Research on Micromechanical Behavior of Current Collector of Lithium-Ion Batteries Battery Cathode during the Calendering Process

Abstract

Calendering is a crucial process in the manufacturing of lithium-ion battery electrodes. However, this process introduces several challenges to the current collector, including uneven stress distribution, stress concentration, and plastic pits, which ultimately impact electrode consistency and safety. It is important to note that the load exerted on the current collector during calendering cannot be determined solely through experimental means. Moreover, due to the extremely thin nature of the current collector, there is a size effect problem. To address these issues, this study establishes a lithium-ion battery cathode model based on real experimental data and conducts a numerical simulation of the calendering process. By obtaining the load applied to the current collector and incorporating it into the crystal plasticity model, we investigate the mechanical behavior of the current collector at the crystal level during calendering. The results demonstrate that the lithium battery cathode collectors undergo plastic deformation during calendering. Furthermore, current collectors with a smaller number of grains exhibit a more pronounced stress concentration zone, and their stress levels are highly sensitive to the crystal direction. The maximum stress fluctuation range can reach approximately 100 MPa. Conversely, current collectors with a greater number of grains exhibit a more uniform stress distribution during calendering and are less sensitive to the crystal orientation. Their stress levels remain stable within a smaller range, approximately 20 MPa. These findings justify and emphasize the importance of investigating the current collector at the microscopic level, thereby providing valuable research insights for the field of calendering.

1. Introduction

With the increasing urgency of the global energy crisis and climate change, lithium-ion batteries are assuming a more pivotal role in our daily lives and production [1,2]. The electrode, as the fundamental component of the lithium-ion battery, comprises four essential parts: active material particles, a solid phase consisting of a conductive agent and binder, pores, and the current collector. Typically, the current collector employs ultra-thin copper or aluminum foil. Its primary function is twofold: providing support to the electrode’s active material (also known as the electrode backbone) and collecting electrons to conduct them through the external circuit. The current collector is indispensable for enhancing conductivity, reducing internal resistance, and improving battery capacity and safety.

During the calendering process, the current collector experiences compression from the electrode material particles, often resulting in uneven stress distribution and plastic deformation that significantly impact battery consistency and safety. High stress concentrations can lead to plastic deformation or cracking of the current collector, diminishing the mechanical strength of the lithium battery and rendering it susceptible to shocks and vibrations. Furthermore, it can adversely affect battery cycling, reducing efficiency and potentially giving rise to hazards or explosions.

Tao, R. et al. [3] explore the circumferential strain of the current collector during the winding process and reveal its fracture failure during the winding process. Zhu, P. et al. [4] compared six types of current collectors in terms of mechanical properties, electrical conductivity, and electrochemical stability. Doberdò, I. et al. [5] found that the carbon coating on the aluminum foil will have more stable current collector properties, but the too-thick coating will increase the current collector quality. Chen, J. et al. [6] change the surface morphology of electrolytic copper foil by asynchronous rolling and improve the conductivity, interface adhesion, and mechanical properties of copper foil. Wang, C.K., et al. [7] use carbon fiber composite plates instead of traditional graphite plates as fuel cell current collectors. Schlaier, J. et al. [8] proposed a preparation method for copper current collectors suitable for silicon anodes. Hu, Y. et al. [9] found that graphene nanosheets and carbon nanotube (CNT) hybrid paper have a high potential to be used as collectors and binder-free anodes for lithium-ion batteries. Sethuraman, V.A. et al. [10] used in-situ measurement to explore the stress evolution of the electrode during lithium-ion intercalation and deintercalation. Jones, E.M.C. et al. [11] explored the in-situ measurement of electrode strain during electrochemical cycling. Manikkavel, A. et al. [12] explored the fracture failure of electrodes under tensile load.

Currently, there is a limited body of research focused on the mechanical behavior and deformation of current collectors during the calendering process. Additionally, with the aim of achieving higher energy density, current collectors have become ultra-thin, reaching micron-level thickness. They consist of only 1–2 layers of grains in the thickness direction. Under these circumstances, the anisotropy of the current collector is heightened, and the size effect becomes more pronounced [13,14]. Consequently, conventional macroscopic theories are no longer sufficient for investigating the mechanical response and deformation of current collectors during the calendering process. Thus, this paper adopts the crystal plasticity theory to examine the stress variations and deformation characteristics of the cathode current collector in lithium-ion batteries at the micro-scale during the calendering process.

