J Moritz

E Faudot

S Devaux

S Heuraux

Plasma sheath properties in a magnetic field parallel to the wall

Keywords: numbers: 52.40.Kh, 52.65.Rr, 52.40.Fd Plasma sheath, PIC simulations, Magnetic confinement a)

Particle in cell simulations were carried out with a plasma bounded by two absorbing walls and a magnetic field applied parallel to them. Both the sheath extent and the potential drop in it were derived from simulations for different plasma parameters such as the electron and ion temperature T i , particle density and ion mass. Both of them exhibit a power law dependent on the Larmor to plasma ion pulsation ratio Ω i . For increasing values of the magnetic field, the potential drop within the sheath decreases from a few T i /e down to zero, where e stands for the electron charge. The space charge extent increases with Ω i and saturates to 2.15 ion Larmor radius. A simple model of sheath formation in such a magnetic field configuration is presented.

Assuming strongly magnetized electrons, and neglecting collisions and ionizations, a new typical length is evidenced, which depends on the ratio Ω i . The charge separation sheath width is theoretically found to increase from a combination of the electron gyroradius and the ion Debye length for low Ω i ratios up to several ion gyroradii for strongly magnetized ions. Both the calculated sheath extent and plasma potential show a fair agreement with the numerical simulations.

I. INTRODUCTION

Sheaths are found in most of studied plasmas for they arise as soon as a plasma encounters a surface. No matter if it is the limiter confining a fusion plasma, the cathode generating a laboratory one or the probe analysing it, the plasma-wall transition is characterized by a spatially positively charged layer, called the Debye sheath 1 , surrounding the surface. Electron velocity being several orders of magnitude larger than its ion counterpart, an electric field builds up in the sheath for slowing down the electrons and speeding up the ions, so that the charge fluxes equal on the wall. The stability of such an electrostatic structure, which extends over several Debye lengths (λ d ) in the x direction perpendicular to the wall, requires the ion velocity v ix to exceed the ion sound velocity (c s ) at the sheath edge to satisfy the Bohm criterion [START_REF] Bohm | The Characteristics of Electrical Discharges in Magnetic Fields[END_REF][3][4] .

In the presence of a magnetic field B tilted by an angle ψ with respect to the normal to the wall surface, and discarding the two cases where ψ = 0 (equivalent to the unmagnetized case) and ψ = π/2 (investigated in this paper), the plasma-wall transition is split into 3 parts: the Debye Sheath, the magnetic presheath and the collisional presheath. The ions are accelerated along the magnetic lines in the later presheath until their parallel (to the magnetic field) velocity is of the order of c s cos ψ at the magnetic presheath edge 5,6 . Within the magnetic presheath, also called Chodura sheath, which extents over a few ion Larmor radius, ions are redirected toward the wall in order to satisfy the Bohm criterion at the entrance of the Debye Sheath. The potential drop within the Debye sheath and the magnetic presheath, as well as the role of the magnetic field angle and strength on the different regions have been investigated by several authors since the original work of Chodura [7][8][9][10] .

When B is applied parallel to the wall, ions and electrons mobility mainly depends on their Larmor gyroradius (R L and r L for ions and electrons respectively), leading to a perfectly confined plasma if no other mechanism allows them to drift across the magnetic lines. These mechanisms have been investigated in the literature. For highly collisional plasma, electron mobility is enhanced by collision so that the ions must be accelerated at the vicinity of the wall 11,12 . This leads to a classical negative potential drop within the sheath (∆φ < 0). In the collisionless case, Theilhaber and Birdsall showed using 2D particle in cell (PIC) simulations that Kelvin-Helmholtz instability due to velocity shear within the sheath generates an ion flux across the field lines. ∆φ is then positive to push the ions back into the plasma and the case, i.e. if B, still parallel to the wall, is tilted with respect to the axis perpendicular to the simulation plane. This leads to 1D sheath behaviour with a particle flux null at the wall 14 . In further studies, authors faced the impossibility of solving the Poisson equation from a kinetic theory and used numerical calculations to derive scaling laws. They found that s scales with R L /λ d and a ∆φ of the order of the ion temperature 12,[15][16][17] , but no simple expression connecting s, or ∆φ, with the plasma parameters such as the ion and electron temperature and mass (T i , T e , m i and m e resp.), or with B, has ever been derived.

In this paper, we investigate the sheath formation in a parallel to the wall magnetic field, in the case of a perfectly confined plasma with no collision, ionisation nor turbulent fluxes.

Such assumptions lead to a particle flux null at the wall once the steady state is reached as explained in ref. 14,15 . The absence of flux at the wall could be seen as very restrictive regarding some experimental studies which have indeed indicated that the flux received by plasma facing components tangential to a flux surface does not vanish due to a possible funneling effect 18,19 , or to turbulent transport or simply to the difficulty to perfectly align the magnetic field with the surface. This is however still an open question as other authors have experimentally shown results at variance with this fact 20 .

Assuming a perfect parallel alignment of the magnetic field with respect to the wall and a perfect confined plasma is justified by the possibility to obtain a scaling of the sheath extent and of the floating wall potential with the magnetic field strength both numerically and analytically.

We show here by using PIC simulations that the potential drop within the sheath and the sheath extent scale with the ion cyclotron to plasma pulsation ratio Ω i = ω ci /ω pi . The former decreases from a few T i /e in the weakly magnetized regime of the ions (Ω i << 1) to zero for Ω i >> 1 where ions are strongly magnetized. The latter increases with Ω i from a few ion Debye lengths and saturates to 2R L . In the first part of the paper, the results of the PIC simulations are presented for a series of plasma parameters (density, temperature and ion mass). In the second part, a simple model is derived in order to explain the dependency of the sheath extent and the potential drop within it with respect to Ω i .

II. PIC SIMULATIONS

The simulations have been carried out using a 1D3V PIC code developed in the laboratory by one of the authors. The system studied consists in a plasma bounded by two grounded absorbing walls separated of 15R L with B such as ω ce > ω pe , where ω ce and ω pe are the electron cyclotron and plasma pulsations respectively. A cell size of ∆x = 0.1r L has been chosen in order to accurately describe both ion and electron motions. Initially, the superparticles are uniformly distributed on the grid (∼ 100 per cell) and their velocity set randomly from a Maxwellian distribution. The particles are then moved using the Boris pusher method [START_REF] Boris | Proceedings of the Fourth Conference on Numerical Simulation of Plasmas[END_REF] , with the electric field interpolated at the first order on the particles position. No collision nor particle injection are considered in the numerical scheme. To run the simulations in an acceptable time, we used reduced ion-to-electron mass ratio m i /m e from 200 to 600. T e is kept constant to 2 eV in all calculations, which is a representative value of the electron temperature in plasma discharges [START_REF] Lieberman | Principles of plasma discharges and material processing[END_REF] .

Fig. 1a and b present the transient particle fluxes at the wall for two different Ω i ratio.

The plasma parameters used in these simulations are T i = T e = 2 eV, m i = 400m e and n 0 = 10 16 m -3 . Each point in Fig. 1 represents the particle flux integrated over 1000 time iterations. When the ions are weakly magnetized as shown in Fig. 1a (Ω i =0.08), the ion flux Γ i decreases rapidly during 0.1 ion gyroperiod and completely vanishes after 0.55 ion gyroperiod. The characteristic transient time of 0.1 × 2π/ω ci is in that case close to 2π/ω pi , suggesting the importance of the electric field effects. Note that the electron flux Γ e decreases a bit faster than Γ i in this regime. When the magnetic field dominates the ion motion in Fig. 1b, for a larger pulsations ratio (Ω i = 1.56), the ion flux decreases slowly until 0.9 gyroperiod, while the electron flux vanishes after a few time iterations (the electron flux drops to zero after the first point, i.e. in less than 1000 time iterations = 100 electron gyroperiods). The characteristic transient time is then the ion gyroperiod for large Ω i . In all the following results, the different plasma characteristics such as the ion and electron density n i and n e or the plasma potential vs. x are averaged over 2ω -1 ci once the particle flux has vanished, i.e after one gyroperiod as shown in Fig. 1.

With the aim of emphasizing the role of the electric field in the different regimes of Ω i , the acceleration due to the electric field in the Boris pusher subroutine was forced to zero. Then, the lost particles at the wall, and consequently the densities in the plasma, are determined by the gyromagnetic motion only. Comparing the densities with (n e and n i ) and without the electric field (n e0 and n i0 ) in Fig. 2, it can be seen that electrons are always strongly magnetized as expected by the magnitude of B in our simulations leading to ω ce > ω pe . The behaviour of the ions is clearly dependent on the electric field for small Ω i , their density reaching the plasma density at a distance to the wall smaller than R L . For large Ω i , the ion density is weakly dependent on the electric field and decreases over several R L in front of the wall.

In both cases, the space charge close to the wall is negative and an electric field builds up in the sheath in order to repel the ions back into the plasma. This is the opposite situation to what is usually observed when the field lines intercept the wall. In Fig. 3 are shown the normalized plasma potential eφ/T i and the space charge ρ with respect to the distance to the wall x/R L for different Ω i ratios and for the same plasma parameters as previously. When Ω i increases, so does the sheath thickness (the space charge extent), while the potential drop ∆φ within it decreases. We analysed the evolution of ∆φ and s with respect to T i , m i and n 0 . The sheath thickness was determined using the ion density when n i = 0.9 × n 0 , because of the numerical noise around the saturation and to compare the different results without ambiguity. In Fig. 4 are shown the variations of e∆φ/T i and s/R L with respect to Ω i for the different plasma parameters investigated (the Ω i sweep is obtained by changing the magnetic field strength keeping ω ce > ω pe ). From Fig. 4a one can see that e∆φ/T i reaches about 3.7

for Ω i << 1 and decreases rapidly for Ω i < 1 until it drops out for large Ω i ratios. The sheath width saturates at 2.15R L for Ω i >> 1 and quickly decreases for Ω i < 1 (Fig. 4b).

It is important to note here that both quantities (s and ∆φ) depend on the ion mass, the plasma density and the ion temperature. For instance, if T i or m i are increased, so is the potential drop within the sheath in absolute units. However, when s and ∆φ are expressed in reduced units as in Fig. 4, and plotted with respect to Ω i , every single characteristic is rescaled on an unique master curve. The dependence of both the sheath extent and the potential drop within it is then in B/ √ m.n 0 and will be explicitly calculated in the next section. Finally other simulations have been carried out with a larger electron temperature

(T e = 10 eV and T e = 20 eV) and no significant variation to the master curve of Fig. 4 has been evidenced. In this parallel to the wall geometry of the magnetic field, and for such a magnetic field amplitude (ω ce > ω pe ), electrons stick to their field line. The dynamic of the ions only drives the sheath characteristics. Within the range of T e that we have investigated, the results of our simulations hold for either plasma discharges or plasma in the scrape-off layer of tokamaks 23 where the electron temperature is of the order of 25 eV.

