Yue Peng

Guillaume Andrieux

Jean-François Diouris

Magaye Diop

Energy optimisation of an OOK transmitter using high-order orthogonal modulation

Keywords: OOK, wireless sensors, energy efficiency, orthogonal modulation

In this paper, we show that high-order orthogonal modulation can be used to optimize the power consumption of an energy efficient On-Off Keying (OOK) transmitter for short range wireless sensor applications. Our work is based on the characteristics of a high performance OOK modulator that completely turns off during the transmission of zeros and provides energies per bit in the picojoule range. We take into account the limitations of the circuit in terms of maximum modulation rate and constant output power. Based on a bit error rate performance analysis and a circuit energy model, we propose an original approach to find the energy optimal modulation order for a given range constraint.

When considering only the transmitter power consumption, a large improvement in energy per bit can be obtained by using this optimization. When considering a residual power consumption during the transmitter off state, an improvement is still obtained but is less important.

Introduction

Wireless sensors (WS) find applications in various areas like home automation, health, safety, etc. For a large part of these applications, unidirectional communication is enough because only intermittent measurements need to be sent to the management system. In that case, it can be assumed that these devices are only composed of a sensing block associated to a transmitter block. Due to practical constraints, WS are expected to be powered by a limited energy source (battery or energy harvester) for a long period of time. The radio transmission is known to be the major energy consumer. So for energy constrained applications, the optimization of the transmission technique is crucial.

On-off keying (OOK) is the simplest form of amplitude-shift keying that represents digital data by the presence or absence of carrier. It has the advantage of more simple circuits A c c e p t e d M a n u s c r i p t

TETL_A_1477184

than more complex modulations. A good energy efficiency can be expected if the transmitter can be switched off during the transmission of zeros. Design of efficient OOK transmitters can be found in Daly, [START_REF] Chee | An Ultra-Low-Power Injection Locked Transmitter for Wireless Sensor Networks[END_REF][START_REF] Kuan | 44 pj/bit energy-efficiency Kband OOK transmitter for wireless sensor networks[END_REF][START_REF] Daly | An Energy-Efficient OOK Transceiver for Wireless Sensor Networks[END_REF][START_REF] Jung | /bit Energy-Efficient 2[END_REF][START_REF] Raja | A 52 pJ/bit 433-MHz low power OOK transmitter[END_REF][START_REF] Shirai | Dedicated antenna less power efficient OOK transmitter for mm-cubic IoT nodes[END_REF][START_REF] Yousefi | A 430 MHz Fully Integrated High Efficiency OOK Transmitter for Wireless Biomedical Application[END_REF] for VHF, UHF or K-Band.

CONTACT Guillaume Andrieux. Email: guillaume.andrieux@univ-nantes.fr

Especially, the transmitter proposed by [START_REF] Raja | A 52 pJ/bit 433-MHz low power OOK transmitter[END_REF] provides an energy efficiency of 52 pJ/bit with a data rate equal to 10 Mbit/s. Due to the simplicity of the transmitter, the output power is constant and the circuit is matched to small range communications.

From the Shannon capacity theorem, we know that increasing energy efficiency implies sacrificing spectral efficiency [START_REF] Proakis | Digital Communications[END_REF]. It is also well known that this trade-off can be obtained by orthogonal modulations. Increasing the number of symbols reduces the energy per bit at the price of data rate decrease for a given bandwidth.

In this paper we propose to apply high-order orthogonal modulation to an efficient on-off keying transmitter and to study the optimization of the modulation. We show that these modulations can dramatically reduce the energy consumption of the transmitter. Taking into account the circuit characteristics, we propose an original approach to find the energy optimal modulation order for a given range constraint.

The paper is organized as follows. In section 2, we consider an energy efficient OOK transmitter and a circuit energy model based on a real device. Section 3 recalls the definition and performance of orthogonal modulation for non-coherent detection. Section 4 proposes the energy optimization of an OOK transmitter using orthogonal modulation. Section 5 provides numerical results. Finally a conclusion summarizes the obtained results.

OOK transmitter

An OOK transmitter is composed of an oscillator and a power amplifier (or buffer in the simplest case). When transmitting a bit 1, a sine wave generated by the oscillator is transmitted to the antenna through the amplifier. When transmitting a bit zero no signal is transmitted. To reduce the circuit energy consumption, it is important to shutdown the power supply of the circuit during the off state. But this operation is only possible if the start-up time of the oscillator is much lower than the bit duration.

As an example, we consider the 433-MHz OOK transmitter described by [START_REF] Raja | A 52 pJ/bit 433-MHz low power OOK transmitter[END_REF]. The circuit completely turns off the transmitter during the transmission of `0' and employs a speed up scheme to obtain high data rates and low wake up time. From the transmitter realistic parameters, the energy consumption per bit

Orthogonal modulation

As stated in the introduction, an improvement of the energy efficiency at the price of the spectral efficiency can be obtained using high-order orthogonal modulations. We consider this type of modulation defined in figure 1 and by the following = 2 k M symbols, where k is the number of bits per symbol

[( 1) , ] 0 ( ) = 1 (2 ), [1, ], n n t n t n c c s t c o s ft n M π φ - + ∈ (3)
where [ 1, 2] 1 t t is the index function, c t is the pulse duration and 0 f is the carrier frequency. The phase n φ is random because we assume that the transmitter oscillator is switched on and off during each symbol. Due to the presence of this random phase, it is not possible to use a coherent receiver. In the case of a non-coherent detector, the bit error rate of orthogonal modulation, is given by [START_REF] Proakis | Digital Communications[END_REF] as

1 1 12 0 =1 1 ( 1 ) = . 2 1 1 E nk b n M n N n eb M n M P C e M n + - - + - - +  (4)
In the next section, it will be necessary to express the required 0 / b E N as a function of a target eb P . As it is difficult to inverse equation ( 4), we propose an approximation of the bit error probability given by the following expression:

2 0 2 . 4 E b k k N eb P e -  (5)
As seen in figure 2, the proposed expression provides good approximations for eb P under 3 10 -and k between 1 and 8. We can then deduce the expression of the signal to noise ratio (SNR) per bit as a function of the target bit error rate

( ) 0 1 2 (2) 4 , b eb E ln ln P N k   -      (6)
which is obviously a decreasing function of k .

Orthogonal modulation based on OOK can be compared with Minimum Energy (ME) which optimizes energy by minimizing the number of ones which are present in the coded message. Every block of k bits is mapped into a 2 1 kbit codeword. The BER performance of minimum coding is studied in Tang et al.

Energy optimization

With the previously defined OOK transmitter, the total energy per bit using orthogonal modulation can be written , = . 2

h btot k k P E R (7)
From this equation, it is obvious that increasing k or increasing the bit rate R can reduce the energy per bit. But, to obtain realistic results, the limitations of the circuits must be considered.

The first limitation deals with the bit rate which is bounded by the maximum modulation rate of the OOK transmitter and the minimum 1 pulse duration cmin t . From this limitation, the maximum bit rate for an orthogonal modulation using 2 k symbols is

= . 2 max k cmin k R t (8)
This equation illustrates that when increasing the number of symbols, the bit rate must be reduced to take into account the limited bandwidth of the circuit (represented by 1/ cmin t ). Replacing ( 8) in ( 7), we get a new expression of the total energy per bit , = .

h cmin btot k P t E k (9)
This expression is a decreasing function of k . In a more realistic scenario, the control circuits of the modulator should also be considered. Assuming a power consumption c P during the transmission of zero, the total energy per bit can be written

( ) , 2 1 = . k h cmin c cmin btot k P t Pt E k + - (10)
This new expression of , btot k E is a convex function of k and the optimal value of k , minimizing the total energy, can be easily obtained by zeroing the derivative (proof in appendice)

/ 1 1 = , 2 h c L E min P P W e k ln -   +     (11)
where L W denotes the Lambert function. This equation shows that E min k depends only on the ratio of the on and off power consumptions / h c P P . The second limitation concerns the maximum output power out P . As the transmitted symbol energy is out cmin P t × and we have k bits per symbol, the transmitted energy per bit can be written

E P t N k d M kT λ π ×       (13)
From this expression, the maximum range of the device can be deduced

0 = . 4 out cmin b g b P t d E M kk T N λ π (14)
By replacing ( 6) in ( 14) we get = . 4

( 2 ( 2 ) 2 ( 4) )

λ π   +     (16)
In a lot of applications the area of transmission is limited (for example to a room) and it can be interesting to optimize the circuit energy for a given transmission range min d . This problem can be written Increasing the number of bits per symbol k can be interesting in terms of energy optimization but the price to pay is the decrease of spectrum efficiency. This effect can be evaluated using a simple scenario. Assume s M sensors communicating with an access point in a limited area (a house for example). Assume that each sensor send K bits every t T seconds (These K bits include the frame header and the payload). Using a modulation with k bits per symbol, the K bits can be transmitted using s N symbols = ,

s K N k   (18)
where x   denotes the ceiling function. The frame duration f T , to transmit the s N symbols, can be expressed as:

= 2 k f cmin s T T N (19)
Assuming that the sensors are not synchronized, the probability that the 1 s Mother sensors transmit during the first sensor transmission can be written

= 2 ( 1)
.

k cmin collision s s t T K P N M T k   - (20)
This probability is a growing function of k but it must be noticed that, in practical applications, the ratio / cmin f T T is very small so that collision P remains very low. This remark will be illustrated at the end of the next section.

