# 1 experimental and numerical evaluation of residual mechanical performance of carbon/epoxy laminated coupons after integration of solid battery cells for aeronautical applications

Frédéric Laurin, Anne Mavel, Florence Saffar, Alexander Beutl, Helmut Kühnelt

<figure><img src="image_1.png" /></figure>

## To cite this version:

Frédéric Laurin, Anne Mavel, Florence Saffar, Alexander Beutl, Helmut Kühnelt. 1 experimental and numerical evaluation of residual mechanical performance of carbon/epoxy laminated coupons after integration of solid battery cells for aeronautical applications. Composites Science and Technology, 2023, 247, pp.110384. 10.1016/j.compscitech.2023.110384. hal-04571136

HAL Id: hal-04571136

https://hal.science/hal-04571136

Submitted on 7 May 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Experimental and numerical evaluation of residual mechanical performance of carbon/epoxy laminated coupons after integration of solid battery cells for aeronautical applications

Frédéric Laurin,\*a, Anne Mavel\ª, Florence Saffar\ª, Alexander Beutl\ᵇ, Helmut Kühnelt\ᵇ

## Abstract

The present study deals with a numerical and experimental evaluation of the residual mechanical performance of a quasi-isotropic carbon/epoxy laminated composite plate in which solid battery cells have been integrated. Firstly, the mechanical properties of the multifunctional Reinforced Multilayer Stack (RMS) battery cells have been determined thanks to dedicated multi-instrumented tests, while those of the AS4/8552 composite material have been extracted from the literature and validated by comparisons with tensile tests on plates without battery, considered as a reference case. Then, on the basis of the recommendations obtained from a virtual test campaign using FE simulations, a 16-ply laminated composite plate containing 6 solid battery cells was manufactured with a modified curing cycle that preserves the electrical properties of the batteries while ensuring the mechanical properties of the composite material. Various control methods, such as CT-scan and optical analysis, were used to demonstrate the promising quality of the manufactured composite coupon with embedded cells. Finally, a mechanical tensile test was carried out to experimentally determine the reduction in mechanical properties. The analysis of such a test with non-linear FE simulation has allowed a better understanding of the damage and failure process when solid battery cells are integrated into high performance laminated composite structures designed for the aeronautical industry.

**Keywords:** A. Multifunctional composites, B. Mechanical properties behaviour, B. Multifunctional properties, C. Multi-mechanism modelling, D. X-ray computed tomography

<footnote>\ª ONERA, Paris-Saclay University, Châtillon, France</footnote>

<footnote>\ᵇ AIT Austrian Institute of Technology GmbH, Vienna, Austria</footnote>

<footnote>\* Corresponding author. Email address: frederic.laurin@onera.fr (F. Laurin).</footnote>
# Experimental and numerical evaluation of residual mechanical performance of carbon/epoxy laminated coupons after integration of solid battery cells for aeronautical applications

Frédéric Laurin,\*a, Anne Mavel\*a, Florence Saffar\*a, Alexander Beutl\*b, Helmut Kühnelt\*b

## Abstract

The present study deals with a numerical and experimental evaluation of the residual mechanical performance of a quasi-isotropic carbon/epoxy laminated composite plate in which solid battery cells have been integrated. Firstly, the mechanical properties of the multifunctional Reinforced Multilayer Stack (RMS) battery cells have been determined thanks to dedicated multi-instrumented tests, while those of the AS4/8552 composite material have been extracted from the literature and validated by comparisons with tensile tests on plates without battery, considered as a reference case. Then, on the basis of the recommendations obtained from a virtual test campaign using FE simulations, a 16-ply laminated composite plate containing 6 solid battery cells was manufactured with a modified curing cycle that preserves the electrical properties of the batteries while ensuring the mechanical properties of the composite material. Various control methods, such as CT-scan and optical analysis, were used to demonstrate the promising quality of the manufactured composite coupon with embedded cells. Finally, a mechanical tensile test was carried out to experimentally determine the reduction in mechanical properties. The analysis of such a test with non-linear FE simulation has allowed a better understanding of the damage and failure process when solid battery cells are integrated into high performance laminated composite structures designed for the aeronautical industry.

**Keywords:** A. Multifunctional composites, B. Mechanical properties behaviour, B. Multifunctional properties, C. Multi-mechanism modelling, D. X-ray computed tomography

<footnote>\*a ONERA, Paris-Saclay University, Châtillon, France</footnote>

<footnote>\*b AIT Austrian Institute of Technology GmbH, Vienna, Austria</footnote>

<footnote>\* Corresponding author. Email address: frederic.laurin@onera.fr (F. Laurin).</footnote>
# 1. Introduction

Electrification of aircraft systems is key for increasing efficiency and reducing the climate impact of air transport towards the European net-zero goal [1]. The functional integration of structural capabilities and electrical energy storage in the form of structural batteries (SB) is considered as a low TRL technology with the potential to reduce the impact of battery energy storage on the overall aircraft weight. So far, structural batteries have mainly been studied at the material level [2–4]. The influence of the integration of solid battery cells in composites on their mechanical properties, mainly stiffness and strength, has been studied experimentally through tensile [5,6], compression [6,7] or flexural [6,8–10] tests on composite materials designed mainly for the automotive industry, with intermediate mechanical properties associated with a low temperature curing cycle. Therefore, the CleanSky2 THT project SOLIFLY is developing further structural batteries for aeronautical applications, with particular emphasis on their integration into Composite Fibre Reinforced Plastic (CFRP) laminates that are compatible with aeronautical manufacturing processes associated with high performance composite laminates.

The present paper deals with a detailed analysis of multi-instrumented tests carried out on high performance laminated composite coupons with embedded solid battery cells, associated with non-linear finite element simulations, in order to determine the decrease of some classical mechanical properties (stiffness, damage initiation, final failure), but also to determine the modifications due to the integration of solid battery cells in the damage and failure process of composite parts.

Firstly, the mechanical characterization of (i) one of the two solid battery cell concepts developed in the SOLIFLY project and of (ii) the composite material is presented in section 2. Then, in section 3, based on numerical simulations, the curing cycle of the studied high-performance composite material has been modified, in order to avoid degradation of the electrical performance of the battery cells, while ensuring high mechanical properties of the composite material. Finally, a composite plate with battery cells was numerically designed (section 4.1), manufactured (section 4.2) and mechanically tested (section 4.3) to evaluate its residual mechanical performance in the presence of battery cells and compare it with the predictions of the proposed FE model.
# 1. Introduction

Electrification of aircraft systems is key for increasing efficiency and reducing the climate impact of air transport towards the European net-zero goal [1]. The functional integration of structural capabilities and electrical energy storage in the form of structural batteries (SB) is considered as a low TRL technology with the potential to reduce the impact of battery energy storage on the overall aircraft weight. So far, structural batteries have mainly been studied at the material level [2–4]. The influence of the integration of solid battery cells in composites on their mechanical properties, mainly stiffness and strength, has been studied experimentally through tensile [5,6], compression [6,7] or flexural [6,8–10] tests on composite materials designed mainly for the automotive industry, with intermediate mechanical properties associated with a low temperature curing cycle. Therefore, the CleanSky2 THT project SOLIFLY is developing further structural batteries for aeronautical applications, with particular emphasis on their integration into Composite Fibre Reinforced Plastic (CFRP) laminates that are compatible with aeronautical manufacturing processes associated with high performance composite laminates.

The present paper deals with a detailed analysis of multi-instrumented tests carried out on high performance laminated composite coupons with embedded solid battery cells, associated with non-linear finite element simulations, in order to determine the decrease of some classical mechanical properties (stiffness, damage initiation, final failure), but also to determine the modifications due to the integration of solid battery cells in the damage and failure process of composite parts.

Firstly, the mechanical characterization of (i) one of the two solid battery cell concepts developed in the SOLIFLY project and of (ii) the composite material is presented in section 2. Then, in section 3, based on numerical simulations, the curing cycle of the studied high-performance composite material has been modified, in order to avoid degradation of the electrical performance of the battery cells, while ensuring high mechanical properties of the composite material. Finally, a composite plate with battery cells was numerically designed (section 4.1), manufactured (section 4.2) and mechanically tested (section 4.3) to evaluate its residual mechanical performance in the presence of battery cells and compare it with the predictions of the proposed FE model.
## 2. Mechanical characterization of battery cells and composite material

### 2.1 Solid battery cells

The SOLIFLY project focuses on the development of structural batteries using two different concepts, the innovative multifunctional Coated Carbon Fibres (CCF) material and the multifunctional Reinforced Multilayer Stack (RMS) [11]. Both concepts used the same semi solid-state Li-ion battery formulation, NMC|gel electrolyte|Si/graphite. In this article, only the RMS concept, developed by AIT, is considered to illustrate the proposed methodology for integrating battery cells into laminated composite structures.

The various components of an RMS cell are briefly described below. After an extensive experimental campaign to optimize the electrolyte for the RMS approach, a promising formulation was developed. The obtained gel is based on an ionic liquid electrolyte, i.e. 3M LiFSI in PYR₁₃FSI, which is combined with a gelling agent, i.e. PVdF-HFP. The mechanical stability of this electrolyte is further improved by the addition of an inorganic filler material, i.e. SiO₂, which reduces the ionic conductivity, while improving the mechanical properties. NMC811 was selected as the cathode material. In contrast to the conventional battery systems, solid or semi-solid electrolytes have to be added during the electrode preparation process to form so-called composite electrodes. The gel electrolyte without the SiO₂ filler was added to the cathode composition before casting of the electrode. The development of a suitable anode for the envisaged structural battery cell is quite challenging and work is still in progress. Graphite is being used as a more stable alternative to the Si/C composite. A similar approach to the cathode development is being used and composite anodes are being prepared by adding the gel electrolyte to the electrode composition.

Regarding the cell geometry, a schematic outline of the intended cell geometry for the RMS approach is shown in Figure 1. The assembled single-electrode pair cells will have an overall thickness of approximately 210 µm, matching the ply thickness within acceptable limits (of approximately 10%). The electrolyte will be slightly larger than the electrodes to avoid shorting of the cell at the corners of the electrodes. A cross-sectional area of 100 x 70 mm² is targeted for industrial application. At the
## 2. Mechanical characterization of battery cells and composite material

### 2.1 Solid battery cells

The SOLIFLY project focuses on the development of structural batteries using two different concepts, the innovative multifunctional Coated Carbon Fibres (CCF) material and the multifunctional Reinforced Multilayer Stack (RMS) [11]. Both concepts used the same semi solid-state Li-ion battery formulation, NMC|gel electrolyte|Si/graphite. In this article, only the RMS concept, developed by AIT, is considered to illustrate the proposed methodology for integrating battery cells into laminated composite structures.

The various components of an RMS cell are briefly described below. After an extensive experimental campaign to optimize the electrolyte for the RMS approach, a promising formulation was developed. The obtained gel is based on an ionic liquid electrolyte, i.e. 3M LiFSI in PYR₁₃FSI, which is combined with a gelling agent, i.e. PVdF-HFP. The mechanical stability of this electrolyte is further improved by the addition of an inorganic filler material, i.e. SiO₂, which reduces the ionic conductivity, while improving the mechanical properties. NMC811 was selected as the cathode material. In contrast to the conventional battery systems, solid or semi-solid electrolytes have to be added during the electrode preparation process to form so-called composite electrodes. The gel electrolyte without the SiO₂ filler was added to the cathode composition before casting of the electrode. The development of a suitable anode for the envisaged structural battery cell is quite challenging and work is still in progress. Graphite is being used as a more stable alternative to the Si/C composite. A similar approach to the cathode development is being used and composite anodes are being prepared by adding the gel electrolyte to the electrode composition.

Regarding the cell geometry, a schematic outline of the intended cell geometry for the RMS approach is shown in Figure 1. The assembled single-electrode pair cells will have an overall thickness of approximately 210 µm, matching the ply thickness within acceptable limits (of approximately 10%). The electrolyte will be slightly larger than the electrodes to avoid shorting of the cell at the corners of the electrodes. A cross-sectional area of 100 x 70 mm² is targeted for industrial application. At the
current stage, the gravimetric energy density of the assembled RMS cells in coin cell format is
90 W.h/kg, while the volumetric energy density has been measured to be around 200 W h/l.

<figure><img src="image_1.png" /><figcaption>**Figure 1.** a) Image of an RMS battery cell (anode side) and b) details of the RMS cell architecture</figcaption></figure>

During the development process of the battery cells, AIT provided ONERA with dummy cells. These
battery cells are not effective from an electrical point of view, but their architecture is representative of
that of the effective cells with similar mechanical properties. It should be noted that the in-plane size of
the battery cells was modified to 150 mm x 20 mm x 0.21 mm in order to be tested at ONERA. Two
specimens were subjected to tensile tests on an electromechanical testing machine with a maximum
load capacity of 10 kN combined with a 1 kN load cell, due to the small thickness of the specimens.
These tests were multi-instrumented with (i) acoustic emission (using two nano30 sensors attached to
the jaws and analysed with the commercial software MISTRAS) to detect damage events during the
loading, (ii) digital images correlation (using a 12bit CCD camera with a resolution of 2160x4096 pixels
analysed with the commercial software Vic2D®) to measure the strain during the test and to detect any
crack, as shown in Figure 2a. A black and white speckle was applied to the cathode side of the
specimens. Longitudinal and transverse strains were measured using two virtual extensometers located
at the centre of the specimen with lengths of 25 mm and 12.5 mm respectively, as shown in Figure 2b.

The first specimen tested was subjected to tensile loading at a constant displacement rate of 0.5 mm/min until failure occurred in the area of interest and is associated with delamination between the Cu foil and the anode coating, followed by failure of the Cu foil. The failure stress is equal to 36.5 MPa. As can be
current stage, the gravimetric energy density of the assembled RMS cells in coin cell format is
90 W.h/kg, while the volumetric energy density has been measured to be around 200 W h/l.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** *a) Image of an RMS battery cell (anode side) and b) details of the RMS cell architecture*</figcaption></figure>

During the development process of the battery cells, AIT provided ONERA with dummy cells. These battery cells are not effective from an electrical point of view, but their architecture is representative of that of the effective cells with similar mechanical properties. It should be noted that the in-plane size of the battery cells was modified to 150 mm x 20 mm x 0.21 mm in order to be tested at ONERA. Two specimens were subjected to tensile tests on an electromechanical testing machine with a maximum load capacity of 10 kN combined with a 1 kN load cell, due to the small thickness of the specimens. These tests were multi-instrumented with (i) acoustic emission (using two nano30 sensors attached to the jaws and analysed with the commercial software MISTRAS) to detect damage events during the loading, (ii) digital images correlation (using a 12bit CCD camera with a resolution of 2160x4096 pixels analysed with the commercial software Vic2D®) to measure the strain during the test and to detect any crack, as shown in Figure 2a. A black and white speckle was applied to the cathode side of the specimens. Longitudinal and transverse strains were measured using two virtual extensometers located at the centre of the specimen with lengths of 25 mm and 12.5 mm respectively, as shown in Figure 2b.