III. MODEL

In order to understand the evolution of ∆φ and s with respect to Ω i , we propose a very simple model based onto particle motions. We assume a semi-infinite plasma in contact with a conducting and absorbing wall at x = 0 (see Fig. 5) and we focus on the case of strongly magnetized electrons only, i.e ω ce > ω pe . Considering electrons at their thermal velocity v te parallel to the x axis and neglecting the electric field effect on their motion along this direction, after an electronic gyroperiod 2π/ω ce , their flux at the wall vanishes.

The electronic density n e (x) can then be approximated by a step function: n e (x) = 0 for x ≤ r L and n e (x) = n 0 otherwise. The ion mobility towards the wall, perpendicular to the field lines, is larger than the electron one (R L >> r L ). As the electronic flux at the wall cancels, so does the ion one at the equilibrium, and a positive electric field E(x) arises in the sheath in order to repel ions back into the plasma. Considering a single fluid velocity for the ions v i , we assume also that the ion density n i follows a step variation, with n i (x) = 0 for x ≤ s and n i (x) = n 0 above. Although such a step model (SM) is a crude approximation, it has already been successfully applied to model radio-frequency sheaths 24,25 . The electric field is calculated from the Poisson equation ∂E/∂x = e 0 (n i -n e ) for the different regions: 5. Trajectories of the plasma particles. v te , v i and v D are the electron thermal velocity, the ion and the drift velocity respectively. x imin is the minimum abscissa reached by the ion originally at the velocity v i under both B and E(x) action.

E(x) =          n 0 e 0 (s -r L ) for x ≤ r L n 0 e 0 (s -x) for r L ≤ x ≤ s 0 for x ≥ s (1) E(x) r L x imin x,v v i v te B E = 0 s v D Plasma Sheath Wall y FIG.
The aim of the model is to follow the ion motion for the electric field given by Eq. 1 and to self-consistently deduce the minimum s that is necessary to keep the ions into the system (x imin > 0 in Fig. 5). For ions entering the sheath with a speed v(x = s) = -v i directed toward the wall at t = 0, it comes from the Newton equations of motion:

v ix = ω ci ( E(x) B + v iy ) (2a) v iy = -ω ci v ix (2b)
with ω ci the ion Larmor pulsation. Differentiating Eq.(2a) with respect to time for

r L ≤ x ≤ s and assuming ∂E/∂t = 0 gives vix = ω ci v ix ( 1 B ∂E ∂x -ω ci ).
With the initial condition v ix (0) = -v i , v iy (0) = 0 and E from Eq. ( 1), it comes after integration:

v ix (t) = -v i cos ω hi t (3a) v iy (t) = v i ω ci ω hi sin ω hi t (3b)
with ω hi the ion hybrid frequency defined as

ω 2 hi = ω ci (ω ci + n 0 e 0 B ) = ω 2 ci + ω 2
pi and ω pi the ion plasma pulsation.

The time of flight t f of an ion between x = s and x = r L is derived from the integration of Eq.(3a). Replacing t f in Eqs.(3) gives the initial conditions on the ion velocity for its motion through the last region (x ≤ r L ):

v ix0 = -v i √ 1 -λ 2 (4a) v iy0 = ω ci (s -r L ) (4b) with λ = ω hi (s -r L )/v i .
Differentiating the set of equations ( 2) with respect to time and assuming v ix of the form cos(ω ci t + θ), and using the initial conditions (4), it comes the ion position x i (t -t f ) for x ≤ r L and t ≥ t f :

x i (t -t f ) = v ⊥ ω ci (sin(ω ci (t -t f ) + θ) -sin θ) + r L (5) with v 2 ⊥ = v 2 ix0 + (v D + v iy0 ) 2 , v D = E/B is the drift velocity and sin θ = - v D +v iy0 v ⊥
. The minimum drift velocity required to keep the ion inside the plasma is derived from (5). From

x i > 0 and sin(ω ci t + θ) = -1 it comes:

v D > v 2 ix0 -ω 2 ci r 2 L 2ω ci r L -v iy0 (6)
We assume the initial ion velocity at the sheath edge (x = s, t = 0) of the form

v i = αT i m i . Replacing v D = n 0 e 0 s-r L B = ω 2 pi ω ci (s -r L ), v i , v ix0
and v iy0 in Eq.( 6) gives for the minimum sheath size:

s 2 = r 2 L + α 2 Ω 2 i R 2 L 1 + Ω 2 i = r 2 L + αλ 2 di 1 + Ω 2 i ( 7
)
with Ω i = ω ci /ω pi and λ di the ion Debye length. The potential drop within the sheath ∆φ is calculated integrating Eq.1 with the boundary condition φ(0) = 0 as:

e∆φ T i = α 2 - r 2 L R 2 L 1 + Ω 2 i ( 8
)
Neglecting the term ∝ r L in equation 8 (r L /R L << 1) and assuming α = 2, it comes ∆φ T i/e for Ω i ≈ 0, which is the potential drop required to push back into the plasma a non magnetized ion at the thermal velocity. It is worth noting that this result changes when the ion velocity at the sheath edge increases: the potential drop is then larger to push back faster ions. About 99% of the ion velocity is contained between 0 and 3 T i /m i in a

Maxwellian distribution, so that a potential drop of the order of several T i/e is expected in the weakly magnetized regime, i.e α > 2. Moreover ∆φ decreases rapidly to zero with Ω i , where the trajectory of strongly magnetized ions (Ω i >> 1) is slightly affected by electric fields. As the decay of ∆φ with Ω i depends on the density profile chosen, similar calculations have been done with linear density profiles (between the wall and r L for electrons and s for ions) instead of the SM. It leads to a different electric field expression than Eq. ( 1) on the different regions. The motion of the charged particle is then calculated with the averaged electric field E = 1 s s 0 E(x)dx in order to derive a full algebraic expression of s and ∆φ. Actually it only turns Ω 2 i into 3Ω 2 i in Eq.( 7) and ( 8). Then the potential drop within the sheath decays then more rapidly for the linear model (LM) of particle densities.

In Fig. 6 are shown e∆φ/T i and s/R L with respect to Ω i for different values of α using Eq.( 7) and ( 8), compared with the curves obtained with the PIC simulations for n 0 = 10 15 m -3 , T i = 2 eV and m i = 400 m e , which extends over the largest range of investigated Ω i . The calculated variation with α = 7.48, that adjusts the potential drop within the sheath in the weakly magnetized regime of the ions, shows a good tendency with respect to the simulations. The agreement is fairly good using a LM instead of a SM with the same value of α, because the decay of e∆φ/T i is accentuated as explained previously.

Concerning the sheath size variation, a relative good agreement is found for the investigated Ω i for both LM and SM. Moreover, according to Eq.7, for Ω i << 1, s αλ 2 di + r 2 L , so that s ranges between 0.130 and 0.384R L with the different input parameters and α = 7.48. This is very similar to what is evidenced by the PIC simulations in Fig. 4b. It is also emphasized in Fig. 7 where the evolution of the sheath extent normalized to R L and λ di for one set of the plasma parameters is shown. When Ω i << 1, the sheath width is of about 7.5λ di , while it reaches roughly 2R L in the strongly magnetized regime of the ions. Actually, our model holds for ω ce ≥ ω pe , because we neglect the effect of the electric field on the electron motion. It induces a lower bound limit for B ≥ n 0 m e / 0 and for Ω i ≥ m e /m i . In such a case where ω ce = ω pe , r L λ de , the electron Debye length. Assuming T e = T i , we have Eq. ( 7) and ( 8) respectively. The phenomenological laws (9) are superimposed in both figures.

λ de = λ di = λ d and according to Eq. 7, the sheath extent is of about √ α + 1λ d . For weakly magnetized ions, the sheath characteristics do not depend on the magnetic field strength.

Then, its extension scales with the Debye length, just like in unmagnetized sheaths (or when the applied field is titled with respect to the wall), but with a negative space charge instead of a positive one.

The results of the PIC simulations and the model evidence 2 regimes for the potential drop and the sheath thickness. When Ω i < 1 (as long as ω ce > ω pe ), the transient sheath time scales with the plasma frequency instead of the cyclotron frequency. Ions are not considered as magnetized and their mobility is maximum. It induces a maximum potential drop of several T i /e to repel the ions and a sheath length of the order of the ion Debye length.

When Ω i > 1, both ions and electrons are strongly magnetized in the sheath. The mobility for ions is reduced but remains higher than the electrons one so that the potential drop stays positive but tends to 0 for strong magnetic fields. The sheath width saturates at 2 times the ion Larmor radius because no other transport mechanism is involved. The discrepancy between simulations and the models (LM and SM) is explained by the approximations made on the electric field and density variation within the sheath. The particle loss calculation at the wall using a Maxwellian velocity distribution and a uniform distribution in space would lead to a gaussian like profile for the ion density. SM and LM are actually zero and first order approximations of the expected exponential density profile using an average particle velocity.

Using an average velocity is also a source of error because the particles thermal motion is neglected. In the context of radio-frequency sheaths, the use of a step model for electron density is valid as long as the wall potential is larger than T e /e 26 . Although this assumption is not quantitatively correct in the present work, it is meaningful for understanding the sheath formation and providing a correct order of magnitude of its extension in such a magnetic field configuration. Moreover, using similar power law dependences than previously for e∆φ/T i and s/R L , it is possible to find a better agreement with the PIC simulations as shown in Fig. 6. The best agreement compiling all our results was found for a law very similar to the one derived in the context of the step model:

e∆φ T i = 3.89 1 + 3.80Ω 1.29 i and s R L = 4.52Ω 1.53 i + 0.2 1 + 2.03Ω 1.53 i (9)
with error margins of about 5% for e∆φ/T i and 10% for s/R L .

IV. CONCLUSION

We studied the sheath formation in a parallel to the wall configuration of the magnetic field by using PIC simulations and assuming no collision nor flux at the wall except in the transient regime. The numerical results show that the potential drop and the sheath thickness obey to a master curve depending only on the parameter Ω i = ω ci /ω pi and 2 regimes have been identified for the sheath width and potential drop within it. In the weakly magnetized regime of the ions, Ω i < 1, the sheath thickness scales as the classical Debye length, while the potential drop decays rapidly from several T i /e. In the strongly magnetized regime, the sheath thickness scales with R L and the potential drop slowly decreases to 0. A new analytic definition of both parameters has been derived from a simple step model of the particle density. From weakly to strongly magnetized conditions, the model yields a sheath width ranging from λ 2 di + r 2 L to R L , while the potential drop decreases from T i to 0, both with the strong dependence on ion cyclotron frequency to ion plasma frequency ratio, as observed in the PIC simulations.

