Tudor-Bogdan Airimitoaie

Christophe Farges

Loïc Lavigne

Franck Cazaurang

Loic Lavigne

Convertible delta-wing aircraft for teaching and research ⋆

Keywords: convertible aircraft, autonomous vehicles, non-linear systems, experimental test-bench

INTRODUCTION

In recent years, there has been an increased interest in the field of vertical take-off and landing (VTOL) aircraft with a special emphasis on those equipped with fixed-wings (see [START_REF] Bapst | Design and implementation of an unmanned tail-sitter[END_REF]; [START_REF] Gryte | Aerodynamic modeling of the skywalker x8 fixed-wing unmanned aerial vehicle[END_REF]; [START_REF] Airimitoaie | Convertible aircraft dynamic modelling and flatness analysis[END_REF]). VTOL fixed-wing aircraft have the advantage of an increased autonomy with respect to multi-rotors. They are also called convertible because of their capability to fly as multi-copters during take-off, landing and hover and as regular aircraft during fast-forward flight. Figure 1 shows the basic principle of a convertible aircraft. The one presented here is equipped with 6 propeller-engines mounted two by two on three pairs of wings making it similar to a hexa-copter during slow speed flight manoeuvres (configuration (a) in Fig. 1). Nevertheless, the wings can tilt to a horizontal position and allow the aircraft to benefit from aerodynamic lift during high speed forward flight (configuration (b) in Fig. 1). One advantage of this tilt-wing configuration is that the main body stays in an horizontal position during the entire flight, which can be useful for the transportation of certain objects.

Being located in one of the most important centres for aerospace engineering in France, the University of Bordeaux has a long history in the development of aeronautics related educational programs. Among these, automatic control is well represented with two Masters of Science, one ⋆ This paper has been supported by the French Agence Nationale de la Recherche (ANR), Projet MICA ANR-16-CE22-0003, and by the Centre de Ressources IMA (Univ. Bordeaux). © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/bync-nd/4.0/ on aeronautics maintenance and another one on complex systems engineering.

Our endeavour is to improve the teaching of automatic control in these educational programs and the convertible aircraft project presented in this paper offers this possibility. Furthermore, it shows that automatic control cannot be dissociated from other fields of engineering such as mechanical, embedded systems, and avionics and can only enrich them.

The starting point of this program has been the MICA (Model Identification and control of a Convertible Aircraft) research project that focuses on the fault tolerant guidance in the context of convertible aircraft (see MICA ( 2016)). The main idea of the fault detection and isolation (FDI) and fault tolerant control (FTC) that we are aiming to provide is based on the theory of flat systems developed in [START_REF] Lévine | Analysis and Control of Nonlinear Systems. A Flatness-based Approach[END_REF]. Previous research using this approach has shown its suitability for the design of guidance strategies [START_REF] Morio | Robust terminal area energy management guidance using flatness approach[END_REF] and for FDI [START_REF] Torres | Fault detection and isolation on a three tank system using differential flatness[END_REF].

This paper presents our teaching activities around this subject. It presents our experience in the design and building of the convertible. It then describes the main challenges from an automatic control point of view and the educational benefits that can be expected from running a project with this complexity.

The paper is organized as follows. In section 2, are presented the main activities of this project emphasizing its multidisciplinary nature. The non-linear modelling of the convertible aircraft is described in Section 3. This represents the first part of the autopilot control law design.

Concluding remarks are given in Section 4.

PROJECT MAIN ACTIVITIES

The biggest challenge and at the same time to most exciting aspect of this project is its multidisciplinary nature.

It has been a great opportunity to get involved many students from various disciplines of engineering. To coordinate their activities, we have opted for an organisation based on technological bricks, which implies that each group of students has the responsibility of proposing a solution for a smaller problem related to this project. This allows us to increment in steps our expertise for being able to complete the entire project.

There are four main activities in this project: (i) mechanical system design and build, (ii) numerical windtunnel analysis by computational fluid dynamics (CFD), (iii) embedded system design and programming, and (iv) development of automatic control algorithms for the autopilot.

The desired concept of convertible aircraft for this project is a 6-rotors VTOL similar to the one shown in Fig. 1. Nevertheless, for reasons of dependency on the results from parallel activities, it is not possible to do all four previous activities directly on this configuration. As a first step of the project, we have thus decided to: (i) build a quad-copter drone from parts available on the market in order to work on the embedded system (while the convertible aircraft is not finished); and (ii) build a delta-wing aircraft in order to analyse the manufacturing difficulties on a design that is simpler than a 6-rotors / 3 tilt-wings aircraft.We will give more details about these activities in the following.

Computer aided design (CAD) of the mechanical system

The first step in the construction of any modern aircraft is the design of a 3-dimensional computer model. Various CAD software can be used, such as Catia ® , Solidworks ® (commercial) or FreeCAD ® (free). CAD modelling has become a very important part in aircraft manufacturing as it allows to highly reduce the cost and time before marketing of a new product.

The use of CAD software for the design and analysis of various components has the advantage of being more rapid than the construction itself. Modern CAD software benefit from complex functionalities which allow to do various tests such as the analysis of the resistance of the system, the computation of the inertia matrix, the mass, etc. In our aircraft maintenance master's program, students are trained in the use of CAD software for the design of various aircraft components.

The same is true for this project. Let us consider for example the design of the tilt-wing mechanism.1 This component of the convertible aircraft should satisfy the following criteria:

• have a self-lock mechanism in order to avoid spending energy to counteract wind forces while maintaining the wings at a desired angle with respect to the aircraft body; • the complete tilting of the wing should be done sufficiently fast in order to avoid introducing additional delays in the control system; • the effect of the wing tilting on the aircraft inertia matrix should be minimized. An initial design of the tilt-wing mechanism using infinite screws is shown in Fig. 2. The advantage of this solution is that the effect of wind is highly reduced and very little energy is needed to keep the wing at a desired angle. Nevertheless, this kind of mechanism might not be sufficiently fast to a change of angle request from the autopilot.

Numerical wind-tunnel analysis

Another important step in the design of an aircraft is the wind-tunnel analysis of the aerodynamic coefficient functions. As we do not have a convenient facility for this, we have chosen to do a numerical wind-tunnel analysis instead. This implies using CFD algorithms to evaluate the flow of air around the aircraft by numerically solving the fluid flow equations. This is a very complex task and is usually done under some approximations using dedicated CFD software.

During this project we have used either XFLR5 [START_REF] Deperrois | Xflr5 analysis of foils and wings operating at low reynolds numbers[END_REF] or OpenFOAM [START_REF] Jasak | OpenFOAM: Open source CFD in research and industry[END_REF]. The former is a simplified CFD analysis software implementing the lifting line theory and vortex lattice method and it is only accurate at small angles of attack. OpenFOAM allows to analyse complex shapes under more general fluid flow conditions. It can be used to analyse aerodynamic flow at any angle of attack and for various speeds of the aircraft. Nevertheless, properly configuring a CFD analysis is not an easy task and it gets more complicated as one aims to obtain more reliable results.

One of the tasks that has been done using XFLR5, was the configuration of the delta-wing aircraft. The objective was to configure the dimensions in order to improve the flight characteristics of this aircraft. XFLR5 allowed to obtain also an estimation of the inertia matrix and of the aerodynamic coefficients for small angles of attack. The obtained design is shown in Fig. 3. A first test case for OpenFOAM was to evaluate a simple 2dimensional symmetric NACA 0012 wing profile, which is the one chosen for the delta-wing. To assess the numerical wind-tunnel results, these have been compared with [START_REF] Sheldahl | Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis wind turbines[END_REF]. Figure 4 shows the comparison for the lift coefficient and for a Reynolds number Re=5e5.