The first specimen tested was subjected to tensile loading at a constant displacement rate of 0.5 mm/min until failure occurred in the area of interest and is associated with delamination between the Cu foil and the anode coating, followed by failure of the Cu foil. The failure stress is equal to 36.5 MPa. As can be
seen in Figure 2c, a highly non-linear behaviour is measured prior to the final failure while no acoustic
event was recorded prior to the first delamination. To determine the source of such a non-linearity, the
second specimen was loaded to 90% of the previous failure load and then unloaded to zero force. No
acoustic event was recorded during this test. A non-negligible permanent strain was observed after
unloading. In the following, it seems relevant to consider an RMS battery cell as a homogeneous
equivalent material with a plastic behaviour. The initial elastic Young's modulus of the two specimens
is very similar and is equal to E=11 700 MPa, which is the same as that measured during unloading of
the second specimen. The Poisson's ratio was measured at v=0.35 for the second sample only. The
onset of plasticity, estimated from the loss of linearity, was measured at R₀=14 MPa. The observed
variation in the behaviour is probably related to some initial defects. Optical analysis was carried out
on the free edges of the tested specimens prior to testing. Some small initial delamination cracks were
observed between the electrolyte and the anode, probably due to machining. These defects are located
in the part of the specimen clamped in the jaws of the test apparatus, thus limiting their potential effect
on the behaviour. It may be interesting in future work to carry out non-destructive controls, such as
C-scan, to better study the relationship between the initial defects and the variation in the tests.

<figure><img src="image_2.png" /><figcaption>**Figure 2.** a) Electromechanical testing machine, b) measured displacement field and associated virtual extensometers, c) stress/strain curves for the two tested RMS cell specimens.</figcaption></figure>
seen in Figure 2c, a highly non-linear behaviour is measured prior to the final failure while no acoustic
event was recorded prior to the first delamination. To determine the source of such a non-linearity, the
second specimen was loaded to 90% of the previous failure load and then unloaded to zero force. No
acoustic event was recorded during this test. A non-negligible permanent strain was observed after
unloading. In the following, it seems relevant to consider an RMS battery cell as a homogeneous
equivalent material with a plastic behaviour. The initial elastic Young's modulus of the two specimens
is very similar and is equal to E=11 700 MPa, which is the same as that measured during unloading of
the second specimen. The Poisson's ratio was measured at v=0.35 for the second sample only. The
onset of plasticity, estimated from the loss of linearity, was measured at R₀=14 MPa. The observed
variation in the behaviour is probably related to some initial defects. Optical analysis was carried out
on the free edges of the tested specimens prior to testing. Some small initial delamination cracks were
observed between the electrolyte and the anode, probably due to machining. These defects are located
in the part of the specimen clamped in the jaws of the test apparatus, thus limiting their potential effect
on the behaviour. It may be interesting in future work to carry out non-destructive controls, such as
C-scan, to better study the relationship between the initial defects and the variation in the tests.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** a) Electromechanical testing machine, b) measured displacement field and associated virtual extensometers, c) stress/strain curves for the two tested RMS cell specimens.</figcaption></figure>
Based on experimental observations (no acoustic event prior to the final failure, similar measured Young modulus during loading and unloading steps, large residual strain), we decided to consider a plastic behaviour as the constitutive equation of an RMS battery cell, as reported in Eq. 1.

$$ \sigma = C_0:(\varepsilon - \varepsilon_p) \qquad (1) $$

where $\sigma$ is the stress, $\varepsilon$ the strain, $\varepsilon_p$ the plastic strain and $C_0$ the elastic stiffness of the homogenised battery cell, which is assumed to be isotropic. This point is further discussed in the appendix. We have chosen to consider a Von Mises criterion (Eq. 2.1) associated with a classical plastic flow (Eq. 2.2) and an exponential non-linear isotropic hardening [12] (Eq. 2.3) in order to describe the available non-linear tensile behaviour.

$$ f(\sigma, p) = \sigma_{mises} - R(p) \qquad (2.1) $$

$$ \dot{\varepsilon}_p = \dot{p} \frac{\partial f}{\partial \sigma} \qquad (2.2) $$

$$ R(p) = R_0 + Q(1 - e^{b \cdot p}) \qquad (2.3) $$

where $p$ is the cumulative plastic strain and ($Q$, $b$) are the material coefficients associated with the chosen isotropic hardening. As reported in Figure 3, the proposed simple model is able to describe the measured nonlinear behaviour and accurately capture the permanent strain, with a very limited number of parameters. The identified coefficients associated with non-linear isotropic hardening are $Q=24$ MPa and $b=651$. Table 1 summarises the identified material parameters of the proposed model for a homogenised RMS battery cell, which allows a good description of the available tensile test results.

<table><caption>**Table 1.** Identified mechanical properties of the homogenized RMS battery cell.</caption><thead><tr><th>Elasticity</th><th>RMS cell</th><th>Plasticity</th><th>RMS cell</th></tr></thead><tbody><tr><td>E</td><td>11.7 GPa</td><td>R<sub>0</sub></td><td>14 MPa</td></tr><tr><td>v</td><td>0.34</td><td>Q</td><td>24 MPa</td></tr><tr><td></td><td></td><td>b</td><td>651</td></tr></tbody></table>
Based on experimental observations (no acoustic event prior to the final failure, similar measured Young modulus during loading and unloading steps, large residual strain), we decided to consider a plastic behaviour as the constitutive equation of an RMS battery cell, as reported in Eq. 1.

$$ \sigma = C_0:(\varepsilon - \varepsilon_p) \qquad (1) $$

where $\sigma$ is the stress, $\varepsilon$ the strain, $\varepsilon_p$ the plastic strain and $C_0$ the elastic stiffness of the homogenised battery cell, which is assumed to be isotropic. This point is further discussed in the appendix. We have chosen to consider a Von Mises criterion (Eq. 2.1) associated with a classical plastic flow (Eq. 2.2) and an exponential non-linear isotropic hardening [12] (Eq. 2.3) in order to describe the available non-linear tensile behaviour.

$$ f(\sigma, p) = \sigma_{mises} - R(p) \qquad (2.1) $$

$$ \dot{\varepsilon}_p = \dot{p} \frac{\partial f}{\partial \sigma} \qquad (2.2) $$

$$ R(p) = R_0 + Q (1 - e^{b \cdot p}) \qquad (2.3) $$

where $p$ is the cumulative plastic strain and ($Q$, $b$) are the material coefficients associated with the chosen isotropic hardening. As reported in Figure 3, the proposed simple model is able to describe the measured nonlinear behaviour and accurately capture the permanent strain, with a very limited number of parameters. The identified coefficients associated with non-linear isotropic hardening are $Q=24$ MPa and $b=651$. Table 1 summarises the identified material parameters of the proposed model for a homogenised RMS battery cell, which allows a good description of the available tensile test results.

<table><caption>**Table 1.** Identified mechanical properties of the homogenized RMS battery cell.</caption><thead><tr><th>Elasticity</th><th>RMS cell</th><th>Plasticity</th><th>RMS cell</th></tr></thead><tbody><tr><td>E</td><td>11.7 GPa</td><td>R<sub>0</sub></td><td>14 MPa</td></tr><tr><td>v</td><td>0.34</td><td>Q</td><td>24 MPa</td></tr><tr><td></td><td></td><td>b</td><td>651</td></tr></tbody></table>
As the RMS battery cells tested are very thin, approximately 0.21 mm, only tensile tests can be
performed on the specimens to obtain direct measurements of the mechanical properties. It is therefore
not possible to apply other loads to the cell, such as compression or bending, in order to validate the
various assumptions made (choice of an isotropic or a kinematic hardening, insensitivity to hydrostatic
pressure, etc.). Since only tensile loads are considered in this study, both for the battery cells and for
the composite coupons with or without embedded battery cells, the non-linearity modelled here should
be able to consider the load transfer from the battery cell to the composite part in finite element
simulations, and assess its influence on the prediction of the global behaviour and, in particular, the
onset of transverse cracking.

<figure><img src="image_3.png" /><figcaption>**Figure 3.** Comparison of experimental and predicted experimental stress/strain curves for the RMS battery cell.</figcaption></figure>

## 2.2 AS4/8552 composite material

In the SOLIFLY project, it was decided to consider AS4/8552 unidirectional plies with a weight aerial of 194 g/m², which is widely used in the aeronautical industry and has been extensively studied in the literature [13–16]. The mechanical properties used in this study were taken from the literature [14,15] and are given in Table 2. In order to check the relevance of these material data, a quasi-isotropic [(45/90/-45/0)₂]s laminate was manufactured at ONERA using an autoclave considering the curing cycle recommended by the material supplier [13]. The curing cycle consists of two heating plateaus at 110°C
As the RMS battery cells tested are very thin, approximately 0.21 mm, only tensile tests can be
performed on the specimens to obtain direct measurements of the mechanical properties. It is therefore
not possible to apply other loads to the cell, such as compression or bending, in order to validate the
various assumptions made (choice of an isotropic or a kinematic hardening, insensitivity to hydrostatic
pressure, etc.). Since only tensile loads are considered in this study, both for the battery cells and for
the composite coupons with or without embedded battery cells, the non-linearity modelled here should
be able to consider the load transfer from the battery cell to the composite part in finite element
simulations, and assess its influence on the prediction of the global behaviour and, in particular, the
onset of transverse cracking.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Comparison of experimental and predicted experimental stress/strain curves for the RMS battery cell.</figcaption></figure>

## 2.2 AS4/8552 composite material

In the SOLIFLY project, it was decided to consider AS4/8552 unidirectional plies with a weight aerial of 194 g/m², which is widely used in the aeronautical industry and has been extensively studied in the literature [13–16]. The mechanical properties used in this study were taken from the literature [14,15] and are given in Table 2. In order to check the relevance of these material data, a quasi-isotropic [(45/90/-45/0)₂]s laminate was manufactured at ONERA using an autoclave considering the curing cycle recommended by the material supplier [13]. The curing cycle consists of two heating plateaus at 110°C
and 180°C for a duration of 1 hour and 2 hours respectively with a temperature heating rate of 2°C/min.
The pressure applied is 7 bar, applied almost at the beginning of the cure. Two specimens measuring
200 mm x 25 mm x 2.92 mm were machined using a water-cooled diamond saw. The quality of the
produced laminated plate meets the aeronautical standard, as no initial delamination or voids were
observed on the polished free edges or when considering C-scans. Static tensile tests to failure were
carried out using a hydraulic testing machine with a maximum load capacity of 100 kN associated with
hydraulic jaws, as shown in Figure 4a. The tests were instrumented with 2 CCD cameras with a
resolution of 2048x2048 pixels to perform digital images correlation with the commercial software
Vic3D® and to measure the strains during the loading. A virtual strain gauge with a grid size of 7 mm
x 4 mm was used, located in the centre of the specimens, to measure the applied longitudinal and
transverse strains. In addition, 2 nano30 acoustic sensors were bonded to the specimens to monitor the
damage evolution during the loading.

<figure><img src="image_4.png" /><figcaption>**Figure 4.** a) Hydraulic testing machine and failure pattern, b) comparison of experimental and predicted macroscopic experimental stress/strain curves for the laminated composite.</figcaption></figure>

As reported in Figure 4b, the obtained macroscopic behaviour is almost linear at failure, with a
macroscopic modulus, measured between 10% and 50% of the failure load [17], equal to E<sub>xx</sub>=51.5 GPa
with a covariance (CoV) equal to 0.2%. The first detected acoustic events correspond to the appearance
of transverse cracks in 90 plies (first ply failure noted *fpf*) at a longitudinal strain equal to ε<sub>xx</sub><sup>fpf</sup>=0.75%.
The final failure of the laminate is due to the 0-ply failure in tensile fibre mode (last ply failure noted
and 180°C for a duration of 1 hour and 2 hours respectively with a temperature heating rate of 2°C/min.
The pressure applied is 7 bar, applied almost at the beginning of the cure. Two specimens measuring
200 mm x 25 mm x 2.92 mm were machined using a water-cooled diamond saw. The quality of the
produced laminated plate meets the aeronautical standard, as no initial delamination or voids were
observed on the polished free edges or when considering C-scans. Static tensile tests to failure were
carried out using a hydraulic testing machine with a maximum load capacity of 100 kN associated with
hydraulic jaws, as shown in Figure 4a. The tests were instrumented with 2 CCD cameras with a
resolution of 2048x2048 pixels to perform digital images correlation with the commercial software
Vic3D® and to measure the strains during the loading. A virtual strain gauge with a grid size of 7 mm
x 4 mm was used, located in the centre of the specimens, to measure the applied longitudinal and
transverse strains. In addition, 2 nano30 acoustic sensors were bonded to the specimens to monitor the
damage evolution during the loading.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** a) Hydraulic testing machine and failure pattern, b) comparison of experimental and predicted macroscopic experimental stress/strain curves for the laminated composite.</figcaption></figure>

As reported in Figure 4b, the obtained macroscopic behaviour is almost linear at failure, with a
macroscopic modulus, measured between 10% and 50% of the failure load [17], equal to E<sub>xx</sub>=51.5 GPa
with a covariance (CoV) equal to 0.2%. The first detected acoustic events correspond to the appearance
of transverse cracks in 90 plies (first ply failure noted *fpf*) at a longitudinal strain equal to ε<sub>xx</sub><sup>fpf</sup>=0.75%.
The final failure of the laminate is due to the 0-ply failure in tensile fibre mode (last ply failure noted
$lpf$) at an averaged macroscopic strain measured at $\epsilon_{xx}^{lpf}=1.41\%$ with a covariance of CoV=1.0% and an averaged macroscopic stress at $\Sigma_{xx}^{lpf}=706$ MPa with a CoV equal to 0.6%. It can be seen that the material scattering on the two specimens tested is very low even for the measured macroscopic strain.

Such a tensile test on a quasi-isotropic AS4/8552 laminate to failure was simulated using the existing Onera Progressive Failure Model (OPFM) [18,19], which is briefly summarized in this section. The present multiscale failure approach considers the unidirectional ply as the elementary entity of modelling and is predictive for different stacking sequences, using a laminate theory extended to non-linear behaviour [18]. It can be divided into four main steps. Firstly, in order to correctly estimate the failure of a ply in a laminate, it is necessary to accurately estimate the mesoscopic stresses and strains. A non-linear thermo-viscoelastic behaviour has been proposed in Eq. 3.

$$ \sigma = C^{eff}:(\epsilon - \epsilon^{th} - \epsilon^{ve} - \epsilon^{nl}) \quad (3) $$

where $\sigma$ is the mesoscopic stress, $C^{eff}$ the effective stiffness, $\epsilon$ the total strain, $\epsilon^{th}$ the thermal strain (in order to take into account the thermal residual stresses, which are essential to accurately predict the first ply failure), $\epsilon^{nl}$ the non-linear elastic strain (in order to describe the hardening observed experimentally on UD plies subjected to longitudinal tensile loading and in particular on new generations of composites [20]), and $\epsilon^{ve}$ the viscous strain [21] (to take into account the non-linearity observed on UD plies subjected to shear loading, which is essential for accurate prediction of cracks in ±45 plies). Secondly, the prediction of the ply failure within the laminate is performed with a failure criterion, based on Hashin's hypotheses [22], distinguishing the fibre failure mode (noted $f_1$ in Eq. 4) and the in-plane interfibre failure (noted $f_2$ in Eq. 5), and modelling the failure mechanisms in tension (noted $f_1^+$ and $f_2^+$) and in compression (noted $f_1^-$ and $f_2^-$) separately for each failure mode.

$$ \begin{aligned} f_1^+ &= \left(\frac{\sigma_{11}}{x_t}\right)^2 & \text{if } \sigma_{11} \ge 0 \\ f_1^- &= \left(\frac{\sigma_{11}}{x_c}\right)^2 + \left(\frac{\tau_{12}}{S_c^f(1-p\sigma_{22})}\right)^2 & \text{otherwise} \end{aligned} \quad (4) $$

$$ \begin{aligned} f_2^+ &= \left(\frac{\sigma_{22}}{Y_t}\right)^2 + \left(\frac{\tau_{12}}{S_c(1-p\sigma_{22})}\right)^2 & \text{if } \sigma_{22} \ge 0 \\ f_2^- &= \left(\frac{\sigma_{22}}{Y_c}\right)^2 + \left(\frac{\tau_{12}}{S_c(1-p\sigma_{22})}\right)^2 & \text{otherwise} \end{aligned} \quad (5) $$
$lpf)$ at an averaged macroscopic strain measured at $\epsilon_{xx}^{lpf}=1.41\%$ with a covariance of CoV=1.0% and an averaged macroscopic stress at $\Sigma_{xx}^{lpf}=706$ MPa with a CoV equal to 0.6%. It can be seen that the material scattering on the two specimens tested is very low even for the measured macroscopic strain.