The scaling laws governing the sheath length and potential drop we derived in this paper could be used as boundary conditions in finite element plasma codes in which crossfield sheath are not properly implemented. In tokamak or stellarator devices, most surfaces are almost parallel to the magnetic field and the knowledge of such a sheath is essential to determine the relevant boundary conditions of the codes simulating the scrappe-off layer (for instance JOREK 27 and SOLPS 28 ). They can also be useful to floating potential measurements by a Langmuir probe in the special case of the probe collection area being exactly parallel to the magnetic field. Still considering probe, the interpretation of the ion part of the current-tension characteristic requires the knowledge of the sheath size as a function of the applied potential, which could be directly derived from this model. Other PIC simulations have to be run applying such a bias potential. To be applicable this model must obviously be improved by adding collisions or considering a grazing magnetic field angle.

Finally we may expect that in a quiescent plasma regime with a very low collisionality, such an inversion of the potential drop in the sheath could be observed and would validate the applicability of the present model.

FIG. 1

 1 FIG. 1. a) and c) Variation of the ion (Γ i ) and electron (Γ e ) fluxes with respect to the simulation time for different Ω i ratio.

FIG. 2 .

 2 FIG.2. Ion (n i ) and electron (n e ) density for Ω i = 0.08 in a) and Ω i = 1.56 in b). The 0 subscript in n i and n e denotes the results obtained when the electric field is artificially taken to be zero in the code. The parameters of the simulation are T i = 2 eV, m i = 400 m e and n 0 = 10 16 m -3 .

  FIG.3. Variation of the normalized potential eφ/T i a) and of the space charge ρ in b) with respect to the distance to the wall for different Ω i ratio.

FIG. 4 .

 4 FIG. 4. Normalized potential drop within the sheath a) and sheath thickness b) for different plasma constants. The nominal parameters of the simulation are T i = 2 eV, m i = 400 m e and n 0 = 10 16 m -3 . When one of them is changed in a simulation run, T i for instance, both others are kept constant to the nominal values.

FIG. 6 .

 6 FIG. 6. Variation of both normalized potential drop a) and sheath width b) vs. Ω i . The PIC simulation results are shown for n 0 = 10 15 m -3 . The calculated curves with various α come from

FIG. 7 .

 7 FIG. 7. Variation of the sheath width normalized to the ion thermal Larmor radius (R L ) or to the ion Debye length (λ di ) vs. Ω i . The parameters of the simulation are T i = 2 eV, m i = 400 m e and n 0 = 10 15 m -3 . The vertical line denotes the transition between the weakly and the strongly magnetized regime of the ions.


Noterdaeme

M Usoltceva

E Faudot

J Ledig

S Devaux

S Heuraux

G V Zadvitskiy

R Ochoukov

J Moritz

K Crombé

J-M Noterdaeme

Theory of a cylindrical Langmuir probe parallel to the magnetic field and its calibration with interferometry a)

Theory of a cylindrical Langmuir probe parallel to the magnetic field and its calibration with interferometry

I. INTRODUCTION

Specific particle transport in the presence of magnetic field (B) changes the shape of a Langmuir probe IV curve such that the conventional methods of data interpretation become unsuitable 1,2 , especially for a parallel cylindrical probe. Very few attempts 1,2,3 exist on providing a correct theory for density (n) evaluation with such probe. Of those the Laframboise and Rubinstein calculations 2,3 are hardly applicable in practice 1 and our previous theory 1 contains simplifying assumptions that restrict validity limits.

In this paper we develop an accurate theory describing electron collection by a cylindrical Langmuir probe biased to plasma potential (V pl ) (to avoid sheath) and oriented parallel to the magnetic field. This model is an advancement of our previous work 1 and it gives an exact formula connecting plasma density and collected current at V pl . Only the case of a parallel probe is considered, since for a probe at an arbitrary angle to B an exact analytical solution would be excessively complex. At the end the applicability limits of the approximate theory 1 are revised.

Application of the new theory to experimental data on Aline (A LINear Experiment 3,4 ) allows us to draw spatial density profiles, as well as parameter scans. Results are validated with interferometry. A full scan of density as a function of B and the input power is performed for the first time on Aline in magnetized plasma.

II. THEORY FOR A PROBE PARALLEL TO B

The basic idea behind the model presented here is the same as in the previous work 1 : separation of different contributions to the collected current by dividing the electrons into groups according to their speed. The current for each contribution is calculated as a product of charge , flux and collecting area :

( 1 )

In contrast to the previous theory, we consider not only the flux to be dependent on the particle speed but the collecting area as well.

We adapt the cylindrical coordinate system and examine the particle flux through a plane perpendicular to the probe axis (z axis). The collecting area in (1) is an area in this plane which a guiding center of a rotating particle should cross for a particle to be collected. Due to the rotational symmetry no dependency on the azimuth is present. We divide all electrons into 4 fractions:

1) , 2) , 3) , 4)
, where is the speed of an electron with a Larmor radius equal to the probe radius and is the speed of an electron that completes one full rotation ∆ 2 during the same time as it travels the probe length in z direction ( , a) Published as part of the Proceedings of the 22nd Topical Conference on High-Temperature Plasma Diagnostics (HTPD 2018) in San Diego, California, USA. b) Author to whom correspondence should be addressed: mariia.usoltceva@ipp.mpg.de where ⁄ is the electron cyclotron frequency). For experimental applications it would be correct to impose an upper limit for the radial speed as the value when the Larmor radius is equal to the vacuum chamber radius. This is a minor correction and we omit it for the current theoretical formulation.

For each fraction of particles the current is calculated using the same formula, but with its own limits and its own collecting area (with Maxwellian velocity distribution):

2 * , (2)
The assumptions and results for each of them are the following. 1) These particles are "slow" in z direction; they complete a full 2 rotation before reaching the end of the probe. If the perpendicular projection of a particle trajectory intersects the probe projection in at least one point (Fig. 1a,b), a particle is for sure collected. With being the distance between the probe center and the center of a particle trajectory, the collecting area is found as:

2 (3)
Then the integration of (2) gives:

1 1 4 1 √ erf √ ( 4 )
where is nondimensional magnetic field strength 2 and / is the random thermal flux.

2) The same assumption is valid for the second fraction of electrons, except that the integration for is done in different limits (see Fig. 1c and1d):

2 4 (5) 1 4 2 √ erfc √ (6)
3) A particle that is "fast" in z direction might never touch the probe, because it does not complete a full turn on . This case should be approached probabilistically.

There are two sectors of the trajectory projection which correspond to the electron successful collection (Fig. 2). If a particle is in the sector 2 that belongs to the intersection part, it hits the probe perpendicular surface. From the law of cosines,

arccos

. The corresponding probability is

. If a particle is in the sector , on the length in z direction it completes a part of a full turn that is enough to reach the probe. So, a particle hits the parallel probe surface with ∥

. Instead of now we need to use the product of and the full With the limits 0 and we obtain:

(9) 1 1 4 1 √ erf √ * erfc √ (10)
4) Likewise the previous calculation, but with other limits for , for the 4 th fraction we get:

2 4
( 1 1 )

2 2 erfc √ erfc √ (12)
The second term in has an additional factor of 2, to account for the particle collection from the opposite direction of z. It is not done for the first term, as well as for all other current contributions, because the flow of the electrons is limited at the back of the probe tip by the probe body and the manipulator. Only particles with big and big are able to come from the back side. The effective collecting area 1 is the full collected current divided by :

1 * 1 1 √ 1 erfc √ 1 erfc √ √ 2 1 * erfc √ ( 1 3 )
The expression is rather complicated but it is important to see here that for β → ∞ it converges to and for β → 0 to 2 .

III. APPLICATION TO EXPERIMENTAL DATA

Theory validation has been performed using data from the linear plasma device Aline. The experimental conditions were the same as in our previous paper 1 : 25 MHz capacitive RF discharge, magnetic fields of 0.0024-0.1 T, helium, 1Pa. We have performed a scan of a probe position in the direction perpendicular to B (x from -33 mm to +33 mm) at a constant height y = 36 mm above the antenna and at z = 0 mm along B, i.e. directly above the antenna center. In this region densities are expected to be higher than at the position used before 1 . Only one cylindrical probe tip of r pr = 75 µm, L pr = 1 cm was used and it was accurately aligned with B.

IV curves analysis, namely plasma potential and electron temperature calculation, has been done using accurate techniques described in our previous work 1 .

Densities obtained from the Langmuir probe are averaged along x and compared to line-integrated density measured by a 26.5 GHz microwave interferometer MWI 2650 from Miwitron which was chosen because it suits our density range (Fig. 3). Interferometer, used only as a supportive diagnostic for probe calibration, was installed specifically for these tests on a temporary mounting and mechanical shaking caused not high accuracy. The lowest possible interferometry signal to measure was ~1e16 m -3 in our experiments. Above this level errors reached ± 1e16 m -3 . Using intersection method of V pl calculation 1 we make sure that this issue is only present for very low B, less than 0.005 T in our experiments. c) Uncertainties in temperature estimation affecting directly as 1/√ , as well as through the effective area. This should not give significant deviations when is determined self-consistently 1 with . An additional uncertainty in the interferometer density values comes from the fact that the line-integrated signal is divided by a plasma length which is not exactly defined. For all points it was divided by 20 cm, which is fairly realistic for low plasma magnetization and overestimated (up to 2 times) for the higher B. The profile shape variation can be seen even on a small profile part that is accessible for the probe, nearly flat for the 0 T field and with a defined peak for greater field values (Fig. 4).

The coupled power dependence on B was measured for different forwarded power (Fig. 5). The coupling is generally not affected by the probe presence. Now a 2D density profile can be constructed as a function of the coupled power and the magnetic field with both probe and interferometry measurements (Fig. 6). The discrepancies of the results are mostly within 20%, reaching 50% for few points of low interferometry signal.

IV. APPLICABILITY ANALYSIS

An exact formula is undoubtedly preferable to an approximate theory. The equation (13), while being very complex, should be used instead of the inexact effective area formula 1 when a probe parallel to B is considered.

However, construction of similar analytical procedure for an arbitrary angle of inclination is an unjustifiably sophisticated task. Instead we conduct an analysis of the applicability of the approximate theory 1 .