From this figure, one can see that the numerical windtunnel results are close to the experimental wind-tunnel data up to 25 • and they estimate correctly the stall Angle of Attack (AoA) which is an important information for the design of the autopilot control algorithms. At higher AoAs, the numerical wind-tunnel results underestimate the lift coefficient.

Lift coefficient

Lift coefficient vs. AoA

Wind-tunnel data OpenFOAM results

Fig. 4. Comparison of wind-tunnel data from [START_REF] Sheldahl | Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis wind turbines[END_REF] with OpenFOAM results for the NACA 0012 profile for Re=5e5.

Embedded systems design

The hardware part of the autopilot for our project is based on a Raspberry Pi3 with a Navio2 hat [START_REF] Emlid | Model Identification and Control of a convertible Aircraft[END_REF] (see photo in Fig. 5). The software is based on the opensource ArduPilot flight stack. To begin working on the autopilot code, we have started by using a classical quadcopter drone. The main advantage is that quad-copters are easy to build using off-the-shelf components. Another advantage is that the quad-copter can be effectively piloted using PID controllers and a decoupling between roll, pitch, yaw and altitude movements. We have mainly worked with 3 rd year Bachelor students on this part. In order to design Table 1. Parameters of the quad-copter.

the PID control law, a quad-copter model was used. Its parameters are given in Table 1. For the inertia coefficients, students used the parallel axis theorem and the formula for the pendulum natural frequency: ω n = mgr I , where r defines the length of the pendulum and I represents the coefficient of inertia.

NON-LINEAR MODEL AND AUTOPILOT DESIGN

In this section, we describe more precisely the results that have been obtained at this point for the fourth activity of this project which is focused on the autopilot control law design design. There are two important challenges. The first one is to obtain a reliable non-linear dynamic model of the convertible aircraft and the second one is the design of the control law. The next subsections will focus on the non-linear model of the bi-motor delta-wing convertible aircraft.

Basic assumptions and notations

We make the assumption that the Earth is flat and fixed. As such, the ground fixed north-east-down frame (I) is considered to be inertial. For the modelling of the convertible aircraft, three other reference frames are used: the vehicle-carried normal Earth frame (O), the body frame (B) and the aerodynamic frame (A). All coordinate systems are considered right-handed, and their axis are denoted using x, y, z with superscripts i, o, b or a depending on the frame.

Euler angles are used to represent rotations between reference frames. The rotation matrices are denoted as R with a two small-case letters subscript. The first letter indicates the final frame and the second gives the original frame, such as

2 R ob = R z (ψ(t))R y (θ(t))R x (ϕ(t)) (1) = cψcθ -sψcϕ + cψsθsϕ sψsϕ + cψsθcϕ sψcθ cψcϕ + sψsθsϕ -cψsϕ + sψsθcϕ -sθ cθsϕ cθcϕ (2)
for the rotation of a vector from frame B to frame O, where ψ, θ, and ϕ are, respectively, the yaw, pitch and roll angles. In the previous equations, cos, sin, and tan trigonometric functions are abbreviated using their first letter. The elementary rotations are given by

R x (ϕ) = 1 0 0 0 cϕ -sϕ 0 sϕ cϕ , R y (θ) = cθ 0 sθ 0 1 0 -sθ 0 cθ , R z (ψ) = cψ -sψ 0 sψ cψ 0 0 0 1 .
Similarly, the rotation from frame A to frame B is given by

R ba = R y (-α(t))R z (β(t)) = cαcβ -cαsβ -sα sβ cβ 0 sαcβ -sαsβ cα , (3)
where α(t) represents the angle of attack (AoA) and β(t) is called the side slip angle. In the absence of wind, the kinematic speed is the same as the aerodynamic speed and is denoted V a a (t) = [v a (t) 0 0] T . The superscript a added to the vector notation V a (t) indicates that its components are represented in the aerodynamic frame A. The same convention is used with superscripts o or b for any vector when its components are given in, respectively, frame O or B.

An important property of rotation matrices is that they are orthogonal, i.e. they are invertible and the inverse is equal to the transpose (R yz = (R zy ) -1 = (R zy ) T ).

The rotation speed vector of frame B with respect to frame O is denoted Ω bo .

Although very popular, Euler angles are limited by the gimbals lock problem. This manifests itself by the loss of distinguishability between the first and the third rotation angles, when the second one is of 90 • (see [START_REF] Castillo | Modelling and control of mini-flying machines[END_REF]). This is an important issue for us as the conversion from hover to forward flight implies that the conditions for the gimbal lock problem are met. Different solutions exist, such as the use of a second set of vertical Euler angles, rotation matrices, quaternions, modified Rodrigues parameters and more.

System description

Figure 6 shows the delta-wing bi-motor aircraft design considered in this paper. The orientation of the body frame B axes can be observed: x b points towards the front of the aircraft and belongs to its plane of symmetry alongside z b axis, which is perpendicular to x b and points towards the Earth when the delta-wing is in forward horizontal flight. The y b axis is perpendicular to the plane of symmetry and oriented towards the right of the delta-wing. x b , y b , and z b form a right-handed orthonormal coordinate system with the origin at the aircraft's centre of gravity (CG).

Each wing has one propeller-engine and one elevon, which can be controlled independently. The centre of rotation of each propeller is situated in the (x b , y b ) plane and the CG Left/right elevons Fig. 6. Delta-wing bimotor aircraft (view from above). distance to the centre of gravity is given by the variable L on the x b axis and the variable l on the y b axis.

There are 4 control inputs:

• δ el , δ er are the deflection of the left and right elevons;

• ω l , ω r are the rotation speeds of the left and right propeller-engines.

The wings are cut out of extruded polystyrene using a hot-wire technique. The profile used for the wings is NACA0012.

Forces and moments acting on the delta-wing

The main efforts on the aircraft are of gravitational and aerodynamic natures. The later are due either to fixed (surfaces of the left and right wings) or rotating wings (propellers). The gravitational force can be written in frame O:

G o = [0 0 mg] T . (4)
Aerodynamic forces and moments of fixed wings are most easily represented in frame A. It is useful to distinguish between longitudinal and lateral forces and moments. Flight in the vertical plane is influenced by lift and drag forces and the moment around the lateral axis y a (the same as y b during longitudinal flight):

F lif t (t) = 1 2 ρv 2 a (t)SC x (α, q, δ e ), (5)
F drag (t) = 1 2 ρv 2 a (t)SC z (α, q, δ e ), (6)
τ m (t) = 1 2 ρv 2 a (t)ScC m (α, q, δ e ). (7)
These are most significantly influenced by the angle of attack α(t), the pitch rate q(t), and the control δ e (t) = δ el (t) + δ er (t) (see also [START_REF] Beard | Small Unmanned Aircraft -Theory and Practice[END_REF]). The lateral force and moments, on the other hand, depend on the side-slip angle β(t), the roll rate p(t), the yaw rate r(t), and the control δ a (t) = δ el (t) -δ er (t):

F y (t) = 1 2 ρv 2 a (t)SC y (β, p, r, δ a ), (8)
τ l (t) = 1 2 ρv 2 a (t)SbC l (β, p, r, δ a ), (9)
τ n (t) = 1 2 ρv 2 a (t)SbC n (β, p, r, δ a ). (10)
In the previous equations, S is the area of the deltawing, c is the mean chord, b is the wingspan of the aircraft, and ρ is the density of the air. The aerodynamic force and moment vectors in frame A become