Such a tensile test on a quasi-isotropic AS4/8552 laminate to failure was simulated using the existing Onera Progressive Failure Model (OPFM) [18,19], which is briefly summarized in this section. The present multiscale failure approach considers the unidirectional ply as the elementary entity of modelling and is predictive for different stacking sequences, using a laminate theory extended to non-linear behaviour [18]. It can be divided into four main steps. Firstly, in order to correctly estimate the failure of a ply in a laminate, it is necessary to accurately estimate the mesoscopic stresses and strains. A non-linear thermo-viscoelastic behaviour has been proposed in Eq. 3.

$$ \sigma = C^{eff}:(\epsilon - \epsilon^{th} - \epsilon^{ve} - \epsilon^{nl}) \quad (3) $$

where $\sigma$ is the mesoscopic stress, $C^{eff}$ the effective stiffness, $\epsilon$ the total strain, $\epsilon^{th}$ the thermal strain (in order to take into account the thermal residual stresses, which are essential to accurately predict the first ply failure), $\epsilon^{nl}$ the non-linear elastic strain (in order to describe the hardening observed experimentally on UD plies subjected to longitudinal tensile loading and in particular on new generations of composites [20]), and $\epsilon^{ve}$ the viscous strain [21] (to take into account the non-linearity observed on UD plies subjected to shear loading, which is essential for accurate prediction of cracks in ±45 plies). Secondly, the prediction of the ply failure within the laminate is performed with a failure criterion, based on Hashin's hypotheses [22], distinguishing the fibre failure mode (noted $f_1$ in Eq. 4) and the in-plane interfibre failure (noted $f_2$ in Eq. 5), and modelling the failure mechanisms in tension (noted $f_1^+$ and $f_2^+$) and in compression (noted $f_1^-$ and $f_2^-$) separately for each failure mode.

$$ \begin{aligned} f_1^+ &= \left(\frac{\sigma_{11}}{x_t}\right)^2 & \text{if } \sigma_{11} \ge 0 \\ f_1^- &= \left(\frac{\sigma_{11}}{x_c}\right)^2 + \left(\frac{\tau_{12}}{S_c^f(1-p\sigma_{22})}\right)^2 & \text{otherwise} \end{aligned} \quad (4) $$

$$ \begin{aligned} f_2^+ &= \left(\frac{\sigma_{22}}{Y_t}\right)^2 + \left(\frac{\tau_{12}}{S_c(1-p\sigma_{22})}\right)^2 & \text{if } \sigma_{22} \ge 0 \\ f_2^- &= \left(\frac{\sigma_{22}}{Y_c}\right)^2 + \left(\frac{\tau_{12}}{S_c(1-p\sigma_{22})}\right)^2 & \text{otherwise} \end{aligned} \quad (5) $$
where $X_t$ and $X_c$ are the longitudinal tensile and compressive strengths respectively, $Y_t$ and $Y_c$ the transverse tensile and compressive strengths, $S_c$ the in-plane shear strength and $S_c^f$ the in-plane shear strength for the fibre mode. The main improvement of the interfibre failure criterion, over the Hashin criterion, is a better description of the reinforcement of the apparent strength of the material for combined in-plane shear and transverse compressive loadings (due to the introduction of the material parameter $p$, which is easy to identify and equal to to $p = -1/Y_c$). Thirdly, when transverse cracks occur in a ply within the laminate, its mechanical properties are progressively degraded using a thermodynamic degradation approach based on damage modelling [18]. The initial elastic compliance $S^0$ is increased (Eq. 6) by the degradation of the failed ply in the in-plane interfibre mode ($d_2H_2$). The kinetics of the degradation (scalar variable noted $d_2$) is distinguished from the effects of the ply failure (the compliance constants affected by transverse cracking are defined by the fourth-order effect tensor noted $H_2$).

$$C^{eff} = S^{eff-1} \quad \text{and} \quad S^{eff} = S^0 + d_2H_2 \quad \text{with} \quad d_2 = \beta \langle f_2^+ - 1 \rangle_+ \quad \text{and} \quad \dot{d}_2 \ge 0 \quad (6)$$

where $\beta$ is a material coefficient correlated to the kinetics of degradation due to ply failure in the interfibre mode, and $\langle \rangle_+$ corresponds to the Macauley brackets. The effect tensor $H_2$, of which only the components 22, 44, 66 are non-zero (in Voigt notation), can be determined from the knowledge of the elastic properties of the UD plies, as detailed in [18]. Fourthly, for a laminated unnotched coupon, the ultimate failure could be due to the first ply failure in the fibre mode or in transverse compression, which is the case for classical stacking sequences (containing only 0°, ±45° and 90° plies) considered in the aeronautical industry. This multiscale failure approach can be identified by the tests currently performed in aeronautics as described in detail in [18,19]. Table 2 shows only the identified material parameters relevant to the test cases considered in the present study using tests found in the literature [14,23].
where $X_t$ and $X_c$ are the longitudinal tensile and compressive strengths respectively, $Y_t$ and $Y_c$ the transverse tensile and compressive strengths, $S_c$ the in-plane shear strength and $S_c^f$ the in-plane shear strength for the fibre mode. The main improvement of the interfibre failure criterion, over the Hashin criterion, is a better description of the reinforcement of the apparent strength of the material for combined in-plane shear and transverse compressive loadings (due to the introduction of the material parameter $p$, which is easy to identify and equal to to $p = -1/Y_c$). Thirdly, when transverse cracks occur in a ply within the laminate, its mechanical properties are progressively degraded using a thermodynamic degradation approach based on damage modelling [18]. The initial elastic compliance $S^0$ is increased (Eq. 6) by the degradation of the failed ply in the in-plane interfibre mode ($d_2H_2$). The kinetics of the degradation (scalar variable noted $d_2$) is distinguished from the effects of the ply failure (the compliance constants affected by transverse cracking are defined by the fourth-order effect tensor noted $H_2$).

$$C^{eff} = S^{eff-1} \quad \text{and} \quad S^{eff} = S^0 + d_2H_2 \quad \text{with} \quad d_2 = \beta \langle f_2^+ - 1 \rangle_+ \quad \text{and} \quad \dot{d}_2 \ge 0 \quad (6)$$

where $\beta$ is a material coefficient correlated to the kinetics of degradation due to ply failure in the interfibre mode, and $\langle \rangle_+$ corresponds to the Macauley brackets. The effect tensor $H_2$, of which only the components 22, 44, 66 are non-zero (in Voigt notation), can be determined from the knowledge of the elastic properties of the UD plies, as detailed in [18]. Fourthly, for a laminated unnotched coupon, the ultimate failure could be due to the first ply failure in the fibre mode or in transverse compression, which is the case for classical stacking sequences (containing only 0°, ±45° and 90° plies) considered in the aeronautical industry. This multiscale failure approach can be identified by the tests currently performed in aeronautics as described in detail in [18,19]. Table 2 shows only the identified material parameters relevant to the test cases considered in the present study using tests found in the literature [14,23].
<table><caption>**Table 2.** Mechanical properties of the AS4/8552 composite material taken from [14,15]. Other mechanical properties, related to the 8552 matrix, can be found in [23].</caption><thead><tr><th>Properties</th><th>AS4/8552</th><th>Properties</th><th>AS4/8552</th></tr></thead><tbody><tr><td>E<sub>11</sub></td><td>134.0 GPa</td><td>X<sub>t</sub></td><td>1950 MPa</td></tr><tr><td>E<sub>22</sub></td><td>10.0 GPa</td><td>Y<sub>t</sub></td><td>88 MPa</td></tr><tr><td>G<sub>12</sub></td><td>4.9 GPa</td><td>Y<sub>c</sub></td><td>-250 MPa</td></tr><tr><td>ν<sub>12</sub></td><td>0.3</td><td>S<sub>c</sub></td><td>110 MPa</td></tr><tr><td></td><td></td><td>β</td><td>50</td></tr></tbody></table>

As shown in Figure 4b, the predictions at the laminate scale, with the identification based on data found in the literature, are in very good agreement with the experimental data. Indeed, the global stiffness is mainly due to the knowledge of the longitudinal modulus of the elementary UD ply (assumed equal to $E_{11}=134\text{GPa}$) and the transverse strain is strongly related to the Poisson ratio (equal to $\nu_{12}=0.3$). The first ply failure occurs in the 90 plies (predicted with a transverse tensile strength equal to $Y_t=88\text{MPa}$) and the final failure due to fibre failure (predicted with a tensile strength equal to $X_t=1950\text{MPa}$), are also accurately predicted. The proposed model is able to predict the damage scenario up to the final failure for a quasi-isotropic laminated composite plate (without any battery).

# 3. Alternative composite curing cycle to meet battery cell constraints

## 3.1 Constraints on the curing cycle due to battery cell integration

Thermal and pressure stability are key issues for autoclave manufacturability. In the battery cell, the component with the lowest thermal stability is the gel electrolyte. The ionic liquid is thermally stable up to 200°C, but at temperatures around 160°C, the electrolyte shows an exothermic reaction that could degrade the electrochemical performance and needs to be further investigated. In conclusion, it seems mandatory to reduce the maximum curing temperature below 160°C, while ensuring a similar curing rate of the matrix in order to maintain the mechanical performance of the composite part. It is interesting
<table><caption>**Table 2.** Mechanical properties of the AS4/8552 composite material taken from [14,15]. Other mechanical properties, related to the 8552 matrix, can be found in [23].</caption><thead><tr><th>Properties</th><th>AS4/8552</th><th>Properties</th><th>AS4/8552</th></tr></thead><tbody><tr><td>E<sub>11</sub></td><td>134.0 GPa</td><td>X<sub>t</sub></td><td>1950 MPa</td></tr><tr><td>E<sub>22</sub></td><td>10.0 GPa</td><td>Y<sub>t</sub></td><td>88 MPa</td></tr><tr><td>G<sub>12</sub></td><td>4.9 GPa</td><td>Y<sub>c</sub></td><td>-250 MPa</td></tr><tr><td>ν<sub>12</sub></td><td>0.3</td><td>S<sub>c</sub></td><td>110 MPa</td></tr><tr><td></td><td></td><td>β</td><td>50</td></tr></tbody></table>

As shown in Figure 4b, the predictions at the laminate scale, with the identification based on data found in the literature, are in very good agreement with the experimental data. Indeed, the global stiffness is mainly due to the knowledge of the longitudinal modulus of the elementary UD ply (assumed equal to $E_{11}=134\text{GPa}$) and the transverse strain is strongly related to the Poisson ratio (equal to $\nu_{12}=0.3$). The first ply failure occurs in the 90 plies (predicted with a transverse tensile strength equal to $Y_t=88 \text{ MPa}$) and the final failure due to fibre failure (predicted with a tensile strength equal to $X_t=1950 \text{ MPa}$), are also accurately predicted. The proposed model is able to predict the damage scenario up to the final failure for a quasi-isotropic laminated composite plate (without any battery).

### 3. Alternative composite curing cycle to meet battery cell constraints

#### 3.1 Constraints on the curing cycle due to battery cell integration

Thermal and pressure stability are key issues for autoclave manufacturability. In the battery cell, the component with the lowest thermal stability is the gel electrolyte. The ionic liquid is thermally stable up to 200°C, but at temperatures around 160°C, the electrolyte shows an exothermic reaction that could degrade the electrochemical performance and needs to be further investigated. In conclusion, it seems mandatory to reduce the maximum curing temperature below 160°C, while ensuring a similar curing rate of the matrix in order to maintain the mechanical performance of the composite part. It is interesting
to note that the electrolyte, conventionally composed of flammable organic solvents, was replaced with a non-flammable PVdF-based gel electrolyte using a non-flammable ionic liquid. The porous electrodes in the RMS stack are filled with the ionic liquid or gel electrolyte. High pressure applied at the beginning of the curing cycle can cause diffusion of the ionic liquid from the battery cell into the composite. It is therefore necessary to reduce the pressure compared to the recommended pressure. It was thus decided to reduce the pressure from 7 bar to 3.2 bar, which is the pressure recommended by the material supplier for sandwich composites. It is relevant to use this pressure because the battery cells can be considered as the core part in a laminated composite material. Particular attention has therefore been paid to reducing the maximum temperature in the curing cycle.

## 3.2 Numerical design of the composite curing cycle

Numerical simulations were carried out (i) in order to determine an optimized curing cycle, taking into account the constraints imposed by the battery cells, and (ii) in order to obtain a cure rate of the composite material that is similar to that obtained with the reference curing cycle, considering a maximum curing temperature of 180°C. To this end, two different analytical models were considered. The first simple model, proposed by Nelson [24], estimates the evolution of the curing rate of the composite material, noted $\alpha$, as a function of time $t$ and temperature $T$, as shown in Eq. 7.

$$ \frac{d\alpha}{dt} = K\alpha^m(1-\alpha)^n \quad \text{with} \quad K = A e^{-\frac{E}{RT}} \qquad (7) $$

The parameter $R$ is the well-known universal gas constant and ($K$, $m$, $n$, $E$) are material parameters to be identified. The second more advanced model has been proposed by Garstka et al. [16] and is given in Eq. 8. The parameters ($K$, $m$, $n$, $c$, $\alpha_{C0}$, $\alpha_{CT}$, $E$) are material parameters to be identified. This model has been successfully used to estimate the cure behaviour of the AS4/8552 composite in [16].

$$ \frac{d\alpha}{dt} = \frac{K\alpha^m(1-\alpha)^n}{1+\exp(c(\alpha-(\alpha_{C0}+\alpha_{CT}T)))} \quad \text{with} \quad K = A e^{-\frac{E}{RT}} \qquad (8) $$

In order to identify the material properties of these two models, Differential Scanning Calorimetry (DSC) tests were carried out on uncured prepreg samples. The protocol chosen was an isothermal study of the curing kinetics for two different temperatures, 140°C and 160°C. At these temperatures, the
to note that the electrolyte, conventionally composed of flammable organic solvents, was replaced with a non-flammable PVdF-based gel electrolyte using a non-flammable ionic liquid. The porous electrodes in the RMS stack are filled with the ionic liquid or gel electrolyte. High pressure applied at the beginning of the curing cycle can cause diffusion of the ionic liquid from the battery cell into the composite. It is therefore necessary to reduce the pressure compared to the recommended pressure. It was thus decided to reduce the pressure from 7 bar to 3.2 bar, which is the pressure recommended by the material supplier for sandwich composites. It is relevant to use this pressure because the battery cells can be considered as the core part in a laminated composite material. Particular attention has therefore been paid to reducing the maximum temperature in the curing cycle.

