Sabine Le Roux
email: sabine.leroux@mines-albi.fr

Mehdi Salem
email: mehdi.salem@mines-albi.fr

Anis Hor
email: anis.hor@isae-supaero.fr

Improvement of the bridge curvature method to assess residual stresses in selective laser melting

Keywords:

stresses Ti-6Al-4V alloy

Introduction

Additive manufacturing (AM) processes, and in particular selective laser melting (SLM), are recognized as a promising technology due to its ability to produce complex and lightweight customized components. These are directly fabricated from a sliced 3D-CAD model, without requiring expensive part-specific tooling [START_REF] Bremen | Selective laser melting, a manufacturing technology for the future[END_REF]. Despite its many advantages, the SLM process is still under development, especially for aeronautical applications. Among the current challenging research topics, most studies focus on the material densification, microstructure and mechanical properties [START_REF] Kruth | Consolidation phenomena in laser and powder-bed based layered manufacturing[END_REF][START_REF] Mani | Measurement Science Needs for Real-Time Control of Additive Manufacturing Powder Bed Fusion Processes[END_REF][START_REF] Leuders | On the mechanical behaviour of titanium alloy TiAl6V4 manufactured by selective laser melting: fatigue resistance and crack growth performance[END_REF][START_REF] Zhang | Selective laser melting of titanium alloys and titanium matrix composites for biomedical applications: a review[END_REF][START_REF] Liu | Microstructure, defects and mechanical behavior of beta-type titanium porous structures manufactured by electron beam melting and selective laser melting[END_REF][START_REF] Simonelli | Effect of the build orientation on the mechanical properties and fracture modes of SLM Ti-6Al-4V[END_REF], while some others are dedicated to process monitoring, improving surface quality and reducing residual stresses [START_REF] Bremen | Selective laser melting, a manufacturing technology for the future[END_REF][START_REF] Mani | Measurement Science Needs for Real-Time Control of Additive Manufacturing Powder Bed Fusion Processes[END_REF][START_REF] Townsend | Surface texture metrology for metal additive manufacturing: a review[END_REF][START_REF] Mercelis | Residual stresses in selective laser sintering and selective laser melting[END_REF][START_REF] Knowles | Residual stress measurements and structural integrity implications for selective laser melted Ti-6Al-4V[END_REF]. The SLM process belongs to the family of powderbed fusion (PBF) technologies [START_REF] Astm | Standard Specification for Additive Manufacturing Titanium-6 Aluminum-4 Vanadium With Powder Bed Fusion[END_REF], whereby a thin layer of powder spread on a substrate is selectively melted by a computer controlled laser beam and consolidates by heat diffusion. The part is built layer by layer, by repetition of these steps for successive powder beds [START_REF] Keller | Thermo-mechanical simulation of additive layer manufacturing of titanium aerospace structures[END_REF][START_REF] Li | Efficient multiscale prediction of cantilever distortion by selective laser melting[END_REF]. During production, the material experiences large localized temperature gradients due to rapid heating and cooling within a short time associated to the scan pattern of the high energy focused laser beam. Due to the layered build-up, the latter melting layer may re-melt or reheat the underlying layers. This results in high thermally-induced internal stresses which can detrimentally affect the mechanical performances and thus the reliability and life of the components in service [START_REF] Rossini | Methods of measuring residual stresses in components[END_REF]. When removing the part from the base plate, the residual stresses are released by shrinkage and bending deformation, causing dimensional inaccuracies [START_REF] Simonelli | Effect of the build orientation on the mechanical properties and fracture modes of SLM Ti-6Al-4V[END_REF][START_REF] Mercelis | Residual stresses in selective laser sintering and selective laser melting[END_REF][START_REF] Knowles | Residual stress measurements and structural integrity implications for selective laser melted Ti-6Al-4V[END_REF][START_REF] Kruth | Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method[END_REF][START_REF] Cheng | Stress and deformation evaluations of scanning strategy effect in selective laser melting[END_REF]. The distortion or even cracking of the part can sometimes happen during the process when the stresses reach critical levels. Understanding and controlling the development of the residual stresses inducing the component distortion is a critical issue and one of the current challenging research topics in SLM manufacturing [START_REF] Bremen | Selective laser melting, a manufacturing technology for the future[END_REF].

Residual stresses can be generated in many structures and components during various thermal or thermo-mechanical manufacturing processes such as welding, forming, heat treatment, machining, etc. [START_REF] Withers | Residual stress and its role in failure[END_REF][START_REF] Leggatt | Residual stresses in welded structures[END_REF][START_REF] Masubuchi | Analysis of Welded Structures: Residual Stresses, Distortion, and Their Consequences[END_REF][START_REF] Kleiner | Analysis of residual stresses in high-pressure sheet metal forming[END_REF][START_REF] Sridhar | Effect of machining parameters and heat treatment on the residual stress distribution in titanium alloy IMI-834[END_REF]. Over the years, various techniques have been developed to evaluate residual stresses, such as X-ray and neutron diffraction, ultrasonic velocity, magneto-acoustic emission, hole drilling, instrumented sharp indentation, crack compliance, layer removal, etc. [START_REF] Withers | Residual stress. Part 1-measurement techniques[END_REF][START_REF] Kandil | A Review of Residual Stress Measurement Methods, A Guide to Technique Selection[END_REF][START_REF] Wang | Residual stress in metal parts produced by powder-bed additive manufacturing processes[END_REF]. These methods can be classified depending on their characterization scale and their destructive or non-destructive nature. Mechanical methods (e.g., sectioning, contour, hole-drilling, ring-core, curvature) are used to characterize type I macro-stresses which vary over large distances (namely the dimensions of the part). These destructive techniques are based on the deformation measurement during or after complete or partial release of the residual stresses upon disturbing the mechanical equilibrium of the part. Non-destructive "physical" methods, such as diffraction analysis, are more relevant for assessing residual stresses of type II and type III, which occur respectively at the grain level or on the atomic scale [START_REF] Mercelis | Residual stresses in selective laser sintering and selective laser melting[END_REF][START_REF] Withers | Residual stress. Part 1-measurement techniques[END_REF]. However, the measurement uncertainties obtained by these methods depend on the material being analyzed. In particular, the correct evaluation of residual stresses in titanium alloys is difficult due to the overlap of the diffraction peaks associated with their poorly defined shape [START_REF] Moussaoui | Studying the measurement by x-ray diffraction of residual stresses in Ti6Al4V titanium alloy[END_REF][START_REF] Dai | Distinction in corrosion resistance of selective laser melted Ti-6Al-4V alloy on different planes[END_REF].

The curvature method, which consists in measuring the deflection or curvature of a part caused by the addition or removal of material containing residual stresses, is generally used to determine post-process thermal stresses within coatings and layers [START_REF] Withers | Residual stress. Part 1-measurement techniques[END_REF][START_REF] Kandil | A Review of Residual Stress Measurement Methods, A Guide to Technique Selection[END_REF][START_REF] Larsson | Deflection measurements as method to determine residual stress in thin hard coatings on tool materials[END_REF]. It can be applied to SLM components since the additive manufacturing is based on melting of successive layers, for example to optimize process parameters (such as laser power, scan speed and strategy, layer thickness, preheating, etc.) known to have a significant effect on the residual stresses [START_REF] Withers | Residual stress. Part 1-measurement techniques[END_REF][START_REF] Kruth | Selective laser melting of iron-based powder[END_REF]. Thus, several studies [START_REF] Li | Efficient multiscale prediction of cantilever distortion by selective laser melting[END_REF][START_REF] Zaeh | Investigations on residual stresses and deformations in selective laser melting[END_REF][START_REF] Buchbinder | Investigation on reducing distortion by preheating during manufacture of aluminum components using selective laser melting[END_REF][START_REF] Papadakis | Numerical computation of component shape distortion manufactured by selective laser melting[END_REF][START_REF] Yadroitsava | Residual stress in SLM Ti6Al4V alloy specimens[END_REF] were performed using an overhang "cantilever" test geometry selected to cause significant distortions, to investigate the influence of process parameters or to validate distortion prediction models. The method consists in determining the difference between the height of the specimen arms before and after separation from the support structure, on few points (usually about ten) along the longitudinal axis of the specimen. However, the measurement accuracy is limited to a hundred or a few hundred micrometers, due to the method of cutting the supports, and to the high surface roughness which is not filtered in the profile [START_REF] Buchbinder | Investigation on reducing distortion by preheating during manufacture of aluminum components using selective laser melting[END_REF]. In-situ measurements can be useful to monitor the PBF process during the part build [START_REF] Mani | Measurement Science Needs for Real-Time Control of Additive Manufacturing Powder Bed Fusion Processes[END_REF][START_REF] Tapia | A review on process monitoring and control in metal-based additive manufacturing[END_REF][START_REF] Everton | Review of in-situ process monitoring and in-situ metrology for metal additive manufacturing[END_REF]. Thus, Denlinger et al [START_REF] Denlinger | Effect of inter-layer dwell time on distortion and residual stress in additive manufacturing of titanium and nickel alloys[END_REF] used a laser displacement sensor to measure in situ deflection of a rectangular parallelepiped substrate material free to distort at one extremity, in order to investigate the residual stresses accumulated during the building of Ti-6Al-4 V and Inconel 625 parts by laser-based directed energy deposition. In addition, the authors determined the pre-and post-process plate profiles at ten points along the top of the substrate using a coordinatemeasurement machine.

The changes in the plate profile and out-of-plane distortion of the substrate were then calculated by subtracting the pre-process from the post-process measurements. But this asymmetric geometry, as the cantilever, enables to assess the residual stress only in one direction, because it concentrates the stresses along the specimen axis. For their part, Kruth et al [START_REF] Kruth | Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method[END_REF] investigated the amount of residual stresses in Ti-6Al-4 V parts produced by SLM using a bridge-shaped geometry specifically designed. Their so-called "bridge curvature method" (BCM) consists in determining the residual stress by finite elements simulation using on the curling angle α. This parameter is defined as the deviation from the normal position of the planes at the bottom of the pillars cut off from the base plate by wire EDM. It is determined using a 3D-CNC vision measuring machine. However, the measurement accuracy of the curling angle may be affected by a poor quality of the specimen cut, whereas the value of the calculated stress is very sensitive to the accuracy of this measure.