F a a (t) = [-F lif t F y (t) -F drag ] T and τ a a (t) = [τ l (t) τ m (t) τ n (t)] T .
A common representation used for the longitudinal aerodynamic coefficients non-linear functions is given by:

C x (α, q, δ e ) = C xα (α) + C xq c 2v a q(t) + C x δe δ e (t) (11) C z (α, q, δ e ) = C zα (α, Re) + C zq c 2v a q(t) + C z δe δ e (t) (12)
C m (α, q, δ e ) = C mα (α) + C mq c 2v a q(t) + C m δe δ e (t) (13)

Lift, drag, and pitch moment are non-linear functions depending primarily on the angle of attack α(t). One solution to approximate them (proposed in Phung ( 2015)) uses sigmoid functions as

C xα (α) = c 1x + c 2x sin 2 (α) (14) C zα (α, Re) = c 1z sin(2α)σ(α, α 0 (Re))+ + c 2z sin(2α)(1 -σ(α, α 0 (Re))) (15) C mα (α) = 1 2 -sin 2 π 2 + α 2 . ( 16
)
In ( 15), α 0 (Re) represents the stall angle, which depends on the Reynolds number (Re), and σ(α, α 0 (Re)) denotes the sigmoid function: α-α0(Re) . For various Reynolds numbers, the stall angle α 0 (Re) can be obtained either using wind-tunnel or computational fluid dynamics (CFD) studies.

σ(α, α 0 (Re)) = 1 1 + e α-α0(Re) + 1 1 + e 180 • -
For lateral aerodynamics, the following functions are commonly used:

C y = C y0 + C y β β + C yp b 2v a p + C yr b 2v a r + C y δa δ a (17) C l = C l0 + C l β β + C lp b 2v a p + C lr b 2v a r + C l δa δ a ( 18
)
C n = C n0 + C n β β + C np b 2v a p + C nr b 2v a r + C n δa δ a (19)
In [START_REF] Beard | Small Unmanned Aircraft -Theory and Practice[END_REF] the following equations for the propulsion force and torque of one propeller are proposed, respectively,

f pi (t) = 1 2 ρS prop (k motor δ i (t)) 2 -v 2 a (t) , (20)
t pi (t) =k t [k Ω δ i (t)] 2 , ( 21
) where i ∈ {l, r} designates either the left or the right propeller and S prop is the area swept out by the propeller. The vector of propulsion forces is given, in the body frame B, by:

F b p (t) = [f p l (t) + f pr (t) 0 0] T .
(22) Taking into account also that the two propellers have opposite senses of rotation, the propeller induced torque on the body of the convertible aircraft is given by

M b t (t) = [t p l (t) -t pr (t) 0 0] T . ( 23
)
Each propulsion force induces also a moment that can be written (in frame B), as:

M b pi (t) = ------→ (CG, O i )| B ∧ [f pi (t) 0 0] T . ( 24
)
In the previous equation, ------→ (CG, O i )| B gives the coordinates of the point of application for each of the two propulsion forces in the Body frame (i ∈ {l, r}). Considering a symmetric positioning of the two propellers in the plane formed by x b and y b and with distances x p on axis x b and y p on y b , then the total moment from the propulsion forces can be written as

M b p (t) = [0 0 y p • (f p l (t) -f pr (t))] T . (25)
Let denote the total force vector from propulsion and aerodynamic elements, in frame A, as

F a (t) = X a (t) Y a (t) Z a (t) =F a a (t) + R ab F b p (t). ( 26
)
The total torque vector is given, in frame B, by

τ b (t) =   L b (t) M b (t) N b (t)   =τ b a (t) + M b t (t) + M b p (t). ( 27
)

Estimation of aerodynamic coefficient functions

Wind-tunnel aerodynamic coefficients data for the NACA 0012 profile are given in [START_REF] Sheldahl | Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis wind turbines[END_REF] for angles of attack (AoA) ranging from 3 0 • to 180 • and different Reynolds numbers in the range 4 • 10 4 to 7 • 10 5 . These data points can be interpolated to obtain continuous variations with respect to the AoA and the Reynolds number using sigmoid and trigonometric functions as described in [START_REF] Phung | Conception, modeling, and control of a convertible mini-drone[END_REF].

For some common symmetrical NACA profiles, windtunnel data are given in [START_REF] Sheldahl | Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis wind turbines[END_REF]. Students applied the previously described technique to the lift, drag and pitch moment coefficients. Figure 7 shows a comparison of the wind-tunnel data and the estimation of the lift coefficient. Drag coefficient estimation is compared to the wind-tunnel data in Fig. 8.

Non-linear dynamic model

There are different ways of choosing the frames for writing the translational and rotational equations of motion. Here, we have chosen to write them both in frame B using the Newton-Euler formalism (another solution is given in 3 For symmetric profiles, this is the same as having -180 • to 180 • . (32)

The elements of Ω b bo are denoted Ω b bo = [p q r] T and [•] × defines the skew-symmetric operator:

[Ω a ao ] × = 0 -r q r 0 -p -q p 0 .

Equations ( 28)-( 31) together with formulation of forces and moments given in Section 3.3 can be used to write a non-linear simulator of the convertible aircraft. This is also the first step before design the autopilot control law.

CONCLUSIONS

This paper describes the progress of the convertible aircraft project at the University of Bordeaux with emphasis on the results obtained during student projects. The complexity of this project stands on its multidisciplinary nature. An important aspect is the effective transmission of results between different activities. The final beneficiary of the entire work are the students working on the automatic controller design, which have to integrate information from other student teams into their own work. This can be seen in the modelling part described in this paper. Ongoing work focuses on the design of the autopilot control law using a feedforward-feedback architecture.

Fig. 1 .

 1 Fig. 1. Hover (a), horizontal flight (b), and transition (c) for a tilt-wing convertible aircraft.

Fig. 2 .

 2 Fig. 2. 3D design of tilt-wing mechanism using infinite screw.

Fig. 3 .

 3 Fig. 3. XFLR5 model of the delta-wing aircraft.

Fig. 5 .

 5 Fig. 5. Photo of Raspberry Pi 3 with Navio2 hat used for implementing the drone autopilot. Param. Symbol Value Mass m 1.6 kg Local acceleration of gravity g 9.8 m/s 2 Length of arm l 0.375 m Inertia on x b axis Ixx 3.35e-2 kg • m 2 Inertia on x b axis Iyy 3.73e-2 kg • m 2 Inertia on x b axis Izz 4.39e-2 kg • m 2 Propeller thrust coefficient k 6.9e-6 kg • m Propeller torque coefficient d 7.57e-7 kg • m 2

Fig. 7 .

 7 Fig. 7. Lift coefficient wind-tunnel data compared with the interpolation result.

Fig. 8 .

 8 Fig. 8. Drag coefficient interpolation compared to windtunnel data for Re=16e4. Airimitoaie et al. (2018)). The complete set of differential equations is given byξ =R ob V b a ,(28)m dV b a dt + Ω b bo ∧ mV b a =R ba F a + R T ob G o , (29) Ṙob =R ob Ω b bo × ,(30)d(IΩ b bo ) dt + Ω b bo ∧ IΩ b bo =τ b ,(31)where ξ = [x y z] T gives the position of the center of mass of the aircraft relative to frame I and I is the aircraft matrix of inertia I = I xx 0 -I xz 0 I yy 0 -I xz 0 I zz .(32)

There exist two types of convertible aircraft, tilt-wing or tilt-rotor, depending on whether the wing tilts entirely or just the propellerengine part. In this project we have chosen a tilt-wing configuration.