## 3.2 Numerical design of the composite curing cycle

Numerical simulations were carried out (i) in order to determine an optimized curing cycle, taking into account the constraints imposed by the battery cells, and (ii) in order to obtain a cure rate of the composite material that is similar to that obtained with the reference curing cycle, considering a maximum curing temperature of 180°C. To this end, two different analytical models were considered. The first simple model, proposed by Nelson [24], estimates the evolution of the curing rate of the composite material, noted $\alpha$, as a function of time $t$ and temperature $T$, as shown in Eq. 7.

$$ \frac{d\alpha}{dt} = K\alpha^m(1-\alpha)^n \quad \text{with} \quad K = A e^{-\frac{E}{RT}} \qquad (7) $$

The parameter $R$ is the well-known universal gas constant and ($K$, $m$, $n$, $E$) are material parameters to be identified. The second more advanced model has been proposed by Garstka et al. [16] and is given in Eq. 8. The parameters ($K$, $m$, $n$, $c$, $\alpha_{C0}$, $\alpha_{CT}$, $E$) are material parameters to be identified. This model has been successfully used to estimate the cure behaviour of the AS4/8552 composite in [16].

$$ \frac{d\alpha}{dt} = \frac{K\alpha^m(1-\alpha)^n}{1+\exp(c(\alpha-(\alpha_{C0}+\alpha_{CT}T)))} \quad \text{with} \quad K = A e^{-\frac{E}{RT}} \qquad (8) $$

In order to identify the material properties of these two models, Differential Scanning Calorimetry (DSC) tests were carried out on uncured prepreg samples. The protocol chosen was an isothermal study of the curing kinetics for two different temperatures, 140°C and 160°C. At these temperatures, the
evolution of the global heat flow $W_f$ was measured and allowed the curing rate of the epoxy matrix to be estimated. The evolution of the curing rate $\alpha$ during the DSC tests in the second phase (temperature plateau) is shown in Figure 5a for the thermal loads at 140°C and 160°C. Two samples have been considered for each configuration in order to obtain an estimate of the material scattering, which is quite large considering the four samples. This scattering can be caused by the small size of the DSC prepreg samples (with a weight of ~5 mg). Indeed, at these dimensions, the $W_f$ of the sample may be different from that of a global prepreg, and therefore the resin mass estimation may be poor. The parameters of the two models were identified from the four available test data and the values are given in Table 3. As shown in Figure 5a, the two models are able to reproduce the measured curing rate evolution. Due to significant material scattering, this identification should be treated with caution.

<table><caption>**Table 3.** Identified material parameters of the Nelson and Garstka models [16,24] for the material AS4/8552 using DSC tests</caption><tbody><tr><td>Nelson's model [24]</td><td>A (s<sup>-1</sup>)</td><td>E (kJ/mol)</td><td>m</td><td>N</td></tr><tr><td>AS4/8552</td><td>7.9 10<sup>6</sup></td><td>80.3</td><td>0.47</td><td>1.59</td></tr><tr><td>Garstka's model [16]</td><td>A (s<sup>-1</sup>)</td><td>E (kJ/mol)</td><td>m</td><td>N</td><td>C</td><td>α<sub>C0</sub></td><td>α<sub>CT</sub></td></tr><tr><td>AS4/8552</td><td>7.9.10<sup>6</sup></td><td>80.3</td><td>0.47</td><td>1.59</td><td>39.5</td><td>-0.96</td><td>5.3 10<sup>-3</sup></td></tr></tbody></table>

To validate the identified model, an additional isothermal study of the curing kinetics was performed at 180°C (material supplier's recommended temperature) and at 155°C. One sample was considered at each temperature.

As shown in Figure 5b, the predictions of the two models are in very good agreement with all the experimental data, those used for identification and those used for blind predictions. Therefore, considering the two models, different curing cycles with a maximum temperature below 160°C and different durations were numerically considered in order to obtain a configuration with a curing rate at the end of the second temperature plateau close to 1, the value obtained by the two models for the reference case. Finally, as shown in Figure 6, the chosen modified configuration consists of maintaining a first plateau at 110°C for 1 hour and then applying a second plateau at 155°C for 3 hours. The curing
evolution of the global heat flow $W_f$ was measured and allowed the curing rate of the epoxy matrix to be estimated. The evolution of the curing rate $\alpha$ during the DSC tests in the second phase (temperature plateau) is shown in Figure 5a for the thermal loads at 140°C and 160°C. Two samples have been considered for each configuration in order to obtain an estimate of the material scattering, which is quite large considering the four samples. This scattering can be caused by the small size of the DSC prepreg samples (with a weight of ~5 mg). Indeed, at these dimensions, the $W_f$ of the sample may be different from that of a global prepreg, and therefore the resin mass estimation may be poor. The parameters of the two models were identified from the four available test data and the values are given in Table 3. As shown in Figure 5a, the two models are able to reproduce the measured curing rate evolution. Due to significant material scattering, this identification should be treated with caution.

<table><caption>**Table 3.** Identified material parameters of the Nelson and Garstka models [16,24] for the material AS4/8552 using DSC tests</caption><tbody><tr><td>Nelson's model [24]</td><td>A (s<sup>-1</sup>)</td><td>E (kJ/mol)</td><td>m</td><td>N</td></tr><tr><td>AS4/8552</td><td>7.9 10<sup>6</sup></td><td>80.3</td><td>0.47</td><td>1.59</td></tr><tr><td>Garstka's model [16]</td><td>A (s<sup>-1</sup>)</td><td>E (kJ/mol)</td><td>m</td><td>N</td><td>C</td><td>α<sub>C0</sub></td><td>α<sub>CT</sub></td></tr><tr><td>AS4/8552</td><td>7.9.10<sup>6</sup></td><td>80.3</td><td>0.47</td><td>1.59</td><td>39.5</td><td>-0.96</td><td>5.3 10<sup>-3</sup></td></tr></tbody></table>

To validate the identified model, an additional isothermal study of the curing kinetics was performed at 180°C (material supplier's recommended temperature) and at 155°C. One sample was considered at each temperature.

As shown in Figure 5b, the predictions of the two models are in very good agreement with all the experimental data, those used for identification and those used for blind predictions. Therefore, considering the two models, different curing cycles with a maximum temperature below 160°C and different durations were numerically considered in order to obtain a configuration with a curing rate at the end of the second temperature plateau close to 1, the value obtained by the two models for the reference case. Finally, as shown in Figure 6, the chosen modified configuration consists of maintaining a first plateau at 110°C for 1 hour and then applying a second plateau at 155°C for 3 hours. The curing
rates obtained are $\alpha$=0.99 for Nelson's model and $\alpha$=0.97 for Garstka's model respectively, very close to the estimates obtained for the recommended curing cycle.

<figure><img src="image_5.png" /><figcaption>**Figure 5.** a) Isothermal study of curing rate at 140°C and 160°C with DSC to identify the 2 models, b) validation of the models by comparison with additional DSC tests at 180°C and 155°C.</figcaption></figure>

In conclusion, the optimised curing cycle for the AS4/8552 unidirectional ply, which ensures the constraints related to the electrical performance of the RMS battery cells, determined through a virtual manufacturing campaign considering the proposed modelling of the cure kinetics, considers a pressure of 3.2 bar and a maximum curing temperature of 155°C, applied over 3 hours, after an initial plateau at 110°C for 1 hour.

<figure><img src="image_6.png" /><figcaption>**Figure 6.** Estimation of the curing rate using the Nelson and Garstka models for a) the reference and b) the modified curing cycles.</figcaption></figure>
rates obtained are $\alpha$=0.99 for Nelson's model and $\alpha$=0.97 for Garstka's model respectively, very close to the estimates obtained for the recommended curing cycle.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** a) Isothermal study of curing rate at 140°C and 160°C with DSC to identify the 2 models, b) validation of the models by comparison with additional DSC tests at 180°C and 155°C.</figcaption></figure>

In conclusion, the optimised curing cycle for the AS4/8552 unidirectional ply, which ensures the constraints related to the electrical performance of the RMS battery cells, determined through a virtual manufacturing campaign considering the proposed modelling of the cure kinetics, considers a pressure of 3.2 bar and a maximum curing temperature of 155°C, applied over 3 hours, after an initial plateau at 110°C for 1 hour.

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Estimation of the curing rate using the Nelson and Garstka models for a) the reference and b) the modified curing cycles.</figcaption></figure>
## 3.3 Validation of optimized curing cycle for composites with embedded battery cells

In order to check the relevance of the proposed curing cycle, some mechanical tests were carried out on 16-ply [(45/90/-45/0)$_2$]s quasi-isotropic specimens manufactured either with the reference or with the modified curing cycle. For the two curing cycles considered, two different mechanical tests were performed: (i) Inter-Laminar Shear Strength (ILSS) tests, corresponding to a standardized short three-point bending (ASTM D2344 standard [25]), in order to estimate the influence of the curing cycle on the out-of-plane shear strength. Indeed, this strength is strongly related to the chemical state of the epoxy matrix and such a test is discriminant to compare the two curing cycles. (ii) Tensile tests on a quasi-isotropic laminate, which is a standardized test (AITM 1-007 standard [17]), and that will be considered later for the manufacture of a composite laminate with embedded RMS battery cells. Firstly, in order to study the possible evolution of the volume fibre ratio for the different curing cycles, the total thickness of all the 16-ply quasi-isotropic specimens was measured with a calliper at 5 different locations in the specimen prior to the test. The laminate thickness was measured at $t_{QI}^{ref}=2.91$ mm and $t_{QI}^{mod}=2.93$ mm for the reference and modified curing cycles respectively, with a difference close to the accuracy of the calliper measurement, meaning that no significant variation in fibre volume ratio is expected.

Interlaminar shear strength tests were performed at ONERA on an electromechanical testing machine with a maximum load capacity of 150 kN, as shown in Figure 7a. The radius of the load span is 3 mm and 2 mm for the two support spans. The distance between the two support spans is equal to 5 times the total thickness of the laminate, which in this case is 15 mm. The dimensions of the specimens were measured to be 35 mm x 20 mm x 2.92 mm. 4 samples per curing cycle were tested at a loading rate of 0.5mm/min. A nano30 acoustic sensor was attached to the specimens in order to monitor the damage evolution. The first significant acoustic events were recorded at the peak load. As shown in Figure 7b, the post mortem failure patterns are very similar for the specimens manufactured using the two different curing cycles.
## 3.3 Validation of optimized curing cycle for composites with embedded battery cells

In order to check the relevance of the proposed curing cycle, some mechanical tests were carried out on 16-ply [(45/90/-45/0)$_2$]s quasi-isotropic specimens manufactured either with the reference or with the modified curing cycle. For the two curing cycles considered, two different mechanical tests were performed: (i) Inter-Laminar Shear Strength (ILSS) tests, corresponding to a standardized short three-point bending (ASTM D2344 standard [25]), in order to estimate the influence of the curing cycle on the out-of-plane shear strength. Indeed, this strength is strongly related to the chemical state of the epoxy matrix and such a test is discriminant to compare the two curing cycles. (ii) Tensile tests on a quasi-isotropic laminate, which is a standardized test (AITM 1-007 standard [17]), and that will be considered later for the manufacture of a composite laminate with embedded RMS battery cells. Firstly, in order to study the possible evolution of the volume fibre ratio for the different curing cycles, the total thickness of all the 16-ply quasi-isotropic specimens was measured with a calliper at 5 different locations in the specimen prior to the test. The laminate thickness was measured at $t_{QI}^{ref}=2.91$ mm and $t_{QI}^{mod}=2.93$ mm for the reference and modified curing cycles respectively, with a difference close to the accuracy of the calliper measurement, meaning that no significant variation in fibre volume ratio is expected.

Interlaminar shear strength tests were performed at ONERA on an electromechanical testing machine with a maximum load capacity of 150 kN, as shown in Figure 7a. The radius of the load span is 3 mm and 2 mm for the two support spans. The distance between the two support spans is equal to 5 times the total thickness of the laminate, which in this case is 15 mm. The dimensions of the specimens were measured to be 35 mm x 20 mm x 2.92 mm. 4 samples per curing cycle were tested at a loading rate of 0.5mm/min. A nano30 acoustic sensor was attached to the specimens in order to monitor the damage evolution. The first significant acoustic events were recorded at the peak load. As shown in Figure 7b, the post mortem failure patterns are very similar for the specimens manufactured using the two different curing cycles.
<figure><img src="image_7.png" /><figcaption>**Figure 7.** a) ILSS test setup, b) load/displacement curves and c) failure patterns for specimens subjected to ILSS tests and manufactured with two different curing cycles (reference and modified).</figcaption></figure>

Indeed, as expected, delamination cracks are observed at the 90/45 interfaces, and a small indentation is also observed in the upper 45 ply. The global stiffness of the specimens measured in the linear part of the curve (between 10% and 50% of the failure load) and the peak load (corresponding to the onset of delamination at the 90/45 interfaces) are very similar whatever the considered curing cycles. Indeed, the averaged global stiffness for the reference cycle is $S=6990$ N, while, for the modified cycle it is $S=7203$ N, i.e. a slight increase of +3.1%. The averaged failure load for the specimen cured with the reference cycle is equal to $F_r = 5009$ N (with a CoV of 3.7%) and for the modified cycle, it is equal to $F_r = 4860$ N (with a CoV of 5.5%), which means a slight decrease of -2.8%, similar to the material scattering. In conclusion, the out-of-plane shear strengths, which are strongly related to the state of the matrix, are similar for the modified curing cycle compared to the reference cycle.

Additional tensile tests on quasi-isotropic laminates were carried out at ONERA using the same hydraulic testing machine and instrumentation as described in section 2.2. The macroscopic strain/stress curves are also very similar up to final failure as shown in Figure 8a.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** a) ILSS test setup, b) load/displacement curves and c) failure patterns for specimens subjected to ILSS tests and manufactured with two different curing cycles (reference and modified).</figcaption></figure>

Indeed, as expected, delamination cracks are observed at the 90/45 interfaces, and a small indentation is also observed in the upper 45 ply. The global stiffness of the specimens measured in the linear part of the curve (between 10% and 50% of the failure load) and the peak load (corresponding to the onset of delamination at the 90/45 interfaces) are very similar whatever the considered curing cycles. Indeed, the averaged global stiffness for the reference cycle is $S=6990$ N, while, for the modified cycle it is $S=7203$ N, i.e. a slight increase of +3.1%. The averaged failure load for the specimen cured with the reference cycle is equal to $F_r = 5009$ N (with a CoV of 3.7%) and for the modified cycle, it is equal to $F_r = 4860$ N (with a CoV of 5.5%), which means a slight decrease of -2.8%, similar to the material scattering. In conclusion, the out-of-plane shear strengths, which are strongly related to the state of the matrix, are similar for the modified curing cycle compared to the reference cycle.