The crystal plasticity theory takes into account the microstructure of materials and establishes a connection between the microscopic deformation behavior of materials and their macroscopic mechanical response. It is a method of research at the microscopic scale. This theory has found extensive application in studying various aspects, including tensile and compression behaviors, anisotropy, size effects, and the forming limits of materials at the micro scale. The crystal plasticity theory has always been a hot topic for scholars. The idea was first proposed by Taylor, G.I., et al. [15,16,17,18,19,20,21]. Later, it was widely used under complex loading conditions to explore the deformation process and texture evolution of single-crystal and polycrystalline materials. Huang, Y.G. [22] combines crystal plasticity theory with the finite element method, called CPFEM (crystal plasticity finite element method), and develops UMAT for single crystal plastic deformation. Lu, C., et al. [23] investigated the texture evolution and heterogeneity during equal channel angular pressing (ECAP) of an aluminum single crystal by CPFEM. Khan, A.S. et al. [24] used CPFEM to simulate the deformation of pure aluminum along two orientations at different strain rates. Chen, S.D., et al. [25] used CPFEM to find that asymmetric rolling is more effective in generating plastic deformation. Through CPFEM, Zhang, H. et al. [26] found that the mechanical properties of copper foil were affected by grain size, sample size, and crystal orientation. Fan, W. et al. [27] explore the uneven deformation of stainless steel foil during stretching by CPFEM.

2. Materials and Methods

The preparation of lithium battery electrodes involves four main processes: stirring, coating, drying, and calendaring, as illustrated in Figure 1. In this study, lithium battery cathodes were prepared using Li[Ni_0.5Co_0.2Mn_0.3]O₂ (NCM) as the active material (90%-wt), carbon black (CB) as the conductive agent (5%-wt), polyvinylidene difluoride (PVDF) as the binder (5%-wt), and aluminum foil as the current collector. The aim was to investigate the calendering process.

To begin, NCM, CB, and PVDF powders were mixed in a planetary vacuum mixer (MSK-SFM-16) for 20 min. Subsequently, 1-Methyl-2-pyrrolidinone (NMP) was added as a solvent and stirred using a combination of low and high speeds. This mixing process is crucial for achieving a thorough blending of the electrode material particles, binder, and conductive agent, resulting in the formation of a stable suspension (slurry). The solid content of the slurry after mixing was $\mathsf{\eta }$ = 50%.

Next, the prepared slurry was uniformly coated onto one side of the current collector (aluminum foil with a thickness of 17 μm) using a slot-die coating machine (CPC2005A1). This coating process ensures a consistent and even distribution of the slurry on the collector.

Finally, the coated lithium battery cathode was placed in a hot air-drying oven and subjected to a temperature of 90 °C for a duration of 6 h. This drying process facilitates the evaporation of the solvent from the slurry, allowing for the formation of a solid-state conductive network between the electrode’s active material and the conductive agent.

The calendering process involves the use of two rollers to reduce the thickness of the lithium battery electrode. Calendering serves multiple purposes, including increasing energy density, enhancing bond strength, improving conductivity, and extending the lifespan of lithium-ion batteries. As a result, it is an indispensable step in the electrode preparation process.

In this study, the calendering of lithium battery cathodes was performed using a double roller calender machine (MSK–2300A). The rollers have a diameter of 200 mm and a length of 330 mm. The calendering speed was set at 1 m/min. Different degrees of calendering for the lithium battery cathodes were achieved by adjusting the roller gap. The thickness of the calendered lithium battery cathode was measured using a micrometer (MDH–25MB), as depicted in Figure 2.

3. Numerical Simulation

3.1. Lithium-Ion Cathode Model

The cathode of a lithium-ion battery consists of the upper coating and the lower current collector, which is typically made of aluminum foil. Figure 3 illustrates this configuration. The upper coating is composed of active material particles (NCM), a conductive agent (CB), and a porous structure. The active material particles and conductive agent (CB) are bound together by a cohesive bulk network formed by a binder.

