Investigation of the mechanical behaviour of lithium-ion batteries by an indentation technique

International Journal of Mechanical Sciences 105 (2016) 1–10

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International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci

Investigation of the mechanical behaviour of lithium-ion batteries by an indentation technique Sina Amiri a,b, Xi Chen b, Andrea Manes a, Marco Giglio a a b

Politecnico di Milano, Department of Mechanical Enigneering, via La Masa 1, 20156 Milano, Italy Department of Earth and Environmental Engineering, Columbia University, 500 West 120th Street, New York, NY 10027, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 23 March 2015 Received in revised form 15 September 2015 Accepted 30 October 2015 Available online 10 November 2015

Indentation is an alternative technique for the measurement of a material's elastoplastic properties. It can be used when the classical tensile test approach is not feasible (thin film, very small components, etc.). This paper presents the results of experiments in which this technique has been exploited to investigate the mechanical properties of the multi-layered structure of lithium-ion batteries with the aim of gaining a better understanding of their mechanical integrity. Indentation tests were performed separately on different layers of a lithium-ion battery using a Berkovich indenter. In order to perform the tests, fused silica substrate (which has well-known mechanical properties) was used to constrain the samples. The elasticity of the anode and the current collectors were obtained from the unloading curve of the measured indentation load–displacement data. Also, the individual stress–strain curves were calculated through reverse engineering of the loading curve. A commercial finite element software (ABAQUS) was used to perform numerical simulations comprising axisymmetric elements representing the Al and Cu foil current collectors. Micro-tensile tests were also carried out on these foils. Agreement was obtained between the outcomes of the micro-tensile and the results of the reverse engineering of the indentation tests. A micro-structure analysis was also performed to give an insight into the structure of the battery components which is necessary for small scale mechanical characterization. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Indentation Lithium-ion battery Film Elastic modulus Constitutive law

1. Introduction Energy in the form of electricity can be generated from different renewable sources, such as wind and solar, which have a high potential to meet the growing demand with low emission. The utilization of the generated electricity from these sources requires efficient electrical energy storage and batteries are one of the most appropriate storage system. A rechargeable Lithium-ion battery consists of two electrodes separated by an electrolyte for ionic conduction. Energy conversion in the lithium-ion (Li-ion) batteries takes place via reversible intercalation/de-intercalation processes of the lithium ions between the electrodes. This kind of battery has become more popular with the growing use of mobile devices and its popularity has been further augmented due to its increasing usage in hybrid electric vehicles. However, three safety issues have an impact on the use of Li-ion batteries: the electrical, thermal and mechanical integrity. The aim of the present paper is to investigate the mechanical properties of the components, thus addressing the third issue. E-mail address: [email protected] (S. Amiri). http://dx.doi.org/10.1016/j.ijmecsci.2015.10.019 0020-7403/& 2015 Elsevier Ltd. All rights reserved.

A Li-ion battery cylindrical cell is composed of layers of electrodes made of coated aluminium and copper foils and a separator, a polymeric component, which is rolled or stacked inside the casing. The coated foils are about 0.1–0.2 mm thick and the uncoated foils (current collectors) have a thickness of 10–13 μm. The number of layers in the battery cells depends on the application. Generally, when an electrical current is applied to the Li-ion battery in a charging process, lithium ions moves out of the cathode (LiCoO2) and become trapped inside the anode storage medium which is usually graphite. Conversely, during a battery discharge process, the lithium ions travel back to the cathode and produce an electrical current. The understanding of the mechanical integrity requires a deep insight into the mechanical behaviour of Li-ion battery cells. Different possible scenarios have already been investigated and published in the literature. Sahraei et al. [1] performed tests on pouched and bare lithium-ion cells under five loading conditions such as through-thickness compression, inplane unconfined compression, in-plane confined compression, hemispherical punch indentation and three-point bending. The individual compression stress–strain curves were calculated from the measured load–displacement data for the active anode