Additional tensile tests on quasi-isotropic laminates were carried out at ONERA using the same hydraulic testing machine and instrumentation as described in section 2.2. The macroscopic strain/stress curves are also very similar up to final failure as shown in Figure 8a.
<figure><img src="image_8.png" /><figcaption>**Figure 8.** a) Load/displacement curves and b) failure patterns for the tensile test specimens manufactured with two different curing cycles (reference and modified cycles).</figcaption></figure>

Indeed, the averaged macroscopic modulus for the reference cycle is $E_{xx}=51.5$ GPa while, for the modified cycle, it is $E_{xx}= 52.3$ GPa, i.e. a slight increase of +1.5%. The cumulative acoustic energy curves are also very similar, although it is difficult to precisely define the onset of damage. In order to quantitatively compare the different specimens, the acoustic energy threshold was arbitrarily set at 20000 e.u., the value corresponding to the first significant acoustic events. The onset of transverse cracking in the 90 plies is measured at $\Sigma_{xx}^{fpf} = 390$ MPa, and for the modified curing cycle at $\Sigma_{xx}^{fpf} = 360$ MPa, i.e. a decrease of -7.7%. The values are very similar when considering the noise recorded at the beginning of the damage process. Finally, the failure patterns are similar as shown in Figure 8b, and the macroscopic failure stress has been increased by +10.4% with the modified curing cycle, the macroscopic stress at failure evolving from $\Sigma_{xx}^{lpf} = 706$ MPa to $\Sigma_{xx}^{lpf} = 788$ MPa for the reference and modified curing cycles respectively. This increase could be due to a higher viscosity of the matrix with the modified curing cycle, which therefore better distributes the load to the adjacent fibres after a premature fibre failure in the 0 plies.

To conclude, based on simulations, a modified curing cycle was proposed, reducing the maximum temperature from 180°C to 155°C and increasing the duration of the second temperature plateau from 2 hours to 3 hours. The pressure was decreased from 7 bar to 3.2 bar, the same pressure used for the
<figure><img src="image_10.png" /><figcaption>**Figure 8.** a) Load/displacement curves and b) failure patterns for the tensile test specimens manufactured with two different curing cycles (reference and modified cycles).</figcaption></figure>

Indeed, the averaged macroscopic modulus for the reference cycle is $E_{xx}=51.5$ GPa while, for the modified cycle, it is $E_{xx}= 52.3$ GPa, i.e. a slight increase of +1.5%. The cumulative acoustic energy curves are also very similar, although it is difficult to precisely define the onset of damage. In order to quantitatively compare the different specimens, the acoustic energy threshold was arbitrarily set at 20000 e.u., the value corresponding to the first significant acoustic events. The onset of transverse cracking in the 90 plies is measured at $\Sigma_{xx}^{fpf} = 390$ MPa, and for the modified curing cycle at $\Sigma_{xx}^{fpf} = 360$ MPa, i.e. a decrease of -7.7%. The values are very similar when considering the noise recorded at the beginning of the damage process. Finally, the failure patterns are similar as shown in Figure 8b, and the macroscopic failure stress has been increased by +10.4% with the modified curing cycle, the macroscopic stress at failure evolving from $\Sigma_{xx}^{lpf} = 706$ MPa to $\Sigma_{xx}^{lpf} = 788$ MPa for the reference and modified curing cycles respectively. This increase could be due to a higher viscosity of the matrix with the modified curing cycle, which therefore better distributes the load to the adjacent fibres after a premature fibre failure in the 0 plies.

To conclude, based on simulations, a modified curing cycle was proposed, reducing the maximum temperature from 180°C to 155°C and increasing the duration of the second temperature plateau from 2 hours to 3 hours. The pressure was decreased from 7 bar to 3.2 bar, the same pressure used for the
sandwich material. To ensure that the mechanical properties of the composite with the modified curing cycle are similar to those obtained with the reference cycle, ILSS and tensile tests were performed on quasi-isotropic laminates and it was shown that the mechanical properties were very similar.

# 4. Numerical and experimental evaluation of the residual mechanical performance of a composite laminate with embedded battery cells

## 4.1 Numerical design of a composite laminate with RMS battery cells

The numerical methodology to consider the mechanical effect of the integration of battery cells in a laminated composite plate is detailed in [11], and briefly described in this section. As shown in Figure 9a, the battery cells, considered as a homogeneous material to limit the computation time, are explicitly introduced into the finite element mesh within the composite laminates. Fully integrated quadratic elements were chosen, which are generic wedge elements called c3d15, used for each unidirectional ply in the laminate (one element in the thickness of each ply or battery cell). The finite element simulations are performed taking into account the proposed plastic behaviour for the battery cells and the OPFM model for the different non-linearities (mainly transverse cracks in the present case) encountered in the composite material. For simplicity, the composite plies are assumed to be perfectly bonded to each other and to the battery cells. This assumption appears to be relevant for the tensile loads studied and the high fracture toughness composite material considered, but is questionable for other loads, such as compression or bending, where failure could be due to buckling associated with local delamination. The finite element simulations are performed with the in-house software Z-set, developed jointly by ONERA and the Ecole des Mines, using an implicit solver. The boundary conditions applied to the FE simulations consist of fixing the lower free edge and imposing the uniaxial displacement on the upper free edge at a constant displacement rate. Finite element simulations are considered without geometric non-linearities due to the low strain at failure of the carbon/epoxy laminates considered. As recommended in [11], the global stiffness of a composite plate with battery cells decreased linearly with the volume of integrated cells. Thus, the volume of integrated cells for the manufactured plate was designed to have a measurable effect on the global stiffness (i.e. higher than the material scattering). Furthermore, it has been numerically demonstrated in [11] that the shape of the battery cell has no effect
sandwich material. To ensure that the mechanical properties of the composite with the modified curing cycle are similar to those obtained with the reference cycle, ILSS and tensile tests were performed on quasi-isotropic laminates and it was shown that the mechanical properties were very similar.

# 4. Numerical and experimental evaluation of the residual mechanical performance of a composite laminate with embedded battery cells

## 4.1 Numerical design of a composite laminate with RMS battery cells

The numerical methodology to consider the mechanical effect of the integration of battery cells in a laminated composite plate is detailed in [11], and briefly described in this section. As shown in Figure 9a, the battery cells, considered as a homogeneous material to limit the computation time, are explicitly introduced into the finite element mesh within the composite laminates. Fully integrated quadratic elements were chosen, which are generic wedge elements called c3d15, used for each unidirectional ply in the laminate (one element in the thickness of each ply or battery cell). The finite element simulations are performed taking into account the proposed plastic behaviour for the battery cells and the OPFM model for the different non-linearities (mainly transverse cracks in the present case) encountered in the composite material. For simplicity, the composite plies are assumed to be perfectly bonded to each other and to the battery cells. This assumption appears to be relevant for the tensile loads studied and the high fracture toughness composite material considered, but is questionable for other loads, such as compression or bending, where failure could be due to buckling associated with local delamination. The finite element simulations are performed with the in-house software Z-set, developed jointly by ONERA and the Ecole des Mines, using an implicit solver. The boundary conditions applied to the FE simulations consist of fixing the lower free edge and imposing the uniaxial displacement on the upper free edge at a constant displacement rate. Finite element simulations are considered without geometric non-linearities due to the low strain at failure of the carbon/epoxy laminates considered. As recommended in [11], the global stiffness of a composite plate with battery cells decreased linearly with the volume of integrated cells. Thus, the volume of integrated cells for the manufactured plate was designed to have a measurable effect on the global stiffness (i.e. higher than the material scattering). Furthermore, it has been numerically demonstrated in [11] that the shape of the battery cell has no effect
on the global stiffness and a limited effect on the damage initiation. Therefore, a rectangular shape was
chosen for the battery cells for the sake of simplicity.

<figure><img src="image_9.png" /><figcaption>**Figure 9.** a) Mesh and boundary conditions of the FE simulation of a laminate with battery cells, b) cumulative plastic strain (p) in the cells and failure criterion (f₂) in the 90 plies at failure load.</figcaption></figure>

Finally, it has been numerically demonstrated that an important geometric parameter for damage initiation is the distance between the free edges of the specimens and the edges of the battery cells. In fact, when the stress gradient generated by the introduction of the battery cells interacts with the stress gradient induced by the free edge effects, it leads to the premature appearance of transverse cracks, as illustrated by the f₂ criterion field in the 90 ply in Figure 9b. Therefore, the estimation of the distance between the edge of the coupon and the edge of the battery cell depends on (i) the ratio between the transverse Young modulus of the UD plies and the Young modulus of the battery cells (which will induce local overstressing), (ii) the transverse strength of the UD ply considered and (iii) the size of the specimen, which should be consistent with the experimental testing machine available in the laboratory.

For the present configuration, it was numerically determined that the ratio of the width of the battery to the width of the plate should be greater than 1.5 and the distance between the edge of the cell and the edge of the coupon should be at least 10 mm.
on the global stiffness and a limited effect on the damage initiation. Therefore, a rectangular shape was
chosen for the battery cells for the sake of simplicity.

<figure><img src="image_11.png" /><figcaption>**Figure 9.** a) Mesh and boundary conditions of the FE simulation of a laminate with battery cells, b) cumulative plastic strain (p) in the cells and failure criterion (f₂) in the 90 plies at failure load.</figcaption></figure>

Finally, it has been numerically demonstrated that an important geometric parameter for damage initiation is the distance between the free edges of the specimens and the edges of the battery cells. In fact, when the stress gradient generated by the introduction of the battery cells interacts with the stress gradient induced by the free edge effects, it leads to the premature appearance of transverse cracks, as illustrated by the f₂ criterion field in the 90 ply in Figure 9b. Therefore, the estimation of the distance between the edge of the coupon and the edge of the battery cell depends on (i) the ratio between the transverse Young modulus of the UD plies and the Young modulus of the battery cells (which will induce local overstressing), (ii) the transverse strength of the UD ply considered and (iii) the size of the specimen, which should be consistent with the experimental testing machine available in the laboratory.

For the present configuration, it was numerically determined that the ratio of the width of the battery to the width of the plate should be greater than 1.5 and the distance between the edge of the cell and the edge of the coupon should be at least 10 mm.
Considering these numerical recommendations, it was decided to manufacture a composite plate with electrically non-functional RMS battery cells for the sake of simplicity. Therefore, as shown in Figure 10, six battery cells have been integrated only in the central 90 plies and ±45 plies of a 16-ply quasi-isotropic [(45/90/-45/0)$_2$]s laminate, a lay-up which is widely used in the aeronautical industry. The battery cells have been integrated considering 2 blocks of 3 consecutive battery cells, so that in future work only 2 copper foils (one for the anode and one for the cathode) per cell block will be integrated to extract the current from the composite coupon. In fact, thin and narrow copper foils are used as current collectors and are inserted at the 90/45 interface between the plies. The connections between the copper current collectors and the battery cell are made using a silver clay as a bonding and conductive agent and then the copper current collectors are then coated with an insulating paint to prevent short circuits.

The dimensions of the quasi-isotropic laminate, after machining with a water-cooled diamond saw, are 200 mm x 30 mm x 2.92 mm. The free length of the sample is 150 mm, with the remainder of the sample clamped in the hydraulic jaws. The in-plane size of the battery cells is 100 mm x 20 mm to obtain an in-plane section of approximately 2000 mm² for each battery cell.

<figure><img src="image_10.png" /><figcaption>**Figure 10.** Geometrical configuration for a 16-ply quasi-isotropic composite plate with 6 RMS cells.</figcaption></figure>

For this configuration, the FE model contains approximately 1 million degrees of freedom and the mesh is shown in Figure 9a. The present model predicts a -7% decrease in the global stiffness of the laminate (-4.4% with elasticity in the RMS cells) and a -28% decrease in the onset of transverse cracks in the 90 plies (-24% with elasticity in the RMS cells). Indeed, as shown in Figure 9b, the integration of the
Considering these numerical recommendations, it was decided to manufacture a composite plate with electrically non-functional RMS battery cells for the sake of simplicity. Therefore, as shown in Figure 10, six battery cells have been integrated only in the central 90 plies and ±45 plies of a 16-ply quasi-isotropic [(45/90/-45/0)$_2$]s laminate, a lay-up which is widely used in the aeronautical industry. The battery cells have been integrated considering 2 blocks of 3 consecutive battery cells, so that in future work only 2 copper foils (one for the anode and one for the cathode) per cell block will be integrated to extract the current from the composite coupon. In fact, thin and narrow copper foils are used as current collectors and are inserted at the 90/45 interface between the plies. The connections between the copper current collectors and the battery cell are made using a silver clay as a bonding and conductive agent and then the copper current collectors are then coated with an insulating paint to prevent short circuits.

The dimensions of the quasi-isotropic laminate, after machining with a water-cooled diamond saw, are 200 mm x 30 mm x 2.92 mm. The free length of the sample is 150 mm, with the remainder of the sample clamped in the hydraulic jaws. The in-plane size of the battery cells is 100 mm x 20 mm to obtain an in-plane section of approximately 2000 mm² for each battery cell.

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Geometrical configuration for a 16-ply quasi-isotropic composite plate with 6 RMS cells.</figcaption></figure>

For this configuration, the FE model contains approximately 1 million degrees of freedom and the mesh is shown in Figure 9a. The present model predicts a -7% decrease in the global stiffness of the laminate (-4.4% with elasticity in the RMS cells) and a -28% decrease in the onset of transverse cracks in the 90 plies (-24% with elasticity in the RMS cells). Indeed, as shown in Figure 9b, the integration of the
plasticity in the battery cells induces a redistribution of the stresses in the vicinity of the battery cells, especially in the 90-plies, and thus has a non-negligible influence on the two quantities of interest.

In addition, the composite coupon should be able to store 1 W.h of electrical energy, considering 200 W.h/l for the battery cells. Assuming a density of 1.54 g/cm³ for the composite material and 2.31 g/cm³ for the battery cells, the mass of the coupon was increased by +5% compared to the reference coupon.

## 4.2 Manufacturing of a composite plate with RMS cells

The protocol for manufacturing of a quasi-isotropic laminated composite plate with embedded RMS cells is detailed in Figure 11 and can be decomposed in 6 main steps. First, the unidirectional plies were manually cut in the different directions (0°, 90°, ±45°) from the prepreg roll. For the plies containing battery cells, the shape of the cell was previously manually cut into the prepreg ply with a scalpel.

<figure><img src="image_11.png" /><figcaption>**Figure 11.** Proposed manufacturing protocol for a composite plate with 6 RMS cells.</figcaption></figure>

The battery cells are then integrated into the uncured prepreg plies during the manual lay-up process. Three single-electrode layer cells were stacked consecutively in two 45/90/-45 blocks of plies with a total thickness slightly greater than the 3 corresponding plies. The composite laminate with battery cells was then placed in a vacuum bag, using the same bleeder cloth than as in the reference cycle. The
plasticity in the battery cells induces a redistribution of the stresses in the vicinity of the battery cells, especially in the 90-plies, and thus has a non-negligible influence on the two quantities of interest.

In addition, the composite coupon should be able to store 1 W.h of electrical energy, considering 200 W.h/l for the battery cells. Assuming a density of 1.54 g/cm³ for the composite material and 2.31 g/cm³ for the battery cells, the mass of the coupon was increased by +5% compared to the reference coupon.