In the present study, an improved methodology derived from the BCM is proposed to accurately assess the part distortion of Ti-6Al-4 V bridge-shaped specimens produced by SLM. Profile and 3D surface measurements are performed on the upper surface using optical microscopy before and after removing the specimen from the base plate. The surface topographies are filtered and analyzed to determine the magnitude of distortion and additional parameters expressing the shape of the curvature. The repeatability of the method is assessed by statistical analysis, and the results of 2D and 3D measurements are compared.

Experimental procedure

Material and specimens

SLM experiments were performed on a ProX® DMP 200 machine from PHENIX SYSTEMS. Titanium alloy Ti-6Al-4 V was used as powder material, chosen for many applications as aerospace and biomedical industries owing to its good strength-to-weight ratio, high fatigue and corrosion resistance, good bio-compatibility associated to a good formability and heat treatability [START_REF] Zhang | Selective laser melting of titanium alloys and titanium matrix composites for biomedical applications: a review[END_REF][START_REF] Wang | Residual stress in metal parts produced by powder-bed additive manufacturing processes[END_REF]. The powder was plasma-atomized, resulting in a particle size ranging from 15 μm to 70 μm and a median diameter d 50 of about 35 μm. A parallelepiped bridge shape, shown in Fig. 1, was selected to emphasize residual stresses during and after the manufacturing [START_REF] Kruth | Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method[END_REF]. Specimens were manufactured in a protective argon atmosphere to prevent oxidation, using a non-preheated Ti-6Al-4 V base plate and without supporting structures. The invariant manufacturing parameters are reported in Table 1. Various laser scan strategies were investigated, as indicated in Fig. 2.

Measurement of distortions

Non-contact optical measurement techniques

The specimens were removed from the SLM support plate by electro-erosion. The distortions due to residual stresses that developed during the building process were released during the cutting. The surface of the specimen was measured using an Extended Field Confocal Microscope (EFCM, Altimet AltiSurf 520), based on the principle of chromatic coding (Fig. 3a): -focusing of a white light source reflected on the surface of the sample, -beam splitting of the polychromatic light source into its constituent wavelengths by an accurate distance-measuring sensor incorporating special chromatic lenses (each wavelength being able to focus only on a point situated at a specific distance from the sensor, thus creating a continuum of monochromatic imaging points), -activating the distance-sensing ability of the sensor by matching the central wavelength of the reflected beam to the exact height of the focused point, via a spectrometer [START_REF] Cohen-Sabban | Quasi-confocal extended field surface sensing[END_REF].

The scanning was carried out through a CHR-150 controller (Stil S.A.) connected to the profilometer and provided a topographic image representing the surface height z as a function of the surface coordinates (x,y). In order to improve the sensitivity of the sensor to reflected light, dark background correction was systematically performed before measurement.

A Focus Variation Microscope (FVM, Alicona InfiniteFocus SL) was also used to measure the specimen surface. As detailed in Figure 3b, this technique is based on exploiting the small depth of focus of an optical system with vertical scanning to provide topographical and colour information from the variation of focus [START_REF] Danzl | Focus variation-a robust technology for high resolution optical 3D surface metrology[END_REF]. Although less accurate on altitude coding than EFCM, this technique had the advantage here of being faster for the acquisition of large areas.

Profile measurements

Profile measurements were performed by EFCM on the specimen top surface in both X and Y directions, using a chromatic sensor having a 350 μm depth of field (whose full features are given in Table 2). A fairly low sampling frequency of 100 or 300 Hz (depending on the specular properties of the surface) was used to limit the amount of non-measured points, which typically represented between 1 and 5% of the scanned area. Three profiles of 18.8 mm length and five profiles of 9 mm length, spaced about 4 mm apart and crossing the specimen respectively along the X and Y axes, were acquired. The profiles were spaced apart by about 4 mm. The lateral resolution of the profiles was selected to 1 μm, and the measuring speed to 100 μm/s in order to improve the signal. An example of a raw profile measured along X direction is given in Fig. 4a.

The repeatability of the measurements was evaluated on three selected specimens produced with different laser scan angles ϴ (i.e. 0°, 45°and 90°). Five different acquisitions were performed by the same operator, over several days/weeks. For each measurement, the specimen was removed from the motorized table and then replaced.

Surface topographies

The topography of upper surface of the specimens (about 19.3 mm × 9.3 mm, i.e. 90% of the total area excluding extreme edges) was scanned by EFCM. Due to high z variation of the surface, a chromatic optical probe with a large depth of field (3 mm) had to be used. A scanning speed of 1 mm/s and a low sampling frequency (100 Hz) were selected. The lateral resolution was set to 10 μm along both X and Y directions to reduce the acquisition time.

Surface measurements were also carried out by FVM, chosen for its ability to measure a wide z ranges characteristic of shape defects. The specimens were mounted on a motorized stage and illuminated with ring light. A 10 × objective lens was used, giving a XY range of 22.32 mm × 11.25 mm constituted of 12 × 7 fields of view. Vertical resolution was set at 200 nm and lateral resolution at 3.9 μm. Once captured, the raw height maps were cut to the same size (i.e. 19.3 mm x 9.3 mm) as surface topographies acquired by EFCM.

Using the same protocol as for the profiles, five different surface maps were scanned on each specimen to estimate the measurement repeatability with both measuring systems. In order to precisely quantify the distortions due to the residual stresses, topographic measurements were performed before and after separation of the parts from the base plate. The raw profiles were processed using the surface metrology software Mountains Map® (DigitalSurf). The first step consisted to interpolate non-measured points by considering the value of their nearest neighbours. Then, the profile was levelled by least mean squares (LMS) subtraction to correct the non-parallelism between the optical sensor and the surface of the specimen. To describe the bending due to the release of residual stresses, the points of the profile were fitted by a second-order polynomial function expressed as:

= = + + z f x ax bx c ( ) , 2 (1)
where z is the altitude of the points of the profile, x the coordinates of these points, and a, b and c are the coefficients of the function. The magnitude of distortion was finally assessed by calculating the parameter Pt, which corresponds to the total depth of the concave shaped curve of Fig. 4b. A sensitivity study showed that there was little difference (less than a few micrometres) in the Pt value determined using a polynomial of degree 2, 3 or even 4. On the other hand, a polynomial of higher degree (5 or more) would take into account waviness defects which are rather the signature of the process (for example, the weld tracks, balling, and unmelted powder). Therefore, it was decided to set the degree of the polynomial function at 2.

Surface topography processing

The processing procedure was the same as for profiles, except that the operations were carried out on surfaces (Fig. 5a). First, the nonmeasured points were interpolated and the surface levelled by LMS plane subtraction. The distortion was fitted by a quadratic polynomial surface expressed as a function of x and y as:

= = + + + + + z x y ax by cxy dx ey f f( , ) , 2 2
(2

)
where z is the altitude of the points of the surface, x and y are the coordinates of these points, and a, b, c, d, e and f are the coefficients of the function. Then, standardized flatness parameters such as the peakto-valley (or total) flatness deviation FLTt and the root mean square (or quadratic) flatness deviation FLTq were calculated on the resulting surface shown in Figure 4b, without additional filtering. According to ISO 12781-1 [START_REF]Geometrical Product Specifications, (GPS) -flatness -part 1: vocabulary and parameters of flatness, International Organization for Standardization[END_REF], FLTt is defined as:

= + FLTt FLTp FLTv, ( 3
)
where FLTp is the value of the largest positive local flatness deviation from the least squares reference plane and FLTv is the absolute value of the largest negative local flatness deviation from the least squares reference plane.

FLTq was determined from the following equation:

∫ = FLTq A LFD dA 1 , A 2 (4)
where LFD represents the local flatness deviation and A the surface area of the flatness feature.

FLTt was considered as the most useful flatness parameter from a metrological point of view [START_REF] Nadolny | Analysis of flatness deviations for austenitic stainless steel workpieces after efficient surface machining[END_REF].

In addition, curvature attributes were determined using a Matlab® routine. Curvature describes how much the curve deviates from straight line, in a given direction and at a particular point of the curve [START_REF] Roberts | Curvature attributes and their application to 3D interpreted horizons[END_REF]. For a function f(x), the curvature k(x) can be expressed in terms of second derivatives as:

= + k x d dx d dx ( ) f/ (1 ( f/ ) ) . 2 2 2 3/2 (5)
In a three-dimensional space defined by orthogonal (x,y,z) axes where x and y represent the map axes and z the depth axis, a surface can be described by a function z = f(x,y) which was equivalent in our case to a quadratic polynomial (Eq. 1). The curvature tensor K can be expressed by the following relation:

⎜ ⎟ = ⎛ ⎝ ⎞ ⎠ = ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ K K K K K .
The normal curvatures can be defined by planes which are orthogonal to the surface. The intersection of these two orthogonal planes with the surface describes the principal curvatures (K max and K min ). The maximum curvature K max and the minimum curvature K min correspond respectively to the curvatures calculated in the directions O max and O min , for which the curvatures take the largest and the lowest absolute values.

