in cylindrical lithium-ion batteries, RSC Adv. 7 (2017) 14360–14371. [18] B. Dixon, A. Mason, E. Sahraei, Effects of electrolyte, loading rate and location of indentation on mechanical integrity of li-ion pouch cells, J Power Sources 396 (2018) 412–420. [19] W.W. Wang, S. Yang, C. Lin, Y.D. Li, State of charge dependent constitutive model of the jellyroll of cylindrical Lithium-ion cells, IEEE Access 6 (2018) 26358–26366. [20] J. Xu, B.H. Liu, D.Y. Hu, State of charge dependent mechanical integrity behavior of 18650 Lithium-ion batteries, Sci. Rep. 6 (2016) 21829–21839. [21] W. Li, Y. Xia, J.E. Zhu, H.L. Luo, State-of-Charge dependence of mechanical response of lithium-ion batteries: a result of internal stress, J. Electrochem. Soc. 165 (2018) 1537–1546. [22] J. Xu, Y. Jia, B. Liu, H. Zhao, H. Yu, J. Li, S. Yin, Coupling effect of state-of-health and state-of-charge on the mechanical integrity of lithium-ion batteries, Exp. Mech. 58 (2018) 633–643. [23] T. Kisters, E. Sahraei, T. Wierzbicki, Dynamic impact tests on lithium-ion cells, Int. J. Impact Eng. 108 (2017) 205–216. [24] Y.K. Jia, S. Yin, B.H. Liu, H. Zhao, H.L. Yu, J. Li, J. Xu, Unlocking the coupling mechanical-electrochemical behavior of lithium-ion battery upon dynamic mechanical loading, Energy 166 (2019) 951–960. [25] J. Xu, B.H. Liu, L.B. Wang, S. Shang, Dynamic mechanical integrity of cylindrical lithium-ion battery cell upon crushing, Eng. Fail. Anal. 53 (2015) 97–110.
5. Conclusions In this investigation, two types of 18650 Li-ion batteries, namely NCA and NCM batteries, are compressed between two plates at various loading rates. The following conclusions can be obtained from the experimental results which can enrich the knowledge of mechanical properties for Li-ion batteries. (1) NCM and NCA Li-ion batteries show similar mechanical, elec trical and thermal responses under dynamic loadings. Hence, the difference of cathode material has little effect on the mechanical property of 18650 Li-ion batteries. However, it should be mentioned that the structure design of battery packs in EVs should be designed differently for the safety of different Li-ion batteries, even for 18650 Li-ion batteries with different cathode materials. (2) For NCA and NCM Li-ion batteries, the general trend of their mechanical responses at different loading rates is similar. (3) Both NCA and NCM Li-ion batteries exhibit strain rate hardening behaviors, namely their resistances to deformation increase as loading rate increases. NCM Li-ion batteries show obvious strain rate hardening behaviors at low loading rates while NCA Li-ion batteries can only show strain rate hardening behaviors until the loading rate increases to a certain value. (4) For compression tests at high loading rate, many layers of elec trodes inside both NCA and NCM Li-ion batteries have broken after compression tests. This may cause safety issues for 18650 Liion batteries at high SOCs. The constitutive model of the jellyroll at various loading rates is proposed based on the experimental results. A FEM of the jellyroll is established to validate the proposed constitutive model. The established FEM shows good simulation accuracy and it can be used to simulate mechanical behaviors of 18650 Li-ion batteries under dynamic loading cases. It can also be utilized to evaluate the crashworthiness of Li-ion batteries in the case of impact accidents and provide valuable guid ance for the structure design of battery packs in EVs.
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[26] I. Avdeev, M. Gilaki, Structural analysis and experimental characterization of cylindrical lithium-ion battery cells subject to lateral impact, J Power Sources 271 (2014) 382–391. [27] J. Xu, B.H. Liu, X.Y. Wang, D.Y. Hu, Computational model of 18650 lithium-ion battery with coupled strain rate and SOC dependencies, Appl. Energy 172 (2016) 180–189.
[28] G. Kermani, E. Sahraei, Dynamic impact response of lithium-ion batteries, constitutive properties and failure model, RSC Adv. 9 (2019) 2464–2473. [29] W.W. Wang, S. Yang, C. Lin, Clay-like mechanical properties for the jellyroll of cylindrical Lithium-ion cells, Appl. Energy 196 (2017) 249–258. [30] L. Greve, C. Fehrenbach, Mechanical testing and macro-mechanical finite element simulation of the deformation, fracture, and short circuit initiation of cylindrical Lithium-ion battery cells, J Power Sources 214 (2012) 377–385.