The parentheses (t) are dropped out in some of the following equations to save space.

ACKNOWLEDGEMENTS

We would like to thank all the students that contributed to this work during their projects and those that contributed during their internships: Gemma Prieto Aguilar, Daniel Monier-Reyes and Hend Triki (Univ. of Bordeaux, France), Bhavika Wani and Kevin Timmel (Univ. Cincinnati, USA), Jihène Kraiem (ENIT, Tunisia). Without them, this work would not have been possible.


Tiphaine Bazin

François Rouzé-L'alzit

Alain Demourgues

Isabelle Julien

Sylvain Catros

Caroline Bertrand

Eric Champion

Thierry Cardinal

Manuel Gaudon

Ceramic Powder Bed Laser Sintering (CPBLS) on copper-doped hydroxyapatite: Creation of thin (5-50 µm thick) consolidated ceramic patterns

Keywords: Laser Sintering, Ceramic, Hydroxyapatite, Thin Films

Introduction

Besides conventional shaping processes, the development of 3D printing has favoured the production of complex pieces/devices in small series while reducing production time since some steps such as the manufacture of moulds are no longer necessary. The evolution of digital modelling and simulation tools allows the production of complex shapes whether at the geometric or hierarchical level. Indeed, objects with cavities, inclusions or honeycomb-like structures can be easily printed [START_REF] Chartier | Additive Manufacturing to Produce Complex 3D Ceramic Parts[END_REF][START_REF] Chen | 3D printed hierarchical honeycombs with shape integrity under large compressive deformations[END_REF][START_REF] Yadroitsev | Hierarchical design principles of selective laser melting for high quality metallic objects[END_REF][4][START_REF] Liu | Aerospace applications of laser additive manufacturing[END_REF][START_REF] Dimas | Tough Composites Inspired by Mineralized Natural Materials: Computation, 3D printing, and Testing[END_REF][START_REF] Ning | Additive manufacturing of carbon fiber reinforced thermoplastic composites using fused deposition modeling[END_REF]. Many additive manufacturing techniques have thus emerged depending on the type of material used and the intended application. All these techniques are based on the same manufacturing principle: the shaping of a three-dimensional part by a stack of successive layers, each of which undergoes a two-dimensional structuring.

In the biomedical field, especially in bone reconstruction, additive manufacturing has grown considerably in recent years [START_REF] Rengier | 3D printing based on imaging data: review of medical applications[END_REF][START_REF] Vail | Materials for biomedical applications[END_REF][START_REF] Wiria | Selective laser sintering adaptation tools for cost effective fabrication of biomedical prototypes[END_REF][START_REF] Duan | Selective laser sintering and its application in biomedical engineering[END_REF][START_REF] Mazzoli | Selective laser sintering in biomedical engineering[END_REF][START_REF] Shirazi | A review on powder-based additive manufacturing for tissue engineering: selective laser sintering and inkjet 3D printing[END_REF]. Indeed, it offers the possibility of reconstructing damaged areas thanks to the design of personalized parts with a complex architecture, adapted to the patient's morphology [START_REF] Champion | Advanced processing techniques for customized ceramic medical devices[END_REF]. Implants made of ceramics, and more particularly of calcium phosphates (hydroxyapatite: HA, mainly), promote intimate contact with natural bone. Their shaping by additive manufacturing is mainly done by stereolithography, which is the most widespread and popular technique today for designing ceramic parts [START_REF] Chia | Recent advances in 3D printing of biomaterials[END_REF][START_REF] Chartier | Stereolithography of structural complex ceramic parts[END_REF]. This technique makes it possible to manufacture complex shaped parts with a resolution of the order of 10 microns via the laser light curing of a ceramic suspension. But after shaping, sintering (conventional conditions) is necessary in order to consolidate the final ceramic part, which can represent an important limitation for various applications. In another process: indirect selective laser sintering process, a polymer is typically used with the ceramic powder as binder. On hydroxyapatite compounds, most of the works are focused on the manufacture of HA-polymer composites in which the amount of HA constitutes a minor part. Among the biocompatible polymers used, mention may be made of polyetheretherketone (PEEK) [START_REF] Tan | Scaffold development using selective laser sintering of polyetheretherketonehydroxyapatite biocomposite blends[END_REF][START_REF] Zhang | In vitro biocompatibility of hydroxyapatite-reinforced polymeric composites manufactured by selective laser sintering[END_REF], polyamides [START_REF] Kumaresan | Design, analysis and fabrication of polyamide/ hydroxyapatite porous structured scaffold using selective laser sintering method for bio-medical applications[END_REF][START_REF] Dabbas | Selective Laser Sintering of Polyamide/Hydroxyapatite Scaffolds[END_REF] or polycaprolactone (PCL) [START_REF] Williams | Bone tissue engineering using polycaprolactone scaffolds fabricated via selective laser sintering[END_REF][START_REF] Eosoly | Selective laser sintering of hydroxyapatite/poly-ε-caprolactone scaffolds[END_REF]. Only few papers reported works on "direct selective laser sintering of bio-ceramics" (what is called herein CPBLS process), and less again on HA-based compounds. From CPBLS, 3D devices of complex shape can be sintered directly from a powder bed (coated using scrapers or rollers) or a powder film (produced by tape casting or dip coating), without additives. The selective laser sintering process consists of selectively sintering the particles of a powder bed (metal, ceramic, polymer, glass) using an infrared laser beam. The two main types of lasers used are the CO 2 laser with a radiation of 10.6 m wavelength and the Nd: YAG laser, 1.06 m wavelength.

Irradiation of the powder by the laser beam, at a temperature below its melting point, thermally activates the diffusion of the atoms causing the formation of bridges at the interface between adjacent particles (local sintering phenomenon). Hence, direct laser sintering consists of consolidating the bed of powders by diffusion of the atoms like in the conventional solidstate route. In a recent study, Shuai et al. investigated the selective laser sintering of nanosized hydroxyapatite particles: sintered parts built with 300 µm thick layers could be designed using a laser beam with a diameter of 4 m and a power of 50 W. The low speeds used, ranging from 50 to 300 mm.min -1 , made it possible to increase the laser-material interaction time and therefore to promote the diffusion of atoms. In the two studies conducted by Shuai et al. [START_REF] Shuai | Processing and characterization of laser sintered hydroxyapatite scaffold for tissue engineering[END_REF][START_REF] Shuai | The microstructure evolution of nanohydroxapatite powder sintered for bone tissue engineering[END_REF], the influences of energy density (2 -5 J.mm -2 ) and beam power (between 2 and 10 W) on the sintering efficiency of HA nano-powder were studied. Besides the composition/morphology/structure of the powder, four very important laser parameters control the CPBLS process of ceramics as HA.