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and cathode materials. In another study Sahraei et al. [2] proposed a simple model of a single cell. This model was developed for the safety assessment of batteries under mechanical abuse conditions. They performed various tests on a 18,650 lithiumion cell such as indentation by a hemispherical punch, lateral indentation by a cylindrical rod, compression between two flat plates, and three-point bending. However, further studies in the literature focus more on the behaviour of the battery cell as an assembly while the individual mechanical behaviour of the lithium-ion battery components needs more attention. An indentation test, as an advanced version of a conventional hardness test, is widely used in different structural applications and in various engineering research fields such as automotive and aerospace industries. Since indentation tests can be implemented in a relatively non-destructive manner and provide an array of information about the material under investigation, several studies have been performed to evaluate the behaviour of the materials by this technique. Indentation tests further require a low amount of sample preparation and many research efforts have thus been undertaken to probe the elastic and plastic properties of bulk material with this technique [3–7]. However, when a multilayer structure is under evaluation, the problem is more complex than for a bulk material because the substrate can influence the indentation load–displacement curve. Its effect depends on several factors: hardness, elastic modulus, and the yield stress of both film and substrate. Different scenarios have already studied such as a film on an elastic or elastoplastic substrate [8–10]. Moreover, several studies measuring the fracture toughness of brittle [11] and of ductile materials [12] have been performed due to its application potential in macro to nanoscales. In this work we present an indentation approach to individually characterize both coated and uncoated copper current collectors as well as uncoated aluminium current collectors in the Liion battery. Specifically, we have studied the mechanical properties of copper and aluminium films on the fused silica substrate. The aluminium/fused silica layered structure is almost elastically homogeneous whereas the copper/fused silica configuration is not. The effect of this elastic modulus mismatch on the indentation properties is taken into account by using Gao's theory. Reverse engineering is adopted through an extensive finite element analysis to define the plasticity of the current collectors. A data comparison in order to validate the novel indentation approach was enabled by conducting micro-tensile experiments on these uncoated films. Furthermore the elastic properties of the anode have been investigated in the cases in which the material of the deposited coating is graphite.

2. Theoretical background 2.1. Indentation on the bulk material Indentation is a non-destructive method used to investigate the mechanical behaviour of a bulk material. Oliver and Pharr [13] have shown that the elastic modulus of the material can be obtained by analysing the unloading part of a load–displacement curve. The reduced modulus, En , has been determined from the measurement of the contact area, Ac, and the compliance term of the specimen which corresponds to the inverse of the unloading slope calculated at the maximum indentation depth, i.e. C ¼ ðdh=dPÞh ¼ hmax , as follows: En ¼

pffiffiffiffi π pffiffiffiffiffi  2βα Ac C  C f

ð1Þ

The projected contact area (Ac) between the indenter and the material is a function of the contact depth hc and this parameter, which has to be carefully calculated, is discussed in detail. Cf is the frame compliance of the instrument. β is a correction factor that depends on the indenter shape, where β ¼ 1 for axisymmetric indenters and β ¼1.034 for a Berkovich indenter [14]. Considering the fundamental concept of contact mechanics, when two objects (i,ii) are in contact, the indenter and the sample in the indentation test, the relation between the reduced modulus (En ) of contact and the elastic modulus of two the objects (Ei, Eii) can be expressed as follows:  1 1  ν2i 1  ν2ii þ ð2Þ En ¼ Ei Eii where νi and νii are the Poisson's ratios of the two objects which are in contact [15]. Generally, in the indentation experiment, deflection of the load frame affects the evaluated reaction force and can be registered by the depth sensor. Therefore, an error proportional to the load is introduced to the displacement reading and the measurement of the instrument compliance is necessary to minimise this error. This correction results in a shift of the indentation load–displacement curve to the left. The compliance of a nanoindenter can be measured by a series of tests at increasing loads on a standard specimen. Moreover, in order to evaluate the contact area (Ac) and consequently the contact stiffness (S), the geometry of the Berkovich indenter is assumed to be ideal. However, in practice such a perfect indenter can't be manufactured and instead of a perfectly sharp tip, the indenter has a radius. Therefore, for a given contact area, hc, the actual area is higher than the one based on the perfect sharp tip. The correction factor, α, is usually obtained through a series of tests on a specimen with a known hardness and a Young's modulus. Area correction can be the most important factor and has a significant effect on the accuracy of the results. However, it becomes progressively less important as the indentation depth increases. In addition, the deformation mode around the indentation is an important factor in the indentation test which affects the calculation of the contact area between the indenter and the sample. In the presence of sinking-in, the Oliver–Pharr method [13] is wellknown and widely used where the contact depth (hc) is calculated from the maximum depth (hm), the compliance of the indentation instrument (C) and the maximum applied load (Pm): hc ¼ hm  ϵCP m

ð3Þ

where ϵ is a factor which depends of the shape of the indenter. For a flat punch indenter, ϵ equals 1 whereas for spherical and a conical indenter ϵ is equal to 0.75 and 0.72 respectively [13]. In practice, this factor varies between 0.72 and 0.78 due to geometrical imperfections of indenter. In this study, the constant value of 0.75 is used [13]. In the case of a piling-up deformation mode around the indentation the Oliver–Pharr method is not applicable since it underestimates the contact area; therefore Bec et al. [16] have introduced another approach to calculate the contact depth in this mode as follows: hc ¼ αðhm  CP m Þ where

ð4Þ

α equals 1.2.