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Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Investigation of mechanical property of cylindrical lithium-ion batteries under dynamic loadings Wenwei Wang a, Sheng Yang a, b, *, Cheng Lin a, Weixiang Shen b, Guoxing Lu b, Yiding Li a, Jianjun Zhang b a b
National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing, 100081, China Faculty of Science, Engineering and Technology, Swinburne University of Technology, John Street, Hawthorn, Victoria, 3122, Australia
H I G H L I G H T S
� Two types of 18650 Li-ion batteries are performed dynamic compression tests. � Two types 18650 Li-ion batteries both exhibit strain rate hardening behaviors. � Establishing a finite element model of cylindrical Li-ion batteries suitable for dynamic loadings. A R T I C L E I N F O
A B S T R A C T
Keywords: Lithium-ion battery Mechanical abusive conditions Dynamic loading Constitutive model
Understanding of mechanical property of lithium-ion batteries is the key to unlock complicated and coupled behaviors of thermal runaway, which is triggered during electric vehicle collision. In this study, mechanical behaviors of cylindrical lithium-ion batteries under dynamic loadings are investigated. Two types of 18650 lithium-ion batteries, namely LiNiCoAlO2 and LiNiCoMnO2, are chosen to perform compression tests at various dynamic loadings. Experimental results indicate that these two types of 18650 lithium-ion batteries exhibit strain rate hardening behaviors, namely their resistances to deformation enhance as loading rate increases. LiNi CoMnO2 batteries show obvious strain rate hardening behaviors at low loading rates while LiNiCoAlO2 batteries can only show strain rate hardening behaviors until the loading rate increases to a certain value. The constitutive model of the jellyroll of lithium-ion batteries is proposed to describe these mechanical behaviors under dynamic loadings and it is validated by a finite element model of lithium-ion batteries. The proposed constitutive model can be utilized to evaluate the crashworthiness of lithium-ion batteries in the case of impact accidents and provide valuable guidance for the structure design of battery packs in electric vehicles.
1. Introduction The introduction of electric vehicles (EVs) can significantly reduce the dependence on oil fuel and the emission of greenhouse gas, which is beneficial to environmental improvement. Lithium-ion (Li-ion) batteries have been the primary energy storage for EVs due to its advantages over other energy storage, such as high energy/power density, long cycle life, high working voltage and low self-discharge rate [1–4]. As EVs need high capacity and energy density of Li-ion batteries to meet the demand for long driving mileage, the safety and reliability of Li-ion batteries have become more and more important. Many safety measures are taken in Li-ion batteries to avoid catastrophic failures including pressure relief vents, current interrupt devices, ceramic-coated separators, positive
temperature coefficient current-limiting switches as well as battery management systems (BMSs) [5,6]. However, in the case of EV collision, the poor thermal stability of Li-ion batteries may lead to fire and even explosion due to the existence of its flammable electrolyte. Many attentions are paid to deformation behaviors, voltage and thermal responses of Li-ion batteries under mechanical abusive condi tions in recent years. Yang et al. analyzed the stiffness of an 18650 Li-ion battery during compression tests and revealed that its deformation process could be divided into three stages [7,8]. Chung et al. revealed the deformation and failure mechanism of Li-ion batteries under trans verse loading [9]. They found that the angle between fault line and battery plane is consistently constant and approximately 62� . Li et al. recorded the voltage and temperature responses of Li-ion batteries
* Corresponding author. National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing, 100081, China. E-mail address: [email protected] (S. Yang). https://doi.org/10.1016/j.jpowsour.2020.227749 Received 19 October 2019; Received in revised form 24 December 2019; Accepted 12 January 2020 Available online 14 February 2020 0378-7753/© 2020 Elsevier B.V. All rights reserved.
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during mechanical abusive tests [10]. They found that peak force is strongly related to open circuit voltage (OCV) drop and battery tem perature rise. Wang et al. developed a detailed finite element model (FEM) to study mechanical properties of cylindrical Li-ion batteries under four common loading conditions and proposed a short-circuit criteria based on separator failure [11]. Zhu et al. utilized scanning electron microscope (SEM) to investigate the deformation mechanisms of Li-ion batteries components under micro tests and found that defor mation mechanisms between cathode and anode coatings are different [12]. Zhang et al. revealed the degradation mechanism of trilayer separator of Li-ion battery during charge/discharge cycles and they found that failure stress and strain of a separator decreases when a number of cycles increase [13]. The mechanical properties of graphite anode and the adhesion strength of cathode in Li-ion batteries were studied