According to [START_REF] Buchbinder | Investigation on reducing distortion by preheating during manufacture of aluminum components using selective laser melting[END_REF], the mean curvature K m was defined as the average of the principal curvatures K min and K max [START_REF] Roberts | Curvature attributes and their application to 3D interpreted horizons[END_REF]:

= + K K K ( ) / 2 . m max min (7)
Roberts [START_REF] Roberts | Curvature attributes and their application to 3D interpreted horizons[END_REF] showed that the mean curvature was not particularly useful for describing the surface, since it tends to be dominated by -and consequently visually similar to -the maximum curvature K max which can be considered as a more meaningful attribute. However, since K m helps to derive the principal curvatures, it can be useful to calculate its value from the coefficients of the polynomial function (Eq. 2) using the following equation [START_REF] Rektorys | Differential Geometry[END_REF]:

= + + + - + + K a e b d cde d e (1 ) (1 ) (1
) .

m 2 2 2 23 / 2 (8)
Gaussian curvature K g was defined as the product of the principal curvatures K min and K max [START_REF] Roberts | Curvature attributes and their application to 3D interpreted horizons[END_REF]:

= K K K .
.

g min max (9)
As for K m , this attribute has only limited applications to describe surfaces, but is useful to derive other curvature attributes. K g was calculated as a function of the coefficients of Eq. (2) using the following relationship [START_REF] Rektorys | Differential Geometry[END_REF]:

= - + + K ab c d e 4 ( 1
) . (10)

3. Results

Repeatability of distortion measurements

2D parameters

Statistical results of profile measurements by EFCM, expressed by the standard deviation σ and the coefficient of variation C.V. (or relative standard deviation, defined as the ratio of the standard deviation to the mean), are reported in Tables 3 and4 respectively for the two optical probes of different ranges. First, we note that the two sensors give significantly different mean distortion magnitudes, with an average difference of 7 μm in both X and Y directions. It can be considered that the 3 mm probe should be more suitable due to its greater depth of field and an axial resolution (0.1 μm) sufficiently accurate to measure shape deviations. For both sensors, profile measurements along X give C.V. of less than 8%, attesting to relatively low measurement dispersions. Higher C.V. values, close to or greater than 20%, are obtained along Y direction especially for the specimens built with ϴ = 0°and 90°.

Micrographs of the upper surface of the specimens observed with a scanning electron microscope (SEM) reveals a very coarse and heterogeneous surface quality (Fig. 6). Surface defects such as weld tracks (appearing as ridge-like formations indicating the path followed by the laser while traversing the powder bed), spatter, unmelted and partially melted powder particles (appearing as sphere-like protrusions stuck to the surface), are clearly visible. It is well known that AM processes by powder-bed fusion produces parts with high surface roughness [START_REF] Townsend | Surface texture metrology for metal additive manufacturing: a review[END_REF][START_REF] Leach | Metrology for additive manufacturing[END_REF] and anisotropic properties related to the laser trajectories [START_REF] Simonelli | Effect of the build orientation on the mechanical properties and fracture modes of SLM Ti-6Al-4V[END_REF][START_REF] Dai | Distinction in corrosion resistance of selective laser melted Ti-6Al-4V alloy on different planes[END_REF]. This was confirmed on the investigated specimens by profile measurements carried out according to ISO 4287 [START_REF]BS EN ISO_4287. Geometrical Product Specification (GPS) Surface Texture: Profile Method Terms, Definitions and Surface Texture Parameters[END_REF] and ISO 4288 [START_REF]BS EN ISO_4288. Geometric Product Specification (GPS) Surface Texture Profile Method: Rules and Procedures for the Assessment of Surface Texture[END_REF] standards, which give an arithmetic average roughness Ra ranging between 10 and 20 μm depending on the scan strategy. Such surface heterogeneity can lead to uncertainty and dispersion in the mathematical fit of the polynomial function representative of the flatness deviation. This is particularly critical when the distortion is low, as is the case with profiles along Y whose magnitude is lower to 30 μm. For the specimen built with ϴ = 45°, C.V. is of the same order of magnitude in both directions. This is related to the path of the optical probe when measuring the profiles, because the welds are crossed at 45°both in X and Y directions.

3D parameters

Flatness parameters (i.e. FLTt and FLTq) and curvature attributes (K min , K max , K m, O max ) determined on surface topographies measured by EFCM are reported in Table 5. C.V. values are less than 4% for all investigated specimens, except for the minimum curvature K min which exhibits a greater dispersion (3% < C.V. < 16%) probably due to the particularly low value of this attribute. One can notice the very good repeatability of the orientation O max of the maximum curvature (C.V. < 1%). As can be seen in Table 5, the evolution of flatness and curvatures parameters does not show the same trend as a function of the orientation of the laser scan ϴ. The reason is that curvature attributes are independent on the specimen geometry than the flatness parameters. The second one should therefore be used preferentially when comparing experimental measurements obtained on different geometries.

Fig. 7a andb shows a strong similarity between the surface topographies obtained by FVM and EFCM, respectively. Both reveal the specimen bending and some topographic features such as the weld tracks and unmelted particles appearing as peaks. However, the FVM surface map has a smoother appearance than the EFCM one, certainly because of a less noisy signal (with unmeasured points representing less than 0.05% of the total area). Compared to EFCM, results obtained from the Alicona FVM give slightly lower mean values for all attributes (Table 6). This difference could be due to the lower z-resolution achieved with the principle of FVM. However, FVM provides improved measurement repeatability (C.V. ≤ 1%) except for K min which is again more scattered than other curvature attributes (C.V. up to 5%).

In Table 7 are reported the calculated percentage differences between the parameter mean values measured with FVM and EFCM. Remarkably low differences (≤ 3%) are observed for the two specimens with the largest distortions (i.e. ϴ = 0°and 45°), except for K min due to its poorer repeatability. The differences are somewhat larger for the specimen built at 90°(between 1.7 and 11.3%), especially for the curvatures attributes K max and K m . However, regarding the main orientation of the distortion O max , the difference is always very small (less than 1%) whatever the scan orientation. This parameter can therefore be considered as particularly repeatable and robust.

Comparative measurements before and after cutting

In Table 8 are reported the flatness deviations and curvature attributes measured by EFCM on some specimens built with various laser scan strategies (as described in Fig. 2), before and after the part has been removed from the plate. In addition, the evolution of the total flatness deviation FLTt is graphically shown in Fig. This graph indicates that before cutting, the flatness deviation is relatively low and close for all investigated specimens (FLTt = 36.5 μm + /-3.3 μm). At this stage, the stress relaxation is low and concerns only the free surface layer, resulting in a small bending of the specimen. After cutting, a significant increase is observed on FLTt parameter (164 μm + /-48 μm) for all scan strategies (Table 8). This increase is about 80% on average for both parameters, indicating that most of the tensile residual stresses are released after cutting, thus causing bending of the specimen.

Fig. 8b indicates that the orientation of the maximum distortion O max is very close to 180°(i.e. aligned with longitudinal x-axis) for all specimens before removal from the base plate, while it varies considerably after cutting. An exception is however noted for the specimen built perpendicular to the X-axis (ϴ = 90°) for which O max remains substantially unchanged (although with a higher curvature).

Table 5

Flatness and curvature attributes determined on 3D topographies acquired by EFCM (with a 3 mm optical sensor) on specimens removed from the base plate.

Laser scan orientation

FLTt (μm)

FLTq (μm) K max (mm -1 ) K min (mm -1 ) K m (mm -1 ) O max (°) ϴ =

Discussion

Fig. 9 shows the evolution of the C.V. resulting from repeatability tests as a function of the mean value of the distortion magnitude, for both profile and surface measurements by EFCM and FVM. The repeatability of 3D topographic measurements clearly appears much better compared to 2D profiles. In fact, the flatness and curvature parameters are statistically more representative than the magnitude of distortion estimated from one or a few isolated profiles, which depends substantially on their position on the specimen. This is particularly true on anisotropic or inhomogeneous rough surfaces such as those produced by SLM. As shown by the fitted curve by a power law, the greater the deformation, the better the measurement repeatability. It will therefore be favourable to use a test geometry enabling the greatest possible deformations to be generated.

Unlike many other optical techniques that are limited to coaxial illumination, the maximum slope angle measurable by FVM does not depend solely on the numerical aperture of the lens since it can also be adjusted by the flexibility of the technique in terms of use of light (such as a ring light). This overcomes most limitations when measuring surfaces with strongly varying reflection properties within the same field of view. This advantage has been clearly demonstrated for applications such as measurement of steep surface flanks or welding spot inspections, which have a very irregular shape with steep flanks and difficult reflective behavior [START_REF] Danzl | Focus variation-a robust technology for high resolution optical 3D surface metrology[END_REF]. In our case, the SLM surfaces have many asperities with sharp slopes (Fig. 7), leading to measurement artifacts by EFCM because of the reflection of some surface points outside the angle limit of the optical probe. This may explain the best repeatability observed for topographic measurements made by FVM compared to measurements by EFCM, which is probably also related to better lateral resolution (4 μm for FVM versus 10 μm for EFCM). Furthermore, acquisition times of surface topographies can be particularly long, typically several hours with EFCM for the measurement conditions considered in this study. FVM reduces the acquisition time to a few tens of minutes while ensuring excellent measurement repeatability, therefore it could advantageously be used to assess the part distortion. In Fig. 9, it can also be noticed that the curve shows an inflection point corresponding to a distortion magnitude of about 35 μm, which is equivalent to the median diameter d 50 of the Ti-6Al-4 V powder used for manufacturing specimens. Below this distortion magnitude, C.V. exceeds 5% and then increases drastically. This value can therefore be defined as the quantification limit of the developed method, below which measurements should not be relevant because of the large number of unmelted particles on the surface of SLM parts (as previously illustrated in Fig. 6). Moreover, it may be thought that the presence of these particles on the surface can affect the calculation of the polynomial function representing the distortion. This effect was estimated by applying a morphological filter using a 70 μm diameter sphere (which corresponds to the maximum size of the powder) on the surface, just before the polynomial approximation. The results showed that the value of flatness deviation parameters (FLTt and FLTq) was slightly modified (difference of less than 5%) for the distortion amplitude greater than the quantification limit.