2.2. Indentation on the film The evaluating of the mechanical properties of the films in a multi-layer structure presents particular challenges. When using instrumented indentation tests the main difficulty in the

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Fig. 2. Morphology of the aluminum film.

where, for a Berkovich indenter, ξ equals to (t=½h tan Ψ ). Ψ is the effective semi-angle of an equivalent conical indenter (70.3°) and t is the film thickness.

3. Experimental analysis 3.1. Micro-structure analysis

Fig. 1. Morphology of the copper film: (a) optical microscope image before polishing and (b) SEM image after the polishing and etching process.

characterization of the mechanical behaviour of the films on the substrate arises in the determination to what extent the substrate and the film separately contribute to the measured properties. A key parameter in indentation tests on a multi-layer structure is the critical depth. For a hard film on a soft substrate Cleymand et al. [17] have shown that if the critical depth exceeds 1–2% of the film thickness, the response of the structure is not the intrinsic response of the film. However, for the soft film on the hard substrate configuration this critical normalized indentation depth is different. Xu and Rowcliffe [18] have studied this configuration and have shown that above 20% of the film thickness, the substrate affects the indentation load–displacement curve. Gao et al. [19] have developed a model for indentation as a function of the indenter displacement (h) and the film thickness (t), to express the relative variation of the composite reduced elastic modulus compared to that of the film and of the substrate. In this model, see Eq. (5), depending on the indentation depth, the structure may either behaves globally like the film or in contrast more like the substrate. After a certain fraction of the normalized indentation depth (the indentation depth to the film thickness ratio) that depends upon the properties of the materials of the layers, the composite reduced elastic modulus, Enc , changes gradually from the film reduced modulus, Enf , to the substrate reduced modulus, Ens .  n  E  E n  c s  ϕ ¼  n n  ð5Þ E f  E s  The empirical weight parameter, ϕ, is considered in this model by Gao et al. [19] and expressed as " ! # 2 2 1 1þξ ξ ϕ ¼ arctan ξ þ ð1  2νÞξ ln  ð6Þ 2 2π ð1  ν Þ π ξ2 1þξ

For the micro-structure analysis, Al6061-T6 substrates have been used and the metallic films (Al and Cu) have been mounted on top of them. The samples were carefully polished without any grinding on a 6 μm polishing pad and were finished with a 1 μm pad, with interspersed ultrasonic cleaning after each polishing step. However, neither the anode (graphite) nor the cathode (LiCoO2) was polished prior to the micro-structure analysis due to the softness of the material which can change their properties upon polishing. Non-etched samples of polished metallic films can show possible cracks, pits, etc. but no microstructural details such as grains can be observed because of the lack of contrast-producing features on the surface. The copper film has been chemically etched for 10 s employing 50 ml HNO3 and 50 ml H2 O as etchant. However, the aluminium film has been electro chemically etched to generate a sufficient contrast by applying 20 for 10 s on the surface employing the Barker's reagent (5 ml HBF4, 200 ml H2 O) as an etchant. Scanning electron microscopes (SEM) and optical microscopes have been used to gain a better understanding of the microstructure of the Li-ion battery components. Micro-graphs of the anode, the cathode and the current collectors are shown in Figs. 1–4. The optical microscopic analysis in Fig. 1a shows the morphology of the copper film before polishing and the SEM image after the etching process in Fig. 1b shows visible grains of an approximate average size is 1 μm. The optical microscopic analysis of the morphology of the aluminium film before polishing is shown in Fig. 2. However the process is not straightforward: due to the small thickness of the aluminium film, the polishing and etching procedures were very difficult and may lead to an excessive removal of material thus altering the SEM analysis results. Regarding the coatings of the current collectors, Fig. 3 shows the morphology of the anode with a random distribution of the graphite particles which are attached to each other during the manufacturing process by using binders. These particles do not have a regular shape and the approximate diameter varies from 5 to 25 μm (see Fig. 3b). However, the SEM images in Fig. 4 show the co-existence of different chemical compositions in the microstructure of the LiCoO2 (cathode) coating. These chemical compositions (see regions A and B in Fig. 4) are summarized in Table 1

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Fig. 4. Morphology of the cathode (LiCoO2).