Given the aforementioned characteristics of the lithium-ion battery cathode coating, a discrete element model was employed to capture the mechanical response of the cathode. This approach has been validated and found to be feasible in the relevant literature [28,29,30,31,32,33,34]. The discrete element model allows for a detailed understanding of the interaction and behavior of individual particles within the cathode, offering insights into its mechanical properties and response.

The discrete element modeling of the electrode was conducted by referring to scanning electron microscopy (SEM) images of lithium-ion battery cathodes, as shown in Figure 4. The electrode model parameters are set as in

Table 1. Electrode model parameters.

Materials	Description	Values	Units	Source
Active material particles (NCM)	Young’s modulus (NCM)	1.42 × 1011	Pa	[30,31]
	Density	4.75	g/cm2	[30]
	Poisson’s ratio	0.25		[30]
	Coefficient of static friction	0.25		[33]
	Coefficient of rolling friction	0.01		[33]
	Coefficient of restitution	0.25		[33]
Conductive carbon black	Young’s modulus(CB)	4.5 × 10⁸	Pa	[29]
	Density	2.25	g/cm2	Measured
	Poisson’s ratio	0.3		[29,34]
	Coefficient of static friction	0.25		[34]
	Coefficient of rolling friction	0.01		[34]
	Coefficient of restitution	0.25		[29]
Current collector	Young’s modulus	6.89 × 1010	Pa	Measured
	Density	2.7	g/cm2	Measured
	Poisson’s ratio	0.25		Measured
Compression plate	Young’s modulus	1.82 × 1011	Pa	Materials Library
	Density	7.8	g/cm2	Materials Library
	Poisson’s ratio	0.3		Materials Library

. SEM was also used to measure the particle size of the coating. In the model, the active material particles (NCM) and conductive agents (CB) were represented as spherical particles. Active material particles (NCM) and conductive agents (CB) are modeled as spherical particles. The particle size distribution follows a normal distribution, as depicted in Figure 5. This approach allowed for a realistic representation of the particle characteristics and facilitated the analysis of their behavior and interactions within the electrode structure.

The contact between particles follows the Hertz contact model.

The normal force in particles (${\mathrm{F}}_{\mathrm{n}}$):

$${\mathrm{F}}_{\mathrm{n}}=\frac{4}{3}{\mathrm{E}}^{*}\sqrt{{\mathrm{R}}^{*}}{\mathsf{\delta }}_{\mathrm{n}}^{3/2},$$

(1)

where ${\mathrm{E}}^{*}$ is the equivalent modulus of elasticity, ${\mathrm{R}}^{*}$ is the equivalent radius of the particle, and ${\mathsf{\delta }}_{\mathrm{n}}$ is the normal overlap;

$$\frac{1}{{\mathrm{E}}^{*}}=\frac{(1-{\mathrm{v}}_{\mathrm{i}}^2)}{{\mathrm{E}}_{\mathrm{i}}}+\frac{(1-{\mathrm{v}}_{\mathrm{j}}^2)}{{\mathrm{E}}_{\mathrm{j}}}$$

(2)

$$\frac{1}{{\mathrm{R}}^{*}}=\frac{1}{{\mathrm{R}}_{\mathrm{i}}}+\frac{1}{{\mathrm{R}}_{\mathrm{j}}}$$

(3)

where ${\mathrm{E}}_{\mathrm{i}}$, ${\mathrm{v}}_{\mathrm{i}}$, ${\mathrm{R}}_{\mathrm{i}}$ and ${\mathrm{E}}_{\mathrm{j}}$, ${\mathrm{v}}_{\mathrm{j}}$, ${\mathrm{R}}_{\mathrm{j}}$ is the Young’s modulus, Poisson ratio, and radius of each sphere in contact.

