M Rollin

L Penazzi

V Velay

A Dupuy

S Gallet

A New Numerical Strategy for SPF Pressure Profile Computing Based on Statistical Strain Rate Controlling

Keywords: Superplastic forming, Finite Element Modeling, Optimization, Strain Rate Distribution Nomenclature -user specific notations εopt Optimal strain rate ε crit Critical deformation

This paper investigates the designing of Superplastic Forming pressure cycles in order to propose rapid forming sequences that suit industrial strategy, and which enable the control of microstructure evolutions. An optimization algorithm using ABAQUS coupled with MATLAB has been developed in order to improve forming cycles while allowing superplasticity. The numerical strategy is based on an algorithm controlling a statistical maximum of the distribution of strain rate of nonformed elements of part mesh instead of the maximum strain rate on the whole mesh for classical optimization algorithms. The objective of this method is to exclude numerical singularities that are used for pressure controlling in traditional techniques. This paper details firstly the new algorithm and then presents numerical and experimental results for different forming conditions obtained from industrial, classical, and optimized pressure cycles. These tests were performed on Ti-6Al-4V titanium alloys.

Introduction

Superplastic forming (SPF) is a hot forming process for sheet metal. Classical SPF consists in blowing gas under pressure in to a chamber in order to form sheet metal on a mold. SPF has many advantages: it can be used to form complex shapes with a high yield rate, thin and fairly constant sheet thickness and with no significant finishing stage. However, it requires high forming temperatures, and a low strain rate compared to stamping and forging processes in general. In addition, SPF requires particular material with a specific microstructure morphology that promotes superplastic mechanisms.

The key to the SPF process is to control the pressure during forming in order to produce strain rates in a specific range that can be called the superplastic domain.

By this method, the properties of superplastic materials prevent strain localization and promote rather reasonably uniform part thickness. This domain is defined at a constant temperature as the strain rate range that allows high elongation. The domain is dependent on microstructure because the deformation mechanisms asso-ciated with superplasticity (grain boundary sliding, and the accommodation diffusional flow mechanisms) are dependent on grain size and morphology [START_REF] Alabort | On the mechanisms of superplasticity in Ti6Al4V[END_REF].

A lot of work has been done to reduce forming time over recent decades because of the necessity to improve this time-consuming process. A first axis of improvement concerns the material properties, and the objective is to move the superplastic domain. Mohamed et al. [START_REF] Mohamed | Factors influencing ductility in the superplastic Zn-22 Pct Al eutectoid[END_REF] highlighted that reducing the material grain size caused an elevation of the superplastic strain rate range. Since their study, a large body of work has been undertaken on so-called ultrafine grain microstructures, which not only increase the strain rate range, but also lower the temperature of the superplastic domain. Figueiredo et al. [START_REF] Figueiredo | Developing superplasticity in a magnesium AZ31 alloy by ECAP[END_REF] achieved a strain rate ten times higher with 0.2 µm grain size, obtained by an equal-channel angular pressing process with an aluminum alloy. Matsumoto et al. [START_REF] Matsumoto | Ti6Al4V alloy with an ultrafine-grained microstructure exhibiting low-temperaturehigh-strain-rate superplasticity[END_REF] obtained low temperature with high strain rate superplasticity on a Ti-6al-4V alloy produced by simple hot working of an α -martensite microstructure alloy. One problem of these grain size refining processes is that they are difficult to implement industrially. A second axis of improvement concerns the process conditions. The pressure is adjusted in order to form as fast as possible.

Regardless of the superplastic domain, it is important to stay inside its range to ensure the maximum elongation properties.

Finite Element modeling is widely used in the industry to define the appropriate pressure cycle. Optimization of a pressure cycle resides in controlling the pressure during forming so that the strain rate of the part stays within an acceptable range.

In this paper, only the design of the pressure cycle is studied, for a fixed temperature and initial microstructure. The author has developed a statistical approach for the evaluation of the strain rate field, and especially the maximum. The maximum strain rate is the usual value used to regulate pressure, and ultimately define a pressure cycle. The objective of using statistics is to obtain field distribution information, and therefore to exclude numerical singularities in order to obtain physical data. The author's method makes it possible to select appropriate information to improve the forming cycle. However, there are some possible consequences of increasing global strain rate during SPF. Firstly, one important problem is that strain rate sensitivity decreases when the strain rate increases. Alabort et al. [START_REF] Alabort | On the mechanisms of superplasticity in Ti6Al4V[END_REF] illustrated this phenomenon with a contour map of the strain rate sensitivity exponent m as a function of temperature and strain rate. The consequence is that thinning or necking of the part is likely to happen prematurely. Gifkins [START_REF] Gifkins | Grain-boundary sliding and its accommodation during creep and superplasticity[END_REF] investigated the interactions between grain boundary sliding and the accommodation mechanisms. The consequence of increasing strain rate is that GBS is not accommodated, resulting in void growth. Finally, dynamic grain growth is strain rate sensitive. The grain size increase disrupts the grain boundary sliding mechanisms (the main superplastic mechanism), as mentioned by Langdon [START_REF] Langdon | An Analysis of Flow Mechanisms in High Temperature Creep and Superplasticity[END_REF]. Velay et al. [START_REF] Velay | Behavior modeling and microstructural evolutions of Ti6Al4V alloy under hot forming conditions[END_REF] have shown that the grain size is significantly impacted by time exposure and strain rate conditions during superplastic deformation.

In the following sections, the different existing numerical strategies for pressure designing are summarized. Then the authors' method is presented, applied first on a standard geometry, and secondly on an industrial aircraft workpiece. The SPF of the pressure cycle obtained on the industrial part using this new method is compared to that of a "classical method". The previously cited impacts on material and geometry are analyzed in the last part of the paper.

Background

Finite Element (FE) modeling of SPF was introduced in the 1980's by Bellet [START_REF] Bellet | Modelisation numerique du formage superplastique de toles[END_REF] to address the need to improve the thickness profile, surface and mechanical properties of parts, but also to adapt the pressure profile to increase the forming rate while allowing superplasticity. Globally, pressure cycle optimization is based on two different aspects: a reference quantity to target, and a pressure algorithm to control pressure so as to form at the targeted quantity throughout the forming process. The reference quantity is usually an optimal strain rate εopt defined as the highest strain rate for which the strain rate sensitivity exponent m is superior to a critical value. Indeed, m (defined in Equation ( 1)) is a marker of superplasticity.

Woodford [START_REF] Woodford | Strain rate sensitivity as a measure of ductility[END_REF] has pointed out that for some metals, high elongation properties imply a high m value.

m = ∂ln(σ) ∂ln( ε) (1)
• Reference quantity There are different scalar quantities that can be used for forming, but the strain rate is mostly the preferred choice. Garriga-Majo [START_REF] Garriga-Majo | Optimization of the superplastic forming of a dental implant for bone augmentation using finite element simulations[END_REF] compared the strain rate, the flow stress and the energy dissipation rate as quantities to target during simulation. Their results indicated that the energy dissipation rate value gave the best results in terms of forming time, but to the detriment of surface quality. The material model can be coupled with grain size evolution and void growth, which are both major disruptive phenomena for the stability of superplastic deformation. The value of m and therefore εopt evolves throughout the forming process. Ding et al. [START_REF] Ding | On the optimization of superplastic blow-forming processes[END_REF] developed a variable strain rate path. They used the gradient of the strain rate over the sheet, which has the advantage of preserving local thinning. Nazzal et al. [START_REF] Nazzal | Finite Element Modeling and Optimization of Superplastic Forming Using Variable Strain Rate Approach[END_REF] used a variable strain rate approach (similarly to Ding et al.) to perform the SPF simulation of a rectangular box and an industrial aircraft part. They compared a constant with a variable strain rate approach and the forming time reduction was found to be significant. Chung and Cheng developed [START_REF] Chung | The analysis of instability and strain concentration during superplastic deformation[END_REF] and experimented [START_REF] Chung | Fracture criterion and forming pressure design for superplastic bulging[END_REF] a strain sensitive optimization of pressure through a so-called flow localization factor (FLF). This FLF is derived from the instability analysis of Hart [START_REF] Hart | Theory of the tensile test[END_REF],

and makes it possible to take advantage of the excellent necking resistance of superplastic materials. This method led to a considerable improvement in forming time compared to constant or even variable strain rate paths, but gave a less uniform thickness distribution in the tested case.