in Refs. [14,15]. They found that shear strength of adhesion interface is nearly two times of its tensile strength. Zhang et al. inves tigated the mechanical failure behaviors of electrodes in Li-ion batteries and it was found that battery failure behaviors are complicated, which is a combination of tensile and compression failures [16]. The effect of porosity and thickness of electrodes in Li-ion batteries on internal short circuit was studied in Ref. [17]. It was found that both moderate porosity and appropriate increase in the thickness are beneficial to the stabilization of short-circuit voltage. Dixon et al. studied the effect of electrolyte of pouch Li-ion batteries on their mechanical behaviors [18]. It was found that the measured force and displacement of the pouch batteries with electrolyte is lower than those of the pouch batteries without electrolyte. The state of charge (SOC) hardening behaviors of Li-ion batteries were studied in Refs. [19,20] and the SOC-dependence mechanical behaviors of Li-ion batteries were found to be attributed to the internal stress caused by volume expansion [21]. Xu et al. investigated the effect of state of health (SOH) of Li-ion batteries on their mechanical behaviors [22]. They found that the SOH had a large effect on failure stress while its influences on failure strain were minimal. In real-world engineering scenarios, significant concern of EVs is safety performance at the time of vehicle collision, which belongs to dynamic loading conditions. However, the above studies on the mechanical properties of Li-ion batteries and its components were all carried out under quasi-static tests. Few publications focus on the investigation of the mechanical be haviors of Li-ion batteries under dynamic tests. Kisters et al. carried out dynamic impact tests on Li-ion batteries and they found that the peak force would change as the change of the loading rate [23]. Jia et al. reported the voltage response of Li-ion batteries during dynamic loading and they found that faster voltage drop would be induced by higher testing speed [24]. These two studies adopt experimental analysis. Xu et al. investigated the mechanical response of cylindrical Li-ion batteries under dynamic loadings by performing simulation [25]. Avdeev and Gilaki validated the established FEM under lateral impact loading [26], where the FEM was established based on the mechanical response of Li-ion batteries under quasi-static tests. In recent study, Xu et al. developed a FEM for 18650 Li-ion batteries considering strain rate [27]. They validated their model through drop tests. Kermani et al. carried out high speed compression tests on Li-ion batteries and established a FEM for Li-ion batteries based on Johnson-Cook model [28]. This paper is aimed to investigate the mechanical properties of cy lindrical Li-ion batteries under dynamic loadings and establish a FEM to predict their dynamic mechanical behaviors. The purpose to establish this FEM is to obtain the peak force of the Li-ion batteries under dynamic loadings because the peak force has a strong correlation with the trigger of thermal runaway under mechanical abusive conditions. Obtaining the peak force can guide the structure design of battery packs in EVs to ensure that thermal runaway will not be triggered under crash accidents. In this study, compression tests with various speeds are performed on two types of 18650 Li-ion batteries, namely LiNiCoAlO2 (NCA) and LiNiCoMnO2 (NCM) batteries, which have been the first choice of power battery for electrical passenger vehicles due to their advantages in the
aspects of cost, energy density and etc. Experimental results indicate that cylindrical Li-ion batteries with different cathode materials show similar mechanical, electrical and thermal response under the compression tests. General trend of mechanical responses at different loading rates are similar for NCA or NCM Li-ion batteries. They both exhibit strain rate hardening behaviors, namely their deformation re sistances increase as the loading rate increases. However, the strain rate hardening behaviors of NCA Li-ion batteries can’t be obviously observed until the loading rate increases to a certain value. These experimental results have enriched the knowledge of mechanical properties for Li-ion batteries. Besides, the established FEM can also be utilized to evaluate the crashworthiness of Li-ion batteries in the case of impact accidents and provide valuable guidance for the structure design of battery packs in EVs. The remaining part of this paper is organized as follows. Section 2 analyzes the mechanical responses of NCA and NCM Li-ion batteries under compression tests at different loading rates. Section 3 proposes a constitutive model of cylindrical Li-ion batteries suitable for dynamic loadings. Section 4 establishes a FEM to validate the proposed model. Finally, the conclusions are summarized in Section 5. 