## 4.2 Manufacturing of a composite plate with RMS cells

The protocol for manufacturing of a quasi-isotropic laminated composite plate with embedded RMS cells is detailed in Figure 11 and can be decomposed in 6 main steps. First, the unidirectional plies were manually cut in the different directions (0°, 90°, ±45°) from the prepreg roll. For the plies containing battery cells, the shape of the cell was previously manually cut into the prepreg ply with a scalpel.

<figure><img src="image_13.png" /><figcaption>**Figure 11.** Proposed manufacturing protocol for a composite plate with 6 RMS cells.</figcaption></figure>

The battery cells are then integrated into the uncured prepreg plies during the manual lay-up process. Three single-electrode layer cells were stacked consecutively in two 45/90/-45 blocks of plies with a total thickness slightly greater than the 3 corresponding plies. The composite laminate with battery cells was then placed in a vacuum bag, using the same bleeder cloth than as in the reference cycle. The
modified curing cycle was then applied to the laminated composite plate with 6 embedded RMS battery
cells. An aluminium caul plate [26] was placed on the side of the vacuum bag prior to placing the sample
in the autoclave to provide two flat outer surfaces. Furthermore, the heating rate near the plateau
temperature was reduced from 2°C/min to 1°C/min, to avoid a possible thermal overshoot, that could
lead to an unwanted chemical reaction with the electrolyte if reaching 160°C. Finally, the cured laminate
is cut to the above dimensions using a water-cooled diamond saw. The composite plate was then
controlled with X-ray tomography at LMPS Paris-Saclay with two resolutions which are respectively
68µm to observe the whole specimen and 34 µm to zoom in on the central part around the 6 cells of the
specimen, as shown in Figure 12a. The quality of the manufactured composite plate is very promising,
despite the fact that some initial defects are observed with X-ray tomography. Indeed, some initial out-
of-plane ply waviness is observed in the specimen around the battery cells (mainly across the width of
the specimen) because the thickness of a battery cell (~210 µm) is slightly greater than the thickness of
a ply (~182 µm). The use of a caul plate ensured a flat outer surface [26], but increased the amplitude
of very localised initial waviness at the edge of the battery cell in the transverse direction. Some very
localised initial delamination cracks were observed on CT scans in the transverse direction (section A-
A') for maximum crack lengths equal to a maximum of 2 ply thicknesses (less than 0.5 mm). No initial
delamination cracks were observed in the longitudinal direction (section B-B'). Some initial slippage
between the different cell layers was observed (section C-C'). In addition, a decrease in the total
thickness of the laminate with embedded cells, of approximatively one ply thickness, was measured
after the manufacture. This could be due to the introduction of the caul plate, which probably resulted
in a greater flow of matrix out of the composite plate, and thus changing the fibre volume ratio in the
plies. These three points will be improved in the future, by integrating RMS cells with double electrode
layers corresponding to the thickness of a 3-ply block and without the use of a caul plate.
modified curing cycle was then applied to the laminated composite plate with 6 embedded RMS battery
cells. An aluminium caul plate [26] was placed on the side of the vacuum bag prior to placing the sample
in the autoclave to provide two flat outer surfaces. Furthermore, the heating rate near the plateau
temperature was reduced from 2°C/min to 1°C/min, to avoid a possible thermal overshoot, that could
lead to an unwanted chemical reaction with the electrolyte if reaching 160°C. Finally, the cured laminate
is cut to the above dimensions using a water-cooled diamond saw. The composite plate was then
controlled with X-ray tomography at LMPS Paris-Saclay with two resolutions which are respectively
68µm to observe the whole specimen and 34 µm to zoom in on the central part around the 6 cells of the
specimen, as shown in Figure 12a. The quality of the manufactured composite plate is very promising,
despite the fact that some initial defects are observed with X-ray tomography. Indeed, some initial out-
of-plane ply waviness is observed in the specimen around the battery cells (mainly across the width of
the specimen) because the thickness of a battery cell (~210 µm) is slightly greater than the thickness of
a ply (~182 µm). The use of a caul plate ensured a flat outer surface [26], but increased the amplitude
of very localised initial waviness at the edge of the battery cell in the transverse direction. Some very
localised initial delamination cracks were observed on CT scans in the transverse direction (section A-
A') for maximum crack lengths equal to a maximum of 2 ply thicknesses (less than 0.5 mm). No initial
delamination cracks were observed in the longitudinal direction (section B-B'). Some initial slippage
between the different cell layers was observed (section C-C'). In addition, a decrease in the total
thickness of the laminate with embedded cells, of approximatively one ply thickness, was measured
after the manufacture. This could be due to the introduction of the caul plate, which probably resulted
in a greater flow of matrix out of the composite plate, and thus changing the fibre volume ratio in the
plies. These three points will be improved in the future, by integrating RMS cells with double electrode
layers corresponding to the thickness of a 3-ply block and without the use of a caul plate.
<figure><img src="image_12.png" /><figcaption>**Figure 12.** Controls of the manufactured composite specimen with 6 embedded RMS cells using a) CT-scan and b) micrographs taken after failure of an undamaged part of the specimen (away from the failure location).</figcaption></figure>

Moreover, as shown in Figure 12b, some initial voids are also observed on the free polished edges, and also in the X-ray tomography, but the void volume content remains low (estimated below 2.5% after images analysis). In addition, after the test presented in the next section, the specimen was cut far from the failure zone in order to analyse the integration of the battery cells into the composite laminate, as shown in Figure 12b. Again, out-of-plane ply waviness associated with localised delamination cracks is observed at the edges of the battery cells and the observations are consistent with those obtained from the CT-scan.

### 4.3 Evaluation of the residual mechanical performance

Finally, a tensile test on a quasi-isotropic composite plate with 6 embedded RMS battery cells was carried out at ONERA using a hydraulic testing machine with a maximum load capacity of 100 kN and hydraulic jaws, using the multi-instrumentation described in section 2.2. The macroscopic behaviour of the composite plate with 6 embedded RMS battery cells is slightly non-linear until final failure, as shown in Figure 13a. For the composite plate with battery cells, the modulus is equal to $E_{xx}= 43.2$ GPa,
<figure><img src="image_14.png" /><figcaption>**Figure 12.** Controls of the manufactured composite specimen with 6 embedded RMS cells using a) CT-scan and b) micrographs taken after failure of an undamaged part of the specimen (away from the failure location).</figcaption></figure>

Moreover, as shown in Figure 12b, some initial voids are also observed on the free polished edges, and also in the X-ray tomography, but the void volume content remains low (estimated below 2.5% after images analysis). In addition, after the test presented in the next section, the specimen was cut far from the failure zone in order to analyse the integration of the battery cells into the composite laminate, as shown in Figure 12b. Again, out-of-plane ply waviness associated with localised delamination cracks is observed at the edges of the battery cells and the observations are consistent with those obtained from the CT-scan.

### 4.3 Evaluation of the residual mechanical performance

Finally, a tensile test on a quasi-isotropic composite plate with 6 embedded RMS battery cells was carried out at ONERA using a hydraulic testing machine with a maximum load capacity of 100 kN and hydraulic jaws, using the multi-instrumentation described in section 2.2. The macroscopic behaviour of the composite plate with 6 embedded RMS battery cells is slightly non-linear until final failure, as shown in Figure 13a. For the composite plate with battery cells, the modulus is equal to $E_{xx}= 43.2$ GPa,
i.e. a -16% decrease compared to the reference composite plate without battery cells and manufactured using the material supplier's recommended curing cycle.

<figure><img src="image_13.png" /><figcaption>**Figure 13.** a) Comparison of macroscopic strain/stress curves with and without battery cells, and b) failure pattern of the plate with RMS cells analysed by micrograph and CT-scan.</figcaption></figure>

For the composite plate with battery cells, the onset of damage, obtained by analysing the first significant acoustic events, is equal to $\epsilon_{xx}^{fpf}=0.6\%$ (or $\Sigma_{xx}^{fpf}=270$ MPa), while for the reference plate it is equal to $\epsilon_{xx}^{fpf}=0.75\%$ (or $\Sigma_{xx}^{fpf}=390$ MPa), i.e. a -20% decrease in the macroscopic strain (or a -30% decrease in the macroscopic stress) recorded at the first significant acoustic events. The first acoustic events in the plate with RMS cells are probably due to the failure of the cells, since the measured macroscopic strain corresponds to the strain at failure measured on the tested battery cells alone, as described in section 2.1. It also means that the present composite plate should not be subjected to a macroscopic stress higher than $\Sigma_{xx}=260$ MPa, in order to avoid damaging the battery cells and thus ensure the electrical performance of the cells. For the reference plate, the first acoustic events are associated with the transverse cracks in the 90 plies. Finally, the macroscopic strength of the plate with battery cells is equal to $\Sigma_{xx}^{lpf}=503$ MPa, i.e. a decrease of -29% compared to the reference plate. It is also interesting to compare the macroscopic strain at failure, which is equal to $\epsilon_{xx}^{lpf}=1.41\%$ for the reference plate and $\epsilon_{xx}^{lpf}=1.18\%$ for the plate with cells, i.e. a decrease of -16%. The failure occurs in the free area of the specimen for all specimens tested (with and without battery cells) and is due to fibre
i.e. a -16% decrease compared to the reference composite plate without battery cells and manufactured using the material supplier's recommended curing cycle.

<figure><img src="image_15.png" /><figcaption>**Figure 13.** a) Comparison of macroscopic strain/stress curves with and without battery cells, and b) failure pattern of the plate with RMS cells analysed by micrograph and CT-scan.</figcaption></figure>

For the composite plate with battery cells, the onset of damage, obtained by analysing the first significant acoustic events, is equal to $\varepsilon_{xx}^{fpf}=0.6\%$ (or $\Sigma_{xx}^{fpf}=270$ MPa), while for the reference plate it is equal to $\varepsilon_{xx}^{fpf}=0.75\%$ (or $\Sigma_{xx}^{fpf}=390$ MPa), i.e. a -20% decrease in the macroscopic strain (or a -30% decrease in the macroscopic stress) recorded at the first significant acoustic events. The first acoustic events in the plate with RMS cells are probably due to the failure of the cells, since the measured macroscopic strain corresponds to the strain at failure measured on the tested battery cells alone, as described in section 2.1. It also means that the present composite plate should not be subjected to a macroscopic stress higher than $\Sigma_{xx}=260$ MPa, in order to avoid damaging the battery cells and thus ensure the electrical performance of the cells. For the reference plate, the first acoustic events are associated with the transverse cracks in the 90 plies. Finally, the macroscopic strength of the plate with battery cells is equal to $\Sigma_{xx}^{lpf}=503$ MPa, i.e. a decrease of -29% compared to the reference plate. It is also interesting to compare the macroscopic strain at failure, which is equal to $\varepsilon_{xx}^{lpf}=1.41\%$ for the reference plate and $\varepsilon_{xx}^{lpf}=1.18\%$ for the plate with cells, i.e. a decrease of -16%. The failure occurs in the free area of the specimen for all specimens tested (with and without battery cells) and is due to fibre
failure, considering the analysis of the failure pattern optically observed or with CT scan, as reported in
Figure 13b.

The predictions of the finite element simulations presented in section 4.1, considering the plasticity in
the battery cells and the damage in the composite part, were compared with the results obtained. The
measured and predicted macroscopic stress/strain curves for the composite plates with and without
battery cells are shown in Figure 14a. The prediction for the composite plate without battery cells is in
very good agreement with the test results. For the plate with battery cells, the prediction is in good
agreement with the tests until the applied strain reaches 0.6%, after which it is in poor agreement
thereafter. Firstly, the macroscopic stiffness is overestimated by the model. Taking into account the
plasticity of the cells slightly improves the accuracy of the predicted macroscopic stiffness. In fact, the
reduction in the macroscopic modulus due to the introduction of cells was estimated to be -4.4%
(considering the elasticity of the cell) and -6.8% (considering the plasticity of the cell), while the
measured value is -16%, as shown in Figure 14b. This discrepancy is mainly due to the fact that initial
defects (out-of-plane ply waviness due to the greater thickness of the battery cell, initial voids, local
delamination, decrease in the total thickness) are not considered in the simulations for the time being.
The consideration of damage in the composite plies does not affect the macroscopic longitudinal
modulus due to the presence of 0° plies, but plays a non-negligible role in the estimation of the
macroscopic Poisson's ratio, as already observed in the literature [27]. The measured and predicted
decrease in damage onset is then examined for the plate containing the battery cells, as shown in Figure
14b. Considering an elastic behaviour for the cell, the decrease in damage onset is estimated to be -20%
and corresponds to the first transverse crack in the 90-ply starting from the edge of the battery cells.
However, by considering the plasticity of the RMS cells combined with a simple maximum strain
criterion, the first predicted damage event corresponds to the failure of the battery cell itself and induces
a higher decrease in the first damage event estimated at -25%, while the measured value is -30%.
Therefore, the first acoustic events for the plate with RMS battery cells are well predicted by the present
model. In order to improve the accuracy of the predicted macroscopic stress/strain curves after cells
failure, future work could consist of considering the damage process within the battery cells.
failure, considering the analysis of the failure pattern optically observed or with CT scan, as reported in
Figure 13b.

The predictions of the finite element simulations presented in section 4.1, considering the plasticity in
the battery cells and the damage in the composite part, were compared with the results obtained. The
measured and predicted macroscopic stress/strain curves for the composite plates with and without
battery cells are shown in Figure 14a. The prediction for the composite plate without battery cells is in
very good agreement with the test results. For the plate with battery cells, the prediction is in good
agreement with the tests until the applied strain reaches 0.6%, after which it is in poor agreement
thereafter. Firstly, the macroscopic stiffness is overestimated by the model. Taking into account the
plasticity of the cells slightly improves the accuracy of the predicted macroscopic stiffness. In fact, the
reduction in the macroscopic modulus due to the introduction of cells was estimated to be -4.4%
(considering the elasticity of the cell) and -6.8% (considering the plasticity of the cell), while the
measured value is -16%, as shown in Figure 14b. This discrepancy is mainly due to the fact that initial
defects (out-of-plane ply waviness due to the greater thickness of the battery cell, initial voids, local
delamination, decrease in the total thickness) are not considered in the simulations for the time being.
The consideration of damage in the composite plies does not affect the macroscopic longitudinal
modulus due to the presence of 0° plies, but plays a non-negligible role in the estimation of the
macroscopic Poisson's ratio, as already observed in the literature [27]. The measured and predicted
decrease in damage onset is then examined for the plate containing the battery cells, as shown in Figure
14b. Considering an elastic behaviour for the cell, the decrease in damage onset is estimated to be -20%
and corresponds to the first transverse crack in the 90-ply starting from the edge of the battery cells.
However, by considering the plasticity of the RMS cells combined with a simple maximum strain
criterion, the first predicted damage event corresponds to the failure of the battery cell itself and induces
a higher decrease in the first damage event estimated at -25%, while the measured value is -30%.
Therefore, the first acoustic events for the plate with RMS battery cells are well predicted by the present
model. In order to improve the accuracy of the predicted macroscopic stress/strain curves after cells
failure, future work could consist of considering the damage process within the battery cells.
<figure><img src="image_14.png" /><figcaption>**Figure 14.** Comparison of a) measured and predicted stress/strain curves for composite plates with and without cells, and of b) the measured and predicted reduction of mechanical properties due to the introduction of RMS cells in a 16-ply quasi-isotropic composite plate.</figcaption></figure>

The analysis of the test with the FE simulation has helped to accurately determine the damage scenario until the final failure of the laminate with RMS battery cells. Moreover, it tends to show that the first test results are promising and that the residual performance can still be increased by improving the quality of the composite plate by optimising the manufacturing process (introduction of block of battery cells with a total thickness equal to the thickness of 3 unidirectional plies, and without the use of a caul plate).