The tangential force in particles (${\mathrm{F}}_{\mathrm{t}}$):

$${\mathrm{F}}_{\mathrm{t}}=-{\mathrm{S}}_{\mathrm{t}}{\mathsf{\delta }}_{\mathrm{t}}$$

(4)

where ${\mathrm{S}}_{\mathrm{t}}$ is the equivalent tangential stiffness and ${\mathsf{\delta }}_{\mathrm{t}}$ is the tangential overlap.

$${\mathrm{S}}_{\mathrm{t}}=8{\mathrm{G}}^{*}\sqrt{{\mathrm{R}}^{*}{\mathsf{\delta }}_{\mathrm{n}}}$$

(5)

where ${\mathrm{G}}^{*}$ is the equivalent shear modulus, ${\mathsf{\delta }}_{\mathrm{n}}$ is the normal overlap;

Adhesion between particles is characterized by the bond model.

$$\mathsf{\delta }{\mathrm{F}}_{\mathrm{n}}=-{\mathrm{V}}_{\mathrm{n}}{\mathrm{S}}_{\mathrm{n}}\mathrm{A}\mathsf{\delta }\mathrm{t}$$

(6)

$$\mathsf{\delta }{\mathrm{F}}_{\mathrm{t}}=-{\mathrm{V}}_{\mathrm{t}}{\mathrm{S}}_{\mathrm{t}}\mathrm{A}\mathsf{\delta }\mathrm{t}$$

(7)

$$\mathsf{\delta }{\mathrm{M}}_{\mathrm{n}}=-{\mathsf{\omega }}_{\mathrm{n}}{\mathrm{S}}_{\mathrm{t}}\mathrm{J}\mathsf{\delta }\mathrm{t}$$

(8)

$$\mathsf{\delta }{\mathrm{M}}_{\mathrm{t}}=-{\mathsf{\omega }}_{\mathrm{t}}{\mathrm{S}}_{\mathrm{n}}\mathrm{J}/2\mathsf{\delta }\mathrm{t}$$

(9)

$$\mathrm{A}=\mathsf{\pi }{{\mathrm{R}}_{\mathrm{B}}}^2$$

(10)

$$\mathrm{J}=\frac{1}{2}\mathsf{\pi }{{\mathrm{R}}_{\mathrm{B}}}^4$$

(11)

where ${\mathrm{S}}_{\mathrm{n}}$ and ${\mathrm{S}}_{\mathrm{t}}$ are the normal and tangential stiffnesses, respectively, $\mathsf{\delta }\mathrm{t}$ is the time increment, ${\mathrm{V}}_{\mathrm{n}}$ and ${\mathrm{V}}_{\mathrm{t}}$ the normal and tangential velocities, and ${\mathsf{\omega }}_{\mathrm{n}}$ and ${\mathsf{\omega }}_{\mathrm{t}}$ the normal and tangential angular velocities; ${\mathrm{R}}_{\mathrm{B}}$ is the radius of the bond.

3.2. Calendering Process Simulation

The calendering process plays a crucial role in the formation of electrodes, involving the thinning of coated electrodes in the thickness direction by passing them through two rollers. This process serves two main purposes: enhancing the conductivity of the electrodes and reducing their size to increase energy density. Additionally, calendering has the added benefit of leveling the electrode surface and improving adhesive strength.

Since the calendering process is symmetrical, this study focuses on exploring one side of the process, as illustrated in Figure 6a. It is important to note that the thickness of the cathode is significantly smaller than both its width and the diameter of the roller. Therefore, the calendering process of the cathode can be regarded as a flat deformation problem, where the deformation primarily occurs in the plane of the electrode. This consideration allows for a simplified analysis of the calendering process and facilitates the understanding of the mechanical behavior and deformation characteristics of the electrode during this stage. In the calendering process, the bite angle is $\mathsf{\theta }$.

$$\mathsf{\theta }={\mathrm{c}\mathrm{o}\mathrm{s}}^{-1}\left[\left(\mathrm{R}-\mathrm{S}\right)/\mathrm{R}\right],$$

(12)

where R is the roller radius of the calender and S is the reduction of the electrode thickness of the lithium battery.