Numerical results

With the previous expressions, we can evaluate, as an example, the OOK transmitter proposed by [START_REF] Raja | A 52 pJ/bit 433-MHz low power OOK transmitter[END_REF] implementing OOK orthogonal modulation. The used numerical parameters are given in the table 1. We first analyze the total energy per bit using formula (10) with = 0 μW c P (figure 4). It can be shown that the total energy per bit of 52 pJ/bit for OOK modulation can be reduced to 35 pJ/bit for orthogonal modulation with = 3 k and to 17.5 pJ/bit for = 6 k , which represent an energy reduction of respectively 32 % and 66 % compared to the OOK transmitter presented in [START_REF] Raja | A 52 pJ/bit 433-MHz low power OOK transmitter[END_REF].

When taking into account the power consumption of the other circuits, we consider = 1 μW c P

. This small value represents the power consumption of a microcontroller in shutdown mode waiting a timer to wake up. It can be shown in figure 4 that the total energy firstly decreases with k to a minimum value and then increases. This is due to the influence of c P which becomes predominant when the symbol duration is large.

For the given parameters, the minimum energy is obtained for = 8 k which is in agreement with formula (11) which provides = 7.78

Emin k . The obtained optimal total energy per bit is 16 pJ/bit representing an energy reduction of 69 % compared to the OOK transmitter presented in [START_REF] Raja | A 52 pJ/bit 433-MHz low power OOK transmitter[END_REF]. The output power of the OOK transmitter is limited to -12.7 dBm. For that reason, the considered device is only matched to small range communication. Using formulas ( 6) and ( 14 -are plotted in figure 6 as a function of min d . The optimal k decreases with the distance. When a value of 2 is reached it must be noticed that the range cannot be obtained. So considering the particular device and our propagation model, the range is limited to 17 m. Finally, the total energy per bit can be largely reduced by optimizing k for a given range. For example, for a range less than 10 m, the total energy can be reduced to about 5 pJ/bit, i.e. 10 times less than in OOK.

When c P is no more zero, the procedure described at the end of the part 4 must be used to find the optimal k for a given maximum range. ). In the first case, for distances less than 14 meters, the optimal k is now constant equal to 8. A larger value of k would increase the total energy per bit due to the influence of c P . The total energy per bit can be reduced from 52 pJ/bit in OOK to 16 pJ/bit in orthogonal modulation with a maximum range equal to 14 m. Finally, to illustrate the influence of the number of sensors, we consider the simple scenario given at the end of the previous section. The number of sensors is = 20 M . The number of bits transmitted by each sensor is = 16 K and the transmitting period is = 1 t T s. Using expression (20), the probability of collision is plotted in figure 8 as the function of k . As already noticed, the probability of collision increases with k but remains low when the transmission period is much larger than cmin t .

Conclusion

Energy efficient OOK transmitter for short range wireless sensor applications can be improved by using high order orthogonal modulation. An optimization scheme has been proposed using bit error rate performance analysis associated to circuit energy model. It allows to find the number of symbols which provides the minimum energy per bit for a target maximum range. A large improvement in energy per bit can be obtained if the power consumption during the off state is very small or null. Increasing the number of symbols of orthogonal modulation increases the symbol duration and then the channel occupancy. We showed that this effect has little impact in a simple multi-user scenario.

Orthogonal modulation associated to efficient OOK transmitter provides an energy efficient solution for short range wireless sensors. However, to obtain the maximal efficiency, effort must be done on the circuit design to reduce the power consumption when the transmitter is off.

A c c e p t e d M a n u s c r i p t

Figure 1 .

 1 Figure 1. On-Off orthogonal modulation.

Figure 2 .

 2 Figure 2. Probability of a bit error for noncoherent detection of orthogonal modulation, exact (dash line) and approximation (symbol).

  (2005) and[START_REF] Peng | Realistic Energy Consumption Model for On-Off Keying Based Minimum Energy Coding[END_REF] for unknown source statistic. Orthogonal modulation outperforms ME coding in term of required SNR. For example A c c e p t e d M a n u s c r i p t 4 TETL_A_1477184 for = 6 k and for a BER equal to 4 10 -, a SNR per bit of 7 dB is required for non-coherent softdecoding ME coding and 5.5 dB for non-coherent orthogonal modulation.

  power spectral density b k T and a link margin g M , where λ is the carrier wave length, d is the distance, b k is the Boltzmann constant and T the temperature in Kelvin, we can

  other case, the solution is E min k . The constraint is not active because we are in the increasing part of ,

Figure 3 .

 3 Figure 3. Illustration of solving problem (17). btot E (square) and d (o) as a function of k .

Figure 4 .

 4 Figure 4. Total energy per bit versus bit per symbol, (o) = 1 μW c P , (x) = 0 μW c P .

Figure 5 .

 5 Figure 5. Transmission range as a function of k .

  the range decreases when k increases or the target eb P decreases. This figure shows also Monte Carlo simulation results which are in good accordance with analytic results.The parameter k can now be optimized to obtain a given range min d provided by equation (16) saturating the minimum value to 2. The obtain results

Figures

Figure 6 .

 6 Figure 6. Optimal k (o) and bit energy (square) as a function of the distance.

Figure 7 .

 7 Figure 7. Optimal k (o) and total energy per bit (square) versus distance with = 1μW c P (

Figure 8 .

 8 Figure 8. Probability of collision, equation (20) (dash line) and Monte-Carlo simulation (*).

Table 1 .

 1 Parameters for the numerical analysis.

	Parameter	Value	Unit
	h P	1.036	mW
	t	cmin	0.1	µs
	c P	0,1 or 10	µW
	out P	-12.7	dBm
	k	b	23 1.38 10 -×	. J K -	1
	T	300	K
	Mg	30	dB
	λ	0.69	m

Appendix A. Proof of the expression of optimal k

Proof of the expression of optimal k (11): zeroing the derivative of ( 10) with respects to k we get 2 ( (2) 1) = / 1.

Thus replacing the expression of w

The second derivative of ( 10) is


R Kromer
email: robin.kromer@gmail.com

J Cormier

S Costil

D Courapied

L Berthe

P Peyre

High temperature durability of a bond-coatless plasma-sprayed thermal barrier coating system with laser textured Ni-based single crystal substrate

Keywords:

Thermal barrier coating systems are usually build-up with bond coats to ensure a good adhesion of the ceramic top coat and to protect the substrate against oxidation and corrosion. Such system is often subjected to complex thermo-mechanical loading. Because of the very different damage processes encountered during service operations, a simplified system was investigated by removing the bond-coat. Recently adhesion bond strength was enhanced using laser surface texturing of the substrate in thermal spraying processes. Atmospheric plasma spray yttria-stabilized-zirconia thermal barrier coating system was deposited on the Ni-based AM1 single crystalline superalloy without bond coat. Adhesion bond strength was already increased compared to conventional processing method. Top coat durability was evaluated at high temperature and damage mechanisms were studied. Isothermal and cyclic oxidation tests showed durability of 1000 h and 400 cycles at 1100 °C. The oxidation mechanisms at the substrate/top coat interface changed due to fast solidification during the laser texturing process. Then, TBC system was studied under high temperature mechanical solicitation in tension creep. The textured interfaces were not damaged after 1% creep strain while top-coat/substrate interfacial cracking was observed for grit-blasted specimens. Moreover, no preferential crack development in the substrate was observed. Patterns provided an enhanced adhesion by changing the stress distribution near the interface.