2. Experiments and analysis Two types of cylindrical Li-ion batteries with different cathode ma terials, namely NCA and NCM, are chosen to perform compression tests, their specifications are listed in Table 1. We bought these two types of the batteries, where the manufacturers of NCM and NCA Li-ion batteries are Sony and Samsung, respectively. To avoid fire or even explosion under compression tests, all the Li-ion batteries are discharged at constant current (2 A) to their cut-off voltage. INSTRON VHS 8800 as shown in Fig. 1(a) is used to perform compres sion tests at high speed while MTS EXCEED E45 100 KN as shown in Fig. 1(b) is used to perform compression tests at low speed. The indenter of MTS EXCEED E45 100 KN is installed at the top plate while that of INSTRON VHS 8800 is installed at the bottom plate. It should be noted that safety equipment is placed around INSTRON VHS 8800 to provide necessary protection. Besides, Phantom V2512 as shown in Fig. 1(a) is placed in front of INSTRON VHS 8800 to record the compression tests at high speed. Load and displacement are measured over time during all compression tests and then load-time relation is converted into loaddisplacement relation for easy comparison of mechanical responses at different loading rates. NCM Li-ion batteries are compressed at 0.5 mm/min, 5 mm/min, 25 mm/min and 3 m/s, respectively. NCA Li-ion batteries are compressed at 0.5 mm/min, 5 mm/min, 25 mm/min, 60 mm/min and 3 m/s, respec tively. All the batteries are compressed between two plates and these compression tests are repeated at least three times to make sure the credibility of experimental data. Their experimental results are shown in Fig. 1 (c) and (d), respectively. The videos of NCM and NCA Li-ion batteries compression tests performed at 3 m/s can be downloaded from the supplementary material (S1–S2). The strain rate for cylindrical Li-ion batteries can be calculated as:
Table 1 Specifications of two types of 18650 Li-ion batteries. Items Normal Capacity Normal Voltage Full Charge Voltage Discharge cut-off Voltage Maximum Discharge Current Size Cathode Material Anode Material
2
Specifications NCM Li-ion battery
NCA Li-ion battery
2100 mAh 3.6 V 4.2 V 2.5 V 30 A 65 x 18 x 18 (mm) LiNiCoMnO2 LixC6
2500 mAh 3.7 V 4.2 V 2.5 V 20 A 65 x 18 x 18 (mm) LiNiCoAlO2 LixC6
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exhibit strain rate hardening behaviors, namely their abilities to resist deformation increase as the loading rate rises. On the other hand, we also see the differences between the mechanical responses of NCM and NCA Li-ion batteries. Firstly, the measured maximum force of NCA Liion batteries is different from that of NCM Li-ion batteries at the fully discharged state. It indicates that the structure design of battery packs in EVs should be designed differently for the safety of different Li-ion batteries, even for 18650 Li-ion batteries with different cathode mate rials. Secondly, For NCM Li-ion batteries, their strain rate hardening behaviors can be obviously observed from their mechanical responses at low loading rates, namely 0.5 mm/min, 5 mm/min and 25 mm/min. For NCA Li-ion batteries, their mechanical responses at 0.5 mm/min, 5 mm/ min and 25 mm/min are almost the same. Their strain rate hardening behaviors can’t be obviously observed until the loading rate increases to 60 mm/min. Thirdly, there are still some differences before the displacement of 4 mm. This is due to the difference in those gaps inside NCM and NCA Li-ion batteries. The appearance of an NCM and an NCA Li-ion battery after the compression at 3 m/s is showed in Fig. 1 (c) and (d), respectively. It can be found that many layers of electrodes inside the Li-ion batteries have broken after the compression test. To further investigate the safety performance of NCM and NCA Li-ion batteries under dynamic loadings, compression tests are performed on the NCM and NCA Li-ion batteries at the SOC of 0.4. INSTRON 5985 is used to conduct these compression tests with the loading rate of 60 mm/ min, as shown in Fig. 2 (a). The battery voltage and temperature are recorded simultaneously by HIOKI MR 8880 and FLUKE TI 400 (i.e. an infrared camera) during the compression tests. Fig. 2 shows the exper imental results for the NCM Li-ion battery while Fig. 3 shows the experimental results for NCA Li-ion battery. For the NCM Li-ion battery, the maximum force is 92.47 kN at 7.83 s, as shown in Fig. 2 (a), the voltage rapidly decreases from 3.64 V at 8 s to 2.12 V at 8.5 s and then decreases to 0.01 V at 10.5 s, as shown in Fig. 2 (b) and the temperature slowly increases from 17:03 � C at 8.88 s to its maximum value of 102:78 � C at 86.58 s and then starts to slowly decrease, as shown in Fig. 2 (c). For the NCA Li-ion battery, the maximum force is 90.817 kN at 7.83 s, as shown in Fig. 3 (a), the voltage rapidly decreases from 3.64 V at 8.3 s to 1.65 V at 8.85 s and then decreases to 0.07 V at 8.9 s, as shown in Fig. 3 (b), and the temperature slowly increases from 20:38 � C at 9.99 s to its maximum value of 112:51 � C at 74.37 s and then starts to slowly decrease, as shown in Fig. 3 (c). It can also be observed from Figs. 2 and 3 that the general trends of the voltage and temperature responses of the NCM Li-ion battery are almost the same as those of the NCA Li-ion battery but the maximum temperature for the NCA Li-ion battery after the trigger of internal short circuit is slightly higher than that of the NCM Li-ion battery.
Fig. 1. (a) INSTRON VHS 8800; (b) MTS EXCEED E45; (c) Measured me chanical responses for NCM Li-ion batteries at different loading rates; (d) Measured mechanical responses for NCA Li-ion batteries at different loading rates.