Based on extensive calendering test measurements, it has been consistently observed that the value of “θ” remains extremely small. This finding suggests that the deformation of the cathode during calendering primarily occurs in the normal direction [28,29,30,31,32,33,34]. Based on this understanding, we simplify the calendering process as a compression process primarily in the normal direction, as depicted in Figure 6b. To investigate this phenomenon, a 600 × 600 micro-element is selected as the representative volume element (RVE) model. The RVE model allows for a focused analysis of the deformation behavior and mechanical response of the cathode during the calendering process, providing valuable insights into its overall performance and characteristics.

In Figure 6b, the top compression plate is subjected to downward compression, simulating the effect of the roller during the calendering process. The middle part represents the cathode coating, where the main deformation takes place. Lastly, the bottom metal plate represents the current collector of the lithium-ion battery cathode, which is typically made of aluminum with a thickness of 17 μm. This configuration allows for a representation of the key components involved in the calendering process and facilitates the examination of their mechanical behavior and interactions.

As shown in Figure 7, this paper simulates five degrees of calendering and electrode thickness (150–190 $\mathsf{\mu }\mathrm{m}$). After drying, the cathode of the lithium-ion battery does not ensure uniformity in the thickness direction. Thus, D1 only serves to level the surface of the electrodes and ensure consistency. With the exception of D1, the depression rate “ε = 10%” is controlled for each calendering. The simulation can not only obtain the microstructure evolution behavior of the electrode but also the real mechanical behavior between the coating particles and the current collector.

3.3. Current Collector Model

To achieve higher energy density, the current collector material used for the lithium battery cathode is an ultra-thin aluminum foil, with a thickness of merely 17 μm and only 1–2 layers of grains in the thickness direction. Due to its extremely thin nature, this material exhibits pronounced anisotropy and a more significant size effect compared to large-scale materials. Consequently, conventional macroscopic deformation theories are not applicable in this context. Hence, in this section, a crystal plasticity finite element method is employed to establish a crystal model of the current collector. This approach enables the exploration of the mechanical properties of the cathode current collector during the calendering process at the crystal scale. By considering the microstructural aspects, a more accurate understanding of the deformation behavior and performance of the current collector can be attained.

3.3.1. Crystal Plasticity Theory

The crystal plastic constitutive model proposed by Asaro, R.J., et al. [35,36] was used in this study. The total deformation gradient F is decomposed into the plastic component of sliding along the slip system and the elastic component of lattice distortion and rigid rotation.

$$\mathrm{F}={\mathrm{F}}^{\mathrm{e}}·{\mathrm{F}}^{\mathrm{P}},$$

(13)

$${\mathrm{s}}^{*\left(\mathsf{\alpha }\right)}={\mathrm{F}}^{\mathrm{e}}{·\mathrm{s}}^{\left(\mathsf{\alpha }\right)},$$

(14)

$${\mathrm{m}}^{*\left(\mathsf{\alpha }\right)}={\mathrm{m}}^{\left(\mathsf{\alpha }\right)}·{\left({\mathrm{F}}^{\mathrm{e}}\right)}^{-1},$$

(15)

where ${\mathrm{s}}^{\left(\mathsf{\alpha }\right)}$ and ${\mathrm{m}}^{\left(\mathsf{\alpha }\right)}$ are the unit vectors of the initial slip direction and slip plane normal of the $\mathsf{\alpha }$-th slip system. ${\mathrm{s}}^{*\left(\mathsf{\alpha }\right)}$ and ${\mathrm{m}}^{*\left(\mathsf{\alpha }\right)}$ are the slip direction and slip plane normal after the deformation of the $\mathsf{\alpha }$-th slip system.

The velocity gradient (L) is obtained by the derivative of the deformation velocity to the position. The velocity gradient (L) can also be decomposed into a plastic deformation part ${\mathrm{L}}^{\mathrm{p}}$ and elastic deformation part ${\mathrm{L}}^{\mathrm{e}}$.

$$\mathrm{L}=\dot{\mathrm{F}}·{\mathrm{F}}^{-1}={\mathrm{L}}^{\mathrm{e}}+{\mathrm{L}}^{\mathrm{p}},$$

(16)