• Pressure algorithms Robert has summarized [START_REF] Robert | Contribution to the numerical simulation of sheet metal forming proceses -application to incremental sheet forming and superplastic forming[END_REF] three main types of algorithms. Firstly, there are the proportional corrective algorithms developed initially by Doltsinis [START_REF] St | Some developments in the numerical simulation of metal forming processes[END_REF].

They consist of a continuous function which can take account of different parameters like the control quantity, material parameters, etc. Since Doltsinis' work, a large number of increment functions have been developed with more or less complexity. For instance, Xiang et al. [START_REF] Xiang | Numerical simulation of cavity damage evolution in superplastic bulging process[END_REF] used a function of the relative difference of targeted and maximum strain rates, whereas Hwang et al. [START_REF] Hwang | Study on superplastic blow-forming of 8090 AlLi sheets in an ellip-cylindrical closed-die[END_REF] used a function of the logarithm of the ratio of both quantities. Then, Bellet [START_REF] Bellet | Modelisation numerique du formage superplastique de toles[END_REF] developed the band algorithm which consists in using different ranges of strain rate ratio values around one, where each range is linked to a constant corrective pressure factor. Finally, there are the post-treatment methods proposed by Carrino et al. [START_REF] Carrino | A posteriori optimization of the forming pressure in superplastic forming processes by the finite element method[END_REF]. The technique consists in running a simulation with a known constant pressure cycle, and then correcting the pressure by adjusting the associated maximum strain rate during forming. This type of algorithm requires two simulations, but is easy to implement.

Each improvement cited above enables forming to be completed as fast as possible, thus reducing the forming time. However, the basic principle of these numerical strategies is based on a single element among thousands of others, and sometimes more. This method would work if FE simulation could ensure that perfect continuous stress and strain rate fields were obtained, which, by definition, is not the case. Obviously this hypothesis is not the optimal one for two main reasons, namely contact solving issues and mesh singularities. Indeed, the contact algorithms can lead to stress discontinuities due to penetration and interference solving. Typically, for the passage of the sheet on a small curvature radius, these problems are frequent (Figure 1). Moreover, large deformations can lead to distorted elements, even if the initial mesh has been structured and adapted to the major strain axis. These elements regularly produce singularities in the stress field. The principle of the method developed in this paper is to free the pressure cycle optimization from these discontinuities which lead to an overestimation of the strain rate ratio and limit the forming time.

Optimization technique

There are two important aspects in this method that differ from the classical strategies presented in section 2. The first one consists in replacing the classical maximum strain rate εmax that is used in the strain rate ratio. The term to be used here will be called the maximum of the distribution of strain rate εi max . The second difference resides in the pressure incrementation. In order to be industrially feasible (and also to limit numerical iterations), the pressure is incremented considering not every increment but the integration of the strain rate distribution over a specific step time. Both aspects are detailed hereafter. Henceforth, the presented method will be called the "Strain Rate Distribution-based" (SRD) method, in opposition to the classical one, the "Local Maximum Strain Rate-based" method (LMSR).

Statistical Maximum

The solution retained to determine a maximum from the strain rate field is to model it by a Gaussian distribution. Therefore, it is possible to fix a maximum by knowing the average and the standard deviation of the strain rate field. However, the shape of the distribution does not fit a normal-centered distribution insofar as the part is formed, because more and more elements get in contact and deformed at a limited rate due to friction shear stresses. The second assumption made is to select only the elements which are not in contact for the computation of the distribution of strain rate. The selection is made by a contact pressure criterion. This is an easy way to avoid the problem and also to reduce the forming time by focusing only on the high strain rate elements. This hypothesis is valid because the key point is to stay below the optimal strain rate.

P(X < µ + 2σ) = µ+2σ -∞ 1 σ √ 2π e -1 2 ( X-µ σ ) 2 ) dX 0.98 (2)
µ = 1 N Ω k∈Ω X k (3) σ = 1 N Ω k∈Ω (X k -µ) 2 (4)
Gaussian theory says that for a population (or a set of elements) which has an associated data, 98.1 % of the elements have their data below the average data of the set of elements plus twice its standard deviation. This probability is defined in Equation ( 2) where P, µ and σ represent respectively the density probability function of X, the mean value and the standard deviation of X.

εGM = µ + 2σ (5)
Applying this technique to the strain rate field, the singular elements can be excluded or at least, their number taken in the computation of εi max will be limited. For the rest of the paper, the maximum of strain rate distribution will be called the "Gaussian Maximum" (GM) of strain rate field εGM and is defined by Equation ( 5).

Figure 2a represents the comparison of the histogram density (% el ), the associated "Normalized Probability Density Function" (NPDF) for the "Whole mesh" (Wh) and the "non-contact" (NC) set of elements Ω N C . Ω N C is defined by Equation [START_REF] Langdon | An Analysis of Flow Mechanisms in High Temperature Creep and Superplasticity[END_REF] where Ω W h , P c el , k, P i are respectively the set of all elements of the part, the contact pressure of an element, a pondering coefficient equal to 0.2 and the forming pressure. The data was taken from an increment of the SPF simulation from which Figure 1 was extracted. The NPDF data was related to the total number of elements to highlight the proportion of elements between the whole mesh and the selected elements. This figure clearly confirms a best fit of data in the case where non-contact elements are taken compared to the whole mesh at this forming stage

Ω N C = {el ∈ Ω W h | P c el > kP i } (6)
Three maximums are represented in Figure 2a, the gaussian maximums of both probability functions εWh GM and εNC GM , and the "Local Maximum" max el∈Ω W h ( εel ) (written max( εel )). εWh GM is considerably higher than the local maximum, which indicates that the Gaussian distribution is not efficient in this case. On the contrary, εNC GM is below the local maximum. Figure 2b is a zoom of Figure 2a in the high strain rates area. The % el of whole mesh set is split by εNC GM value into W h -and W h + sets to highlight the elements excluded by the method. It reveals that the elements which are excluded by this technique correspond to a small percentage of all the elements (0.67 %). Figure 2c represents these excluded elements on the part. By comparing these elements with their associated strain rate in Figure 1, it is interesting to observe that they correspond to discontinuous elements. To conclude, this method is reasonably efficient for selecting only the elements that are relevant to fit the distribution of strain rate and finally compute its maximum.

% el -Wh - % el -Wh + εNC GM (b) (c)

Pressure incrementation

As mentioned previously (in section 2), the pressure is corrected over a step and not at each increment in the simulation. For each increment that the FE software computes, the average strain rate < εel > i and the standard deviation of the distribution of strain rate s( εel ) i are computed. < εel > i and s( εel ) i are defined in equations ( 7) and [START_REF] Bellet | Modelisation numerique du formage superplastique de toles[END_REF], where εel , i and Ω i are respectively the equivalent strain rate of an element, the increment number and the set of the non-contact elements Ω N C at the increment i whose size is

N Ω i . < εel > i = 1 N Ω i el∈Ω i εel (7) s( εel ) i = 1 N Ω i el∈Ω i ( εel -< εel > i ) 2 (8)
Ω i = {el ∈ Ω W h | P c el > kP i } (9)
Then, the maximum of the distribution of strain rate of an increment εi max is computed with Equation [START_REF] Garriga-Majo | Optimization of the superplastic forming of a dental implant for bone augmentation using finite element simulations[END_REF]. Finally, the average maximum of the distribution of strain rate of a step < εi max > n is time-step integrated as defined in Equation [START_REF] Ding | On the optimization of superplastic blow-forming processes[END_REF] where t i , N and t N are respectively the time of increment i, the number of increments in step n and the time of step n.