dε = dt ¼ v=ð2RÞ
(1)
where v is the loading rate and R is the radius of Li-ion batteries. The strain rate for 60 mm/min and 3 m/s is 5:5 � 10 2 s 1 and 1:67 � 102 s 1 , respectively. The strain rate for 60 mm/min belongs to quasistatic compression. But it should be noted that the radius of 18650 Li-ion batteries is small, so the whole process of compression test at 60 mm/ min takes around 8 s. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.jpowsour.2020.227749 As observed in Fig. 1(c) and (d), we see the similarities between the mechanical responses of NCM and NCA Li-ion batteries. Firstly, the experimental data at the loading rate of 3 m/s for both NCM and NCA Liion batteries have good repeatability. Secondly, NCM and NCA Li-ion batteries have similar mechanical behaviors at the same loading rate. The general trend of mechanical responses at different loading rates is almost same for NCM and NCA Li-ion batteries. Thirdly, the measured load for NCM and NCA Li-ion batteries both slowly increases in the early stage and then increases exponentially. The reasons are: 1). The coating materials of cathode/anode are porous. 2). There are some gaps among each layer of the jellyroll, between metal casing and the jellyroll and within the hollow metal core. They account for slow increase in load response in the early stage. The jellyroll becomes densified as the compression continues. This accounts for significant increase in load response subsequently. Moreover, NCM and NCA Li-ion batteries both
3. Mechanical characteristics for jellyroll under dynamic conditions The deformation process of NCM and NCA Li-ion batteries at different loading rates are similar. Regardless of the indenter installed at the top or bottom plate, it will result in the same deformation. Hence, we choose the top plate as a moveable indenter to describe the deformation process under dynamic compression tests as shown in Fig. 4. It should be mentioned that a rectangular coordinate system (x, y, z) is used to describe the geometry of a Li-ion battery due to the flat contact area between the battery and two plates. H is the compression load and w is the vertical displacement of the top plate. Besides, experimental results indicate that the mechanical responses of both NCM and NCA Li-ion batteries at high speed are similar with those at low speed in the aspect of general trend, as depicted in Fig. 1(c) and (d). In our previous study, it was found that the whole deformation process of Li-ion batteries under quasi-static loading cases can be divided into three distinct stages [7,8]. Hence, Gaussian functions are 3
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Fig. 3. (a) Measured Load-time curve for NCA Li-ion battery at the SOC of 0.4; (b) Measured voltage response; (c) Measured temperature response.
Fig. 2. (a) Measured load-time curve for NCM Li-ion battery at the SOC of 0.4; (b) Measured voltage response; (c) Measured temperature response.
chosen to fit these curves measured at different loading rates as follows HðwÞ ¼ a0 *expð ððw
b0 Þ=c0 Þ2 Þ
(2)
where a0 , b0 and c0 are the fitting parameters corresponding to different loading rates which are listed in Table 2. The curve fitting function in MATLAB is used to fit the experimental data and obtain the values of these fitting parameters. Fig. 5 shows the analytical fitting curves for NCM Li-ion batteries while Fig. 6 shows those for NCA Li-ion batteries. It should be noted that the mechanical response for the NCA Li-ion battery at 0.5 mm/min is almost same as that at 5 mm/min. Hence, for NCA Li-ion batteries, the measured data for the 0.5 mm/min compression test isn’t analyzed and processed in this paper. The measured load-displacement data of a Li-ion battery can be used to establish its corresponding stress-strain relationship and the detailed process to develop this relationship can be found in Ref. [8]. Fig. 7 shows the calculated equivalent stress and strain of NCM Li-ion battery at different loading rates while those calculated results for NCA Li-ion batteries are shown in Fig. 8. Several conclusions can be obtained from these calculated stress-strain curves as follows. Firstly, NCM Li-ion batteries have the similar constitutive model with NCA Li-ion batteries. The reasons are shown as follows. The deformation is mainly attributed from the porous coating materials of the electrodes during the compression of a Li-ion battery [29,30]. The coating materials of
Fig. 4. Schematic description of Li-ion battery deformation compressed be tween two plates.
cathodes of NCM and NCA Li-ion batteries are both porous although their material compositions are different. Secondly, for both NCA and NCM Li-ion batteries, the stress starts to increase exponentially when the strain exceeds 0.2. This is due to the porous coating materials of elec trodes, the gaps among each layer of the jellyroll, between the jellyroll and the steel casing and within the metal core. The densification of the jellyroll accounts for significant increase in load response subsequently. Thirdly, NCM Li-ion batteries and NCA Li-ion batteries both have the similar constitutive model at different loading rates. The reason is that 4
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Table 2 Fitting parameters a0 , b0 and c0 for NCM and NCA L-ion batteries at various loading rates. Loading rete
NCM Li-ion batteries
NCA Li-ion batteries
0.5 mm/min
5 mm/min
25 mm/min
3 m/s
5 mm/min
25 mm/min
60 mm/min
3 m/s
Coefficient a0
74.99
75.96
87.11
61.67
102.8
95.43
90.95
72.18
Coefficient b0
10.26
9.927
10.19
6.835
9.981
9.766
9.566
7.014
3.771
3.56
3.836
2.377
3.028
3.019
3.105
2.087
Coefficient c0
Fig. 5. Measured force-displacement relations at various loading rates when a NCM Li-ion battery is compressed between two rigid flat plates and their analytical fittings: (a) v ¼ 0.5 mm/min; (b) v ¼ 5 mm/min; (c) v ¼ 25 mm/min; (d) v ¼ 3 m/s.
the constitutive model is established based on the measured load-displacement curves which are similar at different loading rates. Finally, the internal stress of an NCA or NCM Li-ion battery increases as the loading rate increases when the same deformation occurs inside it.