The plastic part of the velocity gradient can be expressed as

$${\mathrm{L}}^{\mathrm{P}}={\sum }_{\mathsf{\alpha }=1}^{\mathrm{N}}{\dot{\mathsf{\gamma }}}^{\left(\mathsf{\alpha }\right)}{\mathrm{s}}^{\left(\mathsf{\alpha }\right)}{\mathrm{m}}^{\left(\mathsf{\alpha }\right)},$$

(17)

The rate dependent crystal plasticity model establishes the relationship between the shear strain rate ${\dot{\mathsf{\gamma }}}^{\left(\mathsf{\alpha }\right)}$ and the resolved shear stress ${\mathsf{\tau }}^{\left(\mathsf{\alpha }\right)}$ for each slip system. The slip system is activated when the shear stress ${\mathsf{\tau }}^{\left(\mathsf{\alpha }\right)}$ is greater than a certain critical value.

$${\dot{\mathsf{\gamma }}}^{\left(\mathsf{\alpha }\right)}={{\dot{\mathsf{\gamma }}}_0}^{\left(\mathsf{\alpha }\right)}\mathrm{sign}\left({\mathsf{\tau }}^{\left(\mathsf{\alpha }\right)}\right){\left|\frac{{\mathsf{\tau }}^{\left(\mathsf{\alpha }\right)}}{{{\mathsf{\tau }}_{\mathrm{c}}}^{\left(\mathsf{\alpha }\right)}}\right|}^{\mathrm{n}},(\left|{\mathsf{\tau }}^{\mathsf{\alpha }}\right|\ge {{\mathsf{\tau }}_{\mathrm{c}}}^{\left(\mathsf{\alpha }\right)}),$$

(18)

$${\dot{\mathsf{\gamma }}}^{\left(\mathsf{\alpha }\right)}=0,(\left|{\mathsf{\tau }}^{\mathsf{\alpha }}\right|<{{\mathsf{\tau }}_{\mathrm{c}}}^{(\mathsf{\alpha })}),$$

(19)

where $\mathrm{sign}\left(\mathrm{x}\right)=1$ if $\mathrm{x}\ge 0$, $\mathrm{sign}\left(\mathrm{x}\right)=$−1; if$\mathrm{x}<0$; ${{\dot{\mathsf{\gamma }}}_0}^{\left(\mathsf{\alpha }\right)}$ is the reference shear strain rate of the slip system $\mathsf{\alpha }$ that is a constant for all the slip systems; n is the rate sensitive coefficient; ${\mathsf{\tau }}^{\left(\mathsf{\alpha }\right)}$ is the resolved shear stress of the slip system $\mathsf{\alpha }$; ${{\mathsf{\tau }}_{\mathrm{c}}}^{\left(\mathsf{\alpha }\right)}$ represents the dislocation slip resistance or critical resolved shear stress of the slip system $\mathsf{\alpha }$.

In this study, the model proposed by Bassani, J.L., and Wu, T.Y. [37] is used to characterize the hardening behavior of the current collector.

$${\dot{{\mathsf{\tau }}_{\mathrm{c}}}}^{\left(\mathsf{\alpha }\right)}={\sum }_{\mathsf{\beta }=1}^{\mathrm{N}}{\mathrm{h}}_{\mathsf{\alpha }\mathsf{\beta }}\left|{\dot{\mathsf{\gamma }}}^{\left(\mathsf{\beta }\right)}\right|,$$

(20)

$${\mathrm{h}}_{\mathsf{\alpha }\mathsf{\alpha }}=\left[\left({\mathrm{h}}_0-{\mathrm{h}}_{\mathrm{s}}\right){\mathrm{sech}}^2\left(\frac{\left({\mathrm{h}}_0-{\mathrm{h}}_{\mathrm{s}}\right){\mathsf{\gamma }}^{\left(\mathsf{\alpha }\right)}}{{\mathsf{\tau }}_1-{\mathsf{\tau }}_0}\right)+{\mathrm{h}}_{\mathrm{s}}\right]\times \left[1+{\sum }_{\begin{array}{c}\mathsf{\beta }=1\\ \mathsf{\beta }\ne \mathsf{\alpha }\end{array}}^{\mathrm{N}}{\mathrm{f}}_{\mathsf{\alpha }\mathsf{\beta }}\tan \mathrm{h}\left(\frac{{\mathsf{\gamma }}^{\left(\mathsf{\beta }\right)}}{{\mathsf{\gamma }}_0}\right)\right],\left(\mathsf{\alpha }=\mathsf{\beta }\right),$$