The simplicity of the resulting formula (17) in the previous work 1 is achieved by neglecting the fact that the collecting areas depend on a particle speed. Moreover, no distinction for different speeds in z direction is drawn. Consequently, the effective area is not an exact expression but an approximation. Limits to its application can be set by revising separately the two terms of equation ( 11) 1 . 1. The "non-magnetized" flux defined by the condition of the radial speed to be bigger than is said to be collected by the whole probe area , which is an overestimation. In reality, an electron with strikes a probe no later than one revolution of the cyclotron orbit: * 2 / , so all such particles are collected by a smaller area 2

. Only particles with bigger than are collected randomly along the whole probe length. For the equation ( 17) to be applicable they should constitute the majority of the velocity distribution. It is roughly true when the mean thermal velocity ̅ is bigger than . The described overestimation seems to be significant for bigger magnetic fields and smaller , when most of the electrons have smaller than the limit. However, for bigger magnetic fields the limitation leads to a small number of particles in , since is also quite big (depending on the temperature). Quantitatively the conditions for the first remark to be insignificant can be expressed as:

̅

for any ̅ and ̅ (14)

2. The second limitation concerns the "magnetized" flux. If a center of the cyclotron rotation of an electron with lies outside the perpendicular probe projection but at a distance no longer than r ce from it, the electron trajectory intersects the probe and such a particle is collected. However, it may be collected not only by the perpendicular surface as was assumed previously, but also by a part of the parallel surface proportional to its speed . The "magnetized" flux is large only in strong magnetic fields. At the same time most of the electrons have speeds , so the additional area 2 is quite small. The second correction is always very small and negligible compared to the effect of the first correction. Finally, the criteria of the applicability of the approximate theory are those described by ( 14). When they are not satisfied, the effective area is overestimated up to the factor of / . A more precise overestimation value can hardly be provided.

We can review the application to the experimental data carried out in the previous work 1 for two cylindrical probe tips. For the smaller tip of r pr = 75 µm, L pr = 1 cm, the equation ( 14) gives that is acceptable only for 0.0076 T and 0.114 T at 5°, which means that for nearly the whole range of B the resulting densities are underestimated. The bigger probe (r pr = 0.5 mm, L pr = 1 cm) data gave larger span of reliable results: 0.0076 T and 0.017 T, so only a small part in between these two values resulted in overestimated and underestimated .

We plot the equation ( 13) from this paper and (17) from the previous work 1 for 0° (Fig. 7 and8) to check the results from the paragraph above and thus the validity of the assumptions (14). All curves are for a constant temperature of 5 eV. The boundaries of B are prolonged beyond the ones used in the experiment to see the upper threshold value where the two theories start to match. The lower threshold values are not observed. The values of the upper threshold in both cases are twice bigger than those obtained from ( 14). This can serve as a guidance to take the criteria for the approximate theory applicability as those in (14) but with a factor of 2 for ̅ . After some transformations they look like:

, for any and 2

The second criterion should be quite correct for a broad range of parameters at 0° and even more so for non-zero angle, since the overestimation of the area reduces with the angle. The first criterion might be applicable for some non-zero angles, but this question requires further investigations.

The comparison above is done for 0° but was around 5° in the experiments 1 , so the real overestimation of is somewhat lower than what we predict for a parallel probe. The experimental data (Fig. 7 1 ) shows that the underestimation of for the small probe is maximum of the factor of 2 compared to the big probe. One of the reasons for that is the non-zero angle, but there might be other factors which affected the current collection.

V. CONCLUSION

An exact analytical solution is given for the electron current collected at V pl by a cylindrical Langmuir probe oriented parallel to the magnetic field. All electrons are divided in 4 fractions according to their radial and parallel to B velocities. The effective collecting area is derived as the sum of the 4 current contributions divided by the electron charge and random thermal flux.

The constructed theory for interpretation of a cylindrical Langmuir probe data allowed for the first time to obtain reliable density profiles in magnetized plasma on Aline. Results are obtained for a broad range of the magnetic fields as well as the coupled power levels.

Interferometry measurements of line-integrated densities have been carried out for the same range of parameters. Values that are well above the noise level of 1e16 m -3 match the densities obtained with the probe with up to 20% error. Possible causes of errors are listed.

The preceding approximate theory 1 for a cylindrical probe at an arbitrary angle is compared to the exact model for the parallel probe orientation and applicability criteria are formulated. The overestimation of the collecting area by the approximate theory seems big, but the experimental underestimation of density is only of the order of 2.

FIG. 1 .

 1 FIG.1. Limiting cases for a particle to be collected, a)&b) for , c)&d) for . A dark circle represents the probe projection, a dashed circle -electron trajectory projection.

FIG. 2 .

 2 FIG. 2. Example of an intersection illustrating sectors 2 and .

FIG. 3 .

 3 FIG. 3. Densities measured with Langmuir probe (dotted lines with circle markers) compared to interferometry (solid lines with cross markers) for different power levels. Possible sources of errors in the Langmuir probe results are: a) RF oscillation of the potential, leading to a shift in IV characteristics. They are eliminated by the compensation circuit of our probe. b) Inaccurate V pl evaluation, leading to wrong current values.Using intersection method of V pl calculation1 we make sure that this issue is only present for very low B, less than 0.005 T in our experiments. c) Uncertainties in temperature estimation affecting directly as 1/√ , as well as through the effective area. This should not give significant deviations when is determined self-consistently1 with . An additional uncertainty in the interferometer density values comes from the fact that the line-integrated signal is divided by a plasma length which is not exactly defined. For all points it was divided by 20 cm, which is fairly realistic for low plasma magnetization and overestimated (up to 2 times) for the higher B. The profile shape variation can be seen even on a small profile part that is accessible for the probe, nearly flat for the 0 T field and with a defined peak for greater field values (Fig.4).The coupled power dependence on B was measured for different forwarded power (Fig.5). The coupling is generally not affected by the probe presence. Now a 2D density profile can be constructed as a function of the coupled power and the magnetic field with both probe and interferometry measurements (Fig.6). The discrepancies of the results are mostly within 20%, reaching 50% for few points of low interferometry signal.

FIG. 4 .

 4 FIG. 4. Spatial density profiles for various B.

FIG. 7 .

 7 FIG. 7. Comparison of the approximate and exact theories for r pr = 75 µm. The arrow indicates the intersection.

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European

Commission.


K R Ramakrishnan

N Le Moigne

O De Almeida

A Regazzi

S Corn

Optimized manufacturing of

Keywords: A, Biocomposite B, Mechanical properties D, Microstructural analysis E, Compression moulding

come

Optimized manufacturing of thermoplastic biocomposites by fast induction-heated compression

moulding: influence of processing parameters on microstructure development and mechanical behaviour K.R. Ramakrishnan, Nicolas Le Moigne, Olivier de Almeida, Arnaud Regazzi,

S. Corn

To cite this version: K.R. Ramakrishnan, Nicolas Le Moigne, Olivier de Almeida, Arnaud Regazzi, S. Corn. Optimized manufacturing of thermoplastic biocomposites by fast induction-heated compression moulding: influence of processing parameters on microstructure development and mechanical behaviour.

Composites Part A: Applied Science and Manufacturing, 2019, 124, pp.105493. 10.1016/j.compositesa.2019.105493. hal-02169387

Introduction

Natural fibres are considered as potential substitute to traditional composite reinforcements due to their low density, high specific mechanical properties, relative worldwide abundance and low cost, and positive environmental profile [START_REF] Shah | Can flax replace E-glass in structural composites? A small wind turbine blade case study[END_REF]. Bast fibres such as flax, hemp, kenaf, jute and ramie are extracted from the periphery of the stems, and have a hierarchical structure with bundles of packed elementary fibres built up of a layered cell wall structure, i.e. the primary and secondary cell walls [START_REF] Bos | In situ ESEM deformation of flax fibres[END_REF]. The secondary cell wall, mainly made of cellulose microfibrils as reinforcements and hemicelluloses as matrix components, is responsible for the high tensile strength and stiffness of elementary fibres, due to high cellulose content and low microfibrillar angle towards the fibre direction. In particular, the specific longitudinal stiffness of flax fibres in tension can even be higher than that of glass fibres due to the low density of flax [START_REF] Pil | Why are designers fascinated by flax and hemp fibre composites? Compos Part A[END_REF].

In this regard, bast fibres such as flax are intended to be used in structural composite applications [START_REF] Pickering | A review of recent developments in natural fibre composites and their mechanical performance[END_REF]. However, the potential of flax fibres as reinforcements in structural composites can only be realized by taking advantage of twistless long fibre yarns, and the study of woven flax fibres reinforced thermoplastic biocomposites is therefore of great interest. There is limited literature on the influence of the type of flax fibres, the typical length of fibres and fabric architecture, the resin system used, and the composite manufacturing process on the mechanical performances of thermoplastic biocomposites. Moreover, it is noteworthy that the composite manufacturing process can be more influential on the final properties of flax fibre reinforced thermoplastic composites than for carbon and glass fibre composites. Indeed, natural fibres used as reinforcement in composites are exposed to high temperatures during composites manufacturing, especially in the case of semi-crystalline thermoplastics matrices that require high processing temperatures for melting and flowing. Liang et al. [START_REF] Liang | Thermo-compression forming of flax fibre-reinforced polyamide 6 composites: influence of the fibre thermal degradation on mechanical properties[END_REF] pointed out that for plant fibre based composites, the choice of manufacturing conditions and thermoplastic matrices are limited by the high melting point of some thermoplastics and the consecutive thermal degradation of natural fibres at high temperatures, due to the presence of thermally sensitive constituents such as waxes, pectins, hemicelluloses and lignin. Gassan and Bledzki [START_REF] Gassan | Thermal degradation of flax and jute fibers[END_REF] noted that heating (under air atmosphere) of fraction ratios [START_REF] Zhang | Commingled natural fibre/polypropylene wrap spun yarns for structured thermoplastic composites[END_REF]. This improvement could be explained by enhanced fibre orientation and dispersion and better packing of the laminate due to improved resin impregnation during manufacturing.

The manufacturing process used for the consolidation of composites also has a great influence on the thermal degradation of flax fibres. Because of the high processing temperatures required for lowering the matrix viscosity and accelerating the impregnation process, fibre degradation may occur during the heating stage and affect the final properties of composites regardless the consolidation process. Hot press compression moulding is commonly used for the manufacturing of long fibre reinforced thermoplastic composites. Hot presses are efficient systems for applying the high temperatures and pressures that are required for ensuring full consolidation of thermoplastic composites [START_REF] Hoa | Principles of the manufacturing of composite materials[END_REF][START_REF] Kim | Effect of pressure on the impregnation of thermoplastic resin into a unidirectional fiber bundle[END_REF]. However conventional hot presses with platens equipped with cartridge heaters exhibit limited heating rates, usually below 5 °C/min. Natural fibre degradation can therefore be already well advanced at the isothermal stage. To overcome this problem, Kazmi et al. [START_REF] Kazmi | Sheet forming of flax reinforced polypropylene composites using vacuum assisted oven consolidation (VAOC)[END_REF] proposed a vacuum assisted oven consolidation (VAOC) technique. The effect of different pressure and temperature cycles on the consolidation quality of flax/PP composites manufactured using this VAOC technique was investigated and an optimum processing cycle to reduce the manufacturing time without significantly altering the mechanical properties of the laminates was proposed. Another alternative technique for limiting the exposure time of natural fibres and thereby reducing the consequential thermal degradation is the use of fast heating manufacturing systems. Such approach is a key to better control the processing of woven natural fibres reinforced thermoplastic composites and hence reach the mechanical performances expected for structural applications.