The 3D approach provides different parameters which are very relevant in understanding the distortion phenomena in relation to the process parameters. Besides the amplitude parameters (FLTt and K max ), the main orientation (O max ) of the distortion highlights the effect of the laser scanning strategy. Fig. 10 shows the distortion shapes extracted from the height maps for various scanning orientations ϴ. It reveals that O max coincide with the vertical axis (at x = 10 mm) only for ϴ = 0°( Fig. 10a), while the axis of bending changes when ϴ departs from 0°( Figs. 10b andc). Since the residual stresses are generated mainly along the laser scan direction, the resulting distortion is oriented perpendicular to ϴ. Parry et al [START_REF] Parry | Understanding the effect of laser scan strategy on residual stress in selective laser melting through thermo-mechanical simulation[END_REF] recently established through thermo-mechanical simulation that the greatest stress component develops parallel to the scan vectors.

Changing the orientation of the laser scanner varies not only O max , but also the distortion magnitudes along X and Y, without however reversing the values by varying ϴ from 0°to 90°(Tables 3 and4). The difference in distortion amplitude along X and Y is inherent to the asymmetric geometry of the bridge specimen (whose length is twice as large as its width). This geometry naturally promotes bending at the thinnest area of the specimen, i.e. along X-axis (as illustrated in Fig. Thus, the distortion magnitude along X for ϴ = 0°remains higher than along Y for ϴ = 90°. In addition, the maximum deformation is induced by a unidirectional laser scan along the x-axis (ϴ = 0°) which also leads to the longest scan vectors, while the minimal deformation is observed for ϴ = 90°which exhibits the shortest scan vectors (Fig. 8a). Several experimental and numerical works [START_REF] Mercelis | Residual stresses in selective laser sintering and selective laser melting[END_REF][START_REF] Kruth | Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method[END_REF][START_REF] Kruth | Selective laser melting of iron-based powder[END_REF][START_REF] Zaeh | Investigations on residual stresses and deformations in selective laser melting[END_REF][START_REF] Keller | New method for fast predictions of residual stress and distortion of AM parts[END_REF] have reported a link between the length of the scan vectors and the residual stresses. These considerations further underline the relevance of 3D measurements, since the resulting parameters (especially O max ) make it possible to better explain and correlate the results with the process parameters, that would not be from simple profile measurements. It must be emphasized that all the results discussed above were obtained on the specimens removed from the base plate.

Measurements made on the specimens prior to separation from the support plate revealed much smaller distortion magnitudes than after cutting (about 80% lower). Moreover, the distortion amplitude before cutting is close to the quantification limit allowed by the measurement method (35 μm). This distortion can be neglected in the present study, since the distortion after cutting reflects the total released residual stresses. However, the distortion before cutting should be considered when its magnitude is significant, and this in order to precisely correlate the distortions with the residual stresses. Based on a numerical model developed to predict the distortion of SLM manufactured parts, Li et al [START_REF] Li | Efficient multiscale prediction of cantilever distortion by selective laser melting[END_REF] found that the tensile stress in a cantilever specimen decreased of 70% when it was removed from the support. With this kind of geometry, the distortion is relatively high before cutting and must be taken into account.

As previously shown (Fig. 8b), the orientation of the distortion before cutting seems independent of the scan strategy (O max close to 180°w hatever the laser scan orientation, the hatch angle, etc.). In fact, the orientation of the main deformation O max corresponds to the maximum curvature K max , which represents the deflection rate over a given length (Eq. 5). Since profile measurements along X and Y revealed that before cutting, the distortion amplitudes are very close in both directions, and the geometry of the bridge specimen is asymmetric (X = 2Y), then the curvature K max is logically maximum in the direction (Y). It is only after cutting that the impact of the orientation of the weld seams on O max is effective. A comprehensive investigation to determine the effect of laser scan strategy on residual stresses and validate these assumptions is planned.

Conclusions

A new method, based on the bridge curvature method (BCM) and non-contact optical measurements of the specimen surface (by EFCM or FVM), was developed to assess the distortions for application to SLM manufactured parts. Repeatability tests revealed that measurements on 3D surface topographies are more robust than 2D profile measurements. An excellent repeatability was obtained in particular on surface height maps measured by FVM. However, surface defects such as unmelted powders can affect the measurement accuracy of the distortion when its magnitude is less than 40 μm, which corresponds to the median size of the powder particles.

Compared to 2D methods and associated criteria reported in the literature, flatness deviation parameters (such as FLTt and FLTq) and curvature attributes (such as the mean curvature K m or the maximum curvature K max ) proposed in our approach are more reliable as representative of the overall deformation of the specimen. In addition, the 3D approach makes it possible to have a better knowledge of the deformation distribution on the specimen, and especially to determine unambiguously the maximum distortion and its associated orientation. It was also shown that, before the specimen was removed from the base plate, the flatness deviation remains low and quasi-independent of the scan strategy, while it increases on average by 80% after cutting of the specimen.

This methodology can be applied to study the effect of process parameters such as the laser scan strategy and the part geometry on deformations and residual stresses, using bridge-shaped specimens or any other type of specimen (such as cantilever) provided that it has a flat upper surface. The 3D mapping of the surface deformation could also help validate thermo-mechanical simulation of the process used to predict residual stresses and distortions in SLM manufactured parts.

Fig. 1 .

 1 Fig. 1. Geometry and dimensions (in mm) of the SLM bridge-shaped specimen.

Fig. 2 .

 2 Fig. 2. Various laser scan strategies investigated: unidirectional scan pattern with a scan angle ϴ = 0°a) or 45°(b), rotating scan pattern with a hatch angle β = 90°( c), and inward concentric scan pattern (d).

Fig. 3 .

 3 Fig. 3. Schematic diagram of topographic measuring devices: a) extended field confocal microscope (AltiSurf 520)[START_REF] Cohen-Sabban | Quasi-confocal extended field surface sensing[END_REF]; (b) focus variation microscope (Alicona Infinite Focus)[START_REF] Danzl | Focus variation-a robust technology for high resolution optical 3D surface metrology[END_REF].

Fig. 4 .

 4 Fig. 4. Typical raw profile levelled by LMS subtraction (a) and estimation of flatness deviation on the fitted quadratic polynomial function calculated from the raw profile (b).

Fig. 5 .

 5 Fig. 5. Typical surface height maps measured on the top of the SLM specimens by EFCM: (a) levelled raw surface, (b) distortion defect approximated by a quadratic polynomial surface (both surfaces are represented with a normalised scale, either in top or in perspective view).

Fig. 6 .

 6 Fig. 6. SEM micrographs of the surface of the specimens built with ϴ = 0°(a) and ϴ = 45°(b), which show the weld tracks and many unmelted particles adhered on the surface.

Fig. 7 .

 7 Fig. 7. Levelled surface height maps of the specimen built with ϴ = 45°, measured by EFCM with a 3 mm optical sensor (a) and by FVM with 10 × objective (b).

Fig. 8 .

 8 Fig. 8. Evolution of the total flatness deviation FLTt (a) and of the orientation O max of the main curvature (b) of specimens built with various scan strategies, before and after removal from the base plate.

Fig. 9 .

 9 Fig. 9. Evolution of the coefficient of variation versus the mean distortion magnitude (all data determined from profile and surface measurements are represented).

Fig. 10 .

 10 Fig. 10. 3D height maps showing the distribution of the distortion for different laser scan orientations ϴ, after removing the specimen from the base plate: a) ϴ = 0°, c) ϴ = 45°, d) ϴ = 90°(the white dotted line indicates the main orientation of the distortion ϴ max ).

Table 1

 1 Manufacturing parameters kept constant on the SLM machine.

	Laser spot	Laser	Scan	Hatch	Layer	Number	Contour scan
	diameter	power	speed	spacing	thickness	of layers
	(mm)	(W)	(mm/	(mm)	(mm)
			s)
	0.07	300	1800	0.085	0.06	233	none

Table 2

 2 Measuring performances of the chromatic sensors used with the extended field confocal microscope (EFCM).

	Total	Working	Axial (z)	Lateral	Precision (μm) Reflection
	depth	distance	resolution	resolution		limit angle
	of field	(mm)	(μm)	(μm)		(°)
	(mm)
	0.35	12	0.01	4	0.1	30
	3	28	0.1	10	1	1

2.3. Extracting and quantifying the distortion 2.3.1. Profile processing

Table 3

 3 Total magnitude of the distortion (Pt) determined on 2D profiles acquired by EFCM (with a 350 μm optical sensor) on specimens removed from the base plate.

	Laser scan orientation	Profile	Mean (μm) Std. dev.	C.V. (%)
	strategy	direction		(μm)
	ϴ = 0°X	168.8	1.85	1.09
		Y	11.2	2.96	26.3
	ϴ = 45°X	101.9	5.84	5.73
		Y	18.4	0.84	4.57
	ϴ = 90°X	56.4	2.41	4.28
		Y	29.6	5.64	19.0

Table 4 Total

 4

	ϴ = 0°X	178.6	2.74	1.53
	Y	23.7	5.25	22.1
	ϴ = 45°X	106.7	3.89	3.64
	Y	11.4	0.79	6.98
	ϴ = 90°X	51.3	3.73	7.28
	Y	26.3	6.59	25.1

magnitude of the distortion (Pt) determined on 2D profiles acquired by EFCM (with a 3 mm optical sensor) on specimens removed from the base plate. Laser scan orientation Profile direction Mean (μm) Std. dev. (μm) C.V. (%)

Table 6

 6 Flatness and curvature attributes determined on 3D topographies acquired by FVM (Alicona, with 10 × objective) on specimens removed from the base plate.