(21)

$${\mathrm{h}}_{\mathsf{\alpha }\mathsf{\beta }}=\mathrm{q}{\mathrm{h}}_{\mathsf{\alpha }\mathsf{\alpha }},\mathsf{\alpha }\ne \mathsf{\beta },$$

(22)

where ${\mathrm{h}}_{\mathsf{\alpha }\mathsf{\alpha }}$ is the self-hardening coefficient; ${\mathrm{h}}_{\mathsf{\alpha }\mathsf{\beta }}$ is the latent hardening coefficient; ${\dot{\mathsf{\gamma }}}^{\left(\mathsf{\beta }\right)}$ is the shear strain rate of the slip system $\mathsf{\beta }$; ${\mathsf{\gamma }}_0$ is the reference shear strain; ${\mathsf{\tau }}_1$ is the critical shear stress saturation value; ${\mathsf{\tau }}_0$ is the initial critical resolved shear stress; ${\mathrm{h}}_0$ is initial hardening rate; ${\mathrm{h}}_{\mathrm{s}}$ is the hardening modulus in the easy slip stage; ${\mathsf{\gamma }}^{\left(\mathsf{\alpha }\right)}$ and ${\mathsf{\gamma }}^{\left(\mathsf{\beta }\right)}$ are the cumulative shear strain of the slip system $\mathsf{\alpha }$ and $\mathsf{\beta }$; q is the latent hardening parameter; ${\mathrm{f}}_{\mathsf{\alpha }\mathsf{\beta }}$ is the interaction coefficient between α and β.

3.3.2. The Polycrystalline Model of Current Collector

In this paper, we establish a current collector polycrystalline model based on the Voronoi method [38].

$$\mathrm{V}\left({\mathrm{a}}_{\mathrm{i}}\right)\in \left\{\mathrm{p}={\mathrm{R}}^2|\mathrm{d}\left(\mathrm{p},{\mathrm{a}}_{\mathrm{i}}\right)<\mathrm{d}\left(\mathrm{p},{\mathrm{a}}_{\mathrm{j}}\right);{\mathrm{a}}_{\mathrm{i}},{\mathrm{a}}_{\mathrm{j}}\mathsf{ϵ}\mathrm{A}\right\},$$

(23)

where A = $\left\{{\mathrm{a}}_{\mathrm{i}}\right\}$ is the set of points in space,$\mathrm{d}\left({\mathrm{p}}_1,{\mathrm{p}}_2\right)$ is the distance between any two points in the space,$\mathrm{V}\left({\mathrm{a}}_{\mathrm{i}}\right)$ is a Voronoi polygon of the point ${\mathrm{a}}_{\mathrm{i}}$.

In this study, a polycrystalline model of the current collector is developed, with dimensions of 600 × 17 μm. The model is constructed based on equiaxed grains, and distinct colors are utilized to represent different grain orientations, as shown in Figure 8.

3.4. The Application of Calendering Load

During the calendering process, the compression plate applies pressure to the cathode coating, causing deformation. Simultaneously, the porosity of the coating decreases, leading to an increase in density. As a result, the load is transferred from the coating particles to the current collector, as determined in Section 3.2. Finally, this load is applied to the surface of the polycrystalline model of the current collector.

4. Results and Discussion

4.1. Morphology Evolution of Current Collector

As depicted in Figure 9. The current collector is not deformed at D1 (leveling of electrode surfaces) and D2 (reduction 15 $\mathsf{\mu }\mathrm{m}$, depression rate “ε = 10%”), with the upper surface remaining horizontal and intact. At D3, the current collector deforms, tiny pits appear, and coating particles begin to embed. As the calendering continues, the plastic deformation of the current collector continues to increase at D4. When the calendering degree reaches D5, the number of collector pits increases significantly, and the depth of the pits also deepens. Most of the coating particles at the junction have obviously been embedded in the current collector.

