The battery breathing effect and its influence on adhesive layers in structural battery packs

Abstract

In this work, two approaches to measure the deformation of a prismatic nickel-manganese-cobalt-battery (NMC) cell due to the battery-breathing-effect during charging is presented. One approach uses an optical system and the second approach uses a test rig with an external load on the cell. The measured deformations are then passed into a numerical model of the battery cell, which is integrated into the battery pack via adhesive bondlines. A structural methyl-methacrylate-adhesive (MMA) is characterized using ARCAN-specimens under different loading angles. From the tests, a Drucker-Prager equivalent stress is deduced which is used to calculate the stress distributions inside the structural adhesive layer on a bonded battery cell. The calculated equivalent stresses are compared to fatigue test data of butt-bonded cylinder specimens to predict the lifetime of the structural adhesive bondline of the battery cell. With the presented methods, the large influence of the battery breathing effect on the lifetime of structural adhesive cell bonds can be shown.

Keywords

Adhesively bonded batteries cell-to-chassis battery breathing effect durability Drucker-Prager equivalent stress

Design challenges in automotive batteries

As battery electric vehicles gain major market shares of the overall car market, their most important component, the battery pack, keeps evolving in a rapid manner. The further development of the design of the battery pack is of utmost importance for automotive companies and therefor new designs are introduced. Nowadays, automotive battery packs consist of battery modules which host several cells and which are integrated into a battery pack. To get rid of these auxiliary structures and to increase the overall energy density of the battery packs, new approaches like cell-to-pack (CTP) or cell-to-chassis (CTC) are being introduced.¹ In these designs, the battery cells are directly integrated into the battery pack to get rid of the module casings. In case of the cell-to-chassis designs, the battery cells are bonded to the battery case using structural adhesives to make them part of the automotive structure and to increase the stiffness of the car body.² The use of adhesives in battery packs increases with the rising level of cell integration. Besides the structural adhesive bondlines, thermal interface materials (TIM) are used to connect the battery cells to cooling plates. These adhesives show a good thermal conductivity and are either classical silicone gap filler materials or polyurethane based materials.³ Furthermore, there are adhesive compression pads or potting materials to bond the cells to each other. These materials are also typically polyurethane- or silicon-based.

During the charging process of the battery cell, the electrode stacks exhibit an expansion. Two mechanisms have to be distinguished: On the one hand the reversible effect which is called battery breathing or reversible swelling. It is based on the lithiation and delithiation of the active material of the cell.⁴ During discharging, this shape of the cell returns to its initial state. Nonetheless, it can threaten the structural integrity of a battery cell.⁵ On the other hand, the irreversible effect is called swelling. This effect is based on lithium plating and the growth of the solid electrolyte interface.⁶ The effect of cell expansion is dependent on the cell chemistry and the battery cell format. Pouch cells show the highest deformations from battery breathing, prismatic cells exhibit fewer deformation due to their stiff casing whereas deformations are very small in case of a cylindrical cell. Regarding the cell chemistry, typical nickel-manganese-cobalt-batteries (NMC) exhibit the battery breathing effect and especially upcoming high-performance cells with silicon added to the electrodes show a high expansion^7,8 In contrast, batteries based on lithium-iron-phosphate (LFP) are nearly unaffected by battery breathing.⁹

Due to the deformation of the cell, the surrounding adhesive bondlines are also affected and can be damaged if not properly designed. Especially structural adhesive bondlines on the cells can be damaged by battery breathing as they only withstand minor elongations and the cell deformations induce high stresses. To ensure the durability of these structural adhesive bondlines, the cell deformations from breathing have to be considered in the design process of an automotive battery. Therefor a methodology is presented to measure the cell deformations due to breathing and to calculate stresses in the adhesive layer of a bonded battery cell. The stresses can then be compared to experimental fatigue data by using an equivalent stress for the adhesive.