(i) Influence of applied energy. During the manufacturing, if the applied energy is too low, the consolidation between the particles and the different layers will be insufficient, causing the creation of pores and delamination of the layers. Increasing the energy applied increases the final density of the parts. A denser and more mechanically resistant structure is then obtained [START_REF] Simchi | Direct laser sintering of metal powders: Mechanism, kinetics and microstructural features[END_REF][START_REF] Amorim | Selective laser sintering of Mo-CuNi composite to be used as EDM electrode[END_REF]. However, at very high energies, the amplification of the thermal gradient induces greater stresses within the material, which can lead to the formation of cracks and curving phenomena [START_REF] Gu | Effects of processing parameters on consolidation and microstructure of W-Cu components by DMLS[END_REF]. Nevertheless, it has been proved that samples irradiated with the same energy density but with distinct power / speed pairs present a different microstructure affecting the density and the final mechanical properties of the part [START_REF] Meyers | Direct selective laser sintering of reaction bonded silicon carbide[END_REF][START_REF] Prashanth | Is the energy density a reliable parameter for materials synthesis by selective laser melting?[END_REF]. The energy applied to a line (J.mm -1 ) or to a volume (J.mm -3 ) is actually proportional to the power of the laser beam and inversely proportional to the laser scanning speed. To take into account only the applied energy is then insufficient for a deep control of CPBLS process.

(ii) Influence of laser power and laser scanning speed. With increasing power and/or decreasing scanning speed, the transferred energy to the matter from the laser is increased [START_REF] Subramanian | Selective laser sintering of alumina with polymer binders[END_REF][START_REF] Song | Experimental Study of the Basic Process Mechanism for Direct Selective Laser Sintering of Low-Melting Metallic Powder[END_REF][START_REF] Tang | Direct laser sintering of a silica sand[END_REF]. Laser sintering is in particular more efficient at low speeds. Indeed, the decrease of the scanning speed increases the time of laser-matter interaction and therefore the energy absorbed by the powder bed is more homogeneous. Conversely, at too high scanning speeds, the laser / material interaction time becomes insufficient to consolidate properly the particles [START_REF] Shirazi | A review on powder-based additive manufacturing for tissue engineering: selective laser sintering and inkjet 3D printing[END_REF][START_REF] Kruth | Binding mechanisms in selective laser sintering and selective laser melting[END_REF]. The laser power-speed couple must therefore be optimized as a function of the desired final properties [START_REF] Tang | Direct laser sintering of a silica sand[END_REF][START_REF] Tang | Direct laser sintering of a copper-based alloy for creating three-dimensional metal parts[END_REF].

(iii) Influence of the thickness of the powder bed. The thickness of the powder bed (or layer) plays an essential role in the geometric precision and density of the final product. In fact, when the laser scans the bed of powder, the energy of the laser is absorbed by a thin layer of particles inducing a high temperature within the particles on the surface, as explained above. The lower the thermal conductivity of the material, the more difficult the heat generated during the laser-material interaction is to transfer to the bottom limit of the powder bed, especially for a thick layer. To ensure better consolidation of the 3D part, the thickness of the layer must be reduced so that the laser penetrates also a part of the previous one, thus promoting sintering between adjacent layers [START_REF] Amorim | Selective laser sintering of Mo-CuNi composite to be used as EDM electrode[END_REF]. When the layers are thinner, the partial fusion of the particles is more homogeneous within the bed of powders which allows the improvement of the geometric precision, the reduction of the surface roughness and the increase of the relative density of the final piece [START_REF] Simchi | Direct laser sintering of metal powders: Mechanism, kinetics and microstructural features[END_REF][START_REF] Amorim | Selective laser sintering of Mo-CuNi composite to be used as EDM electrode[END_REF][START_REF] Kumar | Selective Laser Sintering/Melting[END_REF][START_REF] Juste | Shaping of ceramic parts by selective laser melting of powder bed[END_REF]. The sintering of thin layers also minimizes the temperature gradient and the volume shrinkage of the powder bed, thus reducing the stresses within the material and so crack appearing.

(iv) Influence of the distance between 2 lased lines. Influence of the distance between two lines on the microstructure of the sintered part is similar to that of the thickness of a layer: reducing the spacing between the beads improves geometric precision, decreases surface roughness and increases the rate of densification of the parts and therefore their mechanical resistance [START_REF] Tang | Direct laser sintering of a copper-based alloy for creating three-dimensional metal parts[END_REF][START_REF] Amorim | Selective laser sintering of Mo-CuNi composite to be used as EDM electrode[END_REF][START_REF] Song | Experimental Study of the Basic Process Mechanism for Direct Selective Laser Sintering of Low-Melting Metallic Powder[END_REF][START_REF] Juste | Shaping of ceramic parts by selective laser melting of powder bed[END_REF]. In fact, the greater the distance between two lines, the more the successive sintered beads move apart, forming a part of high porosity. On the other hand, when the distance is short enough for the lines to overlap, the laser beam irradiates the current bead but also the previous one, partially. The matter transport, which then takes place between the adjacent lines, promotes their adhesion and the consolidation of the part. In addition, the partial overlap of the beads makes it possible to compensate the Gaussian dispersion of the laser radiation intensities along the axis of the bead and the thermal conductivity profiles within the material which causes a temperature gradient which decreases from the centre to the outside of the lased line.

The combination of the appropriate parameters would a priori make it possible to modulate the final microstructure of the 3D part such as its geometric precision, its surface roughness and its porosity. However, improving one of these properties can sometimes come at the expense of another, so a compromise must be addressed depending on the application.

In this paper, in order to evaluate the impact of the four main laser parameters, which control the CPBLS process, we focused on dip-coating layers (from thin to thick films) of HA-based compounds dip-coated from ethanol suspension on glass substrates. Preliminary CPBLS tests were applied to HA thick films to roughly determine the set of appropriate laser parameters and the HA powder heat-treatment conditions. One can note that copper-doped compounds are studied since copper leads to control the absorptivity of the powder at the laser wavelength (essential parameter to convert efficiently laser energy into heat) and copper, known for its angiogenic properties, may improve the biological response of HA ceramics in view of their use as biomedical implants [START_REF] Bazin | Synthèse, caratérisations structurales par spectroscopies et mise en fome d'hydroxyapatites dopées au cuivre ou au fer[END_REF][START_REF] Raynaud | Synthèse, frottage et propriétés mécaniques de phosphates de calcium dans le système hydroxyapatitephosphate tricalcique[END_REF].

Experimental

HA Powder preparation

Raw HA was synthesized by co-precipitation. The protocol consisted of adding, at a controlled rate and a constant pH (regulated thanks to ammonia: NH 4 OH, Fisher Scientific), a phosphate solution (di-ammonium hydrogen-phosphate: (NH 4 ) 2 HPO 4 , Fisher Scientific) to a calcium solution (obtained from dissolution of calcium nitrate: Ca(NO 3 ) 2 ,4H 2 O, Sigma-Aldrich). The quantities of the reagents were calculated to obtain a molar ratio Ca/P = 10/6.

The synthesis conditions set were a pH=8.5 with a bath temperature maintained at 85°C. The synthesis was performed under argon gas flow during a maturation period to 5 hours. The asprepared precipitate was then centrifuged and washed with distilled water before being dried in an oven at 100°C. The dried powder was calcined at 600°C for 1 h (10°C.min -1 ramp) to remove reaction by-products such as nitrates. Next, a quantity of copper (II) oxide CuO (Alpha Aesar) was mixed to the HA powder to get a copper concentration of 5 mol%, i.e. to get the chemical composition formula Ca 10 Cu 0.5 (PO 4 ) 6 (OH) 1.5 O 0.5 . The HA-CuO powder mixture was attrition milled to reduce particle size and further promote solid-state reaction.