εi max = < εel > i + 2 × s( εel ) i (10)
< εi max > n = 1 t N N i t i εi max (11)
This < εi max > n value is used in the pressure algorithm instead of the local maximum for LMSR method. The authors chose to use a band algorithm for pressure incrementation. The method is composed by three cases defined in table 1 where R, P and α are respectively the pressure algorithm ratio defined with Equation [START_REF] Nazzal | Finite Element Modeling and Optimization of Superplastic Forming Using Variable Strain Rate Approach[END_REF] for step n, the pressure and the pressure incrementation factor. The cases 1 and 3 correspond to the lower R low and upper bounds R crit for the ratio R beyond which the forming conditions of the step are considered critical. In these cases the step is restarted with a corrected pressure ramp computed with α coefficient. In the case 2, the forming conditions are considered acceptable and the pressure ramp of

CASE IF THEN 1 R n < R low P n,k+1 = α low P n 2 R low < R n < R crit P n+1 = α n P n,k 3 R n > R crit P n,k+1 = α crit P n
R n = < εi max > n εopt (12)

Implementation of the new strategy

The SRD method is implemented on the same basis as the LMSR method (as programmed in ABAQUS ) and presented in Figure 3a, where i and k are respectively the increment, the increment's iteration number and P the pressure.

However, the integration on the time step of εi max can produce an exceedance of εopt . For example, when a portion of the sheet comes into contact with the mold, the strain rate can vary considerably. Figure 4 illustrates a typical evolution of εi max , which induces an exceedance of some εi max values with an average < εi max > n below the εopt . There are three major schemes to evaluate the maximum strain rate of a step (used for pressure algorithm) from maximum of increments. The first one is to select the maximum of all increments. In this case, the problem is that the associated maximum strain rate of the increment can be influenced when high discontinuities happen during particular complex forming phase. A second solution is to apply the same statistical approach than for mesh distribution. The idea is to use the average value < εi max > n and to compute s( εi max ) with Equation ( 13) where N is the number of increments in the step. Then, the new ratio to consider for the pressure algorithm would be R n , defined in Equation ( 14), where twice the standard deviation is again introduced to avoid the problem. This strategy was tested first, Increment 𝑖 FE code : Solving of the increment

𝑃 𝑖 Increment 𝑖 + 1
Pressure algorithm

𝑃 𝑖,𝑘 𝑃 𝑖+1
Find 𝜀 𝑚𝑎𝑥 (a)

Step 𝑛 FE code: Solving of the step

Step 𝑛 + 1

Post treatment:ℛ 𝑛 , 𝒮 𝑛

s( εi max ) = 1 t N N i t i ( εi max -< εi max > n ) 2 (13)
R n = < εi max > n + 2 s( εi max ) εopt ( 14
)
The last solution consists in imposing a maximum variation of εi max beyond what the step is not considered acceptable. When this situation is met, the step is restarted with a smaller time step in order to limit large variations of strain rate distribution.

This variation of εi

max is estimated thanks to the relative standard deviation S n (Equation ( 15)). The time step is regulated as a function of S n in order to prevent the εi max variation in a step becoming too large. Table 2 defines three cases which have an effect on the time step. The values used for S low and S crit are respectively 7.5% and 15%. In the case 1, β low is equal to 3/2, and in the case 3, β crit is equal to 2/3. These values can be changed according to the geometry which influences the forming stability. The weakness of this second method is that some increments of a step can have εi max superior to εopt . The maximum possible strain rate εerr that can be allowed is defined in Equation ( 16), where R max is the maximum acceptable ratio for SRD strategy.

S n = s( εi max ) < εi max > n (15) εerr = R max × εopt (1 + 2S crit ) (16)
Sometimes, during SPF simulation there is no possibility to cross a step without getting S n inferior to S crit . When several iterations are done for a step without getting an acceptable S n value, S crit is momentarily doubled to overcome the step before returning to its initial value once the step is correctly evaluated. Equation [START_REF] St | Some developments in the numerical simulation of metal forming processes[END_REF] gives the computation of pressure as defined in the global algorithm where the pressure is computed before the time step adjustment.

CASE IF THEN 1 S n < S low t n,k+1 = β low t n,k 2 S low < S n < S crit t n+1 = t n,k 3 S n > S crit t n,k+1 = β crit t n,k
P n+1 = P n+1 -P n t n t n+1 + P n = ((α n -1)β n + 1)P n (17)
This procedure was implemented with ABAQUS FE software, MATLAB (for procedure automation) and Python scripts (for the post treatments), as described in Figure 3b. MATLAB manages the creation of step job files and the restarting from previous jobs until the fulfillment of several conditions to detect the end of the forming process. In this section, the proposed method is implemented and compared with a model that has already been used in the literature. This model is the rectangular box used by Nazzal et al. [START_REF] Nazzal | Finite Element Modeling and Optimization of Superplastic Forming Using Variable Strain Rate Approach[END_REF] to develop a variable strain rate approach. The box is 60 cm long by 40 cm wide by 20 cm deep with a 2 cm flange around it, and the sheet metal is 3.175 mm thick. A Norton Hoff power law was selected for use in material modeling (Equation ( 18)). K and m coefficients were obtained from mechanical testing characterization at forming temperature and strain rate range (K=3210, m=0.66). This model is not strain sensitive, which is in contradiction with the definition of a variable strain rate path (VSRP). However, it has been used numerically for comparison purposes. The author's method is independent of pressure algorithms, and can also be combined with other optimization techniques.

In the first step, the presented method is compared with the classical LMSR method proposed by ABAQUS , for three different schemes. The two first schemes consist in forming at a constant targeted strain rate at 10 -4 s -1 and 10 -2 s -1 , regulated on the whole mesh. The third scheme consisted in forming using the VSRP by following the element with the maximum strain. The VSRP was developed by Nazzal et al. [START_REF] Nazzal | Finite Element Modeling and Optimization of Superplastic Forming Using Variable Strain Rate Approach[END_REF], and corresponds to the stability analysis with no initial void fraction (see Figure 5). In the second step, a geometry with a smaller fillet radius (from 40 mm to 6 mm) was tested to promote hard contact conditions and numerical singularities to demonstrate the effectiveness of the method on a geometry closer to an industrial one. Both geometries are shown in Figure 6. Shell elements were used to model the mold and sheet. They were composed respectively of 423 and 445 rigid shell elements R3D4, and by 704 and 2816 deformable shell elements S4R for large and small radius fillets. A surface-to-surface contact algorithm was defined between sheet and mold using a Coulomb friction law with a 0.1 coefficient value.

Results

The pressure cycles obtained for the initial and for the second geometry are presented for each of the three schemes in Figure 7 and Figure 9. A comparison of the strain rate indicators max el∈mesh ( εel ) (written max( εel )) and εi max are presented for SRD pressure cycle simulations respectively in Figure 8 and Figure 10. The differences between LMSR and SRD pressure cycles and strain rate indicators are larger for the second geometry with the small fillet radius. Indeed, there are many discontinuities especially for the simulation with εopt = 10 -4 s -1 (Figure 10a). This confirms the efficiency of the method when contact conditions are severe.

∆ A-B = X A -X B X A (19)
Equation 19 defines for the rest of the paper the relation of relative difference of X A and X B where X B is the reference or initial value of the comparison.

Table 3 summarizes the forming times obtained with the different schemes and methods. A first conclusion is that the author's method clearly decreases the forming times without significantly increasing the pressures. A further conclusion is that the second geometry, with a small radius, gives better results in terms of forming time, especially for εopt = 10 -2 s -1 and VSRP. This is mainly due to the contact conditions that are harder in these case, and thus, promote much singularities that are excluded by the authors strategy. After post-treating the results it appears that most of the elements which overshooted during the simulation were numerical singularities, such as those presented in Figure 2c. However, some elements undergo real deformation and can be excluded by the method. In the next section, microstructure and geometrical analyses are presented to interpret the exclusion of these critical elements for the forming of an industrial part.