	Laser scan orientation	FLTt (μm)	FLTq (μm)	K max (mm -1 )	K min (mm -1 )	K m (mm -1 )	O max (°)
	ϴ = 0°Mean	198.2	53.7	3.84	1.38	2.61	92.2
	Std. dev.	0.95	0.35	0.026	0.054	0.021	0.048
	C.V. (%)	0.48	0.66	0.68	3.96	0.82	0.05
	ϴ = 45°Mean	176.2	37.2	3.13	0.60	1.86	124.0
	Std. dev.	1.09	0.25	0.015	0.027	0.019	0.36
	C.V. (%)	0.62	0.68	0.48	4.56	1.04	0.29
	ϴ = 90°Mean	103.4	22.8	3.15	1.47	2.27	178.6
	Std. dev.	0.80	0.25	0.033	0.023	0.014	0.50
	C.V. (%)	0.78	1.09	1.07	1.53	0.61	0.28

Table 7

 7 Percentage difference between parameters calculated from EFCM and FVM measurements on specimens removed from the base plate.

	Laser scan orientation	FLTt	FLTq	K max	K min	K m	O max
	ϴ = 0°3.1	2.7	2.8	7.0	0.4	0.9
	ϴ = 45°2.2	1.1	2.2	0.0	2.1	1.4
	ϴ = 90°5.7	1.7	11.3	2.1	8.8	0.7

Table 8

 8 Flatness deviations and curvature attributes determined before and after separation of the specimens from the base plate.

	Laser scan	Cutting FLTt (μm) FLTq (μm) K max	K m (mm -1 ) O max (°)
	strategy				(mm -1 )
	ϴ = 0°before	37.6	7.7	1.14	0.81	174.1
		after	204.6	55.2	3.95	2.62	93.0
	ϴ = 90°before	34.2	8.5	2.62	1.34	178.1
		after	109.7	23.2	3.55	2.49	177.4
	h = 45°before	33.2	7.7	2.32	1.19	182.8
		after	170.6	35.3	3.32	2.56	144.5
	h = 105°before	35.0	7.7	2.10	1.18	180.1
		after	116.8	24.8	2.60	2.09	196.1
	Concentric	before	39.8	8.2	2.04	1.22	179.0
	inward	after	203.3	53.5	3.80	3.01	91.6

Acknowledgments

The authors would like to thank the CIRIMAT for providing SLM specimens. Kévin Grondin is greatly acknowledged for its contribution to the development of the Matlab® routine.


F M Schmidt
email: schmidt@mines-albi.fr

S Nakouzi

J Pancrace

Y Le Maoult

F Berthet

CURING SIMULATION OF COMPOSITES COUPLED WITH INFRARED HEATING

Keywords: composite, infrared heating, degree of curing, epoxy resin, carbon fibers, numerical modeling

Because of higher specific strength and stiffness, low weight, and good resistance to corrosion, the use of composite materials in aerospace structures has increased. Aircraft industry has recently begun to investigate Liquid Composites Molding techniques (LCM) through research programs because of its ability to produce large parts at a low cost. In this paper, we have not addressed the filling step during which the resin flows through fibrous media, but we investigate the numerical simulation of curing reinforced RTM-6 by infrared heating. Finite element based program COMSOL Multiphysics™ has been used to simulate the curing process. Thermochemical model has been implemented in order to compute reaction rate as a function of reaction temperature and degree of conversion using a cure kinetic model .

INTRODUCTION

Using thermal radiation to cure the composite is more efficient and effective than standard thermal energy sources. Thermal radiation was successfully used to produce a high quality polymer matrix in less time [START_REF] Chern | On-Line Processing of Unidirectional Fiber Composites Using Radiative Heating: I. Model[END_REF].We assumed the infrared interaction with the composite is a surfacic heat flux on the top surface [START_REF] Chern | On-Line Processing of Unidirectional Fiber Composites Using Radiative Heating: I. Model[END_REF][START_REF] Chern | On-Line Processing of Unidirectional Fiber Composites Using Radiative Heating: II. Radiative Properties, Experimental Validation and Process Parameter Selection[END_REF]. The energy equation was coupled with the exothermic heat released during the curing process in order to predict the composite temperature as a function of time and degree of cure.

LIQUID RESIN INFUSION (LRI)

Liquid infusion process was used is this study to implement the composite; the mould used is a singlesided mould which is sealed with a vacuum bag and the recovery surface is transparent to the infrared radiation. In the LRI, the infusion and the curing process take place at ambient pressure.

INFRARED INTERACTION

Because the graphite fibers embedded in the epoxy resin are very strong infrared absorbers over broad spectral ranges at all wavelengths, the composite has strong absorption bands in some portions of the spectrum as a first approach; we have neglected epoxy absorption in this paper [START_REF] Chern | On-Line Processing of Unidirectional Fiber Composites Using Radiative Heating: I. Model[END_REF][START_REF] Chern | On-Line Processing of Unidirectional Fiber Composites Using Radiative Heating: II. Radiative Properties, Experimental Validation and Process Parameter Selection[END_REF][START_REF] Kim | Transient Thermal Modeling of In-Situ Curing During Tape Winding of Composite Cylinders[END_REF][START_REF] Chern | Thermal Analysis of In-Situ Curing for Thermoset, Hoop-Wound Structures Using Infrared Heating: Part II -Dependent Scattering Effect[END_REF].

BOUNDARY CONDITIONS

The composite is assumed to be a block with (20x10x1mm) dimensions. It is composed of the superposition of a sequence of carbon plies embedded in an epoxy matrix [START_REF] Cunningham | Prediction of the temperature profile with a composit sheets during pre-heating[END_REF]. The infrared radiation is absorbed by the carbon ply present in the top surface of the composite. This incident infrared radiation on the top surface was taken as a boundary condition in COMSOL Multiphysics TM .There is also natural heat convection between this surface and the air present in the oven. The other boundaries are assumed to be adiabatic: the bottom is in contact with a mould and there is no heat exchange between the mould and the composite. The frame of the composite is so thin in comparison to the surface, that we can ignore the heat exchange all around its contour.

! " # $," &' &( = ∇(, " ∇-) + 0 1 ! 1 2 3 &4 &( (1)
Where 2 3 = ultimate heat of reaction, 5 = degree of curing, and the ! " = density, # $," = heat capacity, , " = thermal conductivity of the composite are expressed using the rule of mixture:[8, 9, 10]

! " = B C B D B C E D FB D E C (2)
# $," = # $,1 G 1 + # $,H G H (3)
, " =

I C I D,J (KLM C )I C FM C I D,J (4)
G 1 = M C B D N M C B D N F (KLM C ) B C N (5) G H = 1 -G 1 (6)
Where , H,( = transverse thermal conductivity of the fibers, G = weight fraction, 0 = volume fraction, the subscript Q stands for the fibers, and R for the matrix. The system of equations described above can be solved at each time step in order to calculate the distributions of temperature and degree of curing and their evolution with time.

KINETIC MODELING

GLASS TRANSITION TEMPERATURE

The glass transition temperature is modelled using the DiBenedetto equation:[8]

-S = -ST + (' UV L' UW )X4 KL(KLX)4 (7)
Where -ST and -SY = glass transition temperature of unreacted and full-reacted resin, Z = material constant. These values were deduced from the literature [START_REF] Ruiz | Thermomechanical Properties during Cure of Glass-Polyester RTM Composites: Elastic and Viscoelastic Modeling[END_REF].

KINETIC MODEL

Kamal and Sourour [START_REF] Bailleul | Identification des propriétés thermiques de composites fibres de verre / résines thermodurcissables Application a l'optimisation des procédés de moulage[END_REF] have shown that the following model adequately describes the cure kinetics of an epoxy resin:

[4 [( = (, K + , \ 5 1 )(1 -5) ] (8)
, ^= _ ^exp (-

a b c' ) d = 1, 2 (9)
Where , K and , \ = rate constants with an Arrhenius type of dependence with temperature and R and f = catalytic constants.

Although the model of Kamal and Sourour [START_REF] Bailleul | Identification des propriétés thermiques de composites fibres de verre / résines thermodurcissables Application a l'optimisation des procédés de moulage[END_REF] contains several essential features, it ignores the influence of the glass transition temperature -S on the diffusion of the macromolecules.

This model [START_REF] Bailleul | Identification des propriétés thermiques de composites fibres de verre / résines thermodurcissables Application a l'optimisation des procédés de moulage[END_REF] has been extended in order to reflect the effect of vitrification in the kinetic model of resin transfer molding. This model was also used by [START_REF] Ruiz | Thermomechanical Properties during Cure of Glass-Polyester RTM Composites: Elastic and Viscoelastic Modeling[END_REF] [4

[( = ( I g I h I g FI h + I i I h I i FI h 5 1 )(1 -5) ] (10)
, j = , k exp (- l H ) (11)
Q = Q T + m(---S ) [10] (12)
Where , j = diffusion factor, , k = diffusion rate constant, n = constant having the order of one, -S = glass transition temperature, Q = free volume fraction of the polymer [START_REF] Elsawi | Rheological and kinetic behavior of double-walled carbon nanotubes filled epoxy resin[END_REF], Q T = free volume fraction for a temperature equal to -S , m = thermal expansion coefficient for a temperature above -S .

For an amorphous polymer [START_REF] Nguyen | Systèmes époxy-amines incluant un catalyseur externe phénolique : Cinétique de réticulation-vieillissement hydrolytique[END_REF] which is the case of our composite, Q T = 0,025 and m = 0,00048.

KINETIC PARAMETERS

Kinetic parameters of RTM6 resin are calculated using linear regression algorithms by fitting model equations In the DSC, the rate of heat generation st/sv is recorded with time. As 2 3 is constant for a given curing process, [START_REF] Ruiz | Thermomechanical Properties during Cure of Glass-Polyester RTM Composites: Elastic and Viscoelastic Modeling[END_REF][START_REF] Ruiz | Multi-criteria thermal optimization in liquid composite molding to reduce processing stresses and cycle time[END_REF]12] the rate of the degree of curing is calculated by:

[4 [( = K 2 w [x [( (13)
The degree of curing is obtained by integrating the DSC data and normalizing with 2 w .