Attrition was performed in a 100 mL Teflon bowl in the presence of approximately 50 mL of distilled water, 1 wt% Darvan CN dispersant and 75 g yttrium-stabilized zirconia balls of 1 mm diameter. Attrition speed of 800 rpm was applied for 3 hours. The suspension was then oven dried at 100°C, and with the obtained powder, 10 mm diameter pellets were die pressed by applying a uniaxial pressure of 100 MPa. Finally, the pellets were calcined (ramp 10°C.min -1 ) for 1 hour at 1100°C to obtain a pure Cu-doped HA phase [START_REF] Bazin | Sintering and biocompatibility of copper-doped hydroxyapatite bioceramics[END_REF].

HA Film preparation

In order to study the impact of Cu-doped HA film thickness on laser sintering, controlled thickness layers were developed by the dip-coating technique. This method consists of immersing a substrate, a glass slide, in a ceramic suspension and removing it at a fixed speed to control the thickness of the deposit. The increase of withdrawal rate of the substrate leads to an increase of the wettability forces to the detriment of the gravity forces on the suspension and therefore makes it possible to increase the film thickness deposited on the glass substrate.

The ceramic suspension is produced by adding 30 wt% of Cu-doped HA powder functionalized with 2 wt% of dispersant (Beycostat C213) to ethanol. The thin film is deposited at a withdrawal speed of 400 mm.min -1 . At this speed, corresponding practically to the maximum speed of the device, a film of a few microns thick (<5 µm) is obtained. To increase the total thickness of the thin layer, several successive layers (2, 6 and 12) are deposited on the glass substrate. Between each deposition, the substrate is placed in an oven at 100°C for about 1 min to ensure the drying of the layer just deposited.

HA film laser sintering

The CPBLS experiments have been conducted using a laser system especially designed according to the laboratory specifications by ES Laser (ES17-355). Laser is equipped with IPG Photonics ytterbium fiber laser (YLM-400-AC*Y11) at a monochromatic wavelength of 1.07 m, and a galvanometric mirrors scanner (ScanLab -Hurry scan 20). This equipment has maximum and minimum operating power 400 W and 40 W, respectively. Its focal length was 199 mm and could be adjusted in 100 m increments. The spot size is 50 µm and the maximum lased surface is 75x75 mm 2 .

Laser sintering machine was controlled by SamLight® software which allows the modulation of the laser power (as a % of maximum power), scanning speed (in mm.s -1 ) and focal length (m). The required pattern was also directly drawn from software possibilities.

Characterization techniques

X-ray diffraction patterns were recorded on a Philips X'Pert MPD apparatus equipped with a copper K α1 anticathode (40 kV, 40 mA). Diffraction patterns were collected from 8 to 80° in 2θ with a 0.017° step scan and a counting time of 59 s. Chemical mapping using energy dispersive X-ray spectroscopy (EDS) in scanning transmission electron microscopy (STEM) was performed on a TEM equipped with a field emission gun: JEM 2100F (JEOL, 200 kV) coupled with energy X-ray spectrometer.

UV-Vis-NIR diffuse absorbance spectra were recorded at room temperature from 200 to 800 nm with a step of 1 nm and a band length of 2 nm on a Cary 17 spectrophotometer using an integration sphere. Halon polymer (ChemIndustry) was used as white reference for the blank. A mathematic treatment of the obtained spectra allowed the determination of the L*a*b* space colorimetric parameters, with L the luminosity, a* the green to red axis and b* the blue to yellow axis.

The morphology of the as-prepared particles was observed thanks to a Leica DMI 3000 M inverted microscope using a Leica SFL 100 diode enabling an excitation at 365 nm and the fluorescence collection recorded with a Leica MC 120 HD camera. Microscope objective N PLAN EPI 10×, NA 0.25 was used. For microstructural analyses, SEM investigations were performed using a TESCAN Vega II SBH microscope or JEOL JSM-6700F. The film thickness was measured from SEM cross section views or by the Dektak 150 Surface Profiler (Veeco), allowing the plot of surface profiles thanks to a stylus with a tip radius of 12.5 m and a resolution of 0.8 m.

Results and discussion

First CPBLS experiments on thick films constituted by CuO -HA powder mixture

The first series of sintering experiments by the CPBLS process were carried out on compacted pellets. Based on previous work in the literature showing the possibility to perform the selective laser sintering of a power bed constituted mainly by a white matrix (zirconia) using a dispersion of carbon grains strongly absorbing at the laser wavelength [START_REF] Bazin | Sintering and biocompatibility of copper-doped hydroxyapatite bioceramics[END_REF][START_REF] Ferrage | Dense yttria-stabilized zirconia obtained by direct selective laser sintering[END_REF], we hoped to reproduce this effect. Since the CuO crystallites were black particles (and so hotspots) dispersed into the white HA matrix, we chose to perform these first experiments on mixtures of HA powder (hydroxyapatite) and CuO powder (5 mol% CuO -95 mol% HA) blended in an agate mortar.. Reactive sintering between copper oxide and HA was expected by localized heating of the copper oxide grains inducing Cu 2+ cations diffusion within the surrounding HA crystals, hence leading to the appearance of the Cu-doped HA compound.

Several rounds of irradiation were performed on the pellet surfaces, changing the power and speed parameters of the laser. Based on the linear energy (J.m -1 ) brought to the material by the laser (laser power / laser speed), the experiments can be grouped into three batches: low energy irradiations (series a), irradiations of intermediate linear energy (series b), irradiations of high linear energy (series c). Images from light microscopy (Figure 1.a1, b1, c1, c2) and scanning electron microscopy (Figure 1.a2, a3, b2, b3, c3) are grouped below. The high linear energies cause an excessively high temperature increase, with the formation of bubbles, characteristic of the fusion of the irradiated zones, associated with the presence of cracks.

The intermediate energies lead to a color change of the irradiated area with speckled appearance in optical microscopy (Figure 1.b1). The initially black CuO grains have reacted to the heat effect induced by laser beam, then turned as purple large areoles with the local diffusion into HA matrix. Hence, copper grains behaved like hot spots, leading to Cu 2+ ions diffusion into HA matrix and the appearance of the purple coloration, which is associated with Cu-doped HA compounds. One of the solutions to solve this speckled appearance issue would be to pre-anneal the pellets in order to homogenize the copper distribution into the HA matrix. (estimation by image processing) with a continuous network of particles having formed, with clearly visible inter necks on the SEM images, whereas the green film porosity was around 50-60%). However, despite several attempts to optimize both the chemical composition (CuO/HA concentration ratio) or power/speed of the laser, crack propagations could not be avoided. These cracks then form, all along the laser line (Figure 1.b2), a series of scales of around one hundred microns in diameter (in correlation with the diameter of the irradiation spot of 50 microns for a laser whose adjustment and focusing is perfect).

For the lowest linear energies the reactive sintering is not very advanced, no sintering neck is detectable, and the CuO grains are still present. Moreover, cracks are always detectable, especially in Figure 1.c2.

Figure 1. Optical images or SEM top views on CuO-HA thick films after CPBLS process applied with various energy ranges (a) high energy; b) intermediate energies and c) low energies

Thus, in the case of selective laser sintering, the reaction between HA and CuO cannot take place simultaneously with sintering, unlike by conventional sintering [START_REF] Bazin | Sintering and biocompatibility of copper-doped hydroxyapatite bioceramics[END_REF]. The inhomogeneity of heating between the black grains of CuO and the white hydroxyapatite leads even for the most adequate powers to the appearance of cracks while the distribution of copper is not yet homogeneous. The use of copper-doped HA as starting material on which reactive sintering has already been carried out seems mandatory. The target is to perform a preliminary homogeneous incorporation of the copper element into the matrix in order to achieve the preparation of a monophasic Cu-doped HA pink powder (i.e. with copper being introduced with oxidation state + I) [START_REF] Bazin | Synthèse, caratérisations structurales par spectroscopies et mise en fome d'hydroxyapatites dopées au cuivre ou au fer[END_REF][START_REF] Bazin | Sintering and biocompatibility of copper-doped hydroxyapatite bioceramics[END_REF][START_REF] Ferrage | Dense yttria-stabilized zirconia obtained by direct selective laser sintering[END_REF].