Table 1 Chemical composition of the cathode (LiCoO2). Material name

Weight % C

Weight % O

Weight % Co

Region A Region B

54.66 9.99

18.52 24.57

26.82 65.44

Table 2 Mico-tensile specimen configuration.

Fig. 3. Morphology of the anode with a random distribution of the graphite particles.

Material name

Length (mm)

Width (mm)

Thickness (mm)

Aluminium film Copper film

50 50

10 10

0.0125 0.0106

in which, the element lithium is not considered since generally undetectable in an SEM analysis.

resulting in breaking of the specimen. The experimental set up for the copper film is shown in Fig. 5b.

3.2. Micro-tensile test

3.3. Indentation test

Due to the small thickness of the aluminum and the copper films, the micro-tensile test samples have been carefully prepared to avoid damage to the sample. The films used as micro-tensile specimens are cut into rectangles and the thickness of each film is evaluated as an average value. The dimensions of the specimens are shown in Table 2. A MICROTEST 2000 tensile stage with standard horizontal grips was used to carry out the experiment and to observe plastic behaviour and fracture of the current collectors of the battery cell. During the experiment on the aluminium film, no crack propagation process has been observed and the film breaks suddenly, as shown in Fig. 5a. However, the copper film begins to wrinkle and a micro crack is generated at one side of the specimen. Subsequently the crack propagates to the other side of the film

Indentations have been performed using an indentation system (UMIS-2000, CSIRO, Australia). In the experimental procedure a pyramidal-triangular shaped Berkovich indenter has been used. The samples have been constrained by a clamp on a fused silica support (see Fig. 6a). Because of the effect of the micro-structure on the indentation load–displacement curve, 3  3 matrices are defined on the surface to account for any variation in the obtained curve (see Fig. 6b). For the metallic films (Cu and Al), a variation of less than 10% which depends upon the location of the indentation relative to the grains has been observed. For instance, the material is harder near the grain boundaries than in the centre of the grain. To overcome this variation in indentation several indentation matrices were randomly positioned on the surface of the film under the same experimental conditions. The tests have been

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Fig. 5. Aluminium film (a) and copper film (b) specimens under a micro-tensile test.

Fig. 7. Finite element model during the loading on the copper/fused silica structure.

4. Finite element analysis

Fig. 6. (a) Indentation experiment set-up. (b) The 3  3 matrix on which the indentation tests are performed.

performed under load control keeping the load at maximum for 15 s. All the indentation tests are carried out sufficiently slowly to avoid any dynamic effects. All of the tests have been performed under ambient conditions to avoid any noise during the test that could have minor effects on the results.

The plastic behaviour of the current collectors has been evaluated in this work adopting a reverse engineering method that uses finite element analysis. A series of numerical simulations have been performed and the experimental and numerical indentation load–displacement curves have been compared. An extensive trial and error procedure has been followed to attain the material parameter set that fits the experimental data best. The finite element analysis of the indentation experiment has been carried out using the commercial finite element solver ABAQUS STANDARD (version 6.11). An axisymmetric model, with

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Fig. 8. Effect of the FEM model mesh density on the indentation applied load.

over 15,000 and 8000 four-node axisymmetric elements for the film and substrate respectively, has been constructed to simulate the semi-infinite film/substrate system (Fig. 7). The indenter, made of diamond and considerably stiffer than the target materials, is approximated as a perfectly rigid part. A conical surface with a half apex angle of 70.3° is used to model the widely used Berkovich indenter [20]. The Coulomb's friction law, with a coefficient of 0.15, which has a minor effect on the indentation [4] is used. Regarding the plastic behaviour of the film, the stress–strain σ– ϵ curve of a stress-free film can be expressed by a power law form as following:

σ ¼ Ef ϵ for ϵ r σ yf =Ef

and

σ ¼ Rf ϵnf

for ϵ Z σ yf =Ef

ð7Þ

where Ef is the film elastic modulus and σyf is the film yield stress;  n nf is the work hardening exponent and Rf ¼ σ yf Ef σ yf f is the work hardening rate of the film. In this constitutive law, when nf is zero, Eq. (7) represents the behaviour of the material as elasticperfectly plastic. The parameter set, (Ef, σyf and nf), characterizes the mechanical behaviour of the metallic film on the substrate. In general, the power law elastic–plastic relationship is suitable for metals and alloys with nf varying between 0.0 and 0.5. A fine mesh near the contact regions and a gradually coarser mesh further away from these areas has been adopted to achieve an accurate analysis in a reasonable time. An average size for the mesh elements in the contact region is 50  50 nm2. The minimum number of elements used in the contact area between the indenter and the film is not less than 80 at the maximum applied load. In this study, both film and substrate are assumed to be isotropic. A convergence analysis has been performed to evaluate the mesh sensitivity. For the analysis of the mesh effect, an indentation with a rigid conical indenter, with a half apex angle of 70.3°, on a semi infinite bulk material is considered. The axisymmetric model is adopted with a maximum depth, h, of 1.5 μm. The density of a reference mesh is defined as 1 where the dimension of the minimum element is 50  50 nm2. The mesh density is ρ if its element size is 1/ρ times the defined reference mesh. The mesh is finer than the reference if ρ 4 1 and coarser if ρ o1. To better understand the mesh effect in finite element analyses, different mesh densities have been studied which vary from 0.25 to 2. Fig. 8 shows that the applied indentation force converges to a value with an increasing mesh density. A mesh density that is at least larger than 1 is recommended for a highly accurate analysis.

Fig. 9. Compound elastic modulus as a function of a normalized indentation depth for the copper/fused silica configuration.

5. Results and discussion 5.1. Evaluation of the elasticity As discussed in the indentation tests, the deformation mode around the indentation clearly influences the results and the selection of the methodology is a very important criteria. In fact, the methodologies of Oliver–Pharr [13] and Bec et al. [16] are wellknown for the analysis of sinking-in and piling-up phenomenon respectively. These two methodologies calculate the contact area of the indenter in different ways. In the copper/fused silica configuration, in which the elastic modulus of the copper film is expected to be 1.5–2 times higher than the elastic modulus of the fused silica substrate, the presence of the sinking-in phenomenon is feasible and the Oliver–Pharr method is applied to calculate the contact area in the presence of the discontinuity in the elastic modulus through the structure. Fig. 9 presents the evolution of the compound elastic modulus versus a normalized indentation depth (the ratio of the indentation displacement and the film thickness) for the copper/fused silica configuration. The compound elastic modulus varies continuously as a function of the normalized indentation depth. This trend shows that if the indentation depth exceeds 30% of the film thickness, the elastic modulus of the fused silica substrate becomes dominant. On the other hand, if very shallow indentation depths are considered by using a high-end commercial nanoindenter to ignore the substrate effect, many experimental issues arise from measurements at such a small scale. One of these issues is the surface roughness of the film which renders the determination of the contact area very difficult. This difficulty is further augmented by the shape of the commercial indenter tip, which is blunt at the nanoscale. These observations necessitate the consideration of the Gao's model [19] to calculate the contribution of the substrate effect on the obtained indentation data. Therefore, the weight parameter ϕ, usually called the Gao's function, of this model is evaluated using Eq. (6) on the complete range of the indentation data. Theoretically, the elastic modulus of the substrate is determined when ϕ is null, whereas that of the film is obtained when this parameter equals 1 where no fitting parameter has been introduced into the weight function. Fig. 10 shows the variation of the compound elastic modulus as a function of ϕ. The knowledge of the elastic modulus of the substrate and of the compound modulus of the copper/fused silica film configuration through the film thickness enables the calculation of the intrinsic elastic modulus of the copper film. Fig. 11 shows the calculated intrinsic elastic modulus

S. Amiri et al. / International Journal of Mechanical Sciences 105 (2016) 1–10

Fig. 10. Compound elastic modulus as a function of ϕ for the copper/fused silica configuration.

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Fig. 13. Elastic modulus of the aluminium film as a function of a normalized indentation depth.

Table 3 Evaluated reduced and intrinsic elastic modulus of the components of a lithium-ion battery.

Copper film Aluminium film Anode (graphite)

Fig. 11. Intrinsic elastic modulus of the copper film as a function of a normalized indentation depth.