4.2. The Stress of Current Collector in Calendering Process

During the calendering process, the stresses in the current collector do not distribute uniformly and exhibit significant stress concentrations. The simulation results also reveal the presence of plastic pits at D3, which aligns with the findings in Section 4.1. These pits are associated with significant stress concentrations. As the calendering process progresses, the phenomenon of stress concentration becomes more pronounced and intensified (as depicted in Figure 10). This suggests that the stress concentration phenomenon in the current collector is exacerbated throughout the calendering process.

As the calendering process progresses, there is a general linear increase in the maximum stress experienced by the current collector. However, during the transition from D3 to D4, the rate of stress increases significantly and slows down. This can be attributed to the yielding of the current collector at D3, where plastic deformation occurs (confirming previous findings). As the calendering process further advances, the current collector undergoes the yielding stage, leading to a substantial increase in stress levels once again (as illustrated in Figure 11). This phenomenon highlights the dynamic nature of stress accumulation throughout the calendering process.

4.3. The Number of Grains and Current Collector Stress

In this section, three polycrystalline models of the current collector were established, as depicted in Figure 12. These models consist of 30, 90, and 300 grains, respectively, with each grain possessing a random orientation. Subsequently, a calendering simulation was conducted specifically for D5.

As depicted in Figure 13a, the current collector with fewer grains exhibits a significantly uneven distribution of stress, even displaying a penetrating stress concentration zone. However, as the number of grains increases (Figure 13b), the stress concentration phenomenon diminishes. The presence of grain boundaries contributes to concentrating the high-stress areas primarily on the surface grains without spreading downward. When the grain size reaches 300 (Figure 13c), there is a coordinated deformation between the grains and an increase in grain boundaries, impeding the movement of dislocations. Consequently, the high-stress area is greatly reduced, resulting in a more uniform stress distribution. A current collector with a uniform stress distribution offers several advantages for the mechanical properties of lithium batteries. Firstly, it exhibits enhanced mechanical properties, enabling lithium batteries to withstand greater shocks and vibrations. Secondly, it better ensures the structural integrity of the electrode, thereby reducing the degradation of electrode performance.

4.4. Crystal Orientation and Current Collector Stress

The three current collector models, which contain 30, 90, and 300 grains, respectively, are given five random crystal orientations, and the D5 calendering simulation is performed.

From the comparison shown in Figure 14, it is evident that the current collector with fewer grains is more sensitive to crystal orientation. The maximum stress in the current collector containing 30 grains exhibits significant variation with different crystal orientations. However, this sensitivity gradually diminishes as the number of grains increases. When the number of grains reaches 300, the maximum stress in the current collector is hardly affected by the crystal orientation. Regardless of the changes in crystal orientation, the maximum stress value of the current collector remains stable within a small range.

5. Conclusions

In this study, a discrete-element model of the lithium battery cathode was developed using SEM images of the prepared cathodes. The calendering process was simulated using this discrete element model, allowing the determination of the load on the current collector, which is not accessible through experimental means. Subsequently, a polycrystalline model of the current collector was established based on the crystal plasticity theory, and the load was applied to its surface. The investigation aimed to understand the mechanical properties of the lithium battery cathode current collector during the calendering process at the micro-scale. The main conclusions drawn from the study are as follows:

(1)

The stress distribution in the cathode current collector is non-uniform during calendering, exhibiting significant variations.

(2)

Plastic deformation occurs in the cathode current collector during the calendering process.

(3)

The current collector with fewer grains experiences more pronounced stress concentrations and is more sensitive to crystal orientation.

(4)

As the number of grains increases, the stress distribution in the current collector becomes more uniform, and it becomes less sensitive to crystal orientation.

This study provides insights into the micromechanical behavior of the current collector cathode during calendering, considering the realistic microstructure and material properties of lithium battery cathodes. It offers research ideas for further exploration of the calendering process. In the future, additional studies focusing on current collectors at the microscopic crystal level, such as current collectors with gradient grain size and typical texture, will fill certain research gaps in battery energy density, cycle life, battery capacity, and safety.