Furthermore, these experiments show that on compacted powder pellets, the appearance of cracks seems to be difficult to avoid and can constitute a major lock. To increase the chances of success in terms of densification without appearance of cracks under laser irradiation, experiments on thin layers, opening the possibility to tune the laser amplitude effect with the film thickness were carried out. Indeed, on the one hand, the thin layer deposition could give a more elastic character to HA ceramics and on the other hand, the adhesion with the substrate could limit the appearance of cracks.

The thermal pre-treatment was optimized by coupling structural (XRD), colorimetric (UVvisible-NIR spectroscopy) and chemical (EDS mapping) characterizations (Figure 2).

While the HA-CuO initial mixture (95 mol% -5 mol%) exhibits broad HA peaks reflecting the nanometric character of the starting HA powder obtained by coprecipitation with addition of CuO peaks, the diffractograms obtained after annealing for 4 hours at 1100°C

show the presence of a single phase of hydroxyapatite (Cu-doped HA). In addition, EDX maps show that the distribution of copper in the bulk of the HA grains is homogeneous.

Finally, while the HA-CuO precursor mixtures exhibit a grey coloration (the HA matrix being a white compound and cupric oxide being black) the Cu-doped HA phase exhibits a pink coloration, characteristic of the incorporation of copper in the monovalent state of oxidation in insertion sites of the HAP structure [START_REF] Bazin | Synthèse, caratérisations structurales par spectroscopies et mise en fome d'hydroxyapatites dopées au cuivre ou au fer[END_REF][START_REF] Bazin | Sintering and biocompatibility of copper-doped hydroxyapatite bioceramics[END_REF].

CPBLS process on Cu-doped HA thin films

The Cu-doped HA film prepared from dip-coating were characterized from electronic microscopy. Cross-sections views (SEM) of the 3 final films obtained using 2, 6 and 12 successive coatings (Figure 3a) have been realized in order to determine their thickness.

Thickness evolution versus the number of successive coatings is plotted (Figure 3b). Thin films 5, 13 and 30 m thick are thus obtained. The increase of film thickness is proportional to the number of successive deposits (linear evolution). Among the parameters used, the power-speed pair of parameters for which a "continuous" laser line is observed, i.e. minimizing the delamination, melting or cracking phenomena, is the one combining the highest speed and the lowest power, that is to say for the lowest linear energy: 40 W -250 mm.s -1 (linear energy E = 0.16 J.mm -1 ). The application of higher energy causes the central area of the bead to melt, starting to reveal a vitreous phase in its centre. Another very interesting lesson is that the process performed using the same linear energy but with a couple of different speed -power parameters (couples 40 W -50 mm.s -1 and 80 W -100 mm.s -1 ) leads to different results, in particular the width of the material line marked by the laser can be changed drastically. Thus, the linear energy received from the laser by the Cu-doped HA film does not appear to be a sufficient parameter to be fully discriminating (relevant) and therefore cannot be the only one to be taken into account with a view to optimizing the process. The two laser parameters: laser speed and laser power have to be studied separately.

Comparing the three films prepared with different thicknesses (5, 13 and 30 m), the width of the detectable lased line well depends on both the following three parameters: the scanning speed, the laser power and the film thickness. To illustrate the problematic complexity, the observed lased line width was thus plotted as a function of the scanning speed for the three different film thicknesses at a power of 60 W (Figure 5a) and as a function of the scanning speed for the three experimented laser powers on films with the intermediate thickness (13 m thick) (Figure 5b). Line widths were averaged from 5 measurements taken on a single line. The line width evolution curve obeys a power law of the form y = a × x b (with a > 300 and b < 0) associated to a very large and sudden increase of width below a "critical" speed of approximately 50-100 m. One can note that with the aim to produce dense parts by CPBLS, optimal conditions are reached while partial overlap takes place between the successive lased lines. The extreme sensitivity of the lased line width to the different parameters (laser speed, laser power, film thickness) forces the operator to adapt the line interspace for each single set of parameters. Also, very interestingly, the intensity of the impact of the film thickness on the CPBLS effects is about the same order of magnitude than the one of the laser power. It can be posed that the film thickness is linked to the lased line width when the film thickness is lower than the shape of the potential heated volume in depth, limiting hence the efficient laser power transferred to the HA material (substrate no absorbs laser wavelength). So it can be deduced from these experiments that from the possibility to well control the film thickness using dip-coating process, a focus on the impact of the film thickness has to be managed.

These results show the importance of the Cu-doped HA film thickness on the sintering reaction advancement. In the next step, it was decided to "draw" square-shaped patterns from successive and contiguous lased lines, i.e. using for each single set of parameters a hatching space (hs) between two successive lines adjusted to the width of the line previously determined, in order to avoid areas undergoing "double" heating. Square-shaped patterns by succession of parallel and adjacent laser lines are thus produced at a power of 40 W. Firstly, two laser tests to design sintered square patterns, for the films which are 13 and 30 m thick, were carried out respectively at a speed of 250 and 750 mm.s -1 and with a spacing between the beads of 60 and 40 m, respectively. The SEM images of the square patterns (sintered areas) confirm the previous optical microscopy results obtained on films submitted to the sintering along a single lased line, namely that the irradiation of the material by the laser causes formation of delaminated chips of material superficial parts (Figure 6). For films of such thicknesses, sintering a two-dimensional pattern, as expected, does not solve the chipping problem. For a 5 m thick film, i.e. the film leading to the most original and interesting results, the SL was carried out at speeds of 5, 10 and 30 mm.s -1 , at a power of 40 W. The hatching space between the laser lines was set at 80 m regardless of the scanning speed, as this width remains roughly around 80 m over this speed range.

For speeds of 5 and 10 mm.s -1 , continuous square patterns of white coloring compared to the non-lased parts of the film are observed whereas threads (ribbons) form and peel off the substrate using laser scanning speed equal to 30 mm.s -1 (Figure 7). SEM images were taken on each of the samples as well as on a non-sintered zone. At minimum speed, the layer is uniform, no melting or cracking phenomenon is observed while at a speed of 10 mm.s -1 , cracks begin to appear to finally form ribbons corresponding to each laser line at a speed of 30 mm.s -1 . Irradiating the material at a very low rate could thus help to attenuate the thermal gradient and promote more diffuse stress relaxation along the lased line. On the contrary, despite a lower linear energy, laser sintering for higher scanning speed induces thermal gradients and therefore greater stresses, and causes the separation of each lased parts (with ribbon shapes) independently of each other. The mechanical cohesion of the ribbons obtained at a speed of 30 mm.s -1 (these ribbons are easily handled after their separation) suggests that the sintered areas (square patterns) at lower speed (therefore at higher energy) also have acquired a certain mechanical cohesion. Indeed, the thermal gradients could be minimized for these low speeds, allowing a 20 reorganization of the sintered material without micro-cracking. Using these low laser scanning speeds, the energy received by the material being greater, the average temperatures reached during the lasing can be higher. The progress of the sintering is therefore greater at low speeds. Nevertheless, the SEM images at high magnifications do not reflect a progress in the sintering visible for the lased areas compared to the unlased-lased areas: absence of clearly identified sintering necks, reduction of porosity. However, the observation of ribbons peeling off for fast scanning speeds, suggests that the irradiation of the material by the laser beam could have allowed the consolidation of the powder bed thanks to the development of necks between the particles corresponding to the first step of the sintering process.