In this study, a compression moulding system based on induction technology was used to manufacture consolidated lightweight composites from commingled flax/PP fabrics. This system allows mould heating and cooling rates of about 40 °C/min, and hence shorter compression moulding cycles [START_REF] Bessard | Melt state behaviour of PEEK and processing window interpretation for fast compression moulding process[END_REF]. The effect of processing conditions on the microstructure and mechanical properties of the biocomposites were studied for a better understanding of their process-microstructureproperty relationships. Accounting of respective thermal properties of flax and PP fibres, flax/PP biocomposite laminates were manufactured with varying processing parameters in terms of thermal cycles and applied pressures. Tensile tests were conducted on the resulting biocomposites to determine the influence of the processing conditions on their elastic and ultimate properties.

Materials and methods

Materials

The material chosen for the study was a woven commingled fabric of flax/polypropylene (PP), supplied by Composites Evolution as Biotex flax/PP with surface density of 400 g/m 2 and made from twistless flax fibres and PP fibres in a balanced 2 × 2 twill architecture. Additionally, flax fabrics, also supplied by Composites Evolution without the commingled PP as Biotex Flax was used for the mechanical testing of flax yarns and fabrics. The biochemical composition of flax was analysed by Fibre Recherche Développement® (FRD, Troyes, France) according to Van Soest method (standards NF EN ISO 13,906 and NF V18-122): cellulose (79.6% ± 0.9), hemicelluloses (5.5% ± 0.5), lignin (7.6% ± 0.3), solubles (6.9% ± 0.2) and ashes (0.4% ± 0.1).

Manufacturing of flax/PP biocomposites

Compression moulding was chosen for the fabrication of the composite laminates because of its high reproducibility and low cycle time [START_REF] Faruk | Biocomposites reinforced with natural fibers: 2000-2010[END_REF]. The commingled fabrics were moulded into flax fibre reinforced thermoplastic composite laminates by applying a heating and pressure cycle to melt the PP fibres and impregnate the flax reinforcement, lignocellulosic based materials to temperatures of 100-250 °C could cause alterations in either their physical or chemical structures such as depolymerization, hydrolysis, oxidation, dehydration, decarboxylation and recrystallization, which in turn resulted in changes in the physical properties of natural fibres. The thermal degradation of flax fibres is dependent on both the temperature and duration of exposure. For example, prolonged exposure of 2 h at temperature of 210 °C results in reduction in the tenacity of flax fibres of roughly 70% [START_REF] Gassan | Thermal degradation of flax and jute fibers[END_REF]. Gourier et al. [START_REF] Gourier | Mechanical analysis of elementary flax fibre tensile properties after different thermal cycles[END_REF] studied the effect of thermal cycles (under air atmosphere) on the mechanical behaviour of elementary flax fibres, and found that modifications in the fibre structure and the interactions between components occur at high temperatures such as 250 °C. In order to minimize fibre damages, Van de Velde and Baetans [START_REF] Van De Velde | Thermal and mechanical properties of flax fibres as potential composite reinforcement[END_REF] reported that exposing flax fibres for 15 min at 180 °C results in lower residual tensile stress and strain than when exposed for two hours at 120 °C. Based on their results, the authors recommended that composite production temperatures higher than 180 °C should be avoided, unless the processing duration is short.

The thermal degradation of flax fibres then constitutes a strong limitation regarding their use for the development of high performance thermoplastic biocomposites. Indeed, Bourmaud et al. [START_REF] Bourmaud | Influence of processing temperature on mechanical performance of unidirectional polyamide 11-flax fibre composites[END_REF] who studied the effect of the processing temperature on mechanical performances of unidirectional flax fibre reinforced polyamide 11 (PA 11) composites found that a thermal cycle of 8 min at 210 °C reduces both the stiffness and strength of the composite. As a consequence, the mechanical performances that can be expected with flax fibres composites are restricted by the use of low melting temperature thermoplastic matrices with limited mechanical properties. For instance, John and Anandjiwala [START_REF] John | Chemical modification of flax reinforced polypropylene composites[END_REF] recommended the use of PP as matrix as it requires a relatively low processing temperature. Van de Velde and Kiekens [START_REF] Van De Velde | Effect of flax/PP panel process parameters on resulting composite properties[END_REF] studied the effect of processing parameters, i.e. temperature and time, in a hot-press setup on the mechanical properties of non-woven flax/PP composites, and also recommended a maximum processing temperature of 200 °C to preserve the mechanical properties of flax fibres. Different recommendations regarding exposure of natural fibres to temperature can thus be found in literature and are highly dependent of the residence time and the expectation in terms of physical properties toward the targeted application.

Different strategies have been investigated to preserve the integrity of natural fibres during composite manufacturing, in particular by reducing their exposure time to high temperatures. In this regard, the use of woven commingled fabric made of flax fibres and polypropylene (PP) fibres is one of the solutions that can reduce the thermal degradation of flax fibres during composite fabrication. These woven products are made of hybrid wrap yarn consisting of two components; a yarn core with twist-free staple fibres of flax and PP, and a PP filament wound around the core, limiting defibrillation during weaving and composite manufacturing processes. Further details on the structure of the natural fibre/thermoplastic fibre hybrid yarn and the weaving process using wrap spinning method were given by Baghaei et al. [START_REF] Baghaei | Characterization of thermoplastic natural fibre composites made from woven hybrid yarn prepregs with different weave pattern[END_REF] and Zhang and Miao [START_REF] Zhang | Commingled natural fibre/polypropylene wrap spun yarns for structured thermoplastic composites[END_REF]. The main advantage of hybrid yarns containing both matrix and reinforcing components in its structure is that the commingled structure improves the impregnation efficiency by the thermoplastic resin during composite manufacturing due to the lowest effective resin flow distance [START_REF] Bar | Studies on flax-polypropylene based low-twist hybrid yarns for thermoplastic composite reinforcement[END_REF][START_REF] Bourban | Material phenomena controlling rapid processing of thermoplastic composites[END_REF]. This was confirmed by Kannan et al. [START_REF] Kannan | Effect of reinforcement on the mechanical and thermal properties of flax/polypropylene interwoven fabric composites[END_REF] who observed that the interwoven fabric structures provide shorter resin flow time and good matrix impregnation compared to other possible preforms. A comparison of the thermal degradation of flax/PP composite to pure flax and PP yarns showed a positive shift in the degradation temperature of the composite, and it was hypothesized that the improved thermal stability of the composite was due to the good degree of matrix covering the flax yarns, achieved with the interwoven fabric. Furthermore, it was reported that wrap yarn with a twistless natural fibre core wrapped by a PP filament led to composites which demonstrated a significant improvement in flexural modulus over those with conventional twisted yarn structure, in a range of fibre volume followed by a cooling cycle for the PP crystallisation and consolidation of the laminates. In this study, we used a fast compression moulding system based on induction technology (3iTech® from Roctool). The pilot plant consists in a vertical press of 1000 kN capacity, a 200 kW medium-frequency induction generator, a water cooling unit that can supply cold water up to 100 L/min and a flat tool of 400 × 400 mm 2 moulding area (Fig. 1).

Eight plies of the flax/PP commingled fabric were cut to 280 × 280 mm 2 , and placed between the two rigid steel plates of the hydraulic press. Based on the supplier datasheet, the initial flax fibre volume fraction of the fabrics was 40% and the estimated consolidated thickness of 0.30-0.35 mm per ply, which corresponds to a theoretical final thickness of the composite laminate of 2.4 mm. The fabrics were pre-dried at 70 °C overnight before composite manufacturing in order to remove the excess moisture.

Composite panels were manufactured by placing the stack of commingled fabrics [0-90] 8 between the two rigid steel plates of the hydraulic press at room temperature and considering several processing parameters, i.e. temperature, pressure and consolidation time, for the manufacturing of the flax/PP composite laminates. All laminates were prepared following a specific thermal/pressure cycle comprised of three main phases: an initial heating period with gentle pressure to ensure a good contact and thermal conduction within the flax/PP commingled fabrics, followed by an isothermal phase during which pressure was applied and molten PP could impregnate flax fibres, and the final cooling phase during which PP crystallization and consolidation of the composite laminates occurred. The operating temperatures were chosen based on the thermal stability analysis conducted on the flax and PP fibres as detailed in Sections 2.3 and 2.4.

Thermal properties of polypropylene, flax fibres, and biocomposites

Differential Scanning Calorimetry (DSC) tests were carried out using Netzsch DSC 214 Polyma (Netzsch, Germany), in order to determine the melting temperature (T ) m and the melting enthalpy (ΔH ) m of PP within both fabrics (as fibres) and composites (as matrix). 15-20 mg of pure PP fibres were extracted from the commingled fabrics, and then heated from -40 to 220 °C at 10 °C/min in sealed aluminium pans. Nitrogen was used as a purge gas with flow rate of 40 ml/min. Same tests were conducted on 15-20 mg samples cut from the composite laminates. The degree of crystallinity of PP within the fabrics and the biocomposites was calculated according to Eq. ( 1):

⎜ ⎟ = ⎛ ⎝ × ⎞ ⎠ × X H χ H Δ Δ 100 c m m m 0 (1)
In Eq. ( 1), χ m and H Δ m are the mass fraction (equals to 100% for pure PP fibres) and melting enthalpy of PP (calculated between 120 and 185 °C), respectively. H Δ m 0 is the melting enthalpy of a pure PP crystal, i.e. 207 J/g [START_REF] Blaine | Polymer heats of fusion[END_REF].

DSC tests were also performed on flax fibres extracted from the commingled fabrics. No drying procedure was applied to the fibres before running the DSC experiments.

The thermal stability of flax and PP fibres was evaluated by thermogravimetric analysis (TGA). 15 mg of pure flax or PP fibres were extracted from the fabrics. The change in mass versus temperature was measured from 30 °C to 800 °C with a heating rate of 20 °C/min in

= ν ρ ρ χ f c f f (2) = - ⎛ ⎝ ⎜ + -⎞ ⎠ ⎟ ν ρ χ ρ χ ρ 1 1 p c f f f PP (3) = - ν ρ ρ χ χ (1 ) f c f f d f (4) = - ⎛ ⎝ ⎜ - + - - ⎞ ⎠ ⎟ ν ρ χ χ ρ χ χ ρ 1 (1 ) 1 (1 ) p c f d f f f d f PP (5) = + × - χ ρ ρ ν ν 1 1 1 f PP f fi fi (6)
The microstructure of the flax/PP laminates manufactured at different processing conditions was observed across their thickness using a scanning electron microscope (SEM) (Quanta FEG 200, FEI Company). Samples were embedded in a clear epoxy resin and polished with progressively fine polishing papers. The polished cross sections were carbon coated and the acceleration voltage was set to 12.5 keV.