4. Validation of the method: Industrial workpiece

Simulation of the case

This method was applied to optimize the forming cycle of an AIRBUS A350

part. This workpiece is half of a T-duct in Ti-6Al-4V alloy (Figure 11a). The initial thickness of the blank was around 3.2 mm. A chemical milling (1.5 mm depth) was applied in the center area to generate a pocket. This enabled to promote material deformation to be facilitated in this area and limited the thinning of the sheet in the useful portion of the part. This detail is an important issue and will be discussed later to point out the limitations of certain hypotheses of this strategy.

A quarter of the part was modeled (Figure 11b). A VISCO step was used with material model described in previous section 3.4. The blank had 18741 quadrilateral shell elements with a reduced integration (S4R) and the mold had 3524 rigid quadrilateral shell elements (DS4). The contact was modeled with a "surface-to-surface" algorithm with a finite sliding approach. The Coulomb friction law was chosen with a coefficient of 0.1. In addition to the strain rate distribution based method, the classical LMSR method was computed in order to provide a reference to compare with. The results of the SRD method (which are presented later) come from a whole simulation computed with the complete pressure cycle instead of the pressure step files obtained from initial computing. As regards the CPU time issues for solving complete SPF, SRD methods spent only one and a half times more than LMSR methods ( The pressure implementation cycles obtained with the LMSR and SRD methods are presented in Figure 12. In order to remove numerical artifacts like pressure oscillation, to simplify the cycle and also to ease implementation in the press automate, the curves have been smoothed. The SRD method has greatly improved the forming time. It has been divided approximately by three compared with the forming time for LMSR simulation (from 200 to 67 min). The forming time saving is particularly high for this geometry due to the pocketing surface that lead the pressure profile for LMSR strategy. This case is very specific and enables to test the limits of the method in terms of consequences on material and geometrical specifications. Some other industrial geometries such as air inlet of reactors, and other fairing parts of the pylon were tested regarding to those two numerical strategies. The global time saving is approximately around 30 to 50 % of reduction according to geometries.

Critical deformation

The objectives of performing SPF simulation with both pressure cycles numerically obtained are to analyze the impact on the formability of the part, on the final thickness, and the microstructure. Hence, to validate the model, microstructural analysis must be carried out on sample cuts on formed parts. A critical deformation field was computed (Equation ( 20)) to target different areas to investigate. This field (Figure 13) was only computed for the SRD method because the LMSR method has no critical deformation by definition. The critical strain rate field represented in Figure 13a highlights three main areas

ε crit = ε> εopt εdt ( 20
)
ε + crit = ε> εerr εdt ( 21
) (a) (b)
where the part has deformed over the optimal strain rate:

• Zone A: the most important critical deformation can be divided into two portions. The first corresponds to the initially pocketed area of the blank (see Figure 13b, the blue zone). Logically this surface played its role and has not been taken into account by the SRD method (elements in contact with the mold). The second portion is the rest of the zone. These elements have critical strain due to the passage of a "hard" contact area of the mold with a small radius of curvature and a strong bi-directional deformation in the corner of the pocketed area.

• Zone B: this zone is also due to "hard" contact conditions

• Zone C: this zone is constituted by elements which did not follow the hard contact conditions. They are the last-formed elements.

In order to verify the impact of this computed critical deformation, six samples, called observation points, were selected, as defined in Figure 14. Point 1 has the was computed in order to evaluate the elements that were deformed in very critical strain rate conditions compared to what can be called semi-critical strain (between εopt and εerr ). Point 1 is one of the only points that was deformed in very critical conditions (Figure 13b). Point 2 corresponds to an area with mid-strain level and no critical deformation. Point 3 corresponds to a low strain level with a small critical deformation. Point 4 is included in Zone C, with high strain level and critical deformation without contact issues. Finally, point 5 is a control observation which did not undergo deformation. Points 1 and 1 are specific points only used for thickness measurements, described later.

Experimental validation

Two full-size parts were formed. One with an LMSR and the other with an SRD pressure cycle (Figure 12). Both cycles were capable of forming the parts completely.

Figure 15 shows one of the formed part. Different parameters, such as thicknesses and microstructure issues, were investigated. Samples were cut (according to Figure 14) to observe either microstructure aspects, or thickness impacts, or both.

© AIRBUS 2017 -photo by M. ROLLIN

Then, the comparison of pondered experimental thicknesses shows that there is no significant impact of the strategy for the measured points.

Point position initial

Sth 1 1 2 3 4
∆ Sth LM SR-SRD (%) 1.1 0.14 -3.04 -5.17 -2.57 formations. At SPF temperature, in Ti-6Al-4V, there are two phases, α and β, at their equilibrium content. During cooling, the temperature varies very fast and consequently α and β phase proportions also vary. Ahmed and Rack [START_REF] Ahmed | Phase transformations during cooling in α+β titanium alloys[END_REF] have shown that below the beta transus at low, moderate and high cooling rates (between 0 and 30 • C.s -1 ), the transformation of the beta phase can lead to three different transformations. The appearance of these transformations depends principally on the cooling rate. In our case, when the part is removed from the mold, there is a first sequence where the part is cooled down naturally, and also forced convections. The part is also affected by radiative heat transfers which vary along the complex geometry and, finally, the thickness of sheet is not constant. For all these reasons, the cooling rate of the part is totally heterogeneous, and not constant along the cooling sequence, which induces heterogeneous phase transformations. Therefore, simple qualitative comparisons are made hereafter concerning grain morphology, and grain size comparisons are made sample by sample.

SEM micrographs. Micrographs of samples cut on both formed parts were performed with a NOVA nanoSEM 450 Scanning Electron Microscope (Figure 16 with ×2000 magnification factor). The micrographs were performed with back scattered electron detector, at 8.0 kV beam voltage, 5.0 mm working distance with a beam deceleration mode which bring topological details of the surface. Grain growth issues. The grain size (GS) is also an important parameter of the microstructure characteristics at the end of forming, for several reasons. Indeed, aeronautical standards impose a maximum GS to respect material specifications. In addition, the GS influences the properties of the material in terms of strain hardening and yield strength. It can be clearly observed (Figure 16) that the LMSR cycle has promoted a larger grain growth than the SRD method. growth due to higher strain rates, as mentioned in section 1. However, by comparing two areas which have undergone safe and very critical deformation, respectively point 1 (ε crit =0.77, ε + crit =0.25) and point 2 (ε crit = ε + crit =0), the grain size has grown larger in the safest conditions. One explanation is that the effect of time is enhanced with the deformation, but that the weight of time is more important than strain rate at this temperature.

Conclusions

The current process used by most FE software to implement SPF pressure designing does not take account of numerical issues which influence the forming time in an upward direction. The Gaussian theory for determining the maximum strain rate, which controls pressure algorithms, is a simple way to put aside the singular elements and significantly reduces the forming time. This new strategy was applied on an industrial part and the SPF was successful. The forming time of the tested industrial workpiece which is a particular case, was reduced by 67 %. For more classical geometries the time saving is around 30-50 % according to the complexity of the geometry. The critical issues of SPF have been investigated:

• The thickness distribution is not impacted with the tested geometry.

• The grain growth is logically reduced, and heterogeneous grain growth is not enhanced due to higher strain rates. For this geometry the grain diameter is around 25% less than obtained by classical methods.

• The morphology of the grains is not impacted qualitatively, and no cavities are produced. This means that the deformation mechanisms remain superplastic. This method has allowed improvement of the process while respecting the design specifications imposed by the aeronautics industry.

Appendix

Figure 1 :

 1 Figure 1: (a) Strain rate field during SPF simulation of a part, (b) zoom on discontinuous elements

1 %

 1 s -1 ] dens. of prob.(% of el) 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 2.39.10 -3 s -1 5,68.10 -4 s -1 1.14.10 -3 s -Rate [s -1 ] dens. of prob.(% el ) 5,68.10 -4 s -1

Figure 2 :

 2 Figure 2: illustration of statistical strain rate controlling -(a) Distribution, normal probability function and maximums of Strain rate field for both Wh and NC sets of elements at Figure 1 increment, (b) zoom of (a) graph around εNC GM value and c) representation of excluded elements on part mesh

Figure 3 :(Figure 4 :

 34 Figure 3: Logigrams of pressure algorithms implementation of: (a) classical LMSR method and (b) SRD method

3. 4 .