Fig. 12. Reduced elastic modulus of the aluminium film as a function of a normalized indentation depth.

of the copper film as a function of the normalized indentation depth. The average value obtained for this modulus is 108 GPa. For the aluminium/fused silica configuration the expected elastic modulus of both materials is very similar and the discontinuity in the elastic modulus is insignificant. Therefore, both methodologies are applied to analytically determine the calculation mode of contact area by comparing the value of the elastic

En ðGPaÞ

E ðGPaÞ

Variable 72 1.4

108 68 1.3

modulus with the value in the literature [21], which is 70.1 GPa. Using Eqs. (1) and (2), Figs. 12 and 13 illustrate the reduced and intrinsic elastic modulus of the aluminium film respectively. Fig. 13 shows that the Oliver–Pharr methodology [13] is more appropriate to represent the intrinsic elastic modulus of the aluminium film providing a value that is close to 70.1 GPa, whereas considering the Bec et al. [16] methodology a value of approximately 56 GPa is obtained. The average value obtained for the intrinsic modulus of the aluminium film is 68 GPa. Therefore, the Oliver–Pharr methodology is considered in the following for the aluminium/fused silica configuration to calculate the contact area between the indenter and the aluminium film. Moreover, the anode (graphite) has been considered as a bulk material since the thickness has a large value (90 μm) and is therefore considered as a semi-infinite sample. Since graphite is brittle, sinking-in is the feasible deformation mode around the indentation. Using Eqs. (1) and (2), the reduced and intrinsic elastic moduli are calculated as 1.4 and 1.3 GPa respectively. To conclude, indentation can be employed to determine the elastic modulus of the lithium-ion battery components. However, such analyses necessitate the knowledge of the modulus of the substrate as well as the deformation mode around the indentation, such as sinking-in and piling-up, which is an important phenomenon to take into account. The evaluated elastic moduli of the studied materials in the lithium-ion batteries are summarized in the Table 3. 5.2. Evaluation of the constitutive model The use of a fused silica substrate in the experiments to constrain the components of the lithium-ion battery, firstly requires the perfect understanding of its behaviour and its application to the finite element model. Since the fused silica substrate is brittle and the indentation through the film is not high enough to generate fracture in the substrate, an evaluation of the elastic modulus of the substrate is sufficient to simulate its deformation. Therefore some indentation tests have been performed on the bulk fused

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Fig. 14. Berkovich indent on the surface of the cathode (LiCoO2 ).

Fig. 16. Numerical analysis of indentation for the copper film.

Fig. 15. Experimental indentation load–displacement curve for the copper and aluminium films.

silica substrate and the elastic modulus of 72.5 GPa obtained by the Oliver–Pharr method [13]. The comparison of this value with published data [22] shows good agreement. However, for the current collectors (Cu and Al films), an elastoplastic behaviour is assumed in the finite element analysis in which a work hardening process takes place once the yield stress has been reached. Regarding the elasticity of the metallic films, the values of elastic modulus have been taken from previous extensive analysis (Section 5.1). The plastic behaviour of the films is defined by a power law constitutive model (Eq. 7) and this section is aimed at the determination of the corresponding parameters which can express their flow stress. Moreover, in this section neither the anode (graphite) nor the cathode (LiCoO2) have been analysed since they have very brittle behaviour and no effective work hardening process takes place during the indentation. For instance, in Fig. 14 a Berkovich indentation is shown in which local fracture occurred during the indentation test and the irregular shape of the indent demonstrates the lacking hardening process. To determine the constitutive model parameters for the uncoated films, a series of numerical simulations have been performed in which the experimental and calculated load–displacement curves have been compared. An extensive trial–error procedure has been followed in order to obtain the material parameter set that gives the best fit to the experimental indentation data. Fig. 15 shows the experimental load–displacement results from the loading process of the tests. The most accurate mathematical formulation which can express the experimental relation 2 between the applied load versus the indentation depth is P ¼ ah where a depends on the material. In Fig. 15, a significant difference

Fig. 17. Numerical analysis of the indentation for the aluminium film.