X-ray microtomography imaging experiments were conducted on selected samples to provide a comprehensive description of fibre and porosity volume distribution. Measurements were performed with an EasyTom XL from RX Solutions (France) to record 3D images of the microstructure of composites (voxel size: 3.3 × 3.3 × 3.3 µm 3 ). The Xray source was made of a LaB6 filament (cathode) and a W transmission target (anode), and had an accelerating voltage of 40 kV. A CCD detector of 2048 × 2048 pixels from Princeton Instruments (USA) was used. The samples were cut from the different plates to get a size of approximately 5 × 5 mm 2 . They were placed horizontally in the equipment such as the X-ray beam was always orthogonal to their thickness during scanning. For each processing conditions, materials were tested in duplicate. The scans were reconstructed using the X-Act CT software and then segmented with the ImageJ software [START_REF] Rueden | Image J2: ImageJ for the next generation of scientific image data[END_REF]. Segmentation was achieved using the Trainable Weka Segmentation 3D plugin [START_REF] Arganda-Carreras | Trainable Weka Segmentation: a machine learning tool for microscopy pixel classification[END_REF]. The fibre volume fraction and the porosity were defined as the ratio of the number of voxels corresponding to the volume of fibres and pores, respectively, over the total number of voxels in the cropped region. Pore volumes were assessed with the BoneJ particle analyser and sorted in classes in order to evaluate their distribution [START_REF] Doube | BoneJ: free and extensible bone image analysis in ImageJ[END_REF].

Uniaxial tensile testing on flax/PP biocomposites

A Zwick Z010 testing machine was used to perform tensile tests based on the ISO 527-4 standard for composites. The width and thickness of each sample was measured before every test and the length between the fixing jaws was 110 mm (length of actual samples: 165 mm). Five samples were tested per processing condition and each test was conducted in two stages: a first stage at a crosshead speed of 1 mm/min using an extensometer to determine the tensile modulus (calculated by considering the slope of a linear trendline of the stress-strain curve between a strain of 0.05% and 0.3%), and a second stage at a crosshead speed of 5 mm/min until rupture to determine the tensile strength and strain at break. The tests were conducted in a controlled environment (ca. two hours at temperature of 25 °C and 50% relative humidity). oxygen atmosphere. The kinetics of degradation of flax fibres for different isotherms was also studied by TGA. The thermal cycle applied to flax fibre samples was a two-step process: an initial drying at 110 °C for 5 min followed by a heating ramp to pre-defined temperatures (from 190 °C to 260 °C) and an isothermal stage of 14 min at that temperature, representative of the investigated processing conditions.

Results and discussion

Mechanical properties of flax fibre yarns and fabrics

Flax fibre yarns and fabrics were tested under uniaxial tensile loading using an Instron 5942 tensile test machine with a 500 N load cell. Flax fibre yarns of 100 mm length were tested at a constant crosshead displacement rate of 20 mm/min. Additionally, flax fabrics made of 10 yarns in width were also tested in tension. In addition to sample drying at 70 °C to remove the moisture, the effect of thermal cycles on the mechanical behaviour of flax yarns and fabrics was studied by heating the samples in an oven at different temperatures (200, 220, 240 °C) for duration of 5 and 10 min, corresponding to typical processing temperatures and times. At least 10 samples were tested for each condition.

Microstructural analysis of flax/PP biocomposites

The overall fibre volume fraction ν f and porosity content ν p of the flax/PP composite laminates were calculated with Eqs. ( 2) and ( 3) from the density of the manufactured laminates ρ c measured by gas pycno- metry (Micromeritics AccuPyc 1330) in helium atmosphere after drying the samples minimum 2 h at 70 °C. Measurements were done in triplicate. The density of PP matrix ρ PP was taken as 0.905 g/cm 3 [START_REF] Bernreitner | Designing properties of polypropylene[END_REF], the density of flax fibres ρ f corresponds to the mean value of gas pycno- metry measurements performed on dry flax fibres (ρ f = 1.5204 g/cm 3 ). The fibre weight loss χ d f estimated from TGA data after 7 min or 12 min isotherms (corresponding to 2 min stabilization plus 5 min or 10 min of consolidation at a given temperature, respectively) was also considered in the calculations of ν f and ν p (Eqs. ( 4) and ( 5)). In all these equations, χ f refers to the mass fraction of fibres in dry commingled fabric that was assessed with Eq. ( 6) from the initial flax fibre volume fraction of the fabric provided by the supplier (ν fi = 0.4). For all processing conditions, PP flowing at the edges of the plates was very limited or not preponderant towards the squeezing of the fabrics. Consequently, variations in ν f and ν p are thus assumed to be only due to the formation of pores during processing and/or mass loss due to the degradation of the fibres.

of pure PP was found to be 91.4 J/g, which corresponds to a degree of crystallinity of 44.2% as calculated according to Eq. ( 1). DSC curve of flax fibres exhibits a large endothermic peak around 110 °C primarily attributed to the evaporation of residual moisture in flax fibres.

The thermal stability of flax and PP fibres was evaluated using thermo-gravimetric analysis (TGA). The change in mass versus temperature was measured and is shown in Fig. 3a. In the case of flax fibres, three peaks associated to weight losses are generally observed in the derivative TGA curves of flax fibres. The first mass loss with peak at 98.8 °C is related to the release of water. The second peak at 246 °C which can be seen as a shoulder on the main peak is related to the degradation of low molecular weight and non-cellulosic substances such as hemicelluloses (especially xylan in the case of flax), pectins and waxes [START_REF] Dorez | Effect of cellulose, hemicellulose and lignin contents on pyrolysis and combustion of natural fibers[END_REF]. The third and main peak is associated to the degradation of cellulose which occurs at 356 °C for the flax fabric selected in this study. It should be pointed out that the degradation of lignin generally occurs over a wide temperature range, i.e. from 200 to 500 °C [START_REF] Dorez | Effect of cellulose, hemicellulose and lignin contents on pyrolysis and combustion of natural fibers[END_REF][START_REF] Brebu | Thermal degradation of lignina review[END_REF]. In the case of PP fibres, only one degradation peak is observed in the range 250-440 °C, the maximum in the mass loss derivative being measured at 416 °C (Fig. 3a), hence at much higher temperature than the starting degradation temperature of flax fibres. Thermo-oxydation of non-stabilized PP can occur at moderate processing temperatures of 250 °C [START_REF] Davis | Thermal degradation of polypropylene[END_REF]. However, commercial PP matrices are commonly stabilized allowing processing with limited degradation in this temperature range, also classically used in thermoplastic processes as injection moulding. Thermal degradation processes of PP fibres can thus be considered as negligible towards those occurring in flax fibres in this temperature range.

Exposure time to high temperatures is also critical and the kinetics of thermal degradation of flax fibre for different isotherms (after prior drying at 110 °C) is shown in Fig. 3b. It can be observed significant variations in mass loss over time and the extent of degradation increases drastically with increasing isothermal temperatures. After 10 min, flax fibres lost about 2.0% mass when heated at 220 °C, while mass losses reached 3.6 and 6.0% at 240 °C and 260 °C, respectively.

Based on the biochemical composition analysis (see Section 2.1), flax fibres used contain almost 80% of cellulose and 20% of non-cellulosic components, i.e. lignin, hemicelluloses, and low molecular weight soluble. The mass losses recorded after exposure 10 min at 240 °C and 260 °C (i.e. 3.6 and 6.0%) clearly highlight that a large part of the non-cellulosic components (and possibly small amount of cellulose) were degraded over short exposure times. These non-cellulosic components play a key role in the intra and inter-cellular cohesion and transfer loading mechanisms within flax fibre bundles [START_REF] Lefeuvre | Analysis of the role of the main constitutive polysaccharides in the flax fibre mechanical behaviour[END_REF][START_REF] Fuentes | Effect of the middle lamella biochemical composition on the non-linear behaviour of technical fibres of hemp under tensile loading using strain mapping[END_REF][START_REF] Fernández | Role of flax cell wall components on the microstructure and transverse mechanical behaviour of flax fabrics reinforced epoxy biocomposites[END_REF], and such extensive degradation should thus have a great influence on the resulting mechanical properties of flax fabrics and flax/PP composites.

The thermal stability study was completed by tensile tests performed on flax yarns and fabrics heated at various temperatures. Dried flax yarns exhibited large variations in their mechanical behaviour. The stiffness and overall mechanical response were highly variable (see supplementary data S1). It was observed that some yarns show damage initiation at small displacements but the elementary fibres and/or fibre bundles continued to withstand the load until full rupture. For some tests, the failure in the yarns was more brittle and a sharp drop in the force can be seen. The peak force varied from 15.7 N to 35.8 N while the maximum displacement at rupture also varied from 8.6 mm to 14.3 mm. Scatter in strength of natural fibres due to their intrinsic properties and measurement methods is often reported in literature [START_REF] Bensadoun | Impregnated fibre bundle test for natural fibres used in composites[END_REF]. Considering the tested yarn length (i.e. 100 mm), sliding between the twisted fibres also occurred and should also be one of the reason for the large scattering in yarns strength. Consequently, it was not possible to identify a pattern in the mechanical response of the flax yarns after the heating cycles. Nevertheless, it was possible to observe tendencies on the flax fabrics made of ten yarns and tested in the longitudinal direction. It can be observed in Fig. 4, that increasing the isothermal temperature reduces drastically the stiffness and the peak force of the fabric, attesting that the thermal degradation of the non-cellulosic components measured by TGA has a pronounced effect on the mechanical response of the flax fabrics. Exposure to temperatures higher than 200 °C turned out to be detrimental for the mechanical performances of flax fibre fabrics, mainly due to early breakage of elementary fibres within the yarns. According to Bourmaud et al. [START_REF] Bourmaud | Influence of processing temperature on mechanical performance of unidirectional polyamide 11-flax fibre composites[END_REF], exposure to higher temperatures lead to significant modification of the flax fibres such as its biochemical composition and macromolecular arrangement. These modifications affect the sliding of cellulose microfibrils within the cell walls, and therefore lead to a decrease of Young's modulus and strength of the fibres. Van de Velde and Baetens [START_REF] Van De Velde | Thermal and mechanical properties of flax fibres as potential composite reinforcement[END_REF] showed that the removal of water occurring at 120 °C makes the fibre more brittle. Indeed, water acts as plasticizer in the fibre microstructure. Degradation of pectins at around 180 °C, which are mostly present in the middle lamella and hold the elementary fibres together, had a faster and detrimental effect on the mechanical properties of the green and underretted fibres.