 4 Numerical Validation: Rectangular box 3.4.1. Model

1 ]Figure 5 :Figure 6 :

 156 Figure5: Variable optimal strain rate path with no initial void fraction[START_REF] Nazzal | Finite Element Modeling and Optimization of Superplastic Forming Using Variable Strain Rate Approach[END_REF]

Figure 7 :

 7 Figure 7: Comparison of pressure cycles obtained with LMSR (solid line) and SRD (dashed line) method (a) εopt = 10 -4 s -1 , b) εopt = 10 -2 s -1 and c) VSRP) with large fillet radius geometry

Figure 8 :

 8 Figure 8: Evolution of strain rate indicators during forming of large fillet radius with a) εopt = 10 -4 s -1 , b) εopt = 10 -2 s -1 and c) VSRP

Figure 9 :Figure 10 :

 910 Figure 9: Comparison of pressure cycles obtained with LMSR (solid line) and SRD (dashed line) method (a) εopt = 10 -4 s -1 , b) εopt = 10 -2 s -1 and c) VSRP) with small fillet radius geometry

Figure 11 :

 11 Figure 11: Representation of (a) The mold meshed and (b) the 3D CAD of final part after trimming

Figure 12 :

 12 Figure 12: Comparison of pressure cycles obtained by LMSR and SRD based optimization methods

Figure 13 :

 13 Figure 13: Iso-values of (a) critical deformation ε crit with marked areas and (b) very critical deformation ε + crit

Figure 14 :

 14 Figure 14: Location on the part of observation points

Figure 15 :

 15 Figure 15: View of a workpiece after forming

Figure 16 :

 16 Figure 16: Micrographs of observation points defined in Figure 14 at x2000 magnification for LMSR and SRD methods

CASE IF THEN 1 R 15 3 1 . 15 < 1 . 3 < 5 3

 115115135 n < 0.5P n,k+1 = 2P n,k 1 0.5 < R n < 0.7 P n,k+1 = 1.5P n,k 1 0.7 < R n < 0.85 P n,k+1 = 1.25P n,k 2 0.85 < R n < 0.95 P n+1 = 1.15P n,k 2 0.95 < R n < 1.05 P n+1 = P n,k 3 1.05 < R n < 1.15 P n,k+1 = P n,k /1.R n < 1.3 P n,k+1 = P n,k /1.25 3 R n < 1.5 P n,k+1 = P n,k /1.R n > 1.5 P n,k+1 = P n,k /2

Table 1 :

 1 Pressure regulation table -definition of casesthe next step is computed with α n pressure incrementation factor. The values used for pressure regulation are given table 9 in section 6. However, any other pressure algorithm can be implemented.

Table 2 :

 2 Time step regulation table

  -4 s -1 10 -2 s -1 VSRP

	LMSR (s)	19551	183	1620	30479	318	4100
	SRD (s)	14619	165	1557	19070	215	2849
	∆t LM SR-SRD (%)	25	15	4	37	32	31
			Large Radius			Small Radius

Table 3 :

 3 Comparison of Forming Times

Table 4

 4

	).

Table 4 :

 4 Comparison of numerical solving time for both methods

	Normalized Pressure [bars]	0 0.25 0.5 0.75 1	0	25	50	75	100	125	150	175 LMSR raw LMSR smooth SRD raw SRD smooth	200
							Time [min]

Table 5

 5

	presents

Table 5 :

 5 Comparisons of thicknesses of simulation and measurement at some observation pointsFirstly, when comparing the experimentation with the simulation, it is clear that for Point 1 the thicknesses of the model are more than ten percent lower than experiment for both strategies while all other points have higher thicknesses with the model. This phenomenon can have different origins. One can be the strain rate sensitivity used in the material model. It may not reproduce precisely enough the behavior and a dependency to strain rate could probably improve the results. An other reason can be the pocketing operation that would have not been performed at the tolerance, which has conducted to a limitation of material flow in this region and affected the rest of the part. Table 5 gives the relative thickness differences for experimentation that were pondered by the ratio of nominal (Sth 0 =3.2 mm) and experimental initial thicknesses (Sth LM SR IN I =3.27 mm and Sth SRD IN I =3.27 mm) as defined by Equation 22.

	Sth	Exp	= Sth Exp ×	Sth 0 Sth IN I

Table 6 :

 6 Relative differences of thickness measurements pondered by initial value between LMSR

	and SRD forming strategies at some observation points
	4.3.2. Microstructure evolution
	Microstructure analysis issues. Before analyzing the microstructure of samples cut
	from the formed part, it is important to understand the phase transformation mech-
	anisms that occur during cooling, and what parameters can influence these trans-

Table 7

 7

	summarizes thickness,

Table 7 :

 7 Thickness, critical strain and total strain at observation points

  Table8summarizes these differences. The measurement method consisted in measuring the primary alpha grain diameter. The measurement was taken repeatably with an average relative standard deviation of 18.4 % (between 11% and 31%) with a minimum of twentyfive measurements per micrograph. The average grain size difference of the observed points is 25%. It is complex to dissociate the effect of static and dynamic grain

	Point	1	2	3	4	5
	d LM SR (µm)	8.28 8.32 8.26 7.94 6.76
	d SRD (µm)	5.70 6.41 6.14 6.32 5.10
	∆d LM SR-SRD (%) 31.1 22.9 25.7 20.4 24.5

Table 8 :

 8 Relative grain size difference at some observation points

Table 9 :

 9 Pressure regulation table -data

Acknowledgments

The authors acknowledge AIRBUS Company for its financial support and the AUROCK Company where the forming experiments were performed. The authors are deeply grateful to Serge Tovar from Mines-Albi & Institut Clément Ader for SEM analyses and the discussions regarding the microstructural aspects.


Maxime Rollin
email: maxime.rollin@mines-albi.fr

Vincent Velay
email: bvincent.velay@mines-albi.fr

Luc Penazzi
email: cluc.penazzi@mines-albi.fr

Thomas Pottier
email: dthomas.pottier@mines-albi.fr

Thierry Sentenac
email: thierry.sentenac@mines-albi.fr

Laura Iranzo-Perez
email: flaura.iranzo-perez@mines-albi.fr

𝑓 Alain Dupuy
email: galain.a.dupuy@airbus.com

𝑔 Gaël Khelifati
email: hgael.khelifati@airbus.com

Luc 𝑏

Penazzi

Thomas 𝑐

Pottier

Thierry 𝑑

Sentenac

Laura 𝑒

Iranzo-Perez

Thermo-Mechanical Modeling of Distortions Promoted during Cooling of Ti-6Al-4V Part Produced by Superplastic Forming

Keywords: Superplastic forming, Part Cooling, thermo-mechanical loadings, Residual stresses, Finite Element

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

SPF of parts at AIRBUS is carried out with different titanium alloys. The alloy considered in this paper is the Ti-6Al-4V. Its superplastic properties are well known [START_REF] Ghosh | Mechanical behavior and hardening characteristics of a superplastic Ti-6AI-4V alloy[END_REF], [START_REF] Semiatin | Hot workability of titanium and titanium aluminide alloys -an overview[END_REF]. Indeed, many researcher have highlighted the fact that for couples of temperature and strain rates, associated with an equiaxed grain microstructure, the Ti-6Al-4V provides a very high elongation. This significant deformation occurs due to the superplastic deformation mechanisms of the grain boundary sliding and accommodation thereof [START_REF] Bellet | Modelisation numerique du formage superplastique de toles[END_REF]- [START_REF] Babu | Physically Based Model for Plasticity and Creep of Ti6Al4V[END_REF]. These superplastic deformation mechanisms enables to maintain a stability of the microstructure during deformation. Therefore, SPF parts preserve good properties after forming, in particular for fatigue strength.