improved the computational efficiency while maintaining good simu lation accuracy. High computational efficiency is especially important when an EV crash simulation is carried out which contains thousands of batteries. Hyperworks/Ls-dyna software utilizes explicit time integration and has powerful abilities to perform nonlinear dynamic analysis. It is suit able for crash or large deformation simulation. Therefore, it is used to perform simulation analysis in this paper. To simulate compression test, the models of the jellyroll and two plates are established, respectively, where the solid elements are used to model the jellyroll and the shell elements are used to model the two plates. The grid size for the jellyroll is 0.8 mm and that for two plates is 1 mm. The material property of the jellyroll is set as isotropic, crushable foam (Material type 63) is utilized to model mechanical characteristics of the jellyroll. The rigid material is chosen to model the mechanical characteristics of two plates, which is consistent with the experimental setup. The stress-strain curves depicted in Figs. 7 and 8 are used as the input to the crushable foam to simulate the mechanical behaviors of two types of Li-ion batteries at different loading rates. The other simulation parameters are listed in Table 3. The FEM of the jellyroll is placed on the bottom plate whose six degrees of freedom are fully constrained. The top plate compresses the FEM of the jellyroll at a constant speed which is respectively corresponding to various loading rates used in the experimental program. Surface-tosurface is utilized to define the contact between top or bottom plate and the FEM of the jellyroll. The friction coefficient between the jellyroll and the top or bottom plate are both set as 0.3.
4. Simulation analysis 4.1. Establishment of the FEM This paper selects 18650 cylindrical Li-ion batteries with different cathode materials for investigation. They have almost the same me chanical structure which mainly consists of four parts, namely a steel casing, a positive end-cap, a jellyroll and a metal core. The contributions of the steel casing to the overall strain and stress is small which can be neglected due to its thin thickness (around 0.2 mm), so does the metal core. The positive end-cap has a complicated mechanical structure which is composed of several small parts, but its contribution to the overall stress is also small. Neglecting the above-mentioned three parts in modeling this type of a battery, we establish a FEM of the jellyroll to simulate the mechanical response of a battery for effectively improving computational efficiency. The jellyroll is tightly rolled by five layers, namely two layers of metal foils, one layer of separator and two layers of electrodes. The thickness of each layer is less than 0.5 mm. A detailed FEM of the jellyroll establishing for each layer will generate lots of el ements which will take a long time to compute. In our previous studies [8,19,29], we established a FEM of the jellyroll by integrating five layers into one homogenized representative element (RVE) and significantly 5
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Journal of Power Sources 451 (2020) 227749
Fig. 6. Measured force-displacement relations at various loading rates when a NCA Li-ion battery is compressed between two rigid flat plates and their analytical fittings: (a) v ¼ 5 mm/min; (b) v ¼ 25 mm/min; (c) v ¼ 60 mm/min; (d) v ¼ 3 m/s. Table 3 Simulation parameters. Component
Young’s modulus
Poisson ratio
Density
Jellyroll
Ejellyroll ¼ 1:5 Gpa
0:15
νjellyroll ¼
2:8 g cm
Tensile cut-off value 3
σf ¼ 10 Mpa
4.2. Validation and discussion Fig. 9 depicts the simulated displacement-load curves for NCM Li-ion batteries at different loading rates and Fig. 10 shows those for NCA Liion batteries at different loading rates. Overall, the simulation results for both NCM and NCA Li-ion batteries have a good agreement with their corresponding experimental results. For the NCM Li-ion battery com pressed at 0.5 mm/min, the measured force at 8 mm is 52.08 kN and the corresponding simulation force is 55.05 kN, as shown in Fig. 9 (a). For that at 5 mm/min loading rate, the measured and simulated force at 8 mm is 56.928 kN and 59.57 kN, respectively, as depicted in Fig. 9 (b). The measured and simulated force at 8 mm for an NCM Li-ion battery compressed at 25 mm/min is 63.557 kN and 67.69 kN, see Fig. 9 (c). For a compression test at 3 m/s, the experimental result at 6.08 mm and 6.318 mm is 57.919 kN and 58.2 kN, respectively. The simulated result at 6.0866 mm and 6.286 mm is 59.893 kN and 67.193 kN, respectively, see Fig. 9 (d). When it comes to the NCA Li-ion battery, the measured and simulated value at 8 mm is 66.489 kN and 68.324 kN, respectively, at 5 mm/min loading rate, as shown in Fig. 10 (a). For that at 25 mm/ min loading rate, the measured force at 8 mm is 67.105 kN and the corresponding simulation force is 69.944 kN, as depicted in Fig. 10 (b). The measured and simulated force at 8 mm for the NCM Li-ion battery compressed at 60 mm/min is 70.819 kN and 74.541 kN, respectively, as shown in Fig. 10 (c). For a compression test at 3 m/s, the experimental result at 6.7 mm is 71.398 kN and the simulated result at 6.714 mm is 74.904 kN, see Fig. 10 (d). For a real 18650 Li-ion battery, there are the porous coating mate rials of electrodes and the gaps among each layer of the jellyroll,
Fig. 7. Calculated stress-strain curves for NCM Li-ion batteries at different loading rates.
Fig. 8. Calculated stress-strain curves for NCA Li-ion batteries at different loading rates.