The ribbons obtained at high laser speed were subjected to post-sintering using high temperature treatment. Annealing of the ribbons, which had detached from the substrate during CPBLS, was carried out at 1300°C for 1 h. This additional heat treatment allows the sintering process to continue. Indeed, the SEM images of the annealed ribbons (Figure 8)

show the formation of visible grain boundaries between the particles and shrinkage in the width of the tape of about 10% is also noted. Also, X-ray diffraction analysis, to check the maintaining of the Cu-doped HA phase during the CPBLS process and the post-annealing sintering was performed. All diffraction peaks are well indexed to the hydroxyapatite form, indicating the pure target phase is maintained (Figure 9). The partial densification of the tape materials is due to the drastic thinness of these ribbons: the diameter of each Cu-doped HA grain is nearly equal to the thickness of the ribbon; thus, the densification of such monolayer of grains is difficult. The increase of the ribbon thickness would allow a better densification to be achieved. Herein, the remaining porosity was evaluated at about 7% using the ImageJ software. Some thin microcracks, possibly appearing during laser sintering or handling the ribbons, are also observed on the surface. Thus, on layers of thinner thickness, selective laser sintering makes it possible to ensure mechanical cohesion to the sintered areas. It could then be advantageously followed by a natural sintering step, which would strengthen the part shaped and pre-sintered by CPBLS. Irradiation of the material at a very slow rate allows the formation of necks between the particles and minimizes the thermal gradient along the bead thus preventing cracking of the powder bed.

Reducing the thickness of the films leads to better behavior under laser irradiation.

This should rather come from a decrease in the energy received by the film (due to a film thickness then less than the depth of penetration of the electromagnetic radiation) than from an increase in the elastic properties of the film. This lowering of the received energy allowed us to explore much lower scanning speeds, a key parameter to allow the relaxation of the stresses generated by the start of sintering created under laser. As a result, the production of a pre-sintered film by CPBLS, without cracking phenomenon, was demonstrated on thin film with 5 μm thickness at a power of 40 W and a speed of 5 mm.s -1 (hs = 80 m)

Moreover, we have shown that the CPBLS technique could allow the creation of selfsupported ribbons (with 5 m thickness, 100 m width and few mm length) easy to manipulate and which can be post-sintered thanks to the mechanical strength conferred by the neck well visible between grains produced during the CPBLS process. Only ribbons with a width of around one hundred µm and a thickness of 5 m have been produced here but, with a light adaptation of the protocol, lasing self-supporting ribbons of more complex geometry can be manufactured as shown in the Figure 10.

Conclusion

This paper showed deep and transversal work from the powder synthesis to the ceramic shaping thanks to an original direct selective laser sintering process on copper-doped hydroxyapatite (Cu-doped HA) thin films. Cu-doped HA material was investigated because of its potentiality to be used as bone substitute with angiogenic properties enhanced from copper insertion. Furthermore, copper, as chromophore cation absorbing partly the laser wavelength allows heating from laser irradiation.

HA powder was obtained from co-precipitation process mixing calcium and phosphate precursors at a controlled pH. Then, CuO -HA mixtures were submitted to optimized attrition step before a calcination at 1100°C allowing the obtaining of a violet-colored Cudoped HA powder, monophasic and with sub-micron crystallite size. This powder was formulated to obtain suspension ready to be dip-coated on glass substrates to obtain thin layers with tunable thickness from the number of successive coatings.

Selective Laser Sintering process, was performed on Cu-doped HA layers with different thickness, varying the laser power, the laser scanning speed and the interspace between two lased lines. The success of the ceramic laser sintering: presence or absence of cracks, delamination, mechanical consolidation of the films, but also the control of the lased area (lased line width especially) is shown to strongly depend on the appropriateness of the setting process parameters. As brand new result in regard of the few former studies on ceramic powder laser sintering in literature, it has been shown that the creation of selfsupported ribbons (few mm thick and few mm length) can be easily produced. These ribbons are flexible and rollable and can also be post-sintered at high temperatures (1300°C) to be consolidated (hardened). These last experiments, which can be extended to other refractory ionic compounds, open a new window in different ceramic applications: for instance, winding these as-prepared ceramic threads as source of flexible HA ceramic for biomedical

Figure 1 .

 1 Figure 1.b3 shows that without this pre-treatment, only a partial sintering can be reached.

Figure 2 .

 2 Figure 2. X-ray diffraction patterns of the CuO-HA raw powder mixture (bottom) and the Cudoped HA powder (top) obtained after the annealing treatment at 1100°C (the star indicates the main CuO diffraction peak). Photograph and L*, a*, b* colorimetric parameters associated to the raw mixture and the annealed power. STEM EDS mapping showing the homogeneous cationic distribution (Ca, P, Cu) in the Cu-doped HA phase.

Figure 3 .

 3 Figure 3. SEM cross section views of Cu-doped HA thin films issued for 2, 6 and 12 successive layer coatings and their associated thickness

Figure 4 .

 4 Figure 4. Optical microscope images on the film surfaces after CPBLS process using different set of laser parameters. The two images framed in blue are from two films submitted to a same laser linear energy.

Figure 5 .

 5 Figure 5. Lased line width evolution versus the laser scanning speed for a fixed laser powder value: 60 W (a) or for a fixed film thickness: 13 m (b).

Figure 6 .

 6 Figure 6. SEM micrographs (top view) of square patterns drawn from laser irradiation on thick films (for the film with thickness = 13 m, the laser parameters are fixed such as v = 250 mm.s -1 , hs = 60 m and for the film with thickness = 30 mm, v = 750 mm.s -1 , hs = 40 m)

Figure 7 .

 7 Figure 7. SEM micrographs (top view) of square patterns drawn from laser irradiation on the film with thickness = 5 m, modifying the laser scanning speed between 5 and 30 mm.s -1 .

Figure 8 .

 8 Figure 8. SEM micrographs of one Cu-doped HA ribbon obtained from CPBLS on the 5 m thick film using a scanning speed equal to 30 mm.s -1 and after post-annealing treatment at 1300°C during 1hour.

Figure 9 .

 9 Figure 9. X-ray diffraction pattern recorded on a set of consolidated ribbons from the postannealing treatment at 1300°C (the peak's indexation considering hydroxyapatite crystallographic network, with space group P6 3 /m space group is joined).

Figure 10 .

 10 Figure 10. Illustration of a radial pattern ribbon nest obtained with laser scanning speed of 220 mm.s -1 and laser power of 40 W on a 10 m thick Cu-doped HAP film.

Acknowledgements

The authors thank to the French regional council of Nouvelle Aquitaine for the financial funding given to this study. This work was also supported by institutional grants from the National Research Agency under the Investments for the future program with the reference ANR-10-LABX-0074-01 Sigma-LIM.

application. Also, for the ceramic film remaining on the substrate, the possibility of taking off patterns of accurate shapes created, "tailor made", from the additional manufacturing software, can prove to be a more than interesting alternative to lithography.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.