Introduction

Thermal barrier coatings (TBC) are widely used on nickel-based superalloys substrates submitted to prolonged exposures to combustion gases at high operating temperatures in order to increase gas turbine efficiency and to limit hot corrosion and oxidation issues [START_REF] Cao | Ceramic materials for thermal barrier coatings[END_REF]. A typical TBC system is consisted of three layers: a metallic substrate (generally, a Ni-based superalloy), an alumina-forming metallic bond coat and a ceramic top coat [START_REF] Clarke | Thermal barrier coating materials[END_REF]. The bond coat has two main functions: protection of the base material against oxidation and corrosion attack during high temperature exposure and providing good adhesion of the ceramic top coat [START_REF] Eriksson | TBC bonding coat top coat interface roughness[END_REF]. The latter protects the base material from heat of the flowing combustion gases [START_REF] Hüttel | Investigation of the High Temperature Performance of Thermal Barrier Coating Systems for Steam Turbine Applications[END_REF]. Nevertheless, premature failures due to several mechanisms still limit the TBC systems durability [START_REF] Haynes | Oxidation and degradation of a plasma-sprayed thermal barrier coating system[END_REF]. Damage mechanisms in TBC systems under service conditions are complex and the crack initiation and subsequent propagation, often related to the bond coat strength and microstructure evolutions [START_REF] Jackson | The Effect of Bond Coat Oxidation on the Microstructure and Endurance of Two Thermal Barrier Coating Systems[END_REF][START_REF] Pollock | Oxide-assisted degradation of Ni-base single crystals during cyclic loading: the role of coatings[END_REF][START_REF] Lafata | Oxidation-assisted crack growth in single-crystal superalloys during fatigue with compressive holds[END_REF]. Macroscopic spallation is triggered by maximum in-plane compressive stress and the decrease in ceramic/metal interface bond strength due to aging effects [START_REF] Al-Athel | Modeling decohesion of a top-coat from a thermally-growing oxide in a thermal barrier coating[END_REF]. Interfacial damage is a combination of microstructure evolution and oxide growth. Both are thermally activated and the thermal stresses may modify the interface roughness depending on top coat structure and material. The main damaged mechanisms associated to oxidation and roughness increase are called rumpling, and consists in local interfacial delamination [START_REF] Balint | An analytical model of rumpling in thermal barrier coatings[END_REF]. The elastic and plastic stored energy in the TGO (Thermal Growth Oxide) and imperfections in its vicinity play a significant role in the durability of the full TBC system under cyclic oxidation. In addition, any energy release rate of topcoat, for instance interface defects, play also a major role. The failure occurs through a sequence of crack nucleation, propagation and coalescence events during thermo-mechanical loading applied during service operations in gas turbines [START_REF] Choi | Fracture behavior under mixed-mode loading of ceramic plasma-sprayed thermal barrier coatings at ambient and elevated temperatures[END_REF]. Under high applied stress conditions, a failure mechanism at substrate/bond coat interface may also be observed due to large creep strains and fast creep deformation of the bond coat at high temperatures above the ductile-brittle transition temperature (DBTT) [START_REF] Moridi | Thermo-mechanical stress analysis of thermal barrier coating system considering thickness and roughness effects[END_REF]. Since NiAl(Pt) type bond coats have generally poor creep resistance, a TBC system without bond coat was investigated in the present study. With such a "bond-coatless" TBC system, a mechanical anchoring was used to ensure a good adhesion of the top-coat to the substrate and an alumina-forming superalloy was chosen. For this, a substrate surface laser patterning was used [START_REF] Choi | Fracture behavior under mixed-mode loading of ceramic plasma-sprayed thermal barrier coatings at ambient and elevated temperatures[END_REF]. As presented previously, the patterns increased the in-contact area and provided mixedmode failures to obtain cohesive failures locally [START_REF] Kromer | Laser surface patterning to enhance adhesion of plasma sprayed coatings surface and coatings technology[END_REF]. Thus, the adhesion bond strength of the thermal barrier coating was tripled with laser surface patterning prior-treatment compared to a standard preparation technique (i.e. grit blasting). In the present investigation, the durability and failures mechanisms of this new thermal barrier coating system without bond coat were investigated during isothermal and cyclic oxidation experiments as well as during isothermal creep tests. Yttriazirconia top-coat was deposited on a single-crystal superalloy substrate and this TBC system was investigated during high temperature oxidation and creep conditions corresponding to possible high or intermediate pressure turbine blade and vanes applications as well as high pressure turbine shrouds. A specific attention will be paid to the role of substrate laser texturing in the damage development.

Experimental procedure

Materials

As referred to useful TBC systems, the studied system is composed of a plasma-sprayed YSZ top coat deposited on an AM1 single crystal superalloy substrate. The AM1 is a first generation nickel-based superalloy, whose composition is given in Table 1. Before machining the specimens, single crystalline bars were solution treated at 1300 °C for 3 h followed by air cooling and aged at 1100 °C for 5 h followed by air cooling and at 870 °C for 16 h followed by air cooling [START_REF] Caron | Influence of the γ′ fraction on the γ/γ′ topological inversion during high temperature creep of single crystal superalloys[END_REF]. Buttons were machined from single-crystalline bars with a diameter of 14 mm and a thickness of 1.5 mm. The coated surfaces of these buttons were closed to a (001) crystallographic plane. Creep specimens were also machined from 20 mm AM1 bars. These specimens were machined with the stress axis close to a [001] crystallographic orientation (deviation < 5°). Creep specimens had a gage length of 14 mm and a diameter of 4 mm.

Before thermal spraying, theses specimens were treated by conventional and laser processes. First, grit-blasted surfaces (GB) were used to create a controlled roughness with abrasive-granules (Ra = 3 μm) as a reference. Second, laser surface texturing (LST) was carried out with a pulsed fiber laser (Laseo, Ylia M20, Quantel France). The laser operates at a nominal wavelength of 1.06 μm with a pulse duration of 100 ns, a maximum power of 20 W and variable frequency between 20 and 100 kHz. The laser beam is circular (diameter of 60 μm at the focal point) with a Gaussian energy distribution. Laser patterning consists of series of equidistant lines covered with holes. Several shapes can be defined depending on the X-Y scanners and the number of pulses used. So, the textured substrate has an adhesion area depending on the shape, height, orientation, distribution and density of holes. Optimal pattern dimensions were chosen depending on the spray process (powder size and material viscosity) [START_REF] Kromer | Role of powder granulometry and substrate topography in adhesion strength of thermal spray coatings[END_REF]. The density of holes has been chosen to be 100 patterns•cm -2 to have optimal adhesion strengths [START_REF] Kromer | Laser patterning pretreatment before thermal spraying: a technique to adapt and control the surface topography to thermomechanical loading and materials[END_REF]. Two hole patterns (defined as S{D}) were formed with an outer diameter {D} of 60 and 80 μm and a depth of 40 μm for each pattern. So, three substrate topographies were created: GB, S60 and S80 (Fig. 1). The in-contact area ratio (which represents the ratio in contact between the coating and the substrate per surface unit) were evaluated to 1.8, 2.7 and 3.1 as presented [START_REF] Kromer | Role of powder granulometry and substrate topography in adhesion strength of thermal spray coatings[END_REF].

Then, coatings were deposited using atmospheric plasma spraying with F4 torch (Oerlikon-Metco -Neuwiesenstrasse 158401 Winterthur Switzerland) and standard parameters optimized for the TBC material (Table 2). To ensure repeatability the torch has been mounted on a XYZ robot (ABB robot -Affolternstrasse 44 CH-8050 Zurich Switzerland). Samples were in rotational movement and the torch had a vertical movement for homogeneous coating deposition. Specimens were cooled down to room temperature by Air jet perpendicularly guided. YSZ powder (91.3 wt% ZrO 2 , 7 wt% Y 2 O 3 and 1.7 wt% HfO 2 -Praxair -ZRO 236-1) was chosen as top coat. The particle size varied from 16 μm to 100 μm (d 0.1 -d 0.9 ) with a 63 μm mean particle size. The coating thickness was 300 μm. So, three configurations were evaluated (Fig. 1): grit-blasted and two textured substrates.

Oxidation analysis

A continuous thermogravimetric system was used in the present study for the purpose of quantification and understanding of the oxidation mechanisms [START_REF] Raffaitin | Cyclic oxidation of coated and uncoated single-crystal nickel-based superalloy MC2 analyzed by continuous thermogravimetry analysis[END_REF]. The nature or rate-controlling oxide was monitored (the occurrence of breakaway and changes of the nature of the oxide and its thickness can be studied). The durability of our TBC system without bond coat was studied under isothermal and cyclic oxidation. The main objective was to analyze the impact of the substrate morphological patterning on the time to TC spallation. A special attention was paid to the nucleation of micro-cracking at the interface near the TGO and TGO growth. A SETSYS Evolution Atmospheric Thermo-Gravimetric Analysis (TGA) equipment (Setaram, Lyon, France) was used for long term isothermal and cyclic analysis. A robust and high performance graphite furnace offers high heating and cooling rates (up to 100 °C/min across the entire temperature range) in synthetic air environment (20% O 2 and 80% N 2 ). In this TGA equipment, a symmetrical and hang-down balances detected small mass changes over long term thermal analysis with a precision of ± 2 ng. The system was used to measure mass uptake/loss under isothermal (1100 °C for 100 h) and thermal cycling (100 cycles with 10 min at 100 °C and 1 h at 1100 °C) conditions. The heating and cooling rate used for the experiments was fixed to 90 °C/min. Three samples were investigated for each thermal condition and surface preparation.

LASer Adhesion Test (LASAT)

LASAT is a laser adhesion test allowing the generation of high tensile stresses in materials. In order to produce a laser-generated showwave through a target, a high power laser irradiation is required. When it is focused on a target, the laser-matter interaction leads to an intense plasma formation [START_REF] Berthe | State-of-the-art Laser Adhesion Test (LASAT)[END_REF]. As a response, a shock-wave is generated through the target. Its characteristics depend on several parameters (pulse shape, duration, and energy). A water confinement has been used to constrain the plasma expansion [START_REF] Berthe | Shock waves from a waterconfined laser-generated plasma[END_REF]. When the shock-waves intersect interface or free surface, it is reflected as a release wave. At the same time, a release-wave also propagates in the sample. A tensile stress can hence be generated locally close to a given interface. If tensile stresses near the interface are high enough than the debonding threshold of the interface, it generates a spallation of the coating and thus generates distinctive velocity signals of the back-face detected by VISAR (Velocity Interferometer System for Any Reflector) measurements [START_REF] Barker | Laser inteferometer for measuring high velocities of any reflecting surface[END_REF]. The debonding threshold measurements only work under those specific conditions (Fig. 2). The maximum local stresses indeed need to be located near the interface of the coated system. The laser source used to perform shock-wave experiments was the HEPHAISTOS laser facility (PIMM laboratory, ParisTech, France). The laser has a impulsion time of 7.1 ns with a wavelength at 532 nm (Nd:YAG GAIAclass laser, Thales Laser, France). The beam spatial energy distribution is a "top-hat" and the pulse shape has a near Gaussian distribution. The VISAR device allows measurements of the back-face velocity and permits the identification of damage development. Three samples were The same conditions were used, namely same laser spot and same coating/substrate configurations. Step-by-step, the laser energy has been increased up to reaching delamination after different oxidationtime TBC systems. A limit can be determined when the energy is sufficient for a delamination. It described the threshold of interface debonding. Three tests under and above the specific values for each specimen were performed to increase the reliability of measurements. This test could be performed on small samples used for oxidation tests and enable a local maximum tensile stress evaluations. The defects at the interface are strongly highlighted by the dynamic adhesion tests compared to conventional pull-off tests.