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Fig. 9. Simulated and measured force-displacement curves for NCM Li-ion batteries at different loading rates: (a) v ¼ 0.5 mm/min; (b) v ¼ 5 mm/min; (c) v ¼ 25 mm/min; (d) v ¼ 3 m/s.
Fig. 10. Simulated and measured force-displacement curves for NCA Li-ion batteries at different loading rates: (a) v ¼ 5 mm/min; (b) v ¼ 25 mm/min; (c) v ¼ 60 mm/min; (d) v ¼ 3 m/s.
between the jellyroll and the steel casing and within the metal core. However, the material property of each layer of the jellyroll is integrated into one homogenized representative element in the establishment of
the FEM, which is modeled by solid elements. This simplification ac counts for the relative errors in all simulation results especially in the part from 0 mm to 4 mm. The gaps inside the jellyroll are filled with 7
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electrolyte. The mechanical property of the Li-ion batteries at radial direction is different from that at axial direction. Even the tensile and compression mechanical property of the Li-ion batteries at radial di rection is also different. The material property of the jellyroll is set as isotropic and the electrolyte isn’t considered in the FEM of the jellyroll. This simplification is responsible for the relative errors in the part after 4 mm. For the NCM Li-ion battery compressed at 3 m/s, the relative error at 6.3 mm is large, which is around 20%. For the NCA Li-ion battery compressed at 3 m/s, the relative error between 4.5 mm and 6.5 mm is also large. The reasons for this large error are shown as follows. Under compression tests at 3 m/s, the top and bottom plates are covered by aluminum foil in case that they are corroded by the leak of the elec trolyte. This aluminum foil may cause a Li-ion battery slightly to slip during the compression tests. Furthermore, the compression process of the Li-ion battery can be divided into three steps as shown in the videos. Firstly, the Li-ion battery moves with the bottom plate. Secondly, the Liion battery shoots to the top plate due to its inertia before it is com pressed by the bottom plate. Thirdly, the Li-ion battery is compressed by the bottom plate. Some measurement errors may be caused under this process. Further investigation is needed to reveal the reasons to induce such a large relative error at high loading rate. The mechanical property of each component of an 18650 Li-ion battery at high loading rate is the focus of our future studies. Nonetheless, the overall accuracy of this established constitutive model is sufficiently high to be used to predict mechanical behaviors of 18650 Li-ion batteries under dynamic loadings.
Declaration of competing interest There are no conflicts of interest. Acknowledgements This research was funded by Beijing Science and Technology Pro gram (grant number Z181100004518005). The authors would also like to acknowledge the financial support of China Scholarship Council. References [1] J.P. Tian, R. Xiong, W.X. Shen, J. Wang, Frequency and time domain modelling and online state of charge monitoring for ultracapacitors, Energy 176 (2019) 874–887. [2] R.X. Yang, R. Xiong, H.W. He, Z.Y. Chen, A fractional-order model-based battery external short circuit fault diagnosis approach for all-climate electric vehicles application, J. Clean. Prod. 187 (2018) 950–959. [3] Z.D. Zhang, X.D. Kong, Y.J. Zheng, L. Zhou, X. Lai, Real-time diagnosis of microshort circuit for Li-ion batteries utilizing low-pass filters, Energy 166 (2019) 1013–1024. [4] R.X. Yang, R. Xiong, H.W. He, H. Mu, C. Wang, A novel method on estimating the degradation and state of charge of lithium-ion batteries used for electrical vehicles, Appl. Energy 207 (2017) 336–345. [5] Q.S. Wang, B.B. Mao, S.I. Stoliarov, J.H. Sun, A review of lithium ion battery failure mechanisms and fire prevention strategies, Prog. Energy Combust. Sci. 73 (2019) 95–131. [6] D.P. Finegan, E. Darcy, M. Keyser, B. Tjaden, T.M.M. Heenan, R. Jervis, et al., Characterising thermal runaway within lithium-ion cells by inducing and monitoring internal short circuits, Energy Environ. Sci. 10 (2017) 1377–1388. [7] S. Yang, W.W. Wang, C. Lin, W.X. Shen, Y.D. Li, Investigation of internal short circuits of lithium-ion batteries under mechanical abusive conditions, Energies 12 (2019) 1885. [8] S. Yang, W.W. Wang, C. Lin, W.X. Shen, Y.D. Li, Improved constitutive model of the jellyroll for cylindrical lithium ion batteries considering microscopic damage, Energy 185 (2019) 202–212. [9] S.H. Chung, T.T. Dejean, J.E. Zhu, H.L. Luo, T. Wierzbicki, Failure in lithium-ion batteries under transverse indentation loading, J Power Sources 389 (2018) 148–159. [10] W. Li, Y. Xia, G.H. Chen, E. Sahraei, Comparative study of mechanical-electricalthermal responses of