Methodology of the work

The effect of battery breathing on the durability of structural adhesive bonds in cell-to-chassis designs is investigated using several experimental and numerical procedures, see Figure 1. Starting from the optical measurement of the cell deformations at different states-of-charge (SOC) without an external force on the cell hull, a test rig is designed in the subsequent step to measure the relevant extrusions and intrusions of the cell hull when an external force is applied as this is usually the case when a cell is integrated into a battery pack. Having determined the extrusions and intrusions of the cell hull under load, a battery design for further investigations is presented using three different adhesive systems to account for the expected loads. The structural adhesive as the most critical component of the assembly is then characterized using ARCAN specimens under defined load angles to determine the stiffnesses and yield stresses. Based on these material parameters, a Drucker-Prager equivalent stress is defined to be able to make complex stress states comparable in the following simulations and experiments. The first of these investigations is a model of the breathing cell, the adhesive layers and parts of the surrounding battery pack to assess the maximum stress inside the structural adhesive layer due to cell breathing. Using the parametrized Drucker-Prager equivalent stress, the load level in the structural adhesive is transferred to a butt bonded cylinder specimen and a corresponding nominal stress is calculated. In the last part of the work, cyclic tests of bott-bonded cylinder specimens with the structural adhesive are used to determine a S-N curve of the adhesive. The nominal stresses of the butt-bonded cylinder specimens derived from the numerical simulation of the cell breathing are compared to the S-N curve to determine the influence of battery breathing on the durability of the structural adhesive joint.

Investigation of the battery-breathing-effect

The reversible effect of battery-breathing is investigated using a prismatic battery cell of a capacity of around 500 Wh with an NMC chemistry without silicon in the electrodes, as this is a common type of battery cell and the prismatic form factor is suitable for structural battery concepts using adhesive bonds. The cell has dimensions of 106 mm x 255 mm x 32 mm. The wall thickness is 0.5 mm except for the lower plate and the connector plates which are 1.2 mm in thickness. The hull is made of an aluminum alloy of the 3000 series. To measure the breathing of the cell's outer surfaces, the cells are charged to specific states of charge, namely 1%, 25%, 50%, 75% and 100%, by adjusting the cell voltage to the specific voltages according to the cells data-sheet. The charging rate applied corresponds to slow AC charging. At each of the states-of-charge, a CT-scan with the phoenix ‘v|tome|x s 240’ microCT system from Waygate Technologies and an optical scan with the scanning system ZEISS ATOS^® is performed to determine the cell geometry. In the CT, the cell is positioned on a turntable in front of the detector and scans are performed from different angles. These scans are combined to form a .stl-file of the geometry of the cell at a specific state-of-charge. For the optical ATOS^® measurement, the battery cell is also positioned on a turntable. Before the camera captures images from multiple overlapping directions of the cell, several measurement points are bonded to the cell hull for the correct alignment of the images. From the recorded images of the battery cell, a .stl file is created that represents its geometry. After creating geometry files for each State-of-charge (SOC) in the CT and via ATOS^®, the files for the SOCs of 25%, 50%, 75% and 100% are compared to the files for SOC 0% using the open-source software CloudCompare. Therefore, a single geometry file is aligned to the geometry file of 0%, which acts as a reference geometry. From this comparison, the displacements due to the battery breathing effect can be calculated, see Figure 2 a) for the CT and b) for the ATOS^® analysis.

The CT-measurement creates a rough surface structure on the large sides of the battery cell. Due to the high absorption of the electrodes inside, the signal received by the CT's detector is of insufficient accuracy, whereas the optical measurement yields very smooth surface topographies which makes them suitable for further analysis. Figure 3 depicts the displacement of the cell hull between the SOCs 0% and 100%. The large sides of the battery cell show a displacement of around 0.42 mm due to the expansion of the inner electrode stacks during charging, whereas the upper and lower sides of the cell hull exhibit an intrusion of around 0.2 mm. The relationship between the SOC and the displacement due to cell breathing is not completely linear. Between 0% and 25%, there is a sharp increase in the displacement, followed by a plateau until 50% and a subsequent linear increase to the maximum displacement at 100% SOC.