FITTED KINETIC PARAMETERS

The figure 3 below shows the temperature dependence of factors y1 and y2 [START_REF] Elsawi | Rheological and kinetic behavior of double-walled carbon nanotubes filled epoxy resin[END_REF]which exhibits an Arrhenius type of temperature dependence. The estimated kinetics parameters from the fitting curves used in our simulations are listed in table 1 below.

Table 1: Estimated parameters

Parameter _ K [Rdf LK ] 4.5E6 z K [{/R|}] 74.69E4 _ \ [Rdf LK ] 1.3E6 z \ [{/R|}] 58.37E4 _ k [Rdf LK ] 85.2E28 z k [{/R|}] 2.16E5 R [-] 1.23 f [-] 1.36 n [-] 0.227 2 3 [J/kg] 4.30E5 R [J/(mol-K)]
8.314

NUMERICAL EXAMPLE

The carbon fibers embedded in the epoxy are very strong absorbers in that they absorb infrared energy and convert this energy to heat the epoxy matrix surrounding the carbon fibers. Thermal radiative boundary conditions are imposed on the top surface of the composite and the curing temperature is controlled through the infrared emitters in order to optimize a uniform surface heat flux. The emitters used in our project are halogen lamps given from TOSHIBA LIGHTING; their infrared emission is in the short and medium wavelength. Until now, the composite properties were taken from literature [START_REF] Chern | On-Line Processing of Unidirectional Fiber Composites Using Radiative Heating: I. Model[END_REF][START_REF] Ruiz | Multi-criteria thermal optimization in liquid composite molding to reduce processing stresses and cycle time[END_REF]. Others are assumed to be constants in order to run some initial simulations of a curing process of RTM6 as a matrix combined with a fibrous reinforcement in the form of carbon plies. In this numerical example, a high heat flux of 1600 •/ R² was provided for the first 6 minutes in order to initiate and accelerate resin curing, and for the rest of time, the surface heat flux taken was 1200 •/R². These heat flux values were imposed in a way to cure the composite with less time and do not exceed 220°C in temperature (the degradation temperature of the matrix). We based our studies on an experimental anterior work in the laboratory; where we found that the composite's curing process occurred faster than other heating processes.

NUMERICAL RESULTS

Using COMSOL Multiphysics, the energy equation was coupled with the exothermic reaction in order to predict the temperature distribution in the composite and the degree of cure. The figures 4 and 5 below show the temperature and the degree of curing respectively evolution with time at the center of the composite. The figures 6 and 7 below show the temperature and degree of cure respectively evolution with time and thickness of the composite. These numerical simulations correspond to a 1mm thickness composite; there is no important variation of the temperature or degree of curing with the thickness.

From these simulations, we can deduce that the curing of the composite is accomplished in less time than the others modes of heating.

In the future work, we need to validate our numerical simulations with experimental infrared curing.

CONCLUSIONS

The curing model of resin is investigated in this study. A modification of the Kamal-Sourour curing model is given to account for the diffusion effect. Kinetic parameters of the curing model based on DSC Experiments were estimated using optimization algorithms. The thermal-kinetic model has been developed in COMSOL Multiphysics to simulate the curing process of pure resin with assumed material properties. In-lab software developed to predict the infrared heat flux on the top surface of the composite will be coupled with COMSOL in order to simulate the whole infrared curing process of the composite.

Figure 1 :

 1 Figure 1: Schematic presentation of the LRI process.

Figure 2 :

 2 Figure 2: Schematic presentation of the composite face to the infrared emitters.

  temperature can be evaluated by the Fourier's modal equation assuming an instantaneous equilibrium temperature between the resin and the fibers at each time:[START_REF] Bailleul | Identification des propriétés thermiques de composites fibres de verre / résines thermodurcissables Application a l'optimisation des procédés de moulage[END_REF][START_REF] Ruiz | Thermomechanical Properties during Cure of Glass-Polyester RTM Composites: Elastic and Viscoelastic Modeling[END_REF]

  5, -) with the Differential Scanning Calorimeter experimental data. These experimental DSC data were scanned isothermally for different temperatures: 140, 160, 170 and 180°C.

Figure 3 :

 3 Figure 3: Reaction rate constants k1 and k2.

Figure 4 :Figure 5 :

 45 Figure 4: Temperature evolution versus time at the center of the composite (0.5mm thickness)

Figure 6 :

 6 Figure 6: Temperature evolution versus time and thickness

Figure 7 :

 7 Figure 7: Degree of cure evolution versus time and thickness

ACKNOWLEDGEMENT

The authors would like to thank Mr. Goyot D. for his support. Grateful acknowledgement to TOSHIBA LIGHTING for their financial support and their attention to this work.


Pascal Lamesle
email: lamesle@enstimac.fr

Medhi Salem

Sabine Le Roux

Gilles Dour

Rezai Farhad

Aria

Oxidation and corrosion effects on thermal fatigue behaviour of hot work tool steel X38CrMoV5 (AISI H11)

Keywords: Tool steel, Isothermal fatigue, Thermal fatigue, Environmental effect, Oxidation, Intermetallics, Crack initiation, Crack propagation

Effects of atmosphere and specimen geometry on thermal fatigue (TF) crack initiation and propagation in a low Si content hot work tool steel X38CrMoV5-47HRC were investigated. The TF specimen's geometry enhances the uni-axial TF loading conditions. A high frequency induction heating (3 to 4 MHz) is used. A new TF rig, working under air and/or inert atmosphere with reduced P O2 has been set up. The reduction of P O2 results in localized oxidation sites. Whatever geometry and atmosphere conditions, TF cracks initiate exclusively in the oxide layers. Damage mechanisms are environment dependant. Under laboratory air, parallel macroscopic cracks initiate perpendicular to the hoop stress. Under argon and nitrogen, SEM surface observations show that initiated cracks coalesce by zigzagging along crystallographic paths between non-oxidized zones. In-depth crack propagation mechanism is mainly trans-granular. TF crack initiation life under air and in presence of Fe-Al intermetalllics is decreased in comparison to inert atmosphere.

Introduction

Hot forming tools (rolling [START_REF] Da Silva | Thermal cracking of multicomponent white cast iron[END_REF]. forging, die-casting, in particular high pressure die casting etc) works under transient thermal cycling. They are prone to thermal fatigue (TF), heat-checking ("crack") initiation and propagation. Such cracking is basically related to macroscopic and microscopic local multi-axial loadings. In fact, heat flux density and subsequent temperature distributions change from one region to another in a die inducing different thermal fatigue strains and stress histories [2]. TF damage may be activated and/or coupled with environmental effects (oxidation, corrosion). Investigations on TF crack propagation on tubular specimens are rather difficult mainly because of very complex crack propagation mechanisms under multi-axial loadings. Procedure for determination of crack propagation curves, cracks depth vs. number of thermal cycles is very time consuming. The single edge wedged cross-section specimens [START_REF] Glenny | The Influence of Specimen Geometry on Thermal Fatigue Behaviour[END_REF][START_REF] Meyer-Olbersleben | On thermal fatigue of nickel-based superalloys[END_REF][START_REF] Rézaï-Aria | Fatigue thermique et fatigue isotherme d'un Superalliage à base de Cobalt: Etude Métallurgique de l'endommagement et Modélisation[END_REF] or thin circular-shaped discs match better to TF crack propagation investigations under quasi-uni-axial thermal fatigue loading.

This contribution deals with investigations on TF crack initiation and propagation under various experimental conditions of a low Si double tempered martensitic X38CrMoV5 (47 HRC) steel. TF experiments are conducted both in air and under argon or nitrogen. In order to evaluate the influence of intermetallic phases on cracks initiation, some specimens were pre-aluminized prior to be tested under TF loadings. New TF specimens are used.

Experiments and material

Material and specimens. A quenched and double tempered martensitic tool steel, X38CrMoV5 with low Si content is investigated with a 47HRC hardness (Table 1 The isothermal oxidation behaviour of this hot work tool steel was previously studied [START_REF] Bruckel | Isothermal Oxidation Behaviour of a Hot-Work Tool Steel[END_REF]. The oxide scales, obtained from 600°C to 700°C are formed of an external iron-rich scale (hematite -Fe 2 0 3 ) and an internal scale enriched in Cr (spinel oxide (Fe, Cr) 3 O 4 ) (Fig. 1). Different TF specimen geometries were used. The following results concerned only the specimen called SR1 (Fig. 2). Details of the selection of this geometry are given in [START_REF] Salem | Environmental effect on thermal fatigue damage of low-Si tempered martensitic hot work tool steel X38CrMoV5 (AISI H13)[END_REF].

Thermal fatigue reference cycle and test conditions. The edges of TF specimens are heated by an Hüttinger high frequency induction facility (25kW, 3 to 4 MHz) and cooled by natural convection air, while they are internally cooled by a permanent water-circulation.