Creep tests

Additional tensile creep tests were performed to investigate the mechanical loading and/or temperature history promoting oxide growing of the specific TBC system [START_REF] Subramanian | Thermo-mechanical fatigue failure of thermal barrier coated superalloy specimen[END_REF][START_REF] Riallant | High-temperature creep degradation of the AM1/NiAlPt/EBPVD YSZ system[END_REF]. Besides, the new TBC system needs to be characterized under such thermo-mechanical conditions since several sections of turbine blades are likely to undergo viscoplastic deformation in non-sufficiently cooled sections. Creep tests were performed using a specific set-up developed at Institut Pprime (France). They were performed under constant load. Heating was ensured by a radiant furnace and displacements were measured using a contact less extensometer directly measuring the displacement of flags attached to the gage part of the specimens. The temperature heterogeneity along the gage length was < 5°as demonstrated in previous publication [START_REF] Cormier | Very high temperatyre creep behavior of a single crystal Ni-based superalloy under complex thermal cycling conditions[END_REF]. Creep tests were performed with 120 and 140 MPa initial applied stress at 1100 °C. Tests duration ranged between few up to hundreds of hours to achieve a creep deformation closed to 1% were fixed. A creep strain generally corresponding to the very beginning of the tertiary creep stage of the AM1 Ni-based single crystal superalloy under such creep conditions was determined.

Microscopic observations

Specimens were observed after thermal exposures and creep tests using various scanning electron microscopes (SEM) (SEM JEOL 6400 and 7800F). EDX analyses (SEM 6100 + Quantax EDS 6/10, Bruker and SEM 7800F + EDS-SDD, Jeol) were also used to detect oxides and γ′ depleted layers near the top coat/substrate interface. Such characterizations were performed after careful longitudinal sectioning of the specimens and low temperature embedding in a conductive resin. Mechanical polishing up to a mirror finish was performed for all types of specimen. Several specimens were also etched using a solution made of 2/3 HCl + 1/3 HNO 3 (vol. fractions) at 4 °C to reveal the γ/γ′ microstructure of the substrate. 3. Results

Isothermal and cyclic oxidation

Isothermal oxidation at 1100 °C for 5 h up to 100 h and thermal cycling oxidation from 5 up to 100 cycles at 1100 °C for 1 h were performed for grit blasted (GB) and laser treated (S80 and S60) specimens. The relative mass change for isothermal and thermal cycling oxidation up to 100 h was plotted in Fig. 3 (continuous and dotted-lines respectively). Each single specimen's measurement is calculated per surface unit using image analysis to calculate the area exposed to oxidation. In this way, the additional area due to the presence of holes for textured specimens was taken into account knowing their morphology and the density.

First, a mass gain is observed for each specimen under both isothermal and thermal cycling conditions. Different evolutions of the relative mass change are observed, both during the first hours of oxidation and after 60 h. Moreover, the application of a thermal cycling favors the oxidation of all the specimens by micro-cracks formation, especially for short oxidation durations (below 20 h). The impact of the thermal cycling on the relative mass uptake is in good agreement with Poquillon et al. for two NiAl single crystals [START_REF] Poquillon | Cyclic oxidation kinetics modeling of NiAl single crystal[END_REF]. Then, it is also noticed that the oxidation kinetics are dependent on the surface preparation. Grit-blasted specimens present a faster oxide growth than laser treated ones for the first hours of oxidation. After about 30 h of oxidation, laser treated specimen always exhibit a higher mass uptake compared to grit blasted ones. The relative mass changes were low after 100 h or 100 cycles. It is supposed that a protective layer was grown.

Under high temperature (T > 1000 °C), it was found that the oxide film on AM1 superalloy consists of two layers (Fig. 4), i.e., an inner layer from the side of the metal substrate, which is composed of oriented grains of α-Al 2 O 3 , and an outer layer, which comprises oriented grains of NiAl 2 O 4 spinel [START_REF] Fedorova | High-temperature oxidation of nickel-based alloys and estimation of the adhesion strength of resulting oxide layers[END_REF]. It is also observed that the oxidation of the substrate resulted in a γ′-depleted layer (i.e. without any γ′ particles) as usually observed in the literature [START_REF] Albert | High-temperature oxidation behavior of two nickelbased superalloys produced by metal injection molding for aero engine applications[END_REF]. The two layers of the oxide scale are separated by discrete inclusions of tantalum and titanium oxides (bright spots in the backscattered electron image). So, multi-layer oxides were observed and the transition in oxidation behavior can be deduced with the alumina phase changes. However, the alpha alumina can be defined has a protective layer after 50 h. Such multi-layered oxides were observed for the different specimens (Fig. 4a).

For grit-blasted samples, the plastic deformation induced by the abrasion process changed the oxide growth. Al 2 O 3 oxide was the main TGO. The spinels and inclusions were not clearly defined. Moreover, cracked oxides were noticed for GB after 100 h (see Fig. 4b). It might be the consequences of mixed spallation: cracks propagated through TBC/ TGO or TGO/substrate interface. The misfit leads to compressive stresses and the curvature gives different stresses components. APS TBC has a lamellar structure which is not adapted to support perpendicular stresses (i.e. thermal misfit strains between substrate and TBC). For textured substrates, laser treatments promoted a multi-layered oxide scale similar to the polished substrate (Fig. 4c). Besides, the inclusions were well defined between the inner and outer layers.

Time to spallation of the top-coat under high temperature oxidation

Fig. 5 shows the evolution of the adhesion strength determined by the LASAT test for grit-blasted and laser textured specimens, both after isothermal and cyclic oxidation tests. Four samples were evaluated for each condition.

First the laser adhesion test allowed evaluating the interface topography effect on adhesion [START_REF] Courapied | Laser adhesion test for thermal sprayed coatings on textured surface by laser[END_REF]. It was confirmed by the authors that the laser surface texturing enhanced the adhesion bond strength by mixedmode failures under quasi-static and dynamic stresses [START_REF] Kromer | Laser patterning pretreatment before thermal spraying: a technique to adapt and control the surface topography to thermomechanical loading and materials[END_REF]. Then, after high temperature exposure, the adhesion threshold changed. For isothermal oxidation, an optimal value after 100 h was noticed, meaning that a high interfacial toughness is obtained after such an exposure time, as already observed previously by Vaunois [START_REF] Vaunois | Modélisation de la durée de vie des barrières thermiques par le développement et l'exploitation d'essais d'adhérence[END_REF]. The physicochemical compatibility was optimal between YSZ/TGO after 100 h, corresponding to a TGO scale mainly composed of dense and continuous α-Al 2 O 3 . It is suspected to be linked to a higher substrate/oxide interfacial toughness associated to the formation of a continuous and dense inner α-Al 2 O 3 oxide layer in the TGO. The improvement was higher for S80 due to larger in-contact area. Moreover, the adhesion strength decreased almost linearly after 100 h for isothermal exposure whatever the specimen type. As observed Fig. 6, GB specimens spalled (i.e. a zero adhesion threshold) after 350 h while S60 and S80 would reach spontaneous spallation threshold for durations in the 1500-2000 hours range.

Finally, it was shown that the introduction of a thermal cycling during oxidation tests leaded to a faster decrease of the TC adhesion. GB specimens were observed to spall before 200 h (spallation after 170 cycles). Larger roughness (Ra = 5.3 and 8.2 μm) was investigated to check this behavior. The spallation time was equal to 220 ± 30 and 280 ± 20 μm respectively. So, the morphological patterning had a strong impact on adhesion.

Even if laser treated specimens did not exhibit spallation of the TC after 200 h of thermal cycling, it was observed a spectacular decrease of the adhesion, hence highlighting the detrimental effect of thermal cycling. For these laser treated specimens, a TC spallation life between 400 and 500 cycles was expected (linear extrapolation from the trend presented in Fig. 5). Thermal cycling tests up to such durations would deserve to be performed to confirm this estimation.

Vaunois [START_REF] Vaunois | Modélisation de la durée de vie des barrières thermiques par le développement et l'exploitation d'essais d'adhérence[END_REF] or Liu et al. [START_REF] Liu | Influence of isothermal aging conditions on APS TBC's interfacial fracture toughness[END_REF] presented metallographic characterizations of failure modes in plasma sprayed TBC systems evaluated in isothermal oxidation at 1100 °C. It was found that the durability of commercial quality TBC system is related to progress of degradation modes of bond coat and top layer. During isothermal oxidation test, the bond coat was oxidized to form of a dense alumina and a porous mixed oxide layer between the YSZ top coat and a bond coat made of NiCo-CrAlY alloy. At the moment of oxidation acceleration, the process of crack initiation and propagation was observed mainly in the mixed oxide layer near the YSZ. The observed crack propagation induced the delamination and spallation of top coat after 500 h oxidation. In this study, the lifespan was in the same range of our GB samples without bond coat, even if the interface roughness was lower in our case compared to these previous studies. So, laser surface texturing results can be considered to increase the lifespan under the same conditions.