In contrast to the later use in automotive batteries, where the cells are always kept under an external compressive load to the large sides of the cells to diminish the effect of beathing and swelling, the abovementioned investigations have been performed without external load on the cells and therefore can only give a qualitive picture of the overall deformations of a prismatic battery cell due to the battery breathing effect.

In order to investigate the cell hull displacements from battery breathing of a battery cell affected by an external mechanical load on the large sides, a test rig has been built, see Figure 4. The test rig consists of two massive steel plates on the bottom and on the top, connected via steel bars. On top of the bottom plate, there is a load cell to measure the forces applied to the battery cell before charging and the cell driven force increase during charging. The battery cell is positioned on an aluminum plate above the load cell and is connected to a charging device. On the sides of this module of the test rig, the inductive sensors are clamped to measure the displacements on the cell's bottom and top side. The spring module is positioned on top of the cell to apply a load to the large sides of the cell via four springs and a plastic plate. On the top module, there are four potentiometers measuring the top side displacement of the cell through the pierced plastic plate. Furthermore, there is a screw in the center of the top-plate to pre-stress the four springs by moving the aluminum plate on top of the springs downwards.

The voltage measurement of the cell has to be carried out by directly connecting the electrodes of the cell to the balancer input of the charger to avoid inaccurate voltage measurements due to the high charging currents. A PT100 sensor is bonded to the cells hull to measure the cell temperature for charging safety monitoring. The data of the cell voltage, the load cell, the PT100 sensor, the potentiometers and the inductive sensors are recorded via a data-logger whereas the cell's SOC is calculated from the cell voltage and the datasheet. A charging current of 20 A is applied to load the cell within around nine hours which corresponds to a standard AC-charging speed. This charging speed avoids overheating of the cell and the connectors. A load of 1.6 kN is applied to the battery cell prior to charging via the springs of the test rig. The resulting nominal stress on the cell surface of around 0.06 MPa corresponds to pre-stresses described in literature, see for example.¹⁰ The measured and calculated quantities of the charging process are depicted in Figure 5.

During charging, the cell-voltage increases from 3.2 V to 4.2 V which corresponds to SOCs of around 0% and 100%. After an initial hike, the voltage and SOC increase in a linear manner until the charger decreases the current at the end of the loading process to avoid cell damage. After reaching a SOC of 100%, the beginning of the discharging process to a SOC suitable for storage of the cell is partially recorded. The temperature rises at the beginning of the charging process reaching around 29 °C at a state of SOC of 50% and decreasing again when the charging current is reduced. The force recorded by the load cell is affected by the breathing effect and exhibits the typical initial hike and the following plateau observed in the optical measurements. The cell temperature also has minor influence of the force due to the thermal expansion of the cell and the surroundings. At the end of the charging process, a drop in force in parallel to a drop in temperature can be observed. The positions of the potentiometers on the top side of the battery cell and on the cell's upper and lower sides can be seen in Figure 6, a).

The displacements measured by the potentiometers and the inductive sensors show the same profile observed before. After an initial hike, there is a plateau where the displacement is limited followed by a further increase. On the large sides of the battery cell, the displacement measured is around 0.44 mm. Assuming this displacement spreads symmetrically to both sides of the battery cell, a 0.22 mm displacement can be observed on each side of the cell which is around half as much as determined in the optical measurement without external load. The inductive sensors on the top side of the battery cell exhibit a displacement of around 0.18 mm to around 0.35 mm depending on their position on the top side, see Figure 6, c). On the bottom side of the battery cell, the sensors are positioned on the right side of the cell as there is a cell vent in the center, that allows for the outflow of gases in case of a thermal propagation. In this region, the smallest displacements of the cell are observed, ranging from 0.05 mm to 0.15 mm, see Figure 6, d).

Figure 7 depicts the differences of the cell hull extrusions and intrusions of the optical measurement method, depicted in grey symbols, and the measurement under external load in the test rig: black, blue and red symbols. Comparing the optical measurements performed without external load on the cells, to the measurements in the test rig, significant discrepancies can be observed. Due to the external load applied to the large side of the battery cell, the displacement in this direction is only half as big. In contrast, the cell intrusions on the top and bottom side are larger due to increased stresses in the battery cell hull. It can be concluded that an optical measurement of the cell hull displacements due to the battery breathing effect is a simple and fast way to determine the overall extrusions and intrusions of the cell. But in order to get accurate values for numerical calculations of a cell in a mechanically pre-stressed cell environment, as for example in automotive design processes, it is necessary to measure the cell displacements under load in a test rig, as these values can deviate by a large factor, depending on the cell and external load.