Temperature-times (T-t) cycles are measured by spot-welded thermocouples type-K on the edge. An in-house LabView data acquisition system collects these datas. TF experiments are performed at different T max (600 and 650°C) under identical heating period (about 1s). The minimum temperature (T min ) is set at 100°C (Fig. 3). Experiments are regularly interrupted for SEM examinations of crack initiation and crack propagation inwards from specimen edges. A vacuum chamber is used for TF experiments under inert gas (Fig. 4). The chamber is first put under a secondary vacuum (5x10 -5 mbars), prior introducing inert gas (argon or nitrogen). Table .2 shows the gas impurities contents. Aluminium diffusion coating applied by pack cementation process. X-ray diffraction analyses of the surface of an industrial high-pressure die-casting die (after 20 000 shuts) reveal the presence of iron-aluminium intermetallic phases. The injected aluminium alloys was AS9U3 alloy with high level of silicon content. The X-ray diffraction analyses reveal the presence of binary ironaluminium intermetallic phases and ternary iron-aluminium-silicon intermetallic phases (Fig. 5(a)) [START_REF] Chen | Structure of intermetallic phases formed during immersion of H13 tool steel in an Al-11Si-3Cu die casting alloy melt[END_REF][START_REF] Shahverdi | Microstructural analysis of interfacial reaction between molten aluminium and solid iron[END_REF][START_REF] Gupta | Intermetallic compound formation in Fe-Al-Si ternary system: Part I[END_REF][START_REF] Maitra | Intermetallic compound formation in Fe-Al-Si ternary system: Part II[END_REF]. In order to estimate the role of iron aluminium intermetallic phases on crack initiation, some specimens were pre-aluminizing by pack cementation. This process is usually widely used to confer oxidation resistance on ferrous or nickel alloys. In order to maintain the initial steel microstructure and hardness, it was decided to perform the pack cementation at 550°C, that is lower than the second tempering temperature. The specimen is immersed in a powder's mixture containing pure aluminium (source), a halide salt (activator) and alumina as inert diluent (filler) [START_REF] Xiang | Kinetics of low-temperature pack aluminide coating formation on alloy steel[END_REF]. This pack cementation process allows to form the same binary iron-aluminium intermetallic phases on the surface specimen as industrial die (Fig. 5(b)). It should be emphasized that on the industrial die, different ternary iron-aluminium-silicon intermetallics are observed (Fig. 5(a)). Fig. 6. Cross section of X38CrMoV5 steel aluminized at 550°C for 8h.

Results and discussion.

Crack initiation and propagation mechanisms While the oxide morphology depends upon T max , the oxide scale is always duplex with one layer rich in Cr in contact with steel and one poor in Cr in direct contact with air. These layers have quasi-identical thicknesses [START_REF] Medjedoub | Proceedings of the 7th Int. Tooling Conference: Tooling Materials and Their Applications Forme Research to Market[END_REF] alike under isothermal oxidation tests (Fig. 1). Under air, uniform oxide layer is formed on the edge of TF specimens (Fig. 7(a)). Under inert atmosphere, very early, parallel-localised oxide scales (alike an "atoll") are formed perpendicular to the hoop stress ( ). The "non-oxidised" regions surround these localized oxide-atolls. This specimen geometry is a very promising for in-depth crack propagation investigations. When the crack progresses beyond about the edge tip radii, it becomes a through thickness crack, leading to follow the crack progress via measurements on both disc faces. The TF crack depth vs. of number of cycles curves are reported in Fig. 10. As can be observed, TF crack initiation life under air is decreased in comparison to the inert atmosphere. Similar trend is observed for pre-aluminized specimen tested under inert atmosphere revealing definitively the effect of the binary ironaluminium intermetallics. In both cases, no clear effects on crack propagation rate are observed.

Conclusions

Thermal fatigue behaviour of a low-Si content X38CrMoV5 (AISI H11)-47 HRC is investigated. New thermal fatigue specimen geometries and a new high frequency induction heating under controlled atmosphere (air, inert gas, vacuum) are used. It is observed that oxidation decreases the thermal fatigue crack initiation life. Under test conditions reported here, no clear effect of oxidation on crack propagation rate is observed. Under inert atmosphere, early localized oxidation is observed. Whatever geometry and atmosphere conditions, TF cracks initiate exclusively in the

Fig. 1 .Fig. 2 .

 12 Fig. 1. X-ray maps of the cross section of an oxide scale grown during exposure at 700°C for 90 hours in wet air (pH20 = 198mbars) TF specimens are machined from these bars. The specimen edges are polished along the circumferential direction. Details of TF specimens are given in Fig. 2.

Fig. 3 .

 3 Fig. 3. Typical TF cycle at edge tip of specimens. Heating and cooling period are about 1s and 7s respectively

Argon 1 )Fig. 4 .

 14 Fig. 4. Thermal fatigue rig under controlled atmospher.

FeAl 3 FeAl 3 FeFig. 5 .

 335 Fig. 5. X-ray diffraction pattern on X38CrMoV5 coupons : a) cut from the industrial die b) after aluminizing by pack cementation (8h at 550°C)

Fe 3 Fig. 7 .Fig. 8 .

 378 Fig. 7. Thermal fatigue oxidation mechanisms (T max = 650°C): a) experiment under air after 2500 cycles (generalized oxidation) b) experiment under argon with reduced P O2 after 5000 cycles

Fig. 9 .

 9 Fig. 9. Cross section of the edge tip of TF specimen tested at 650°C under air.

Fig. 10 .

 10 Fig. 10. Variation of cracks depth vs. number of thermal cycles under air and inert atmosphere for X38CrMoV5 with and without a pre-aluminized layer.

  ). Heat treated forged bars are delivered by Aubert & Duval France.

		Table.1 Chemical composition of X38CrMoV5 (AISI H11) (% weight).
	C	Cr	Mo	V	Si	Mn	P	Sn	Sb	Fe
	0.36	5.06	1.25 0.49 0.35	0.36	0.006	0.0022	0.0005	bal

Table .

 .

	2 Gas composition
	H 2 O	O 2	C n H m

oxide layers. Under inert atmosphere, short cracks coalesce by zigzagging along crystallographic paths between non-oxidized zones. In depth crack propagation mechanism is mainly trans-granular both under air and inert atmosphere.

Thermal fatigue experiments performed under inert atmosphere reveal definitely that ironaluminium intermetallic phases decrease the thermal fatigue crack initiation life of low-silicon X38CrMoV5 die steel.

Fe + Al Fe + Al Fe + Al Fe + Al Al Al Fe 2 Al 5 Fe 2 Al 5 Fe 2 Al 5 Fe 2 Al 5 Fe 2 Al 5 Fe 2 Al 5 and FeAl 3 FeAl 3 Fe 2 Al 5 and FeAl 3 Fe 2 Al 5 Fe + Al Fe + Al Fe + Al Al Al Fe 2 Al 5 Fe 2 Al 5


Mouna Ben Salem
email: bensalem@lirmm.fr

Guillaume Aiche
email: aiche@lirmm.fr

Lennart Rubbert
email: lennart.rubbert@insa-strasbourg.fr

Pierre Renaud
email: pierre.renaud@insa-strasbourg.fr

Yassine Haddab
email: haddab@lirmm.fr

Design of a Microbiota Sampling Capsule using 3D-Printed Bistable Mechanism*

Microbiota analysis is a fundamental element for a better understanding of microbiota role, its relationship with the human body and its impact on different pathologies. There is today no non-invasive tool for easy collection of the microbiota in the small intestine. In this paper, we describe the development of such a device that opens the way to new diagnostic techniques. The device is based on a capsule designed as a passive system to maximize the safety during its use. Originality of the design relies in the use of a bistable mechanism obtained using additive manufacturing in order to provide a compact design with integration of opening, sampling and closing functions within the capsule. Design, implementation and initial lab evaluation of sampling are presented.

I. INTRODUCTION

The gastrointestinal (GI) tract is a major organ system in the human body which hosts the microbiota. It is well established that this microbiota has an intimate relationship with the body, and that a microbial imbalance can lead to several diseases such as obesity, cancer and inflammatory bowel disease [START_REF] Qin | A metagenome-wide association study of gut microbiota in type 2 diabetes[END_REF], [?]. The exact correlation between dysbiosis and pathologies is today to be investigated, and sampling of this substance would therefore be beneficial for both fundamental clinical research and diagnostic. The microbiota needed for diagnosis is the bacterial flora located in the small intestine. As the access to the lower part of the GI tract is limited, the conventional techniques used for sampling are invasive, uncomfortable for the patient and most of the time do not reflect the exact intestinal environment [START_REF] Swidsinski | Mucosal flora in inflammatory bowel disease[END_REF]. Hence the development of minimally invasive and representative microbiota sampling tool is greatly needed.

Several capsules have been developed for other medical tasks in the intestine [START_REF] Ciuti | Capsule Endoscopy: From Current Achievements to Open Challenges[END_REF]. Most of them are used for endoscopy, and some to perform actions within the body. This means they integrate active components as camera, batteries and actuators. In this case, integration of components is difficult given strong size constraints. It was yet still possible to achieve different functions, as it is interestingly presented for instance in [START_REF] Yim | Design and Analysis of a Magnetically Actuated and Compliant Capsule Endoscopic Robot[END_REF], [START_REF] Yim | Biopsy using a Magnetic Capsule Endoscope Carrying, Releasing, and Retrieving Untethered Microgrippers[END_REF] with integration of drug delivery and biopsy functions. Passive sampling capsule concepts for microbiota sampling within the small intestine have been proposed in the patents [START_REF] Cinquin | Dispositif de prise d'chantillon intestinal[END_REF], [START_REF] Thélu | Device for intestinal fluid sampling[END_REF]. As an extension, we propose to develop a capsule taking advantage of a bistable mechanism. Designing such sampling capsule as a passive device is of great benefit as safety is an obvious concern for such an ingestible device. In other words, the GI tract will not be exposed to any potentially harmful chemical or electrical component. Such design approach is also in favor of compactness, as we propose to store energy mechanically, without the need to integrate batteries.

Choosing a passive approach for sampling is not necessarily sufficient to solve integration constraints. In addition, we propose to design the capsule using additive manufacturing in order to ease the integration of components required for the sampling and also potentially to minimize costs with a design compatible with single use.

The paper is organized as follows. In section II, the specifications to fulfill are analyzed and then the proposed operating principle is presented. The proposed design is then introduced in section III, starting from the general principle to its implementation using 3D printing and use of PVA foam as a trigger mechanism. Initial experiments are presented in section IV before concluding on the interest of the device and further developments in section V.