**5. Conclusion**

The present work deals with a numerical and experimental evaluation of the residual mechanical performance of a composite laminate made of unidirectional carbon/epoxy plies, widely used in the aeronautical industry, in which solid battery cells have been integrated. The mechanical characterization of the battery cells was carried out using multi-instrumented tests and a plastic model was proposed to describe the measured non-linear behaviour. The AS4/8552 composite material has also been studied and the Onera Progressive Failure Model has been successfully applied to the tests carried out on a composite plate without cells, which is considered as a reference case. The curing cycle of such a high-performance composite laminate was then modified to preserve the electrical performance of the battery cells while maintaining high mechanical properties, which were verified by additional mechanical tests
<figure><img src="image_16.png" /><figcaption>**Figure 14.** Comparison of a) measured and predicted stress/strain curves for composite plates with and without cells, and of b) the measured and predicted reduction of mechanical properties due to the introduction of RMS cells in a 16-ply quasi-isotropic composite plate.</figcaption></figure>

The analysis of the test with the FE simulation has helped to accurately determine the damage scenario until the final failure of the laminate with RMS battery cells. Moreover, it tends to show that the first test results are promising and that the residual performance can still be increased by improving the quality of the composite plate by optimising the manufacturing process (introduction of block of battery cells with a total thickness equal to the thickness of 3 unidirectional plies, and without the use of a caul plate).

**5. Conclusion**

The present work deals with a numerical and experimental evaluation of the residual mechanical performance of a composite laminate made of unidirectional carbon/epoxy plies, widely used in the aeronautical industry, in which solid battery cells have been integrated. The mechanical characterization of the battery cells was carried out using multi-instrumented tests and a plastic model was proposed to describe the measured non-linear behaviour. The AS4/8552 composite material has also been studied and the Onera Progressive Failure Model has been successfully applied to the tests carried out on a composite plate without cells, which is considered as a reference case. The curing cycle of such a high-performance composite laminate was then modified to preserve the electrical performance of the battery cells while maintaining high mechanical properties, which were verified by additional mechanical tests
and compared to the reference case. Following the design of a 16-ply quasi-isotropic laminate plate
with 6 embedded battery cells using non-linear FE simulations, one composite laminated plate has been
manufactured using the modified curing cycle. The mass of the coupon has been increased by 5% and
the specimen should be able to store ~1 W.h of electrical energy, as its electrical functionality is yet to
be proven. The degradation of the macroscopic modulus is about -16% and that of the strength is about
-29%, which could soon be reduced by improving the manufacturing process, in particular by better
controlling the thickness of the battery cells. Future work should consist of experimentally identifying
the missing mechanical properties of the RMS battery cell itself by an inverse method considering cells
in a composite part subjected to relevant loads. In addition, the determination of the strength and fracture
toughness of the cell / composite interface should be determined by non-trivial dedicated tests, as this
is a key parameter for the efficient integration of battery cells, that is currently not considered. As the
manufacturing protocol is now defined, such an experimental study can be carried out soon.

The next step is to manufacture a laminated composite plate with RMS electrically functional battery
cells and measure both mechanical and electrical performance. Particular attention will be paid to the
evolution of the electrical performance as a function of the applied load level and thus to the deformation
of the cell. The influence of damage inside the cell on the electrical performance will also be
investigated.

Acknowledgments

The authors are grateful to the European Commission for supporting the present work, performed within the SOLIFLY project, funded by the Clean Aviation Joint Undertaking under the European Union's Horizon 2020 research and innovation program (Grant Agreement no. 101007577). This publication solely reflects the authors' view and neither the European Union, nor the funding Agency can be held responsible for the information it contains.
and compared to the reference case. Following the design of a 16-ply quasi-isotropic laminate plate
with 6 embedded battery cells using non-linear FE simulations, one composite laminated plate has been
manufactured using the modified curing cycle. The mass of the coupon has been increased by 5% and
the specimen should be able to store ~1 W.h of electrical energy, as its electrical functionality is yet to
be proven. The degradation of the macroscopic modulus is about -16% and that of the strength is about
-29%, which could soon be reduced by improving the manufacturing process, in particular by better
controlling the thickness of the battery cells. Future work should consist of experimentally identifying
the missing mechanical properties of the RMS battery cell itself by an inverse method considering cells
in a composite part subjected to relevant loads. In addition, the determination of the strength and fracture
toughness of the cell / composite interface should be determined by non-trivial dedicated tests, as this
is a key parameter for the efficient integration of battery cells, that is currently not considered. As the
manufacturing protocol is now defined, such an experimental study can be carried out soon.

The next step is to manufacture a laminated composite plate with RMS electrically functional battery
cells and measure both mechanical and electrical performance. Particular attention will be paid to the
evolution of the electrical performance as a function of the applied load level and thus to the deformation
of the cell. The influence of damage inside the cell on the electrical performance will also be
investigated.

Acknowledgments

The authors are grateful to the European Commission for supporting the present work, performed within
the SOLIFLY project, funded by the Clean Aviation Joint Undertaking under the European Union's
Horizon 2020 research and innovation program (Grant Agreement no. 101007577). This publication
solely reflects the authors' view and neither the European Union, nor the funding Agency can be held
responsible for the information it contains.
Appendix

In order to better understand the behaviour of the battery cells at the macroscopic level and to justify some of the modelling choices made, additional tests were carried out on the components of an RMS cell. Two tensile tests were carried out on specimens consisting of a cathode coated on Al foil and an anode coated on Cu foil, respectively, as shown in Figure 15. It should be noted that the thicknesses of the two specimens tested are 52 µm and 109 µm respectively, which makes the test difficult to perform. Only tensile tests are possible for such thin specimens, and these were carried out on an electromechanical testing machine with a maximum load capacity of 10 kN combined with a 1 kN load cell, using the multi-instrumentation described in section 2.2. A virtual strain gauge with a grid size of 7 mm x 4mm was used to measure the longitudinal strain. For the anode and cathode parts, the measured behaviour is highly non-linear up to the final failure, and the low strain at failure for the anode, around 0.8%, can be noted. The Young modulus, measured between 10% and 50% of the failure stress, was experimentally determined to be $E_{xx}^{anode}$ = 13.90 GPa and $E_{xx}^{cathode}$ = 13.55 GPa respectively. For the electrolyte, which is based on a porous LY556 matrix filled with ionic liquid, the Young modulus was assumed to be equal to $E_{xx}^{electro}$ = 3.30 GPa, as reported in the literature [28]. In our opinion, it seems relevant to consider the three elementary constituents as isotropic materials. Due to a lack of information, the Poisson ratios for the three constituents are set to 0.3 by default.

<figure><img src="image_15.png" /><figcaption>**Figure 15.** Measured non-linear behaviour of a) the anode coated on Al foil and b) the cathode coated on Cu foil.</figcaption></figure>

In order to determine the elastic properties of the battery cell knowing the elastic properties of the constituents, the 3D meso/macro change of scale is achieved using the Transformation Field Analysis
Appendix

In order to better understand the behaviour of the battery cells at the macroscopic level and to justify some of the modelling choices made, additional tests were carried out on the components of an RMS cell. Two tensile tests were carried out on specimens consisting of a cathode coated on Al foil and an anode coated on Cu foil, respectively, as shown in Figure 15. It should be noted that the thicknesses of the two specimens tested are 52 µm and 109 µm respectively, which makes the test difficult to perform. Only tensile tests are possible for such thin specimens, and these were carried out on an electromechanical testing machine with a maximum load capacity of 10 kN combined with a 1 kN load cell, using the multi-instrumentation described in section 2.2. A virtual strain gauge with a grid size of 7 mm x 4mm was used to measure the longitudinal strain. For the anode and cathode parts, the measured behaviour is highly non-linear up to the final failure, and the low strain at failure for the anode, around 0.8%, can be noted. The Young modulus, measured between 10% and 50% of the failure stress, was experimentally determined to be $E_{xx}^{anode}$ = 13.90 GPa and $E_{xx}^{cathode}$ = 13.55 GPa respectively. For the electrolyte, which is based on a porous LY556 matrix filled with ionic liquid, the Young modulus was assumed to be equal to $E_{xx}^{electro}$ = 3.30 GPa, as reported in the literature [28]. In our opinion, it seems relevant to consider the three elementary constituents as isotropic materials. Due to a lack of information, the Poisson ratios for the three constituents are set to 0.3 by default.

<figure><img src="image_17.png" /><figcaption>**Figure 15.** Measured non-linear behaviour of a) the anode coated on Al foil and b) the cathode coated on Cu foil.</figcaption></figure>

In order to determine the elastic properties of the battery cell knowing the elastic properties of the constituents, the 3D meso/macro change of scale is achieved using the Transformation Field Analysis
(TFA), which can be seen as an extension of the classical laminate theory to the 3D stress state. More information on TFA can be found in the literature [29,30]. Basically, the TFA method is based on a Representative Volume Element (RVE) (i.e. the multi-layered battery cell) which is divided into a number of sub-volumes (i.e. layers forming the laminate) within which the mechanical fields (stress and strain) are assumed to be uniform. This classical method is used here in order to determine the 3D macroscopic elastic stiffness of the battery cells, knowing the elastic properties of the components (anode, electrolyte and cathode), as shown in Figure 16a. The predicted macroscopic behaviour is in good agreement with the experimental data, with an error of -4.2%.

<figure><img src="image_16.png" /><figcaption>**Figure 16.** a) Comparison between the predicted and measured macroscopic elastic modulus for the battery cell, b) the influence of the Young modulus of the constituents on the macroscopic modulus of the RMS cell and c) predicted Young and in-plane shear moduli for different orientations.</figcaption></figure>

A sensitivity study was then carried out to determine the influence of the constituents on the macroscopic behaviour of the RMS cell. Among the methods found in the literature, the simplest is to vary the input parameters one by one (here a variation of +1% was chosen), while the other parameters are fixed at a nominal value, a method called One-At-a-Time [31,32]. This allows the influence of each input parameter on the output to be assessed independently. This method therefore requires as many calculations as there are input parameters to be evaluated in the model, plus the simulation on the reference configuration. The sensitivity has been calculated by finite difference. However, this simple method has two major limitations: (i) it does not allow any coupling between the input variables to be
(TFA), which can be seen as an extension of the classical laminate theory to the 3D stress state. More information on TFA can be found in the literature [29,30]. Basically, the TFA method is based on a Representative Volume Element (RVE) (i.e. the multi-layered battery cell) which is divided into a number of sub-volumes (i.e. layers forming the laminate) within which the mechanical fields (stress and strain) are assumed to be uniform. This classical method is used here in order to determine the 3D macroscopic elastic stiffness of the battery cells, knowing the elastic properties of the components (anode, electrolyte and cathode), as shown in Figure 16a. The predicted macroscopic behaviour is in good agreement with the experimental data, with an error of -4.2%.

<figure><img src="image_18.png" /><figcaption>**Figure 16.** a) Comparison between the predicted and measured macroscopic elastic modulus for the battery cell, b) the influence of the Young modulus of the constituents on the macroscopic modulus of the RMS cell and c) predicted Young and in-plane shear moduli for different orientations.</figcaption></figure>

A sensitivity study was then carried out to determine the influence of the constituents on the macroscopic behaviour of the RMS cell. Among the methods found in the literature, the simplest is to vary the input parameters one by one (here a variation of +1% was chosen), while the other parameters are fixed at a nominal value, a method called One-At-a-Time [31,32]. This allows the influence of each input parameter on the output to be assessed independently. This method therefore requires as many calculations as there are input parameters to be evaluated in the model, plus the simulation on the reference configuration. The sensitivity has been calculated by finite difference. However, this simple method has two major limitations: (i) it does not allow any coupling between the input variables to be
considered and (ii) it is limited to assessing the sensitivity locally, around a reference solution (this is the reason why tests on constituents to determine their moduli were carried out prior to the sensitivity study). As reported in Figure 16b, it has been shown numerically that the macroscopic elastic behaviour is mainly imposed by the Young modulus of the anode part, then by the cathode and finally by the electrolyte. This result is consistent with the proportion of each component in the RMS cell taking into account the low value of Young modulus associated with the electrolyte. Therefore, in our opinion, it seems relevant to consider that the non-linear behaviour of the cells is mainly imposed by the non-linear behaviour of the anode, associated with a low strain at failure. A further sensitivity study was then carried out to demonstrate the negligible influence of the Poisson ratios of the elementary constituents, which have not yet been measured, on the Young modulus of the battery cells (although it can be noted that they play a non-negligible role on the macroscopic in-plane shear modulus).

<table><caption>**Table 4.** Mechanical properties of the three components (cathode, electrolyte, anode) and estimation of the elastic properties of the RMS battery cell using the TFA method</caption><thead><tr><th>Component</th><th>Properties</th><th>Value</th><th>Properties</th><th>RMS cells</th></tr></thead><tbody><tr><td rowspan="2">Cathode</td><td>E</td><td>13.9 GPa</td><td>E<sub>xx</sub> = E<sub>yy</sub></td><td>11.2 GPa</td></tr><tr><td>v</td><td>0.3</td><td>E<sub>zz</sub></td><td>8.5 GPa</td></tr><tr><td rowspan="2">Electrolyte</td><td>E</td><td>3.3 GPa</td><td>G<sub>xy</sub></td><td>3.0 GPa</td></tr><tr><td>v</td><td>0.3</td><td>G<sub>xz</sub> = G<sub>yz</sub></td><td>4.3 GPa</td></tr><tr><td rowspan="2">Anode</td><td>E</td><td>13.5 GPa</td><td>v<sub>xy</sub> = v<sub>xz</sub> = v<sub>yz</sub></td><td>0.3</td></tr><tr><td>v</td><td>0.3</td><td></td><td></td></tr></tbody></table>

Finally, considering the meso/macro change of scale methodology, the 3D elastic properties of the battery cells have been estimated from the knowledge of the elastic properties of each component. It has been shown numerically that the RMS cell can be considered as quasi-isotropic in the plane, as shown in Figure 16c where the macroscopic longitudinal, transverse and in-plane shear moduli are
considered and (ii) it is limited to assessing the sensitivity locally, around a reference solution (this is the reason why tests on constituents to determine their moduli were carried out prior to the sensitivity study). As reported in Figure 16b, it has been shown numerically that the macroscopic elastic behaviour is mainly imposed by the Young modulus of the anode part, then by the cathode and finally by the electrolyte. This result is consistent with the proportion of each component in the RMS cell taking into account the low value of Young modulus associated with the electrolyte. Therefore, in our opinion, it seems relevant to consider that the non-linear behaviour of the cells is mainly imposed by the non-linear behaviour of the anode, associated with a low strain at failure. A further sensitivity study was then carried out to demonstrate the negligible influence of the Poisson ratios of the elementary constituents, which have not yet been measured, on the Young modulus of the battery cells (although it can be noted that they play a non-negligible role on the macroscopic in-plane shear modulus).