Concept of a bonded battery

For further numerical experimental and numerical investigations, a concept of a bonded battery is presented, see Figure 8. The concept follows the cell-to-chassis design, avoiding the battery modules and integrating the cells directly into the battery case.

Furthermore, the cells are bonded into the case using different adhesives to use the battery as a structural element of the car body. In this concept, a metallic case contains several prismatic battery cells, which can also transfer loads due to their metal casing. On the bottom side, the cells are bonded to the bottom plate with two structural adhesive layers surrounding the cell vent. On the top side of the cell, there is a TIM-adhesive featuring a relatively high thermal conductivity, to connect the cell with a cooling plate. Between the cells, there is a foam material that fixes the cell stack and compensates cell expansion, breathing and swelling while maintaining a load on the cells. Therefore, the foam needs to feature a low poisson's ration to allow a high compression without high stresses.

Properties of an adhesive for cell bonding

The adhesive focused in this work is the structural adhesive joining the cells bottom side to the metal case. This adhesive has to provide an elevated stiffness to increase the overall stiffness of the battery structure. But it also has to provide elevated strain at the yield point to allow deformations caused by the battery breathing effect. Here, a two-component room temperature curing methyl-methacrylate-adhesive (MMA) is used, which is a common choice for structural cell bondings in industrial applications due to its combination of relatively high strength and strain at yield and its crash worthiness.¹¹ To characterize the adhesive, ARCAN-specimens of the shape shown in Figure 9, a) are used.

The shape of the ARCAN specimens doesn’t follow the standard but is optimized for exact strain measurement with bending compensation, internal resistive heating, and exact adjustment of the adhesive layer thickness. For each testing angle, a separate test rig is used. They provide an adhesive layer of 40 mm x 19 mm and thickness of 0.8 mm that is defined by inserting metal sheets of a corresponding thickness between the outer parts of the specimen. The adherends are made of steel and are pretreated by cleaning with isopropanol and by DELO SACO^® blasting to ensure sufficient adhesion. The specimens are cured at room temperature for two days and quasi-statically tested until failure under 0°, 45° and 90° to create different stress states inside the adhesive layer. Strain is measured with one strain sensor at each side of the specimen to account for bending effects, see Figure 9, b). The resulting stress-strain curves are depicted in Figure 10, a). In 0° loading angle, there is a multiaxial stress state in the adhesive layer due to the thin layer of adhesive and the much stiffer adherends that prevent the transverse strain in the adhesive layer. The adhesive exhibits a stiffness $E *$ of around 1100 MPa and a yield strength of 16 MPa. For 90° loading angle, the adhesive layer is subjected to a shear stress state and exhibits an inferior stiffness of 130 MPa and a yield stress of 8 MPa. Using the shear modulus G and the stiffness $E *$ from the tensile test with restricted transverse strain, a Young's modulus of 370 MPa and a Poisson's ratio of 0.433 can be calculated using equations 1 and 2:

v = \frac{E^{*} - 2 G}{2 \cdot (E^{*} - G)}

(1)

E = \frac{(1 + v) \cdot (1 - 2 v)}{(1 - v)} \cdot E^{*}

(2)

As the material parameters for shear and multiaxial tension deviate extremely, the definition of a proper equivalent stress is of utmost importance. As the material behavior of adhesives is dependent on hydrostatic stresses, von-Mises criterion cannot be applied. In contrast, the Drucker-Prager criterion takes hydrostatic and deviatoric stresses into account, see equation 3, and has therefore been chosen to describe the equivalent stress of the MMA-adhesive.