In order to increase production rates, the parts are cooled after forming. The cooling is performed inside the press by gas jet through nozzle covering the whole surface of the part. They are cooled up to a temperature low enough so as to extract the part without deforming the latter during the operation. Once extracted from the mold, it is then cooled to ambient temperature. To cool by gas jet induces inhomogeneous thermal stresses distributed on the surface of the workpiece, which moreover, have an inhomogeneous thickness distribution. The combination of these two phenomena causes the occurrence of plastic deformation and residual stresses, which produces improper final geometry once released after clipping the useful piece,.

In addition to these thermomechanical phenomena, there are also microstructure evolutions during cooling. The order of magnitude of gas jet cooling rates can promote metastable transformation of beta phase during cooling [START_REF] Kubiak | Development of the microstructure and fatigue strength of two phase titanium alloys in the processes of forging and heat treatment[END_REF].The Widmanstätten morphology of these microstructures has higher mechanical properties than classical lamellae morphology obtained by slow cooling [START_REF] Semiatin | Hot workability of titanium and titanium aluminide alloys -an overview[END_REF].

The purpose of this study is to model the different stages of the production process of these parts in order to try to reproduce the influence of cooling strategy on their final geometry. The simulation has been made on Abaqus ® finite element software. In this model, microstructure evolution phenomena related to fast temperature changes cited just above are not taken into account. Only the deformation phenomena related to the thermal stresses on the geometry of the workpiece and the evolution of yield stress as a function of temperature were taken into account.

Model Description.

This paper presents the modeling of forming, cooling and clipping operations of an air inlet part of A320 AIRBUS plane. The geometry of this part is represented in Figure 1.a through the mold geometry, and in Figure 1 The geometry of mold has been discredited with R3D4 discrete rigid elements. The SPF part has been respectively discredited with DS4 Heat transfer elements and S4R deformable shell element [START_REF] Simulia | Abaqus/Standard Users Manual[END_REF]. The different steps of the numerical procedure are defined in the next paragraph.

Multi-step modeling. The different steps included in this model are the SPF, the cooling and the clipping of the part:

 SPF step:
The forming step is modeled with Abaqus/Standard Visco step [START_REF] Simulia | Abaqus/Standard Users Manual[END_REF]. This integration procedure is used to obtain a transient static response in an analysis with time-dependent material behavior. The pressure cycle is computed during the simulation so that to respect a maximum plastic strain rate.

The SPF modeling is made separately and only the thickness field is transferred to the cooling simulation. This reduction comes from the hypothesis that the residual stress field at the end of forming is almost null [START_REF]Superplastic Forming of Advanced Metallic Materials[END_REF], and that there is no hardening or microstructure evolution into the material model, only the geometry has to be transferred to cooling step modeling. A schematic of numerical procedure is represented Figure 2. Material model. The material behavior of Ti-6Al-4V titanium alloy is particularly difficult to model as it have numerous deformation modes on the temperature and strain rate range on our process. Yet, it is possible to split the problem into two different phases in matter of material behavior: the superplastic forming part, and the cooling.

 SPF step Bellet has shown [START_REF] Bellet | Modelisation numerique du formage superplastique de toles[END_REF] that a viscoplastic power law as Norton Hoff law (see Equation 1) enables to model SPF, where 𝜎 0 is the yield stress, 𝐾 the consistency of material and 𝜀̅ ̇𝑝𝑙 the equivalent plastic strain rate. Semiatin & al. and Gosh & Hamilton have shown [START_REF] Ghosh | Mechanical behavior and hardening characteristics of a superplastic Ti-6AI-4V alloy[END_REF], [START_REF] Semiatin | Hot workability of titanium and titanium aluminide alloys -an overview[END_REF] that the strain rate sensitivity parameter m of Ti-6Al-4V is dependent on temperature T, plastic strain 𝜀, plastic strain rate 𝜀ṗ 𝑙 and grain size d. The process of forming at AIRBUS is made for particular small range of temperature and strain rate, during what, both parameters are targeted on optimal values. Moreover, SPF parts do not exceed fifty percent of deformation. In these conditions, the hypothesis has been made that the strain rate sensitivity parameter m remains constant during forming.

𝜎 0 = 𝐾𝜀̅ ̇𝑝𝑙 𝑚 (1) 𝑚 = 𝜕ln (𝜎 0 ) 𝜕ln (𝜀ṗ 𝑙 ) (2)
 Cooling and Clipping step During cooling, the evolution of temperature mainly influences the deformation mechanisms. The strain and strain rate are very low because they are promoted by expansion. The order of magnitude of maximum strain rate under maximum cooling rate undergone is about 𝜀=10 -5 𝑠 -1 . That is why in a first approximation, an elastic perfectly plastic model evolving with temperature has been chosen.

Thermal loadings.

There is different kind of heat transfer during the three steps of cooling. There are schematically described Figure 4.The different boundary equations of conduction, radiation and convection heat transfers are respectively presented in Equation 3-5, where T is the temperature of the part at the boundary, k is the conductivity of the material, 𝜙 𝑐𝑜𝑛𝑑 , 𝜙 𝑟𝑎𝑑 and 𝜙 𝑐𝑜𝑛𝑣 are respectively the conduction, the radiation and the convection flux, 𝜆 is the thermal conductance (or the inverse of the thermal contact resistance), 𝑇 𝑚𝑜𝑙𝑑 is the mold temperature, 𝜖 is the emissivity of the part, 𝜎 𝑟 the Stephan Boltzmann constant, 𝑇 𝑙𝑖𝑚 is the limit temperature for radiation, h the convection coefficient and 𝑇 𝑔𝑎𝑠 is the temperature of gas.

 Press opening: At the beginning of this step, the system is considered at a constant temperature of SPF. There are conduction convection and radiation heat transfers. The limit temperatures 𝑇 𝑚𝑜𝑙𝑑 , 𝑇 𝑙𝑖𝑚 and 𝑇 𝑎𝑖𝑟 of these equations evolve during the step.  Gas jet cooling There are also conduction and radiation (with different limit temperatures than the previous step). Concerning convection, the definition of h coefficient is not uniform, and the limit temperature is constant at gas blown temperature. Mohanty & Tawfek have established [START_REF]Convective Heat Transfer[END_REF] Equation 6 the evolution of h in the case of heat transfer due to a round jet impinging on a flat surface, where r is the radius around the projected center of a nozzle vertically on the surface of the part, ℎ 0 , ℎ 𝑠𝑓 and k are constants. ℎ 𝑠𝑓 represents the "semi-forced" convection promoted by gas flows around nozzles. This model has been characterized in the process conditions.

 Ambient cooling Convection and radiation occur with limits temperatures equal to ambient temperatures.

𝑘∇𝑇 = 𝜙 𝑐𝑜𝑛𝑑 = 𝜆(𝑇 𝑚𝑜𝑙𝑑 -𝑇) (3)
𝑘∇𝑇 = 𝜙 𝑟𝑎𝑑 = 𝜖𝜎 𝑟 (𝑇 𝑙𝑖𝑚 4 -𝑇 4 ) (4)
𝑘∇𝑇 = 𝜙 𝑐𝑜𝑛𝑣 = ℎ(𝑇 𝑔𝑎𝑠 -𝑇) (5)
ℎ(𝑟) = (ℎ 0 -ℎ 𝑠𝑓 ). 𝑒 -𝑘.𝑟 2 + ℎ 𝑠𝑓 [START_REF] Kubiak | Development of the microstructure and fatigue strength of two phase titanium alloys in the processes of forging and heat treatment[END_REF] Model parameters. The parameters that have been used for the different models described above are presented in Table 1 andTable 2

Results

Cooling strategies. Three distinct strategies of cooling have been tested in the model, in order to test the impact of temperature distribution and its evolution during cooling. The temperatures or heat transfers imposed to the part are not all industrially workable and/or used, but they are a mean to understand how does the temperature evolution is important.  "Free" cooling: this strategy consists in letting the part cooling down slowly on the mold up to ambient temperature at the exterior of the press (in "ambient cooling" thermal loadings condition with conduction to the mold whose temperature decrease linearly to ambient).