Choice and monitoring of processing conditions for the manufacturing of flax/PP biocomposites

The processing conditions for the flax/PP composite were chosen based on the results of the thermal analysis of individual constituents. The chosen processing temperature window should be sufficiently high so as to completely melt and flow the PP matrix. Indeed, at higher temperatures, the PP viscosity decreases allowing a better flow and possibly better impregnation within the flax yarns. However, as previously discussed, too high temperatures could degrade drastically flax fibre structure and its resulting mechanical performances. Based on our results, 17 composite laminates were manufactured with contrasting processing parameters so as to highlight the effect of manufacturing conditions on the microstructure and mechanical behaviour of flax/PP composites when using the induction-heated press. The chosen processing parameters, i.e. temperature, pressure and consolidation time used are summarised in Table 1. The nomenclature for the samples follows the rule xC_ym_zb, with × corresponding to the temperature in °C, y to the consolidation time in minutes and z the pressure in bars.

The induction-heated press allowed to continuously monitor the actual temperature, the pressure applied, and the platen position during processing. A typical processing cycle for the manufacturing of a flax/ PP composite at 200 °C is shown in Fig. 5. Maximum heating power was applied for the heating phase (phase 1) and the heating rate was roughly 40 °C/min for all the experiments. When the targeted processing temperature was reached, a stabilization time of 2 min was allowed (phase 2) before applying the pressure and starting the clock to measure the consolidation time (phase 3). It is interesting to note that the position of the upper plate was decreasing in the first minutes of the consolidation due to PP flowing, hence decreasing the thickness of the laminate. At the end of the consolidation phase, the cooling system was turned on (phase 4) and the temperature was allowed to decrease rapidly until 150 °C so as to stop the impregnation and degradation processes (-40 °C/min). The cooling rate was then reduced at this temperature to aid crystallisation of the PP matrix (-5 °C/min) and then increased back to reach ambient temperature (-15 °C/min). The effect of a slow cooling at -2°C/min (plate n°10) and fast cooling -25 °C/min, i.e. without reducing the cooling rate at 140 °C, (plate n°11) was also tested. It should be pointed out that for all the experiments a constant pressure was maintained during the entire consolidation and cooling phases. It must also be noticed that from the moment a constant pressure is applied, the displacement of the press platen is related to the thermal expansion of the mould and material, and to the thickness reduction of flax/PP composite laminate. The consolidation process can therefore be monitored during the isotherm by the decreasing position of the upper plate. As it can be observed, the thickness reduction occurs during the first minutes of the isotherm stage, which indicates that the consolidation of flax/PP composite laminate is almost entirely achieved within five minutes after the application of the pressure.

It is worth mentioning that the composites manufactured at 240 °C during 10 min (plate n°16) and 260 °C during 5 min (plate n°17) were completely destroyed due to the thermal degradation of the fibres. The resulting composite laminates were unusable and not characterized. The images of the resulting composite laminates are shown in supplementary data (S2).

Microstructural analysis of flax/PP biocomposites

The effect of the processing conditions on the crystallisation of PP matrix was investigated with DSC tests performed on the different manufactured composite laminates. The thermograms were very similar for the different manufacturing conditions (see supplementary data S3). Melting peak temperature was not influenced by the processing conditions, roughly 167 °C for all the plates, attesting that the crystals formed upon cooling had the same thermal stability and melted in the same temperature range. In the same cooling conditions, melting enthalpies and degrees of crystallinity varied from 46.1 to 53.4 J/g, and 47.2 to 54.7% (Table 2), respectively. Although DSC tests were achieved on several samples for each plate, it must be noted that the actual fibre weight within the DSC samples could not be perfectly controlled. For this reason, in overall, the variations of the degree of crystallinity cannot be considered significant, and it can be assumed that it was not influenced by the processing conditions. However, the effect of cooling rate on the crystallization of PP was the most influential. For fixed processing conditions (220 °C, 40 bar, 5 min), slow cooling cycle promotes higher degree of crystallinity, i.e. 55.0% instead of 46.4% for the fast cooling cycle (Table 2). A secondary melting peak or shoulder at 150 °C was visible in some processing conditions. This may be attributed to the presence of beta phase crystal which formation could be favoured by higher consolidation pressure, i.e. 40 bar, during crystallization [START_REF] Androsch | Mesophases in polyethylene, polypropylene, and poly(1-butene)[END_REF].

The estimated overall fibre volume fraction and porosity calculated from pycnometry measurements with Eqs. ( 2) and (3) (without accounting for fibre degradation) and Eqs. ( 4) and (5) (accounting for fibre degradation) are presented in Table 2 for the different processing conditions. It can be observed that the different processing conditions had a limited effect on the fibre volume fraction ranging between 37.7 and 39.6% depending on the processing parameters and calculation method (i.e. with or without accounting for fibre degradation). An increase in operating pressure from 20 bar to 40 bar slightly improved the fibre volume fraction of about 1% for the lowest processing temperatures (≤200 °C). The processing temperature had no significant effect on the fibre volume fraction, being in average 39.1%, 38.8% and 39.1% (without accounting for fibre degradation) and 38.6%, 38.1% and 38.4% (accounting for fibre degradation) for 200 °C, 220 °C and 240 °C, respectively.

Fig. 6 shows a 3D interpolated plot of the calculated porosity as function of the consolidation temperature, pressure and time. A porosity fraction lower than 3.9% (3.4% when accounting for fibre degradation) was obtained for all conditions with a minimum porosity fraction of 1.1% (0.6% when accounting for fibre degradation) observed for processing at 200 °C under 40 bar during 10 min. Those relatively low values of overall porosity may be attributed to the thorough mixing between the flax and PP fibres inside the commingled yarns [START_REF] Zhang | Commingled natural fibre/polypropylene wrap spun yarns for structured thermoplastic composites[END_REF][START_REF] Bar | Studies on flax-polypropylene based low-twist hybrid yarns for thermoplastic composite reinforcement[END_REF][START_REF] Kannan | Effect of reinforcement on the mechanical and thermal properties of flax/polypropylene interwoven fabric composites[END_REF], and the resulting good impregnation during manufacturing. Fig. 6a shows that consolidation time has little effect on porosity. In contrast, depending on the processing temperature, a decrease in the overall porosity of up to 2-3% can be observed when increasing pressure. The processing temperature also appears to be a very influential parameter that affected the final composite porosity (Fig. 6b). However, increasing temperature did not result in a progressive reduction of porosity as it could be expected regarding the temperaturedependent behaviour of PP viscosity and flowing. Maximum porosity was reached at intermediate processing temperature, i.e. between 200 and 220 °C. This represents a significant difference with synthetic fibres (as glass or carbon) commingled fabrics for which increasing temperature has a positive effect and results in a decrease of overall porosity due to better matrix flowing and improved fibre impregnation [START_REF] Bourban | Material phenomena controlling rapid processing of thermoplastic composites[END_REF]. According to Pickering et al. [START_REF] Pickering | A review of recent developments in natural fibre composites and their mechanical performance[END_REF] and Madsen et al. [START_REF] Madsen | Plant fibre composites -porosity and volumetric interaction[END_REF], fibre lumens and other inaccessible regions within elementary fibres and/or fibre bundles as well as the limited wettability of natural fibres towards apolar and viscous matrices such as PP, lead to poor impregnation and inclusion of air bubbles during processing and the formation of micro and macro-pores. Besides, it has been shown by Madsen et al. [START_REF] Hans | Properties of flax and hemp composites. Flax Hemp Fibres a Nat[END_REF] that porosity in natural fibre reinforced composites could even increase at high fibre content, if the geometrical compaction limit is reached, due to limited packing ability of natural fibres.

Cross-sectional microstructures of flax/PP composite laminates manufactured in contrasted processing conditions are shown in Fig. 7. Both warp and weft fibre yarns of the different plies are visible in the cross-section of the plate (Fig. 7a andd). As reported by Madsen et al. [START_REF] Madsen | Plant fibre composites -porosity and volumetric interaction[END_REF], different kinds of pores are visible within the composite microstructure including macro-pores which are typically caused by (i) entrapped gas bubbles or voids within the matrix, and micro-pores originating from (ii) natural fibres themselves, (iii) interfacial pores and (iiii) bad impregnation within the yarns. At higher magnification (within the flax yarns), interfacial pores in between the elementary flax fibres and the matrix are observed (see arrow), suggesting poor interfacial adhesion (Fig. 7c andf). For the composite processed at higher temperature, i.e. 240 °C, higher degree of individualization of the elementary fibres (Fig. 7e compared to 7b) can be observed. However, the lumen (central channel) of the elementary fibres shows several microcracks (Fig. 7f) supporting the hypothesis of a thermal degradation of flax fibres and their destructuration at high operating pressure and temperature.

Based on these observations, we postulated that pores might also originate from the release of volatiles during processing resulting from the thermal degradation of flax fibres. In this regard, X-ray tomography experiments were conducted to investigate the local porosity volume distribution within the samples and better depict the influence of the processing temperature, time and pressure on porosity. Fig. 8 shows the 3D images of pores in selected composites. The porosity volume fraction calculated from tomography confirms that the operating pressure and temperature have a great influence on the formation of pores. At 200 °C, increasing the pressure from 20 bar to 40 bar had a drastic effect on the local porosity (Fig. 8a andb) that decreased from 1.81 ± 0.41% to 0.23 ± 0.05%. Increasing the temperature from 200 °C to 240 °C at constant pressure (40 bar) increased the local porosity (Fig. 8c), i.e. 0.78 ± 0.01%, confirming the results in Table 2. It is also interesting to note that slowing down the cooling rate increases the local porosity up to 1.37 ± 0.01% (Fig. 8d), which suggests that longer processing time could also result in the formation of pores. X-ray tomography measurements also give access to the analysis of the distribution of pore volumes (Fig. 9). A clear tendency toward the diminution of the pore size was observed when increasing the operating pressure (200C_5m_20b compared to 200C_5m_40b). This supports the hypothesis that higher pressure favours matrix flowing and fibre impregnation, hence limiting the formation of micro-pores (so called impregnation porosity) within the yarns. Interfacial pores remained due to poor adhesion between PP and flax. In contrast, higher processing temperature and time (240C_5m_40b and 220C_5m_40b (slow)) resulted in the formation of macro-pores between the yarns. This supports the hypothesis that volatiles are formed during processing by the thermal degradation of flax fibres and partially entrapped within the viscous matrix.

Concluding, it has been demonstrated that the processing parameters, i.e. consolidation time, pressure, temperature and cooling rate, have counterbalancing effects on the development of microstructures in commingled flax/PP biocomposites:

-Increasing pressure, temperature and processing time (consolidation and cooling) favours matrix flowing and fibre impregnation, leading to lower porosity and smaller pores, and enhancing crystallization. -But too high processing temperature and time can cause the thermal degradation of the fibres that leads to the formation of volatiles and thereby macro-pores.