F = a \cdot q^{b} - p - p_{t} = 0

(3)

The criterion describes the yield surface in the pressure (p)-von-Mises (q) plane. To determine the material constants a, b and p_t, the stress states inside the adhesive layer of the ARCAN-specimens has to be analyzed. Equation 4 represents the stress tensor in the adhesive layer of the ARCAN-specimen with K being the bulk modulus and G being the shear modulus.

\underline{σ} = [\begin{matrix} (K + \frac{4}{3} G) ε_{x} & 2 G ε_{x y} & 0 \\ 2 G ε_{x y} & (K - \frac{2}{3} G) ε_{x} & 0 \\ 0 & 0 & (K - \frac{2}{3} G) ε_{x} \end{matrix}]

(4)

The strains ε_x and ε_xy can be derived from the strain measurement of the mechanical test ε and the loading angle α, see equations 5 and 6.

ε_{x} = l n (1 + ε \cdot \cos α)

(5)

ε_{x y} = \frac{1}{2} a r c t a n (ε \cdot \sin α)

(6)

From the abovementioned stress tensor with the strains at the yield point, the first and second invariant of the stress tensor I₁, I₂ and the second invariant of the stress deviator J₂ can be calculated, see equations 7–9.

I_{1} = σ_{x} + σ_{y} + σ_{z}

(7)

I_{2} = σ_{x} σ_{y} + σ_{y} σ_{z} + σ_{z} σ_{x} - τ_{x y}^{2} - τ_{y z}^{2} - τ_{z x}^{2}

(8)

J_{2} = \frac{1}{3} I_{1}^{2} - I_{2}

(9)

The hydrostatic stress, which describes the volume changing part of the stress state can be expressed in terms of the first invariant of the stress tensor.

p = \frac{1}{3} I_{1}

(10)

The von-Mises stress describes the shape changing parts of the stress tensor and can be expressed in terms of the second invariant of the stress deviator.

q = \sqrt{3 J_{2}}

(11)

For the three loading angles of the ARCAN specimens, the hydrostatic stress and the von-Mises stress is calculated using the abovementioned equations, see Figure 10, b). The results of the 90° and 45° experiments are quite close due to the relatively low shear modulus compared to the confined tension modulus which adds only minor deviatoric parts to the stress state for 45°. The exponential Drucker-Prager law mentioned in equation 3 is fitted to the experimental data in the p-q plane and the following parameters are derived: a = 0.05, b = 0.27, p_t = 16.5. Neglecting p_t, equation 3 is used as an equivalent stress for the MMA adhesive and is used to compare stress states in the adhesive layer in the following simulations.

Numerical investigation of a bonded battery cell

In order to analyze the stresses inside the structural adhesive layer occurring due to the battery breathing effect, a numerical model of the bonded battery cell and its surrounding is assembled with ABAQUS^®, see section cut view in Figure 11. It consists of the electrode stack, the cell casing, the TIM layer below the battery cell, two structural adhesive layers on top of the cell, a foam material one each of the large sides of the cell, an upper and a lower metal sheet representing the surrounding battery case and two metal sheets parallel to the large sides of the cell compressing the foam material. All materials are modelled as linear elastic and with solid elements. For the structural adhesive and the TIM adhesive, 3 layers of elements have been chosen to model the bondline thickness in order to allow for transverse strain. The relatively thick elastic foam material uses two layers of elements. The material parameters of the structural adhesive are derived from the ARCAN specimens of the MMA-adhesive. A Young's-modulus of E = 370 MPa and a Poisson's ratio of υ= 0.433 are defined. Furthermore, the Drucker-Prager equivalent stress is defined in a user-subroutine as an output variable using equations 3 to 11. The thermal interface material in case of a structural battery designs is typically an elastic 2-component polyurethane adhesive with metal fillers to ensure a thermal conductivity of around 2–3 W/mK. In the numerical analysis this adhesive is defined with a modulus of E = 100 MPa and a poisson's ratio of υ= 0.35. In between the cells, so-called swelling-pads are usually inserted to compensate breathing and swelling effects. In the presented design of a structural battery, a very elastic silicon foam material is used instead. This material is modelled with a Young's modulus of E = 0.084 MPa and a poisson's ratio of υ= 0.2. The aluminum properties are defined as E = 70,000 MPa and υ= 0.35 and the electrodes stiffness is modelled according to Chang et al.¹² with a stiffness of 5000 MPa and an assumed Poisson's ratio of 0.3.