<table><caption>**Table 4.** Mechanical properties of the three components (cathode, electrolyte, anode) and estimation of the elastic properties of the RMS battery cell using the TFA method</caption><thead><tr><th>Component</th><th>Properties</th><th>Value</th><th>Properties</th><th>RMS cells</th></tr></thead><tbody><tr><td rowspan="2">Cathode</td><td>E</td><td>13.9 GPa</td><td>E<sub>xx</sub> = E<sub>yy</sub></td><td>11.2 GPa</td></tr><tr><td>v</td><td>0.3</td><td>E<sub>zz</sub></td><td>8.5 GPa</td></tr><tr><td rowspan="2">Electrolyte</td><td>E</td><td>3.3 GPa</td><td>G<sub>xy</sub></td><td>3.0 GPa</td></tr><tr><td>v</td><td>0.3</td><td>G<sub>xz</sub> = G<sub>yz</sub></td><td>4.3 GPa</td></tr><tr><td rowspan="2">Anode</td><td>E</td><td>13.5 GPa</td><td>v<sub>xy</sub> = v<sub>xz</sub> = v<sub>yz</sub></td><td>0.3</td></tr><tr><td>v</td><td>0.3</td><td></td><td></td></tr></tbody></table>

Finally, considering the meso/macro change of scale methodology, the 3D elastic properties of the battery cells have been estimated from the knowledge of the elastic properties of each component. It has been shown numerically that the RMS cell can be considered as quasi-isotropic in the plane, as shown in Figure 16c where the macroscopic longitudinal, transverse and in-plane shear moduli are
plotted as a function of the angle of an off-axis loading. Analysis of Table 4 shows that, as expected, $E_{xx} = E_{yy}$ and $G_{xy} = E_{xx}/(2(1+\nu_{xy}))$. The out-of-plane elastic properties are estimated to be -30% lower than the in-plane properties but are strongly related to the unknown Poisson ratios of the constituents. The estimated values, with the exception of the Young moduli, need to be considered very carefully. In the present article, it has been decided to consider the RMS battery cell as an isotropic material for the sake of simplicity and because the uncertainty in the out-of-plane properties is not critical for the tensile loads considered.

References

[1] National Academy of Sciences, Transportation Research Board, Transportation Research Circular E-C271: Critical Issues in Aviation and the Environment 2021, 2021.

[2] H. Kuehnelt, A. Beutl, F. Mastropierro, F. Laurin, S. Willrodt, A. Bismarck, M. Guida, F. Romano, Structural Batteries for Aeronautic Applications—State of the Art, Research Gaps and Technology Development Needs, Aerospace. 9 (2022) 31.

[3] F. Danzi, R. Salgado, J. Oliveira, A. Arteiro, P. Camanho, M. Braga, Structural Batteries: A Review, Molecules. 26 (2021) 2203.

[4] L.E. Asp, M. Johansson, G. Lindbergh, J. Xu, D. Zenkert, Structural battery composites: a review, Funct Compos Struct. (2019) 042001.

[5] K. Pattarakunnan, J. Galos, R. Das, A.P. Mouritz, Tensile properties of multifunctional composites embedded with lithium-ion polymer batteries, Compos. Part Appl. Sci. Manuf. 136 (2020) 105966.

[6] S.M. Shalouf, J. Zhang, C.H. Wang, Effects of mechanical deformation on electric performance of rechargeable batteries embedded in load carrying composite structures, Plast. Rubber Compos. 43 (2014) 98–104.

[7] P. Attar, J. Galos, A.S. Best, A.P. Mouritz, Compression properties of multifunctional composite structures with embedded lithium-ion polymer batteries, Compos. Struct. 237 (2020) 111937.
plotted as a function of the angle of an off-axis loading. Analysis of Table 4 shows that, as expected, $E_{xx} = E_{yy}$ and $G_{xy} = E_{xx}/(2(1+\nu_{xy}))$. The out-of-plane elastic properties are estimated to be -30% lower than the in-plane properties but are strongly related to the unknown Poisson ratios of the constituents. The estimated values, with the exception of the Young moduli, need to be considered very carefully. In the present article, it has been decided to consider the RMS battery cell as an isotropic material for the sake of simplicity and because the uncertainty in the out-of-plane properties is not critical for the tensile loads considered.

## References

[1] National Academy of Sciences, Transportation Research Board, Transportation Research Circular E-C271: Critical Issues in Aviation and the Environment 2021, 2021.

[2] H. Kuehnelt, A. Beutl, F. Mastropierro, F. Laurin, S. Willrodt, A. Bismarck, M. Guida, F. Romano, Structural Batteries for Aeronautic Applications—State of the Art, Research Gaps and Technology Development Needs, Aerospace. 9 (2022) 31.

[3] F. Danzi, R. Salgado, J. Oliveira, A. Arteiro, P. Camanho, M. Braga, Structural Batteries: A Review, Molecules. 26 (2021) 2203.

[4] L.E. Asp, M. Johansson, G. Lindbergh, J. Xu, D. Zenkert, Structural battery composites: a review, Funct Compos Struct. (2019) 042001.

[5] K. Pattarakunnan, J. Galos, R. Das, A.P. Mouritz, Tensile properties of multifunctional composites embedded with lithium-ion polymer batteries, Compos. Part Appl. Sci. Manuf. 136 (2020) 105966.

[6] S.M. Shalouf, J. Zhang, C.H. Wang, Effects of mechanical deformation on electric performance of rechargeable batteries embedded in load carrying composite structures, Plast. Rubber Compos. 43 (2014) 98–104.

[7] P. Attar, J. Galos, A.S. Best, A.P. Mouritz, Compression properties of multifunctional composite structures with embedded lithium-ion polymer batteries, Compos. Struct. 237 (2020) 111937.
[8] T.J. Adam, G. Liao, J. Petersen, S. Geier, B. Finke, P. Wierach, A. Kwade, M. Wiedemann, Multifunctional Composites for Future Energy Storage in Aerospace Structures, Energies. 11 (2018).

[9] Y. Zhang, J. Ma, A.K. Singh, L. Cao, J. Seo, C.D. Rahn, C.E. Bakis, M.A. Hickner, Multifunctional structural lithium-ion battery for electric vehicles, J. Intell. Mater. Syst. Struct. 28 (2017) 1603–1613.

[10] P. Ladpli, R. Nardari, F. Kopsaftopoulos, F.-K. Chang, Multifunctional energy storage composite structures with embedded lithium-ion batteries, J. Power Sources. 414 (2019) 517–529.

[11] F. Laurin, A. Beutl, Q. Jiang, H. Kühnelt, Concepts for integrating electrical energy storage into CFRP laminate structures for aeronautic applications, J. Phys. Conf. Ser. 2526 (2023) 012062.

[12] J. Besson, G. Cailletaud, J.L. Chaboche, S. Forest, Mécanique non linéaire des matériaux, edition dunod, 2001.

[13] Hexcel, HexPly_8552_eu_DataSheet, (2020). HexPly_8552_eu_DataSheet.pdf

[14] A.H. Baluch, O. Falco, J.L. Jimenez, B.H. Tijs, C.S. Lopes, An efficient numerical approach to the prediction of laminate tolerance to Barely Visible Impact Damage, Compos. Struct. 225 (2019).

[15] O. Falcó, R.L. Ávila, B. Tijs, C.S. Lopes, Modelling and simulation methodology for unidirectional composite laminates in a Virtual Test Lab framework, Compos. Struct. 190 (2018) 137–159.

[16] T. Garstka, N. Ersoy, K.D. Potter, M.R. Wisnom, In situ measurements of through-the-thickness strains during processing of AS4/8552 composite, Compos. Part Appl. Sci. Manuf. 38 (2007) 2517–2526.

[17] AITM, Airbus Test Method: Determination of Plain, Open Hole and Filled Hole Tensile Strength, Norm AITM 1-0007 Issue 3, 2004.

[18] F. Laurin, N. Carrere, J.F. Maire, A multiscale progressive failure approach for composite laminates based on thermodynamical viscoelastic and damage models, Compos. Part Appl. Sci. Manuf. 38 (2007) 198–209.
[8] T.J. Adam, G. Liao, J. Petersen, S. Geier, B. Finke, P. Wierach, A. Kwade, M. Wiedemann, Multifunctional Composites for Future Energy Storage in Aerospace Structures, Energies. 11 (2018).

[9] Y. Zhang, J. Ma, A.K. Singh, L. Cao, J. Seo, C.D. Rahn, C.E. Bakis, M.A. Hickner, Multifunctional structural lithium-ion battery for electric vehicles, J. Intell. Mater. Syst. Struct. 28 (2017) 1603–1613.

[10] P. Ladpli, R. Nardari, F. Kopsaftopoulos, F.-K. Chang, Multifunctional energy storage composite structures with embedded lithium-ion batteries, J. Power Sources. 414 (2019) 517–529.

[11] F. Laurin, A. Beutl, Q. Jiang, H. Kühnelt, Concepts for integrating electrical energy storage into CFRP laminate structures for aeronautic applications, J. Phys. Conf. Ser. 2526 (2023) 012062.

[12] J. Besson, G. Cailletaud, J.L. Chaboche, S. Forest, Mécanique non linéaire des matériaux, edition dunod, 2001.

[13] Hexcel, HexPly_8552_eu_DataSheet, (2020). HexPly_8552_eu_DataSheet.pdf

[14] A.H. Baluch, O. Falco, J.L. Jimenez, B.H. Tijs, C.S. Lopes, An efficient numerical approach to the prediction of laminate tolerance to Barely Visible Impact Damage, Compos. Struct. 225 (2019).

[15] O. Falcó, R.L. Ávila, B. Tijs, C.S. Lopes, Modelling and simulation methodology for unidirectional composite laminates in a Virtual Test Lab framework, Compos. Struct. 190 (2018) 137–159.

[16] T. Garstka, N. Ersoy, K.D. Potter, M.R. Wisnom, In situ measurements of through-the-thickness strains during processing of AS4/8552 composite, Compos. Part Appl. Sci. Manuf. 38 (2007) 2517–2526.

[17] AITM, Airbus Test Method: Determination of Plain, Open Hole and Filled Hole Tensile Strength, Norm AITM 1-0007 Issue 3, 2004.

[18] F. Laurin, N. Carrere, J.F. Maire, A multiscale progressive failure approach for composite laminates based on thermodynamical viscoelastic and damage models, Compos. Part Appl. Sci. Manuf. 38 (2007) 198–209.
[19] F. Laurin, N. Carrere, J.F. Maire, S. Mahdi, Enhanced strength analysis method for composite open-hole plates ensuring design office requirements, Compos. Part B Eng. 62 (2014) 5–11.

[20] C. Huchette, Analyse multiéchelle des interactions entre fissurations intralaminaire et interlaminaire dans les matériaux composites stratifiés, Doctorate thesis of Université Paris VI, 2005.

[21] A. Schieffer, Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effets du vieillissement thermique, Doctorate thesis of Université de Franche-Comté, 2003.

[22] Z. Hashin, Failure criteria for unidirectional fiber composites, J. Appl. Mech. 47 (1980) 329–334.

[23] M. Nicol, Compréhension et modélisation de l'influence de l'ordre d'empilement sur les scénarios d'endommagement dans des composites stratifiés de plis unidirectionnels, Doctorate thesis of Université Paris Saclay, 2023.

[24] P.H. Nelson, Permeability-Porosity Relationships in Sedimentary Rock, Log Anal. (1994).

[25] ASTM, Standard test method for short-beam strength polymer matrix composite material and their laminate, Norm D2344/D2344M-06a, 2006.

[26] M. Lan, D. Cartié, P. Davies, C. Bailey, Microstructure and tensile properties of carbon-epoxy laminates produced by automated fibre placement: Influence of a caul plate on the effects of gap and overlap embedded defects, Compos. Part Appl. Sci. Manuf. 78 (2015) 124–134.

[27] R. Talreja, Transverse Cracking and Stiffness Reduction in Composite Laminates, J. Compos. Mater. 19 (1985) 355–375.

[28] P.D. Soden, M.J. Hinton, A.S. Kaddour, Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates, Compos. Sci. Technol. 58 (1998) 1011–1022.

[29] G.J. Dvorak, Transformation field analysis of inelastic composite materials, Proc. R. Soc. London Series Math. Phys. Sci. 437 (1992) 311–327.
[19] F. Laurin, N. Carrere, J.F. Maire, S. Mahdi, Enhanced strength analysis method for composite open-hole plates ensuring design office requirements, Compos. Part B Eng. 62 (2014) 5–11.

[20] C. Huchette, Analyse multiéchelle des interactions entre fissurations intralaminaire et interlaminaire dans les matériaux composites stratifiés, Doctorate thesis of Université Paris VI, 2005.

[21] A. Schieffer, Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effets du vieillissement thermique, Doctorate thesis of Université de Franche-Comté, 2003.

[22] Z. Hashin, Failure criteria for unidirectional fiber composites, J. Appl. Mech. 47 (1980) 329–334.

[23] M. Nicol, Compréhension et modélisation de l'influence de l'ordre d'empilement sur les scénarios d'endommagement dans des composites stratifiés de plis unidirectionnels, Doctorate thesis of Université Paris Saclay, 2023.

[24] P.H. Nelson, Permeability-Porosity Relationships in Sedimentary Rock, Log Anal. (1994).

[25] ASTM, Standard test method for short-beam strength polymer matrix composite material and their laminate, Norm D2344/D2344M-06a, 2006.

[26] M. Lan, D. Cartié, P. Davies, C. Bailey, Microstructure and tensile properties of carbon-epoxy laminates produced by automated fibre placement: Influence of a caul plate on the effects of gap and overlap embedded defects, Compos. Part Appl. Sci. Manuf. 78 (2015) 124–134.

[27] R. Talreja, Transverse Cracking and Stiffness Reduction in Composite Laminates, J. Compos. Mater. 19 (1985) 355–375.

[28] P.D. Soden, M.J. Hinton, A.S. Kaddour, Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates, Compos. Sci. Technol. 58 (1998) 1011–1022.

[29] G.J. Dvorak, Transformation field analysis of inelastic composite materials, Proc. R. Soc. London Series Math. Phys. Sci. 437 (1992) 311–327.
[30] N. Carrere, F. Laurin, J.F. Maire, Micromechanical-based hybrid mesoscopic 3D approach for non-linear progressive failure analysis of composite structures, J. Compos. Mater. 46 (2012) 2389-2415.

[31] F. Mathieu, H. Leclerc, F. Hild, S. Roux, Estimation of Elastoplastic Parameters via Weighted FEMU and Integrated-DIC, Exp. Mech. 55 (2015) 105-119.

[32] J. Neggers, F. Mathieu, F. Hild, S. Roux, N. Swiergiel, Improving full-field identification using progressive model enrichments, Int. J. Solids Struct. 118-119 (2017) 213-223.
[30] N. Carrere, F. Laurin, J.F. Maire, Micromechanical-based hybrid mesoscopic 3D approach for non-linear progressive failure analysis of composite structures, J. Compos. Mater. 46 (2012) 2389-2415.

[31] F. Mathieu, H. Leclerc, F. Hild, S. Roux, Estimation of Elastoplastic Parameters via Weighted FEMU and Integrated-DIC, Exp. Mech. 55 (2015) 105-119.

[32] J. Neggers, F. Mathieu, F. Hild, S. Roux, N. Swiergiel, Improving full-field identification using progressive model enrichments, Int. J. Solids Struct. 118-119 (2017) 213-223.