Microstructure observations along cross sections were performed (see Figs. 6 and7). Microstructures close to TC/substrate interface as presented were observed in the as-deposited state (i.e. without any high temperature oxidation), after 100 h of isothermal oxidation at 1100 °C and after 100 cycles in cyclic oxidation. Grit-blasting created a specific roughness by plastic deformation of the substrate and erosion mechanisms. The superalloy microstructure was hence highly deformed at the extreme surface (Fig. 6a). The compressive stresses due to gritblasting affected the microstructure during oxidation (both isothermal and cyclic oxidation) and 4 affected zones were distinguished: 1/ a γ′ depleted layer, 2/ a layer showing cellular recrystallization, 3/ a transition zone and 4/ the substrate standard microstructure, whose γ′ particles have coarsened during thermal exposure (Fig. 6b). The areas of cellular recrystallization were direct linked to the residual stresses introduced during the grit-blasting and are suspected to affect the TGO growth mechanisms [START_REF] Jichun | Surface recrystallization in nickel base single crystal superalloy D6[END_REF]. It was noticed interfacial porosity between the TGO and the top coat promoting crack initiation areas (Fig. 6b). Cracks were indeed observed following this interface during isothermal tests. Besides, few parts of the coating stayed attach to the substrate after thermal cycling tests (Fig. 6c). The difference of thermal expansion coefficients are known to create stresses during the solidification, leading to interfacial and intersplats cracks, as observed in Fig. 6c.

LST created patterns by vaporization and recoil pressure mechanisms [START_REF] Semak | A concept for a hydrodynamic model of keyhole formation[END_REF]. A melted layer with ~1 μm thickness can be observed in the bottom of the pattern in addition to resolidified matter on the edges (Fig. 7a). No evidence of local recrystallization was noticed in the vicinity of the keyholes created by the LST process. A continuous TGO was observed after thermal exposure but no crack initiation was clearly identified after isothermal oxidation tests. The edges were the areas where the first cracks started (arrow Fig. 7b). The maximum solicitation area was supposed on the edges during TGO growth. Therefore, damage development above the hole was observed during thermal cycling treatments (dashed-arrow Fig. 7c). It was observed on the different specimens. A compressive stress state in the hole enabled deviations of cracks in the coating [START_REF] Baker | Stress evolution in thermal barrier coatings for rocket engine applications[END_REF] Thus, the time for TC spallation was limited by the coating mechanical properties due to this failure mode. Indeed, S80-textured specimens have a larger adhesion strength (see Fig. 6) due to larger cohesive area in comparison to S60 (larger section diameter), which supports this assumption.

Creep tests

A viscoplastic deformation at high temperature was introduced by performing tension creep tests to investigate the development of damage with the superposition of a load. It is recalled that creep tests were purposely interrupted after reaching nearly a 1% creep strain. It corresponds to the onset of tertiary creep. Also, we did not want to investigate failed specimens in which the local increase in stress triaxiality in the necking region of the specimen would affect at the coating cracking. The failure mechanisms of the TBC system involved during both long (i.e. applied stress = 120 MPa) and short (i.e. applied stress = 140 MPa) creep tests were investigated in the vicinity of the TGO (i.e. top coat/TGO and TGO/substrate interfaces). The objective was to deduce the major factor of TC spallation such as oxide growth or creep deformation. Fig. 8 shows low (120 MPa) and high (140 MPa) creep curves for grit-blasted and laser textured samples. Cross-sections after creep tests are presented in Fig. 9.

Fig. 9a andb show that an entire top coat/TGO delamination was obtained at the end of creep tests. On the contrary, patterns enabled the coating/substrate contact integrity after the creep tests with no clear proof of crack initiation in this interface (Fig. 9c andd). Laser surface texturing hence allowed a sufficient anchoring compared to gritblasting.

The creep behavior is observed to be very similar between GB (1% creep strain in 525 h) and S80 (1% creep strain in 650 h) specimens for a 120 MPa applied stress. However, with a 140 MPa applied stress, it is observed a pronounced decrease of the time to reach 1% creep strain for the grit-blasted specimen in comparison to the laser-textured one. The earlier onset of tertiary creep for grit-blasted specimens might be explained by the grit-blasting consequences on the extreme surface microstructure of the substrate. It was observed in the present study (see Fig. 10) surface recrystallization after creep tests using grit-blasted specimens, due to surface compressive residual stresses present at the beginning of the tests. No recrystallization has been noticed in lasertextured specimen (only few zones on the plateau). Such a recrystallization mechanism has already been observed previously for similar creep conditions and alloys [START_REF] Furrer | Gamma′ formation un superalloy U720LI[END_REF]. The volume fraction of recrystallized zone under tensile loading has almost no bearing capacity [START_REF] Meng | Effect of surface recrystallization on the creep rupture properties of a nickel-base single crystal superalloy[END_REF], and as a result, the actual stress acting on the unrecrystallized substrate is larger, which is the main cause for the lower creep life of GB specimen, especially for a 140 MPa applied stress. The recrystallized zone was measured to be equal to 24 ± 4 μm for creep tests performed at 120 MPa and 36 ± 7 μm under 140 MPa creep conditions. Taking into account this recrystallized layer, the applied stress was estimated to be 125 MPa instead of 120 MPa and 147 MPa instead of 140 MPa. It is also worth mentioning that the patterns were taken into account in the section computation as they decrease the net bearing capacity of the substrate.

For the sake of comparison, Riallant et al. [START_REF] Riallant | High-temperature creep degradation of the AM1/NiAlPt/EBPVD YSZ system[END_REF] have studied the damage mechanisms of AM1/NiAlPt/EBPVD YSZ system under the same creep conditions. Time for 1% of deformation was evaluated to 500 and 50 h for this TBC "standard" system under 120 and 140 MPa, respectively. They observed YSZ/TGO delamination after 1% of creep deformation. In addition, they noticed porosity at the bond coat/substrate interface. So, for GB specimens, evidences of delamination were observed at the interface of the oxide layer. But, for LST, no debonding was observed, whatever the creep conditions (see Fig. 10b andd). Besides the oxide layers were continuous along the patterns/coating interface. The constant applied loading has only created few cracks on the top coat extreme surface (not shown here). Finally, there were no cracks running through the substrate from the patterns, due to the local stress concentration within the substrate. Hence, this "bond-coatless" system with laser surface texturing enabled a comparable (or even better) durability under high-temperature oxidation and creep conditions.

Discussion

It has been observed in the present study that laser surface texturing seems to be a reliable process to increase the time to spallation of an APS YZS top coat deposited on the AM1 Ni-based single crystal superalloy during isothermal and cyclic oxidation, but also in creep at 1100 °C. This new bond-coat-less TBC system could be considered as a good candidate for high temperature turbine blade, vanes or shrouds applications, especially if the substrate presents intrinsic good oxidation and corrosion resistances.

To explain the possible origins of this improvement in time to spallation compared to a standard grit-blasting process few arguments can be highlighted. Post-processing TGA data (see Fig. 3) to extract the mass gain rate as a function of time enabled a parabolic rate constant evaluation of grit-blasted (GB) and laser textured (S80) specimens. The variations of mass gain versus time can be fitted to a parabola according to Eq. ( 1) [START_REF] Monceau | Determination of parabolic rate constants from a local analysis of mass-gain curves[END_REF]:

= + + t A BΔm CΔm 2 (1)
The kinetics parameters can be evaluated from the coefficients A, B, and C obtained from such a fit. The most important feature is that the second degree coefficient C is always the reciprocal of the "true" parabolic rate constant kp. The fitting of the experimental data to a complete parabola permits a correct evaluation of the kp value independently of the effective oxidation mechanism and/or the occurrence of a transient oxidation regime. Fig. 11 shows the evolution over time of the parabolic rate constant kp for grit-blasted and laser textured samples under isothermal and thermal cycling oxidation tests.