In a first simulation step, the two side plates are moved in direction of the battery cell to compress the foam material until a reaction force of 1.6 kN is reached. In the second simulation step, the electrode stack is expanded linearly to model the breathing effect of the battery and to introduce the deformation to the cell hull. This deformation induces stresses into the TIM, the structural adhesive and the foam material. In case of the structural adhesive and the TIM, these stresses are tensional stresses, due to the intrusion of the upper and lower cell hull, combined with a small portion of shear stress. Maximum stresses are observed along the edges of the adhesive layer, in parallel to the long cell edge. In the foam material, compressive stresses due to the breathing effect can be observed but remain insignificant due to the low stiffness of the material. For the structural adhesive layer, the distribution of the Drucker-Prager equivalent stress is depicted in Figure 12, a). The calculated Drucker-Prager stresses for two adhesive bondline thicknesses of 0.8 mm and 1.6 mm as well as the calculated deformations of the cell hull are depicted in Figure 12, b). The numerically obtained cell deformations match the measured ones quite accurately but there is a deviation for the intrusion on the side of the structural adhesive layer due to the missing cell vent in the numerical model. The Drucker-Prager equivalent stresses in the structural adhesive bondlines reach 14.5 MPa for the 0.8 mm thickness and 12 MPa for the 1.6 mm thickness at the SOC of 100%.

Durability tests of battery adhesive

The reversible battery breathing effect induces stresses into the adhesive layers at each charging cycle. The effect of these cyclic stresses on the durability of the joint is investigated using butt-bonded cylinder specimens with a diameter of 20 mm and a layer thickness of the MMA-adhesive of 0.8 mm, see Figure 13, a). In order to be able to compare the stresses occurring inside the specimen to the stresses in the structural bond of the bonded battery cell, a FE-model of the specimen is created to perform a quasistatic stress analysis and to determine the ratio between nominal stress and Drucker-Prager equivalent stress in the adhesive layer. This nonlinear relationship is shown in Figure 13, b).

Fatigue tests with these butt-bonded cylinder specimens with a thickness of the adhesive layer of 0.8 mm are performed at defined stress levels to determine the number of cycles the specimen is able to withstand until failure. The mean load of each test is defined as 55% of the nominal stress, the load amplitude is defined as 45% of the nominal stress. The resulting relationship between the nominal stress in the adhesive layer and the number of cycles is depicted in Figure 14. The static strength is around 18 MPa and millions of cycles can be endured when the nominal stress is at around 50% of the static strength. The two Drucker Prager stresses for the bondline thicknesses of 0.8 mm and 1.6 mm from the battery cell simulation model, Figure 12, b), are converted to nominal stresses in the butt-bonded cylinder specimen using the relationship in Figure 13, b) and are depicted in Figure 14. The peak stress level of the structural adhesive of the bonded battery cell with a thickness of 0.8 mm is depicted in red (higher stress level) whereas the peak stress level for a 1.6 mm adhesive layer on the cell is depicted in blue (lower stress level). Even tough there is only a minor change in the stress of about 2.5 MPa between the two layer thicknesses of the numerical simulation of the breathing cell, the effect on the fatigue behavior cannot be overrated. While the adhesive peak stress for the 1.6 mm layer could be withstood during about 10,000 charging cycles from SOC 0% to 100% according to the fatigue data predictions, the higher stress in the 0.8 mm bondline of the cell simulation decreases the number of cycles to around 140, which is not enough for a life of an automotive battery even though these batteries are rarely charged whole 0% to 100% cycles and the net capacity of a battery is always smaller than the actual capacity. But this relationship reveals that in the design phase of structurally bonded battery packs, the battery breathing effect has to be considered and is one of the key parameters that can influence the lifetime of a battery pack.