pouch, cylindrical, and prismatic lithium-ion cells under mechanical abuse, Sci. China Technol. Sci. 61 (2018) 1472–1482. [11] L.B. Wang, S. Yin, J. Xu, A detailed computational model for cylindrical lithium-ion batteries under mechanical loading: from cell deformation to short-circuit onset, J Power Sources 413 (2019) 284–292. [12] J.E. Zhu, X.W. Zhang, H.L. Luo, E. Sahraei, Investigation of the deformation mechanisms of lithium-ion battery components using in-situ micro tests, Appl. Energy 224 (2018) 251–266. [13] X. Zhang, J.E. Zhu, E. Sahraei, Degradation of battery separators under chargedischarge cycles, RSC Adv. 7 (2017) 56099–56107. [14] J.E. Zhu, W. Li, Y. Xia, E. Sahraei, Testing and modeling the mechanical properties of the granular materials of graphite anode, J. Electrochem. Soc. 165 (2018) 1160–1168. [15] H.L. Luo, J.E. Zhu, E. Sahraei, Y. Xia, Adhesion strength of the cathode in lithiumion batteries under combined tension/shear loadings, RSC Adv. 8 (2018) 3996–4005. [16] C. Zhang, J. Xu, L. Cao, Z.N. Wu, S. Santhanagopalan, Constitutive behavior and progressive mechanical failure of electrodes in lithium-ion batteries, J Power Sources 357 (2017) 126–137. [17] J. Xu, Y.J. Wu, S. Yin, Investigation of effects of design parameters on the internal short-circuit in cylindrical lithium-ion batteries, RSC Adv. 7 (2017) 14360–14371. [18] B. Dixon, A. Mason, E. Sahraei, Effects of electrolyte, loading rate and location of indentation on mechanical integrity of li-ion pouch cells, J Power Sources 396 (2018) 412–420. [19] W.W. Wang, S. Yang, C. Lin, Y.D. Li, State of charge dependent constitutive model of the jellyroll of cylindrical Lithium-ion cells, IEEE Access 6 (2018) 26358–26366. [20] J. Xu, B.H. Liu, D.Y. Hu, State of charge dependent mechanical integrity behavior of 18650 Lithium-ion batteries, Sci. Rep. 6 (2016) 21829–21839. [21] W. Li, Y. Xia, J.E. Zhu, H.L. Luo, State-of-Charge dependence of mechanical response of lithium-ion batteries: a result of internal stress, J. Electrochem. Soc. 165 (2018) 1537–1546. [22] J. Xu, Y. Jia, B. Liu, H. Zhao, H. Yu, J. Li, S. Yin, Coupling effect of state-of-health and state-of-charge on the mechanical integrity of lithium-ion batteries, Exp. Mech. 58 (2018) 633–643. [23] T. Kisters, E. Sahraei, T. Wierzbicki, Dynamic impact tests on lithium-ion cells, Int. J. Impact Eng. 108 (2017) 205–216. [24] Y.K. Jia, S. Yin, B.H. Liu, H. Zhao, H.L. Yu, J. Li, J. Xu, Unlocking the coupling mechanical-electrochemical behavior of lithium-ion battery upon dynamic mechanical loading, Energy 166 (2019) 951–960. [25] J. Xu, B.H. Liu, L.B. Wang, S. Shang, Dynamic mechanical integrity of cylindrical lithium-ion battery cell upon crushing, Eng. Fail. Anal. 53 (2015) 97–110.
5. Conclusions In this investigation, two types of 18650 Li-ion batteries, namely NCA and NCM batteries, are compressed between two plates at various loading rates. The following conclusions can be obtained from the experimental results which can enrich the knowledge of mechanical properties for Li-ion batteries. (1) NCM and NCA Li-ion batteries show similar mechanical, elec trical and thermal responses under dynamic loadings. Hence, the difference of cathode material has little effect on the mechanical property of 18650 Li-ion batteries. However, it should be mentioned that the structure design of battery packs in EVs should be designed differently for the safety of different Li-ion batteries, even for 18650 Li-ion batteries with different cathode materials. (2) For NCA and NCM Li-ion batteries, the general trend of their mechanical responses at different loading rates is similar. (3) Both NCA and NCM Li-ion batteries exhibit strain rate hardening behaviors, namely their resistances to deformation increase as loading rate increases. NCM Li-ion batteries show obvious strain rate hardening behaviors at low loading rates while NCA Li-ion batteries can only show strain rate hardening behaviors until the loading rate increases to a certain value. (4) For compression tests at high loading rate, many layers of elec trodes inside both NCA and NCM Li-ion batteries have broken after compression tests. This may cause safety issues for 18650 Liion batteries at high SOCs. The constitutive model of the jellyroll at various loading rates is proposed based on the experimental results. A FEM of the jellyroll is established to validate the proposed constitutive model. The established FEM shows good simulation accuracy and it can be used to simulate mechanical behaviors of 18650 Li-ion batteries under dynamic loading cases. It can also be utilized to evaluate the crashworthiness of Li-ion batteries in the case of impact accidents and provide valuable guid ance for the structure design of battery packs in EVs.
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