II. SPECIFICATIONS AND CAPSULE OPERATING MODE A. Identification of specifications

As other capsules, the sampling capsule will be first ingested (Figure 1). This is the first phase during the use of the capsule. After that, it will follow the natural path created by the esophagus and the stomach to reach the small intestine. This is the second main phase of use. As a third phase, sampling is then performed in the small intestine followed by evacuation. Requirements are linked to each of the three phases as described below.

Ingestion of the capsule requires this latter to respect a maximum size defined as the 000 size of pharmaceutical capsules. This means the maximum diameter of the capsule is equal to 9.9 mm, and its maximum length is equal to 26.1 mm.

During its transit in the stomach, the integrity of the capsule must be preserved, while the stomach is an acid environment.

Once located in the small intestine, the capsule must be capable of collecting a sample. The objective is to develop a passive device. As a consequence, a requirement is that the capsule must be specifically sensitive to the pH of the small intestine. Another requirement is the absence of sample contamination once it entered the capsule. Closing of the capsule must avoid any fluid leakage until the device is being naturally evacuated.

B. Proposition of operating mode

As the purpose of the proposed capsule is to sample microbiota, a significant volume needs to be dedicated to sample storing. We therefore choose to have the capsule passively displaced thanks to the peristaltic contractions of the GI tract, and the components of the capsule are thus only dedicated to sampling. The sequence we propose is illustrated in Figure 2 and it can be decomposed as follows.

1. The capsule is initially included into a enteric capsule, such as a gelatin pill coated with a gastro-resistant layer. It can therefore remain sealed until it reaches the small intestine (Fig. 2a).

2. When the capsule arrives in the small intestine, the pH of the environment increases to a more neutral pH. The gelatin-based coating then dissolves. The thickness of the coating can be adapted to modify the time of dissolution and therefore the location of sampling in the small intestine (Fig. 2b).

3. Once the coating is completely dissolved, an opening on the outer surface of the capsule main body makes possible the intestinal liquid to enter. Sample collection is therefore achieved through this inlet orifice (Fig. 2c).

4. A porous foam is present in the capsule for microbiota sampling. This approach is based on the principle described in the patent [START_REF] Cinquin | Dispositif de prise d'chantillon intestinal[END_REF], [START_REF] Thélu | Device for intestinal fluid sampling[END_REF]. This foam forms a kind of sponge that is therefore exposed to the intestinal liquid now entering in the capsule. The sponge absorbs it and swells. We propose in addition to the sampling to use its expansion to create a force that acts on a bistable mechanism embedded in the capsule body. This mechanism acts like a trigger, that is then switched thanks to the sponge to close the inlet orifice (Fig. 2d). The interest of the bistable mechanism is twofold: first, energy is stored in the mechanism by its preload, without loss of space in the capsule. Second, the stable position corresponds to the closing of the capsule, to ensure the absence of fluid leakage.

5. Once the capsule is sealed, it can lead its way out of the human body (Fig. 2e).

III. DESIGN AND MANUFACTURING

A. Key components of the capsule

As outlined hereabove, the capsule is composed of three key components (Figure 2a): First, a shell that constitutes the main body of the capsule. It is a closed envelope, except the inlet orifice for fluid entrance. Second, a sponge that is therefore used as an actuator and a sampler at the same time. Polyvinyl Alcohol (PVA) is a highly absorbent material and expandable when wet. It is therefore suitable for absorbing intestinal fluid [START_REF] Thélu | Device for intestinal fluid sampling[END_REF]. Third, the bistable mechanism to close the capsule.

Using 3D printing, it is possible to consider the design of the bistable mechanism and the capsule outer shell as a single component, which is interesting to respect the maximum admissible size for ingestion. This supposes however the ability to ensure the presence of bistability effect in presence of manufacturing errors, which constitues a first design issue. A second issue is the triggering of the bistable mechanism by the sponge. This supposes a correct selection of sponge and bistable mechanism dimensions. This is performed in two steps, with first the characterization of the sponge which acts as an actuator and second the determination of the mechanism dimensions.

B. Characterization of the actuator

Characterization of the actuator consists in determining the relationship between the sponge displacement during swelling and the force it can generate. A dedicated experimental setup was then built as illustrated in Figure 3, which is composed of a laser-based displacement sensor (Keyence LK-H152) and a flexure beam whose mechanical properties are known in order to convert the measured displacement to force evaluations.

Before testing, the sponge is compressed and placed under the flexure beam. When hydrated it swells and pushes the beam to produce a displacement that is recorded and then converted to a force. With sponges of prismatic shape, of intial dimensions equal 10 x 5 x 10 mm and a compressed height of 2mm, generated forces are between 0.5 N and 1 N.

C. Design of the bistable mechanism

Design of bistable mechanisms was considered in Qiu et al. [START_REF] Qiu | An Electrothermally-Actuated Bistable MEMS Relay for Power Applications[END_REF]. We use here several results of that paper, considering an initially curved beam. In our context, such shape is indeed more interesting than a straight shape as its corresponds to a straight beam buckled in its first mode, without the need for axial preload. It is needed to constrain the second buckling mode so we consider in the end two curved beams clamped together as shown in Figure 4a.

The geometry of the bistable mechanism is defined by thickness t, depth b, span L, initial apex height h as represented in Figure 4a. These parameters are constrained by 1. the capsule space requirement, 2. the force needed to close the capsule, 3. the existence of the bistable effect and 4. the triggering of the mechanism by the sponge force. Following [START_REF] Qiu | An Electrothermally-Actuated Bistable MEMS Relay for Power Applications[END_REF], the bistability condition is expressed by

Q = h t ≥ 6,
the force delivered by the sponge is linked to the mechanism dimensions

f top ≈ 1480 EIh L 3 , f bot ≈ 740 EIh L 3 b c T h L ¡ ¡ ¡ ¡ ! t (a) Geometry f d f top f bot d top d mid d end d bot (b) Force-displacement char- acteristic
Fig. 4: Schematic presentation of the bistable mechanism and the evolution of the force according to the displacement [START_REF] Qiu | An Electrothermally-Actuated Bistable MEMS Relay for Power Applications[END_REF] with I the second moment of area, E the Young's modulus, and the force-displacement relationship is described as represented in Figure 4b with

d top ≈ 0.16h, d bot ≈ 1.92h, d end ≈ 1.99h, d mid ≈ 1.33h
From these relationships and the conditions expressed hereabove, the geometric parameters are determined and reported in Table I. The corresponding CAD design is represented in Figure 5.

D. Manufacturing

Previous synthesis of the bistable mechanism was performed with assumption of linear and isotropic behavior of the material. Since 3D printed materials can exhibit anisotropy, an experimental evaluation of the manufacturing impact was performed. Fused Deposition Modeling technique (FDM, Fortus 400 MC, Stratasys Ltd) is being used for manufacturing, as it allows the production of biocompatible materials. Polycarbonate (PC) was used as material for the initial prototype to validate the concept. As for the final prototype it will be manufactured using ABS M30i (acrylonitrile butadiene styrene) which is biocompatible and sterilizable. Manufacturing of prototypes of the bistable mechanism showed first that the junction between the two curved beams is a weak point in the structure. Second, the ends of the curved beams present flexibilities that impact the bistable behavior. Slight modifications of the intersection between the two beams and their ends was consequently achieved. Initial manufacturing of the capsule showed that the accuracy could also impact the assembly of the capsule with a clearance between the two half shells of the capsule. Additional lugs were then integrated to guarantee the precision during the assembly. Example of the capsule components after these modifications are shown in Figure 6. IV. EXPERIMENTAL EVALUATION After assembly, the bistable mechanism simply needs to be preloaded in the second stable position while the sponge is compressed and added under the mechanism (Fig. 7a). The capsule can then be closed and inserted in the gelatin-based capsule (Fig. 7b).

Since the capsule is dedicated to sampling, the experimental evaluation consisted in immersion of the capsule in a beaker filled with water. Figures 8a and8b show the first phase, with the air exiting the capsule through the inlet orifice to allow the entry of liquid in the capsule. This liquid entry is continuous and completed in 4min 40 sec. Figure 8c correspond to the end of the filling process. Fourteen seconds later, the orifice is closed by the bistable mechanism as shown in Figure 8d.

After the experiment, the capsule was being inspected. We could observe the swelling of the sponge, that reached its maximum possible volume as visible in Fig. 9. A separate experiment showed the sponge is capable of absorbing 200µL, which represents approximately 22.2 10 6 of sampled bacteria considered to be sufficient for microbiota analysis.

V. CONCLUSION In this paper, a capsule for microbiota sampling was proposed. The capsule is passive for safety, based on 3D printing for ease of integration, and uses PVA-based foam for both actuation and sampling. Initial evaluation in lab conditions is encouraging with first demonstration of sampling.

Future work will now be focused on the refinement of evaluation using liquids with viscosity close to the GI liquid. Evolution of the design will also be considered to maximize its robustness to manufacturing uncertainties. After integration of capsule coating, pre-clinical evaluation will then be considered.

Fig. 1 :

 1 Fig. 1: The three main phases of use of the sampling capsule. Figure adapted from [6].

Fig. 2 :

 2 Fig. 2: Decomposition of the sampling capsule operating principle.

Fig. 3 :

 3 Fig. 3: Experimental setup for actuator characterization.

Fig. 5 :

 5 Fig. 5: CAD presentation of the capsule. Sponge is represented before swelling, and the bistable mechanism before the preload.

Fig. 6 :

 6 Fig. 6: Printed components of the sampling capsule, (a): shell, (b): bistable mechanism

Fig. 7 :

 7 Fig. 7: Close-ups on the capsule main components before lab evaluation

Fig. 8 :Fig. 9 :

 89 Fig. 8: Decomposition of liquid entry into the capsule

TABLE I :

 I Bistable mechanism dimensions after synthesis

	Parameter	t	b	L	h
	Value (mm)	0.35	2 18 2.4

*Research supported by the Investissements d'Avenir (Labex CAMI ANR-11-LABX-0004).