between the copper and aluminium films can be observed as the plasticity takes place at very low applied loads. The corresponding a value for the copper and aluminium films are 24.1 and 12:9 mN =μm2 respectively. Fig. 16 has been obtained from numerical simulations in which a range of material parameters for the copper film have been tested in an attempt to reproduce the experimental indentation load–displacement curve (in particular, the corresponding a value). The film yield stress (σyf) and the work hardening exponent (n) were varied in the ranges 0–500 MPa and 0.0–0.5 respectively to cover most metals. The finite element analysis shows that the set of film material parameters which gives a good fit to the experimental data are 170 MPa and 0.11 for the film yield stress and the work hardening component respectively. Similarly, Fig. 17 shows the optimization approach considered for the aluminium film and the obtained values of 50 MPa and 0.30 for yield stress and work hardening component respectively. Additionally to the indentation experiments, micro-tensile tests have been performed in this work to independently verify the results obtained. Micro-tensile tests have been performed on both current collectors (copper and aluminium films) and the values obtained were 210 MPa, 0.1 for copper and 58 MPa, 0.35 for aluminium which represent the yield and the work hardening components respectively. These values were directly obtained from the experiments without considering any optimization procedure.

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Table 4 Comparisons between the material properties from the indentation test and the micro-tensile experiment. Film materials

Copper film Aluminium film

Indentation

Micro-tensile

Difference (%)

σ yf ðMPaÞ

nf

σ yf ðMPaÞ

nf

ϵp;cr

σyf

nf

170 50

0.11 0.30

210 58

0.10 0.35

0.103 0.027

 19  13.8

þ 10  14.3

Fig. 18. Comparison aluminium films.

of

obtained

stress–strain

curves

for

copper

and

Table 4 shows the obtained values from the two experimental approaches; indentation and micro-tensile. Also, the trend of the represented stress–plastic strain for all the cases is illustrated in Fig. 18. Although some difference seems to arise between the results of the indentation and micro-tensile tests nevertheless the comparison is very promising. As already explained, micro-tensile tests on thin films are very complex to perform (Fig. 5) and the results are affected by some factors that may increase the spread of the data. For instance, the thickness of each film is an average, the handling of the specimens is very tough and the micro-tensile test on the copper film shows the creation of wrinkles and micro cracks. Therefore a deviation between the obtained results of these two test approaches is possible. The difficulties in performing the micro-tensile tests and the need to gather consistent mechanical behaviour of the materials of the thin films were the most important motivations of the present investigation in the indentation technique.

6. Conclusion The main aim of the present research has been to individually determine the mechanical properties of the lithium-ion battery components. An indentation analysis which measures their elastic–plastic properties has been presented. To perform these tests the use of a substrate is essential for the support of the samples. Therefore, the effect of the substrate has been taken into consideration during the analysis. In this study, indentation tests with a depth between 8% and 20% of the film thickness were carried out to obtain the indentation parameters. The main contributions obtained are summarized as follows: (i) The elastic modulus of the Li-ion battery components can be evaluated by analysing the indentation results and in some cases the effect of substrate has a significant influence on the final results. Furthermore, since piling-up and sinking-in phenomena

9

can affect the final results significantly, careful attention must be paid to the deformation mode. (ii) For the plastic behaviour of the current collectors, an optimization approach has been followed to obtain representative stress–strain curves for each of them. The effectiveness of this reverse analysis method, which is obtained in an extensive procedure involving numerical analysis and indentation experiments, has been verified by a comparison with the results from microtensile analysis. The stress–strain curves for both metallic films obtained from the reverse analysis are in reasonable agreement with the results from the micro-tensile test. (iii) The approach discussed in this paper is potentially useful for measuring of the elastic–plastic properties of a film on a known elastic substrate where experimental difficulties could hinder the performance of an indentation test on the film. However the phenomena of sinking-in and piling-up need to be taken into account. Finally, indentation is a very promising technique that can be used not only for the investigation of the mechanical behaviour of the battery but also for other structures that are unfeasible to investigate by standard approaches. Moreover, the availability of numerical tools and fast processing may allow efficient optimization procedures. Several other topics can be therefor investigated. For instance, the authors believe that the mechanical behaviour of materials related to the fracture and the anisotropy properties can be explored by means of this methods although their complexity makes these investigations very challenging.

Acknowledgements The authors would like to acknowledge Prof. Tomasz Wierzbicki, the director of the Impact and Crashworthiness Laboratory at MIT, for having inspired this challenging investigation in the mechanical behaviour of the multi-layered structure of lithium-ion batteries. Moreover the authors would also like to acknowledge Prof. Tomasz Wierzbicki for the supply of the lithium-ion battery components used in this work.

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