In the following section, the balanced effects of processing conditions were studied in regard to the mechanical behaviour in the elastic domain and at rupture. From the microstructural analysis, it can be assumed that the mechanical behaviour of the composites is mainly affected by the extent of degradation of flax fibres, and the type of developed pores either interfacial micro-pores or macro-pores in the bulk of the matrix.

Uniaxial tensile behaviour of flax/PP biocomposite

Fig. 10 compares the stress-strain curves of composites manufactured at different temperatures. All composite materials exhibit a similar behaviour, with a quasi-linear elastic domain up to 0.5-0.8% strain until reaching an inflection point (yield point). This inflection point should be related to the viscoplastic behaviour of PP and/or the beginning of damage within the composite structure, i.e. micro-cracks at the interface and within the matrix, which finally leads to the critical fracture of the specimens. The exposure to high processing temperature during composite manufacturing induced a more brittle behaviour, which consequently also resulted in a reduction of composite strength. The median strength and strain at failure indeed decreased from 79.1 MPa to 52.9 MPa and from 2.1% to 1.0%, respectively, when increasing the processing temperature from 190 °C to 240 °C.

In order to analyse the effects of manufacturing conditions on the mechanical properties of flax/PP biocomposites, the Young's modulus and strength were recorded for all conditions and data were interpolated so as to highlight the combined effects of temperature, pressure and consolidation time (Fig. 11).

It can be seen that the pressure had a pronounced positive effect on the Young's modulus (Fig. 11a), higher consolidation pressure being associated to higher modulus, i.e. up to 1 GPa increase from 20 bar to 40 bar. In contrast, pressure had little to no effect on composites strength (Fig. 11b). Based on the microstructural analysis, we assume that the higher Young's moduli obtained with higher pressure are due to better flax fabrics impregnation inducing slightly higher fibre volume fraction, better fibre individualization, and fewer and smaller pores (Table 2 and Figs. 8 and9). It should be noticed that the effect of pressure was somewhat less pronounced at 240 °C. In this case, a high modulus was obtained for both 20 and 40 bar due to better flowing of the matrix and hence better impregnation of the fabrics.

On the other hand, the combined effect of temperature and consolidation time are presented in Fig. 11 (c,d), and it can be seen that the effect of higher temperature and longer time was detrimental for the strength of the composites, which reduced drastically to 52.9 MPa at 240 °C. As discussed above, the drastic decrease of intrinsic mechanical properties of the fibres (Fig. 4) associated to damages within their microstructure (Fig. 7) is responsible for the severe degradation of the ultimate performances of the biocomposites. Furthermore, the development of numerous macro-pores (Figs. 8 and9), related to fibre degradation and consecutive entrapping of volatiles in the bulk of the matrix, greatly amplifies the ultimate performance losses. It is interesting to note that high modulus of the composites could be maintained even when processed at 240 °C for 5 min consolidation (Fig. 11a andc). Thermal degradation of the fibres and formation of macro-pores in these processing conditions is thus not detrimental to the stiffness of the composite.

Finally, the effect of the three cooling cycles on the modulus and strength of the flax/PP composite is shown in Fig. 12. It can be seen that there is no appreciable difference between the fast and optimal cooling condition, while there is a substantial drop in both the modulus and strength for the slow cooling. This shows that when flax fibres are exposed to high temperature for prolonged duration due to slow cooling cycle, thermal degradation and its related consequences on the formation of macro-pores and degradation of fibres, are most likely to occur.

Conclusions

In this study, lightweight thermoplastic biocomposites from commingled flax/PP fabrics were manufactured using a fast induction-heated compression moulding system. The thermal behaviours of flax and PP fibres were evaluated by DSC and TGA analysis. Various and contrasting processing conditions were selected to study their effect on the microstructure development and the mechanical behaviour of the biocomposites. Based on a careful characterization of the physical properties (by DSC, pycnometry) and microstructure (by SEM and X-ray tomography) of the biocomposites, processing/microstructure/mechanical behaviour relationships of the manufactured flax fibres/PP biocomposites were depicted. The balanced effects of processing conditions were identified and described: (i) increasing pressure, temperature and processing time (consolidation and cooling) favours matrix flowing and fibre impregnation, leading to fewer and smaller pores, and enhanced crystallization; (ii) but too high processing temperature and time can cause the thermal degradation of the fibres, leading to the formation of volatiles and thereby macro-pores. Elastic properties of the biocomposites could be maintained even at high processing temperature (240 °C for 5 min of consolidation appearing as the upper limit), but their strength was drastically decreased due to extensive fibre The use of fast processing tools as induction-heated systems can be interesting solutions to overcome the thermal degradation processes occurring with natural fibres reinforced biocomposites. Indeed, fast inductive heating allows overall shorter compression moulding cycles by reducing both the heating and cooling phases while better controlling the impregnation time during the consolidation phase. Thermal degradation is limited during the short heating and cooling phases thus giving the possibility to enhance the consolidation time window. An optimised set of processing parameters can thus be chosen that would allow improvement of the microstructure by limiting porosity and fibre degradation. These results open interesting perspectives for the use of higher melting point matrices and the production of biocomposites with higher mechanical performances. Efficient flowing of the matrix for optimal impregnation of natural fibres fabrics remains a key issue. In this regard, this set of data combining porosity size/distribution vs processing parameters and taking into account natural fibre degradation with a very good control of the processing conditions could provide reliable data for further modelling of compression moulding of commingled natural/polymer fibres fabrics.

Fig. 1 .

 1 Fig. 1. (a) Fast induction-heated compression moulding press, (b) Close view of flax/PP commingled fabric, (c) 8 plies fabric layup and (d) Manufactured composite laminate.

3. 1 .

 1 Fig. 2. DSC heating scan for the first heating cycle of PP fibres and flax fibres. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig. 3. (a) TGA curves for flax fibres (solid lines) and PP (dashed lines) highlighting the main mass loses and degradation peaks, (b) kinetics of thermal degradation of flax fibres at different isothermal temperatures. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 .

 4 Fig. 4. Forcedisplacement curves for flax fabrics made of ten yarns and exposed at different temperatures for 10 min. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .

 5 Fig. 5. Typical processing cycle: measured temperature, pressure and platen position over the whole manufacturing process. Phase 1 (heating), phase 2 (stabilization), phase 3 (consolidation under pressure) and phase 4 (cooling). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .

 6 Fig. 6. Overall porosity based on pycnometry measurements (without accounting for fibre degradation, Eq. (3)) of flax/PP composite laminates for different processing conditions: (a) pressure vs. time, (b) pressure vs. temperature. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7 .

 7 Fig. 7. Microstructure in cross-sections of flax/PP composites as observed by SEM for: 190C_10m_40b (a, b, c); and 240C_5m_40b (d, e, f) laminates.

Fig. 8 .Fig. 9 .

 89 Fig. 8. 3D images of pores in flax/PP composite samples (3800 × 3800 × 1650 µm 3 ) obtained by X-ray tomography experiments for: (a) 200C_5m_20b; (b) 200C_5m_40b; (c) 240C_5m_40b and (d) 220C_5m_40b (slow). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 10 .Fig. 11 .Fig. 12 .

 101112 Fig. 9. Pore volume distribution weighted in volume for: 200C_10m_20b; 200C_10m_40b; 240C_5m_40b and 220C_5m_40b (slow).Fig. 10. Comparison of stress strain curves for different processing temperatures. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 1

 1 Summary of the processing conditions used for the manufacturing of flax/PP composite laminates.

	1	190	10	20	190C_10m_20b
	2	190	10	40	190C_10m_40b
	3	200	5	20	200C_5m_20b
	4	200	5	40	200C_5m_40b
	5	200	10	20	200C_10m_20b
	6	200	10	40	200C_10m_40b
	7	220	5	10	220C_5m_10b
	8	220	5	20	220C_5m_20b
	9	220	5	40	220C_5m_40b
	10	220	5	40	220C_5m_40b (slow)
	11	220	5	40	220C_5m_40b (Fast)
	12	220	10	20	220C_10m_20b
	13	220	10	40	220C_10m_40b
	14	240	5	20	240C_5m_20b
	15	240	5	40	240C_5m_40b
	16	240	10	40	240C_10m_40b
	17	260	5	20	260C_5m_20b

Plate n°Temperature (°C) Time (min) Pressure (bar) Plate_name

Table 2

 2 Biocomposite densities, fibre volume fraction, porosity, melting enthalpy and degree of crystallinity of manufactured flax/PP composites laminates.

	Plate_name	Composite	Fibre volume fraction ν f	Porosity ν p (%)	Fibre volume fraction ν f	Porosity ν p (%) (with	Melting	Degree of
		density ρ c a	(%) (without fibre	(without fibre	(%) (with fibre	fibre degradation, Eq.	enthalpy ΔH m	crystallinity X c
			degradation, Eq. (2))	degradation, Eq. (3))	degradation, Eq. (4))	(5))	(J/g) b	(%) c
	190C_10m_20b	1.124	39.0	2.4	38.5	2.0	50.3	51.5
	190C_10m_40b	1.139	39.6	1.1	39.0	0.7	51.2	52.5
	200C_5m_20b	1.113	38.7	3.3	38.1	3.0	48.4	49.5
	200C_5m_40b	1.137	39.5	1.3	39.0	0.9	46.1	47.2
	200C_10m_20b	1.107	38.5	3.9	37.8	3.4	49.3	50.5
	200C_10m_40b	1.139	39.6	1.1	38.9	0.6	49.1	50.2
	220C_5m_10b	1.123	39.0	2.4	38.5	2.0	48.1	49.3
	220C_5m_20b	1.111	38.6	3.5	38.1	3.1	47.9	49.1
	220C_5m_40b	1.128	39.2	2.1	38.6	1.7	48.9	50.0
	220C_5m_40b	1.136	39.5	1.3	38.9	0.9	53.8	55.0
	(slow)
	220C_5m_40b	1.121	39.0	2.6	38.4	2.2	45.3	46.4
	(fast)
	220C_10m_20b	1.111	38.6	3.5	37.7	2.8	53.4	54.7
	220C_10m_40b	1.116	38.8	3.1	37.8	2.4	46.1	47.2
	240C_5m_20b	1.126	39.1	2.2	38.4	1.7	47.2	48.4
	240C_5m_40b	1.125	39.1	2.3	38.4	1.8	47.5	48.6
	a Average STD: 0.0028.

b Average STD: 2.16. c Average STD: 2.68.

Acknowledgements

This project was funded by the European Union's Horizon 2020 Programme (HERMES project, grant agreement n°636520). The authors would like to thank the Institut Français du Textile et de l'Habillement (IFTH) for performing the tensile tests on flax fibres and fabrics.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.compositesa.2019.105493.