 "Homogeneous" cooling: this strategy consists in applying the thermal loadings described above, but replacing the forced convection coefficient defined by Equation 6with a constant uniform value ℎ 0 . This forced convection has been applied on the whole surface of the part.  "Exterior" cooling: this strategy consists in applying the thermal loadings described above.

The position of gas jet nozzles is represented on Figure 5. The exterior and homogeneous strategies are rather closed, except concerning the location of forced cooling. On the contrary, the free cooling strategy does not contain force cooling, and the mold and lower surface of the part are in contact all along cooling. The Figure 7-a shows firstly that the distortions are not the same according to the different cooling strategies. Secondly, the results for each strategies are far from mold geometry (more than 8 mm on average), what is not as far in reality (whatever the cooling strategy). The Figure 7-b still shows that there is a large difference of impact on distortions between "free" and "homogeneous" cooling strategies. On the contrary, the "exterior" and "homogeneous" cooling strategies have almost no differences.

Conclusions.

A numerical procedure for modeling forming, cooling and clipping operations of SPF part manufacturing has been established. Several strong hypotheses like material behavior but also boundary conditions have been made. These hypotheses lead to acceptable results, but not consistent with reality. The previous results expose several issues on this numerical model:  The fact the two strategies of forced convection give approximately the same results says that either the gradients of temperature in the part have no impact in comparison of the geometry of the part that imposes the deformation through its expansion and the boundary conditions; or, the boundary condition of clamping of the part at the border over constrains the part whereas in reality the frame on which the part is attached deforms.  The non-sensitivity of material model to strain rate (indirectly to cooling rate) could be also a reason of results commented just above.  The comparison of homogeneous forced convection with complete free cooling shows that inside the complexity of the problem, the mold conduction phenomena (related to gradient of temperature in the thickness of part) have an impact on distortions.

Outcomes. Some improvements have to be done to enable better results. The material needs to be strain rate sensitive in order to transcribe the cooling rate effects on material. Moreover, the frame on which the part is attached need to be modeled to see how it supports the part loading and it limits part deformations. An important characterization needs to be done for every model parameters coming from hypotheses (like friction coefficient, emissivity, etc.). Once the model will behave consistently with AIRBUS process, some cooling experiments on SPF presses will be made to compare and fit the model with the reality.

Figure 1

 1 Figure 1 : a) CAO representation of the SPF mold (partial representation of the part for confidentiality issues); b) CAO of the final part obtain after clipping

Figure 2 :

 2 Figure 2: Schematics of multi-step modeling procedure  COOLING step: The cooling is divided in four different steps defined in Figure 3. The opening of the press corresponds to the heat transfers that happened during the opening of the press and the insertion of the extraction/cooling manipulator inside. The gas jet cooling corresponds to the activation of gas blowing. After a certain time, the extraction step is triggered. The extraction system takes the part out of the mold thanks to a frame on which the part is clamped (schematically represented on Figure 1.a by red lines). After extracting the part, it is cooled at ambient temperature up to complete cooling. In the model presented here, the extraction step has been suppressed. The part passes from gas jet cooling to ambient cooling without the transient step between both.

Figure 3 :

 3 Figure 3: Schematics of cooling procedure  CLIPPING operation The clipping operation is made by laser cutting. In the simulation it is virtually made by element removing in a static stress-displacement analysis. It excludes local phenomena during laser cutting.

Figure 4 :

 4 Figure 4: Description of heat transfer during a) The opening of the press, b) The gas jet cooling, c) the Ambient cooling, d) Caption

Figure 5 :Figure 6 :Figure 7 :

 567 Figure 5: Schematic representation of nozzle impingement area (blue area) for "Exterior" coolingImpact of cooling strategy. The easiest way to measure the impact of cooling strategy on final distortions is to quantify the distortions themselves. The deformed meshes after clipping of the different cooling strategies presented previously have been superposed in Figure6-a. The Figure6b represents a cutting view on the node belonging to mold that has been used to superpose the deformed meshes. Indeed the final meshes before clipping have not been deformed the same way, and geometry to be clipped has undergone rotations and translations in addition of inelastic deformations. a) b)

Table 1

 1 .

	Material Parameter				Thermal parameters
	K	m		𝜆		𝜖	ℎ		ℎ 0		ℎ 𝑠𝑓		𝑘
	(MPa)			(𝑊. 𝑚𝑚 -2 . 𝐾 -1 )		(𝑊. 𝑚𝑚 -2 . 𝐾 -1 )	(𝑊. 𝑚𝑚 -2 . 𝐾 -1 )	(𝑊. 𝑚𝑚 -2 . 𝐾 -1 )	(𝑚𝑚 -2 )
	3000	0.75		* 1		* 1	0.02 [9]	0.2* 2		0.05* 2	1. 10 -4 * 2
		: material and thermal models parameters; * 1 : confidential data,* 2 : Forced cooling measurement
	T (°C)	25	100	200	300	400	500	600	700	750	800	850	900
	𝜎 0 (MPa) 950	930	900	850	800	700	500	200	90	45	20	10

Table 2

 2

	: evolution of yield stress as a function of temperature (Cooling material model); extrapolation of data from
	internal and external sources [10], [11]


A S Al-Kindi
email: laure.carassou@irstea.fr

Preliminary assessment of the trophic structure of demersal fish community in the Sea of Oman

Keywords: Sea of Oman, fish diet, stomach contents, stable isotopes, ecosystem-based management

Detailed knowledge on the trophic ecology of marine species is an essential asset for the development of appropriate ecosystem-based management of marine fisheries. In the Sea of Oman, no studies to date have addressed the diet of demersal fish inhabiting soft-bottom habitats, despite the importance of these habitats for local fisheries. This study provides a preliminary investigation of feeding strategies displayed by demersal fish communities at two seasons in the Sea of Oman, Muscat waters, based on stomach content and dorsal muscle δ 15 N, δ 13 C and δ 34 S analyses. A total of 46 fishes from 15 species, 14 families and 7 orders were collected in December 2013 and March 2014. All species displayed a carnivorous diet, with variable contributions of invertebrate and fish prey. While stomach content data suggested that Fistularia petimba (Fistulariidae), Saurida tumbil (Synodontidae) and Ulua mentalis (Carangidae) were mostly piscivorous, their δ 15 N values strongly overlapped with other species found to feed mostly on invertebrates, suggesting a mixed fish-invertebrate feeding on a longer time scale. No significant variations were found between months in terms of mean isotopic values, but larger range values and variances were observed for δ 13 C and δ 34 S in December, possibly indicating the consumption of food resources from more diverse mixture and origin during that month. Only δ 15 N was weakly but significantly related to fish size at the community level, suggesting a poor size-related structuration of the demersal fish community at the spatial and temporal scale examined, consistent with other studies in the study area. However, the low number of samples analyzed limited the scope of our conclusions, and further investigations based on stable isotope methodology are needed to obtain essential biological knowledge for ecosystem-based management of fisheries in the Sea of Oman.

Introduction

The importance of ecosystem-based approaches to fisheries research and management is now increasingly recognized on a global scale [START_REF] Pauly | Towards sustainability in world fisheries[END_REF]Gorospe et al., 2016).

Such approaches indeed allow the incorporation of biological traits characterizing species targeted by fisheries, as well as their interactions with non-commercial species, including their prey and predators, and their environment (Starr et al., 2010;Fogarty, 2013). In particular, understanding the trophic strategies of fishes (who eats what, where and when) remains a vast working challenge for biologists. For example, when consulting the latest available inventories from Fishbase (Froese and Pauly, 2017), among the total 33,600 species recorded in the database (as for July 25 th 2017), information on 'diet' only encompass 2,281 localized records, and information on 'food items' 8,320 records. This means a lot still needs to be done by biologists in order to fully comprehend the complexity of fish trophic strategies, essential information for management policy guidance considering the basal feeding requirements of targeted fish species within their ecosystem of interest. Information on fish diet is particularly scarce in the Arabian Gulf and Sea of Oman, despite the peculiarity of this region in terms of diversity of marine habitats, oceanographic conditions and marine biodiversity (Rastgoo and Navarro, 2017).