As presented, a transition zone can be observed before 1.7 h systematically. The curves decreased fast. The different regions were discussed. Raman spectroscopy analysis was used to evaluate the oxide nature (Fig. 12). The transient oxidation mechanisms can then be confirmed from a θ-Al The first stage showed larger oxidation kinetics for GB than LST specimens. The surface plastic deformation induced faster oxide scale growth and it might be induced by the elastic and plastic stored energy. The concentration differences of specific element were not deduced from EDX analysis. For the second phase, the stable parabolic rate constant is not clear different for the different surface treatments. Audigié [START_REF] Audigié | Modelisation De l'interdiffusion Et Du Comportement En Oxydation Cyclique De Superalliages Monocristallins A Base De Nickel Revetus d'une Sous-Couche Gamma-Gamma′ Riche En Platine[END_REF] shows that kp was equal to 9.5.10 -8 mg 2 •cm -4 •s -1 for polished AM1 superalloy at 1100 °C. In this case, kp value is lightly bigger compared to Audigié rate linked to the thermal tests. According to Fig. 11 where almost similar oxidation kinetics for GB and LST specimens after 2 h of oxidation were noticed, the differences in top coat adhesion between both type of specimen as revealed by the LASAT testing procedure may only result from the nature of the oxide scale, especially the one developed within the first hours of oxidation. Moreover, the cracked TGO as observed for GB specimens in Fig. 5b may also decrease the time to spallation under both isothermal and thermal cycling conditions. This new textured TBC system enables a large durability by increasing the mechanical anchoring mechanisms. The patterns seem to change the distributions of crack propagation [START_REF] Kromer | Laser surface texturing to enhance adhesion bond strength of spray coatingscold spraying, wire-arc spraying, and atmospheric plasma spraying[END_REF]. Ranjbar-Far et al. [START_REF] Ranjbar-Far | Modeling of the residual stresses and their effects on the TBC system after thermal cycling using finite element method[END_REF] have developed a numerical modeling with the finite element code ABAQUS considering a non-homogenous temperature model to study the thermo-mechanical behavior of the thermal barrier coatings system. Among many factors affecting the durability and failure mechanisms of thermal spray coatings during their service life, the residual stresses resulting from the coating process and temperature gradient play an important role. The interface topography affects the residual stress distribution near the interface. Low roughness amplitudes cause straight transversal crack paths, whereas a high amplitude roughness results in kinked crack paths (Fig. 13). Evans and Taylor [START_REF] Evans | Delamination processes in thermal barrier coating systems[END_REF] indeed demonstrated that the presence of a large surface roughness leads to a spatial variation in continuity strains which will result in out-of-plane tensile stresses at the exposure temperature. The development of fastgrowing non-protective oxides due to aluminum depletion (chemical failure) is developed at the tips of bond coat protuberances. It increases with the roughness modification in the cyclic thermal treatments. With flatter interfaces, delamination can proceed by growth of wedge cracks which develop along the TGO/bond coat interface during cooling.

So, oxide micro-cracks might be deduced from a large oxide growth rate after grit-blasting. For a rough interface, stresses in the top coat, TGO and substrate result from thermal expansion mismatch and TGO growth. So, damage can be accumulated near TGO-ceramic interface due to coating structure and oxide micro-cracking. Critical-size crack produces spallation due to large in-plane stresses. Therefore, for laser patterned substrate, compressive stresses were generating in pattern due to the concave shape during coating build-up. Oxides growth caused an increasing tensile stresses in the pattern while pushing the peak regions into compression. Cracks could be seen above peaks and around patterns. They propagated above concave shape due to coating lamellar structure. So, remelted material on the pattern edges could be beneficial and play a role of "snap fastener". Fig. 14 summarizes the damaging mechanisms of grit-blasted and laser textured surfaces as a function of time. The failure mechanisms could be deduced as a "buckling" mechanism for GB specimens. In addition, the fast TGO growth enabled multi-crack location. On the contrary, the top coat intrinsic toughness (inter-lamellar defects and anisotropic structure) is the life limiting factor for LST specimens. The crack propagated above the patterns and the oxide growth was smoother in this case. The lamellar structure helps the buckling mechanisms.

Finally, the TGO thickness evolution has been plotted in Fig. 15 for grit-blasted and laser treated specimens, for isothermal and thermal cycling oxidation treatments. The TGO thicknesses after creep tests have been superimposed in this plot. Parabolic curves are observed and are logically linked to mass rate changes presented previously.

It is observed that creep specimens developed thicker TGO compared to both their stress free oxidation specimens. This could be due to the TGO in the meantime of creep elongation. Besides, for gritblasted samples, it can be deduced an oxide thickness limit for delamination under isothermal oxidation. Then, with stress imposed to the structure such as creep, stresses near the interface accelerated crack initiation and propagation. So, for low applied stress creep tests, the oxide thickness overcome the oxide thickness limit identified from pure oxidation tests. The duration of thermal exposure can be deduced as the main damaging mechanisms in this case. On the contrary, under 140 MPa, the oxide thickness was smaller. So, the mechanical applied stress favored the buckling mechanisms. Finally, for similar creep strains, grit-blasted and laser textured samples have shown pronounced differences in terms of resistance to interfacial crack initiation. The patterns increased adhesion strength due to the complex interface morphology. Time to spallation was deduced to be equal to 1500 h under pure isothermal exposure, without any applied stress (Fig. 6). Despite a larger oxide thickness during creep tests under both 120 and 140 initial applied stresses, the interface was not damaged. The mechanical applied stress, under creeping tests, normally should increase the damaging mechanisms. It is hence suspected that the surface morphology changed the stress distribution near the interface and it seems to be benefic. Future research will be dedicated to laser textured TBC systems with and without bond coat using APS and EB-PVD deposition processes for which failure mechanisms are different. Laser surface treatment strategy needs to be developed to enhance adhesion under thermomechanical solicitations. Topography could be optimized depending on the component (e.g. turbine blade) shapes, thermal gradients or materials.

Conclusions

The impact of the laser patterning on a bond-coat-less TBC coating system has been investigated at 1100 °C, during isothermal and thermal cycling oxidation, as well as during creep tests. According to this work, the following main conclusions can be established:

• Laser texturing of the substrate surface improve the time to spalla- tion during both isothermal and thermal cycling creep tests at 1100 °C compared to a standard grit-blasting process.

• The grit-blasting induces surface recrystallization of the substrate, leading to an earlier onset of the tertiary creep stage.

• The improved time to spallation in creep and thermal cycling oxi- dation after laser patterning of the substrate results from a change in the top coat stress distribution, in addition to the growth of a dense and continuous inner α-Al 2 O 3 TGO.

Fig. 1 .

 1 Fig. 1. Laser surface texturing strategytop view of and cross-sections for (a-d) grit-blasted, (b-e) S80 textured and (c-f) S60 textured surfaces.

Fig. 2 .

 2 Fig. 2. Left -time/position diagram showing the shock wave propagation (red: compression and blue: tension) in a thin coated system (white: substrate and brown: coating) and the debonding of the interface; right -scheme of the corresponding velocity signal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .Fig. 4 .

 34 Fig. 3. Relative mass change as a function of time for isothermal and thermal cycling tests grit-blasted (GB) and laser textured (S80 and S60) sampleserrors of 0.0002 mg•cm -2 .

Fig. 5 .

 5 Fig.5. Adhesion threshold for grit-blasted (GB) and laser textured (S60 and S80) specimens for isothermal (Iso) and cycled thermal (Cycl) teststhree samples were evaluated for each thermal condition and surface preparation.

Fig. 6 .

 6 Fig.6. Cross-sections of GB specimens in the as-processed state (a), after 100 h of isothermal oxidation (b) and 100 thermal cycles (c) at 1100 °C. Four zones:1/ γ′ depleted layer, 2/ cellular recrystallization, 3/ transition zone and 4/ standard microstructurecircles identified interface porosity and intersplats cracks.

Fig. 7 .

 7 Fig. 7. Cross-sections of S80 specimens in the as processed state (a), after 100 h of isothermal oxidation (b) and 100 thermal cycles (c) at 1100 °Ccircle: resolidified ejected material, arrow: crack with isothermal oxidation, Dashed-arrow: crack with anisothermal oxidation.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Creep behavior at 1100 °C/120 MPa (a) and 1100 °C/140 MPa (b).

  2 O 3 to α-Al 2 O 3 phase. As observed by Huang and Peng [39], based on the SEM and Raman analyses, when oxidation starts θ-Al 2 O 3 preferentially nucleates. Then, the θ-Al 2 O 3 nuclei quickly link together to form a continuous layer. Later on, the α-Al 2 O 3 layer grows out-ward under the control of aluminum cation diffusion and inward under the control of oxygen anion diffusion. Thereafter, the α-Al 2 O 3 develops a continuous layer at the interface. Finally, the θ-Al 2 O 3 to α-Al 2 O 3 transformation occurs under high temperature. The oxide volume contraction due to the phase changes can generate micro-cracks, which are visible on the patched surface. The two specific signatures were hence observed using Raman spectroscopy.

Fig. 10 .

 10 Fig. 10. Cross-sections of (a) grit-blasted and (b) laser textured (S80) after isothermal oxidation -recrystallization highlight.

Fig. 11 .

 11 Fig. 11. Parabolic rate constant evolution for grit-blasted (GB) and laser textured (S80) samples under isothermal and thermal cycling oxidation at 1100 °C -three samples were evaluated for each thermal condition and surface preparation.

Fig. 12 .

 12 Fig. 12. Raman spectroscopy results compared to standard θ-Al 2 O 3 to α-Al 2 O 3 -drawing of the oxide layer.

Fig. 13 .

 13 Fig.13. Crack propagation behavior in the TBCs and its dependence on the morphology of the TGO layer and TC/BC interface[START_REF] Courapied | Laser adhesion test for thermal sprayed coatings on textured surface by laser[END_REF].

Fig. 14 .

 14 Fig. 14. Stresses and crack propagation in the TBC after cooling for flat and concave shape combined creep and oxidation.

Fig. 15 .