Furthermore, the fatigue behavior under temperature influence has to be considered, as temperatures during charging or repeated accelerations can reach up to 60 °C in the battery pack and static strength of the MMA adhesive is much lower at these temperatures.

Discussion

The presented method for stress and durability analysis of structural adhesive joints of battery cells stresses the importance of the consideration of the breathing effect of battery cells in the mechanical design process of bonded battery packs. The two measurement methods presented show different results for the cell hull deformations. In the optical scan, where the cell can deform without constraints, a high extrusion of the large sides of the cell and small intrusions of the upper and lower sides of the aluminum cell casing can be observed. In contrast, when using the presented test rig for the measurement of the breathing effect and an external force is applied to the cell, the extrusions on the large sides are smaller and the intrusions on the upper and lower side are increasing. For a general assessment of the cell's breathing effect, the optical measurement is suitable. But if a realistic measurement close to a later application in a cell-to pack or cell-to-chassis battery pack shall be investigated, the use of a specialized test rig with an external force to constrain the breathing effect is necessary. However, the optical measurement can also be used to detect the general extrusions and intrusions for the correct placement of the sensors during the design of the test rig. The measured cell extrusions and intrusions don’t follow a linear characteristic over the charging cycle. The breathing effect rather follows a profile consisting of two ramps, each followed by a plateau. Regarding the FE-simulations, the highest stresses in the structural adhesive layer are tensional stresses due to the cell hull intrusion and can be observed on the edges of the adhesive layer, in parallel to the large edge of the cell hull. The adhesive was modelled using a linear elastic material law. To avoid excessive stresses at the outer edges of the adhesive layer and to get a smoother and more realistic stress distribution, a material model taking into account the plastification effects should be applied in future works. The cyclic durability of the structural MMA-adhesive is very sensitive to the stresses occurring inside the adhesive layer on top of the cell. Therefore, it is of utmost importance to model the stiffness of the surrounding battery pack very accurately, as it has a large influence on the stresses in the structural adhesive layer. A model approach investigating only a part of the battery pack could drastically change the overall stiffness of the structure in the model and yield questionable results.

Summary and outlook

The battery breathing effect of a prismatic NMC battery cell has been investigated using optical measurements without external load and in a test tig with an external load on the large sides of the cell. Even though the overall cell deformations were similar, there were significantly lower deformations on the large sides and larger intrusions on the top and bottom side of the cell when it is charged under an external mechanical load. A concept of a bonded battery has been presented and a structural MMA-adhesive has been characterized using ARCAN-specimens with different load angles to gain material properties for a Drucker-Prager equivalent stress which is integrated into ABAQUS^® as an output variable using a user-subroutine. A numerical model of a bonded battery cell under external load has been created and used to calculate the equivalent stresses occurring in the structural adhesive layer due to the expanding cell stack inside the cell hull. With a numerical model of the butt bonded cylinder specimen, a relationship between nominal stress and Drucker-Prager equivalent stress in the specimen is derived to define corresponding stress states between the structural adhesive layer in the cell breathing simulation and the butt-bonded cylinder specimen. By performing fatigue experiments with the butt-bonded cylinder specimens, a relationship between the nominal stress level and the number of cycles is established. This relationship shows the critical influence the battery breathing effect can have on the lifetime of a structural bondline of a bonded battery cell.

This work only takes into account the battery breathing effect and its influence on the lifetime of a structural adhesive bond. But there are other effects like the progressive swelling of battery cells or the thermal expansion during charging and repeated accelerations of a car, that can have significant influences and the cell deformations and on the adhesive properties. To improve lifetime predictions of bonded batteries, these effects must also be taken into account and combined to complex load cycles. Furthermore, a more accurate model for the stiffness of the surrounding battery pack has to be considered in further investigations.

Footnotes

ORCID iDs

M Griese

T Gutsch

E Stammen

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work presented here is part of the research project 01IF22766N “BreathingBattery“ from the DVS e.V., Düsseldorf. It is supported by the Federal Ministry of Economic Affairs and Energy through the DLR as part of the program for promoting industrial cooperative research (IGF) on the basis of a decision by the German Bundestag.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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