 15 Fig.[START_REF] Caron | Influence of the γ′ fraction on the γ/γ′ topological inversion during high temperature creep of single crystal superalloys[END_REF]. TGO thickness evolution during isothermal and thermal cycling oxidation at 1100 °C for GB, S60 and S80. Data extracted after creep tests at 1100 °C have been added in this plot -three samples were evaluated for each thermal condition and surface preparation.

Table 1

 1 AM1 composition (wt%).

		Ni	Co	Cr	Mo	W	Ta	Al	Ti	C	Fe
	Min	Bal.	6	7	1.8	5	7.5	5.1	1	-	-
	Max	Bal.	7	8	2.2	6	8.5	5.5	1.4	0.01	0.2

evaluated for each thermal condition and surface preparation.

Table 2

 2 Thermal spray parameters for top coat.

Primary gas flow rate [slpm]

Ar 44 H 2 13 Spray distance [mm] 120 Arc current [a] 630 Powder feeding rate [g/mm] 23 Carrier gas flow [L/min] 3.4 Angle injection [°] 90

Acknowledgements

The authors gratefully acknowledge the ANR (Agence National de la Recherche) for financial assistance in the ARCOLE (12-BS09-0009) project. A part of this study is conducted in the framework of the LABEX INTERACTIFS at Institut Pprime UPR CNRS 3346 under contract number ANR-11-LABX-0017.


Silvia Pagliarini
email: silvia.pagliarini@inria.fr

Arthur Leblois
email: arthur.leblois@u-bordeaux.fr

Xavier Hinaut
email: xavier.hinaut@inria.fr

Towards Biological Plausibility of Vocal Learning Models: a Short Review

Sensorimotor learning represents a challenging problem for artificial and natural systems.

Several computational models try to explain the neural mechanisms at play in the brain to implement such learning. These models have several common components: a motor control model, a sensory system and a learning architecture. Our challenge is to build a biologically plausible model for song learning in birds including neuro-anatomical and developmental constraints. In this review, we thus focus on a specific type of sensorimotor learning referred to as imitative vocal learning and examplified by song learning in birds or human complex vocalizations. We aim to compare the various approaches used in existent sensorimotor models relevant for our purpose and to place them in a common framework.

I. IMITATIVE VOCAL LEARNING

Humans and animals such as songbirds show imitative vocal learning. Imitation involves the production of the motor command corresponding to a given experienced sensory stimulus. For instance, a baby imitating a word or a bird imitating a syllable of its tutor. Imitative vocal learning is characterized by several phases [START_REF] Brainard | What songbirds teach us about learning[END_REF]: (i) a sensory phase enables juveniles to build a neural representations of adult vocalizations, which will guide later vocal production [START_REF] Doupe | Birdsong and human speech: common themes and mechanisms[END_REF]; (ii) in the sensorimotor phase, the juvenile then adapts its vocal output to imitate previously heard sounds. During this process, the brain must harness sensory feedback to adaptively modify performance in reference to the object of imitation [START_REF] Mooney | Neural mechanisms for learned birdsong[END_REF]. Interestingly, some neurons, called mirror neurons, called mirror neurons, shows a similar response during the perception and the production of a vocal or motor gesture. Convergence of sensory and motor responses in individual neurons points to a possible mechanism through which auditory and motor signals may be linked to enable vocal learning. More precisely, it suggests the presence of internal models, such as invers or forward model, built through experience and used for vocal production in the brains of humans and songbirds [START_REF] Oztop | Mirror neurons and imitation: A computationally guided review[END_REF], [START_REF] Prather | Precise auditory-vocal mirroring in neurons for learned vocal communication[END_REF], [START_REF] Giret | Evidence for a causal inverse model in an avian corticobasal ganglia circuit[END_REF].

Here we review existing models linked to vocal imitation. Specifically, we are interested in how internal models are learned and motor control is defined. Using an idea of Oudeyer [START_REF] Py Oudeyer | The self-organization of speech sounds[END_REF], we can identify a motor space (corresponding to the articulatory parameters, e.g. the tongue height), a sensory space (corresponding to the physical parameters, such as the frequency of a sound) and the perceptual space (corresponding to the information sent to the brain when perceiving a stimulus, such as a minor number of formants in speech). The perceptual map may be connected with the motor map via an artificial neural network to drive production. Alternatively, vocal production is driven by an internal goal ( [START_REF] Cohen | Social babbling: The emergence of symbolic gestures and words[END_REF]).

Fig. 1: Sensorimotor model components A model for sensorimotor learning includes an input layer, that lies in the perceptual space or conveys the internal representation of a goal. The representation of the vocal output in the motor space is connected to its representation in the sensory space via the motor control apparatus. This sensory output evokes a sensory response. This process is represented by the plane line in the figure . In inverse models, the sensory response is linked to the perceptual input of the model (dotted line). Alternatively, in reinforcement learning models an internal representation of the goal is used as input while the sensory response drives a reward signal (dashed-dot line). Finally, dashed lines show the connection in the case of using a forward model.

Figure 1 summarizes how these three spaces are connected through a learning architecture, a motor control and a sensory system in a sensorimotor model. The properties of the sensory system, shaping the perceptual representation, is beyond the

II. LEARNING ARCHITECTURE

The starting point of a sensorimotor learning model is the input layer. As shown in Fig. 1, it can be given by the definition of the perceptual space or by the internal representation of a goal. The motor output in the motor space is connected with its sensory representation via the motor control system. Finally a sensory response translates the output of the motor control into the input representation. The differentiation in the input and the connections between spaces depend on the type of model one wants to implement and the learning algorithm used. Reinforcement learning mechanisms can be implemented defining the internal representation of the goal and the reward (dashed-dot line in Fig. 1). The introduction of internal models adds the definition of the perceptual space. Inverse models have the aim to provide an appropriate motor command for a given perceptual goal, which is driven by the sensory response (dotted lines in Fig. 1). Forward models describe a causal relationship between motor commands and their corresponding perceptual representations (dashed lines in Fig. 1).

Several learning architectures have been proposed in the literature that connect the input (perceptual or internal goal) to the motor output (in the motor space) through an artificial neural network. The structure of the network varies between models. A Random Recurrent Neural Network (called a reservoir) have been used in Warlaumont and Finnegan [START_REF] Warlaumont | Learning to produce syllabic speech sounds via reward-modulated neural plasticity[END_REF] and Philippsen et al. [START_REF] Philippsen | Learning how to speak: Imitation-based refinement of syllable production in an articulatory-acoustic model[END_REF]. Some other approaches also use neural networks as a modeling architecture, but not a recurrent one ( [START_REF] Doya | A computational model of birdsong learning by auditory experience and auditory feedback[END_REF], [START_REF] Py Oudeyer | The self-organization of speech sounds[END_REF], [START_REF] Pagliarini | A bio-inspired model towards vocal gesture learning in songbird[END_REF]).

The learning rule used to update connections between nodes in the network also differ between models, spacing from reinforcement learning algorithms to associative learning rules. Warlaumont and Finnegan [START_REF] Warlaumont | Learning to produce syllabic speech sounds via reward-modulated neural plasticity[END_REF] implement reinforcement learning based on auditory salience. The salience of a sound is computed from the sound spectrogram ( [START_REF] Coath | The role of transients in auditory processing[END_REF]) that determines the value of the reward signal. Izhikevich's DA-modulated STDP [START_REF] Izhikevich | Solving the distal reward problem through linkage of stdp and dopamine signaling[END_REF] updates the connections between the reservoir and motor neurons 1 . Doya and Sejnowski [START_REF] Doya | A computational model of birdsong learning by auditory experience and auditory feedback[END_REF] update connections using a stochastic gradient ascent algorithm and taking account critic evaluation. Associative learning rules are usually used for building internal models (inverse or forward). For instance, Oudeyer [START_REF] Py Oudeyer | The self-organization of speech sounds[END_REF] uses a Hebbian correlation rule involving the mean activation of neurons over a certain time interval [START_REF] Sejnowski | Storing covariance with nonlinearly interacting neurons[END_REF].

A theoretical model of inverse learning in songbird has been proposed by Hahnloser and Ganguli [START_REF] Hahnloser | Vocal learning with inverse models[END_REF]. We recently did an implementation [START_REF] Pagliarini | A bio-inspired model towards vocal gesture learning in songbird[END_REF] of this theoretical model and we studied how variations in non-linearity and learning rules affect performance. The model includes two neural populations (motor and auditory neurons). Learning is driven by a postdictive Hebbian learning rule. Our model makes an implementation of such theoretical model and extend it. It introduces nonlinearity in the sensory function, which is coherent with the fact that sensory responses in brain are sparse and, indeed, non-linear. In particular, to represent selective responses as observed in various high sensory brain areas (e.g. auditory regions of the pallium in birds display responses selective to tutor syllables or to the bird's own syllables), the auditory activity is defined as a bell-shaped function around a target motor pattern. Learning is driven by a normalized Hebbian learning rule.

Forward and inverse models can also be used together, as in Philippsen et al [START_REF] Philippsen | Learning how to speak: Imitation-based refinement of syllable production in an articulatory-acoustic model[END_REF]. He moves from supervised self-training (thanks to the availability of a forward model) to unsupervised learning when imitation of novel contexts is includes (after the training).

Sensorimotor learning requires a phase of motor exploration, whether in reinforcement learning model or for the implementation of internal (e.g. inverse) models. Different strategies for motor exploration have been studied in the context of vocal learning or in other types of sensorimotor learning. The simpliest exploration mechanism is driven by random motor exploration [START_REF] Moulin-Frier | Curiosity-driven phonetic learning[END_REF], while moresophisticated exploration include random and active motor babbling [START_REF] Forestier | Curiosity-driven development of tool use precursors: a computational model[END_REF], intrinsically motivated goal exploration [START_REF] Forestier | Intrinsically motivated goal exploration processes with automatic curriculum learning[END_REF], or [START_REF] Baranes | Active learning of inverse models with intrinsically motivated goal exploration in robots[END_REF], activegoal exploration [START_REF] Moulin-Frier | Selforganization of early vocal development in infants and machines: the role of intrinsic motivation[END_REF].

III. MOTOR CONTROL

The first step in defining motor control is to choose an appropriate model mapping a motor space onto a sensory space (e.g. muscle command to sound/acoustic representation). Then, we need an appropriate parameter space to describe motor articulations (ideally as function of time).

Air pressure causes vocal folds vibration, which results into a sound wave output. The sound source is the combination between the output of vocal folds vibration and noise. The latter can be due to pressure fluctuations or by the activity of other components of the apparatus (e.g. the glottis). Downstream from the sound source, the vocal tract acts as a resonator, filtering the sound as it travels to the outside world. It modifies the original sound wave and changes the balance between its frequency components. The resonances of the vocal tract are called formants [START_REF] Ladefoged | Elements of acoustic phonetics[END_REF]. A basic model of speech production 1 Actually, they are using only the long term potentiation. therefore includes a sound source (vocal folds) and a linear acoustic filter (vocal tract) [START_REF] Fant | Acoustic theory of speech production: with calculations based on X-ray studies of Russian articulations[END_REF].

A sound wave as source is a common starting point of many works, such as [START_REF] Philippsen | Learning how to speak: Imitation-based refinement of syllable production in an articulatory-acoustic model[END_REF], [START_REF] Amador | Elemental gesture dynamics are encoded by song premotor cortical neurons[END_REF], [START_REF] Doya | A computational model of birdsong learning by auditory experience and auditory feedback[END_REF], [START_REF] Moulin-Frier | Selforganization of early vocal development in infants and machines: the role of intrinsic motivation[END_REF] and [START_REF] Moulin-Frier | Curiosity-driven phonetic learning[END_REF]. Usually sound source is modeled taking inspiration from the mas model of sound production [START_REF] Titze | Mechanical stress in phonation[END_REF], coupling vocal fold tension and air pressure.

The vocal tract has been often modeled as a structure of tubes in literature. For instance Boersma in [START_REF] Boersma | Functional phonology: Formalizing the interactions between articulatory and perceptual drives[END_REF] modeled the vocal tract as a structure of tubes with moving walls. This synthesizer has been used by Warlaumont and Finnegan [START_REF] Warlaumont | Learning to produce syllabic speech sounds via reward-modulated neural plasticity[END_REF]. "VocalTractLab" system developed by Birkholz [START_REF] Birkholz | Vocaltractlab-towards high-quality articulatory speech synthesis[END_REF] defines the vocal tract using several cylindrical sections. This has been used by Philippsen et al. to generate the sound in a vocal learning model [START_REF] Philippsen | Learning how to speak: Imitation-based refinement of syllable production in an articulatory-acoustic model[END_REF]. It has also been used in speech signal filtering [START_REF] Gudhnason | Evaluation of speech inverse filtering techniques using a physiologically based synthesizer[END_REF] or articulatory synthesizer training [START_REF] Prom-On | Training an articulatory synthesizer with continuous acoustic data[END_REF]. Amador et al. [START_REF] Amador | Elemental gesture dynamics are encoded by song premotor cortical neurons[END_REF] and Doya and Sejnowski [START_REF] Doya | A computational model of birdsong learning by auditory experience and auditory feedback[END_REF] model the vocal tract dynamics using ordinary differential equations and a filter. The output is the pressure needed to generate the sound. Amador et al. [START_REF] Amador | Elemental gesture dynamics are encoded by song premotor cortical neurons[END_REF] has been used by [START_REF] Teramoto | Vocal development in a waddington landscape[END_REF] with marmoset. Moulin-Frier et al. [START_REF] Moulin-Frier | Selforganization of early vocal development in infants and machines: the role of intrinsic motivation[END_REF] [13] model vocal production using VLAM (Vocal Linear Articulatory Model [START_REF] Maeda | Compensatory articulation during speech: Evidence from the analysis and synthesis of vocal-tract shapes using an articulatory model[END_REF]) or DIVA(Directions Into Velocities of Articulators).

The output of motor control defines the sensory space. It can be defined by the sound wave, as in [START_REF] Warlaumont | Learning to produce syllabic speech sounds via reward-modulated neural plasticity[END_REF], [START_REF] Teramoto | Vocal development in a waddington landscape[END_REF] and [START_REF] Doya | A computational model of birdsong learning by auditory experience and auditory feedback[END_REF]. The sensory space can also be defined by the formants, obtained tuning the parameter of the motor space (for instance the input of VLAM and DIVA model, as in the works from Moulin-Frier et al. [15] [13] ). More simplistic models do not define the motor control system, leading to a coincidence between motor and sensory space [START_REF] Cohen | Social babbling: The emergence of symbolic gestures and words[END_REF], [START_REF] Pagliarini | A bio-inspired model towards vocal gesture learning in songbird[END_REF].

IV. DISCUSSION

This short review shows that it is difficult to compare the diversity of existing models. One needs to go into the details of each components of the model and the a priori assumptions. In particular, it is not always possible to clearly identify each component: for instance, sometimes the internal representation (e.g. goal) substitutes the perceptual space. The precise features used to represent internal and perceptual space seems to be specific to each model: the comparison between models is thus complex.

The dimensions of the sensory, perceptual and motor spaces also greatly vary among models: thus the learning architectures do not deal with the same task complexity. Actually, the choice of the architecture may constraint the authors to reduce the space dimensions if the architecture could not deal with highdimensional spaces.

The various models try to answer different questions. However, we believe it could be useful to have a common model capable to answer multiple questions and enable the comparison of different experiments. Moreover, it should include more and more the general biological mechanisms. Some models include a developmental aspect (that we did not include in our summarizing table) which changes model parameters over time. In general, modelers tend to define motor control inspired by preexisting models having some biological foundations. However, learning architectures do not always take inspiration from biology.

TABLE I :

 I Model summary

			Topic	Motor space		Motor control	Sensory space	Sensory	Perceptual	Learning
											response	space	/	architecture
											Internal
											representation
	Warlaumont	Humans	Muscle activ-	Praat (lip and	Sound	Auditory	N.A.	Auditory
	2016 [9]			ity time series	jaw)				salience.	salience,
				(900ms)						Random
											RNN	via
											Izhikevich's
											DA-modulated
											STDP
	Philippsen	Humans	26	param.	VocalTractLab	39 formants	Nonlinear	Acoustic rep-	ESN,	non-
	2014 [10]		([-1, 1] 26 )		(Birkholz		([-1, 1] 39 )	function	resentation	dynamic ELM
							[11])
	Oudeyer 2005	Humans	3	param.	de Boer model	4	formants	Nonlinear sen-	2D space	Correlation
	[7]		(multi-agent	([0, 1] 3 )		[12]		(4D space)	sory response	rule
			exp.)
	Moulin-Frier	Humans	7 param.		VLAM [14]	2	formants	NNA	Ep. Mem.	Different
	2014 [13]							([-1, 1] 2 )	exploration
											strategies
	Moulin-Frier	Humans	13 param.		DIVA		2	formants	Mean value	6D-vector	Active-goal
	2014 [15]							([-1, 1] 2 ),	(formants and	exploration
									intensity	intensity)	strategy
									([0, 1])
	Cohen 2018	Humans	Gesture	(3	N.A.		N.A. (identical	Caregiver	Internal goal	PerAc	[16]
	[8]			joint ang.) or			to	motor	choice	(desired	with	reward
				word (2 syll.)			space)	object)	kernels
	Teramoto	Marmoset	3	params.	Resonant		Sound	N.A.	N.A.	Weight change
	2017 [17]		([0, 1.1] 2 ,		vocal tract			influenced by
				const.)							development
											rate
	Doya	1998	Songbird	4 params.		Source-filter	Sound	N.A.	N.A.	Stochastic
	[18]						model	with	waveform	controller and
							amplifier				a critic
	Our	model	Songbird	3	params.	N.A.		N.A. (identical	Nonlinear	[0, 1] 3	Normalized
	[19]			[0.5, 1.5] 3				to	motor	auditory	Hebbian rule
									space)	response

Ep.Mem: Episodic memory of previous experience; DMP: Dynamical Movement Primitives; VLAM: Vocal Linear Articulatory Model; DIVA:Directions Into Velocities of Articulators; GMM: Gaussian Mixture Model; ELM: Extreme Learning Machine; NNA: Nearest Neighbour Algorithm; N.A.: Non Applicable scope of the present review and we cill focus on the learning architecture and motor control In Table

I

, we summarize the proerties of sensorimotor models for vocal learning in humans and animals cited throughout the review.

ACKNOWLEDGMENT

This work was supported by the Inria CORDI-S PhD fellowship grant.