Among the techniques used to study fish trophic strategies, stomach contents have been traditionally employed for decades [START_REF] Hyslop | Stomach contents analysis -a review of methods and their application[END_REF]Cortés, 1997). Although relatively simple to implement, stomach content analyses however present the disadvantage of providing only very recent dietary information, i.e., only prey ingested just prior fish capture can be identified in fish stomachs [START_REF] Hyslop | Stomach contents analysis -a review of methods and their application[END_REF]Cortés, 1997). Moreover, some prey can be ingested without being assimilated by a consumer, resulting in biased estimations of prey contributions (Cortés, 1997). Prey with soft bodies is also likely to be more quickly digested than prey with hard structures, such as shelves or carapaces, resulting in over-or underestimation of prey importance in fish diet. Finally, diet quantification from stomach content analyses requires a large number of samples to be analyzed due to the high variability characterizing stomach fullness and content in most fish species (Cortés, 1997).

Stable isotopes have more recently emerged as a promising complementary methodology to address fish dietary ecology (e.g., [START_REF] Carassou | Assessment of fish trophic status and relationships by stable isotope data in the coral reef lagoon of New Caledonia, southwest Pacific[END_REF]Gning et al., 2010;França et al., 2011;Davis et al., 2012;[START_REF] Carassou | Trophic dynamics of the Cape stumpnose (Rhabdosargus holubi, Sparidae) across three adjacent aquatic habitats[END_REF]. Stable isotopes can be used as natural tracers of the sources of food assimilated by a consumer, relying on the principle that the isotopic composition of the food is reflected in the consumer tissues after some period of time ranging from weeks to months depending on species, environmental conditions and Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008 consumer growth patterns [START_REF] Bosley | Estimating turnover rates of carbon and nitrogen in recently metamorphosed winter flounder Pseudopleuronectes americanus with stable isotopes[END_REF][START_REF] Buchheister | Turnover and fractionation of carbon and nitrogen stable isotopes in tissues of a migratory coastal predator, summer flounder (Paralichthys dentatus)[END_REF]. In this context, stable isotopes of carbon ( 13 C/ 12 C, or δ 13 C) and nitrogen ( 15 N/ 14 N, or δ 15 N) are the most often measured in food web studies (Hobson, 1999;Post, 2002). The combination of stomach content with δ 13 C and δ 15 N analyses is now recognized as a pertinent methodology in order to quantify fish diet and address its spatial and temporal variability in a given ecosystem (Hamidan et al., 2016;[START_REF] Keller | Combined stomach content and δ 13 C/δ 15 N analyses of oilfish, escolar, snake mackerel and lancetfish in the western North Atlantic[END_REF][START_REF] Malek | Trophic structure of a coastal fish community determined with diet and stable isotope analyses[END_REF][START_REF] Olson | Feeding ecology and prey resource partitioning of lenok (Brachymystax lenok) and Baikal grayling (Thymallus arcticus baicalensis) in the Eg and Uur rivers, Mongolia[END_REF]Weidner et al., 2017). In addition to carbon and nitrogen isotopic ratios, sulfur isotopes are also useful to trace the origin of the prey consumed by consumers in aquatic ecosystems [START_REF] Peterson | Stable isotopes as tracers of organic matter input and transfer in benthic food webs: a review[END_REF]Post, 2002;Fry and Chumchal, 2011). The relative composition of 34 S/ 33 S (δ 34 S) in fish muscles, in particular, provides additional information to carbon and nitrogen isotopic ratios to unravel the identity and origin of basal resources used by mobile consumers, in particular prey origin, i.e., benthic or pelagic, as well as the diversity of potential resources constitutive of a consumer's diet [START_REF] Peterson | Stable isotopes as tracers of organic matter input and transfer in benthic food webs: a review[END_REF]Connolly et al., 2004;[START_REF] Jardine | Fish mediate high food web connectivity in the lower reaches of a tropical floodplain river[END_REF]Colborne et al., 2016;[START_REF] Morkūnė | Food sources of wintering piscivorous waterbirds in coastal waters: a triple stable isotope approach for the southeastern Baltic Sea[END_REF].

Only few published studies used stable isotopes to investigate wild fish diets in coastal waters of the Sultanate of Oman [START_REF] Al-Reasi | Evaluating mercury biomagnification in fish from a tropical marine environment using stable isotopes (δ 13 C and δ 15 N)[END_REF][START_REF] Al-Habsi | δ 13 C and δ 15 N elucidation of size-structured food webs in a Western Arabian Sea demersal trawl assemblage[END_REF][START_REF] Mill | Stable isotope data as reef food-web descriptors in a dynamic tropical environment[END_REF][START_REF] Mill | Explaining isotope trophic-step fractionation: why herbivorous fish are different[END_REF]. For example, [START_REF] Al-Habsi | δ 13 C and δ 15 N elucidation of size-structured food webs in a Western Arabian Sea demersal trawl assemblage[END_REF] used carbon and nitrogen isotopic ratios to investigate a potential size-structuration of demersal food webs in the coastal area of the Arabian Sea (located on the south of the country). The same stable isotopes were used to analyze the trophodynamics of coral reef communities from the Arabian Sea and the Sea of Oman (located on the northwest of the country), the two sites being characterized by contrasted influences of regional upwelling [START_REF] Mill | Stable isotope data as reef food-web descriptors in a dynamic tropical environment[END_REF]. The later study [START_REF] Mill | Stable isotope data as reef food-web descriptors in a dynamic tropical environment[END_REF] focused on fish species associated with reef habitats, using many δ 13 C and δ 15 N observations and additional δ 34 S on a restricted number of species, in an attempt to understand reef fishes' reliance on a variety of basal food resources on the reefs, and the influence of upwelling events on their trophic structure. The trophic structure of demersal fish communities in nonreef habitats from the Sea of Oman has never been studied using stable isotope analyses. In the present study, we therefore provide a preliminary analysis of stomach content, δ 13 C, δ 15 N and δ 34 S data to investigate the trophic structure of demersal fish assemblages collected by trawling in soft-bottom Muscat coastal waters.

Material and Methods

Sampling site and methods

Author-produced version of the article published in 1). As fish samples were collected opportunistically in an educational context, potential food resources consumed by fish could not be sampled. Our analysis was therefore restricted to a preliminary description of the overall trophic structure of fish consumers, with no analysis of their relationship with primary producers or any other group of fauna. Each trip consisted in one-day fishing event, with all trips undertaken at similar location. The fishing gear was a bottom trawl characterized by a 30 m 2 opening, with a 12 cm mesh size in the wings and 6 cm mesh size in the bag. A total of 2 to 3 tows were performed at each sampling period. The trawl was towed at day-time during 30 minutes at a speed of about 2 knots. After each tow, fish species were sorted out on the boat and one to six specimens (depending on their availability) of different size for each species were placed on ice and immediately transported back to the laboratory.

Laboratory work

In the laboratory, all fish samples were measured as standard length (cm), except for Aetomylaeus nichofii (banded eagle-ray) for which maximum wing width was measured.

Stomachs of all fishes were removed and preserved in 5 % formaldehyde (Sigma, USA) for

Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

48 hours, before being transferred to 70 % ethanol (Sigma, USA). Stomachs were later cut open and poured in a Petri dish (Bio-rad, USA). Fullness of stomachs were visually estimated (in %) during dissection. Prey were identified to coarse taxonomic categories under a dissecting microscope. The relative abundance of prey categories was quantified by visually estimating the proportion (in %) of different prey items relative to the total space occupied by the total stomach content in the Petri dish.

Samples for stable isotope analyses were prepared for one to three fish per species (replication depending on samples availability; Table 1). For each fish, one piece of dorsal muscle was dissected out, placed in an individual aluminum folder and frozen at -80 °C for further storage. Then, fish muscle samples were defrosted and dried in an oven at 50 °C for 48 hours, before grinding with an ethanol-cleaned mortar and pestle. Samples of dried homogenized muscle powder were finally placed in tin capsules for stable isotope analysis performed at UC Davis Stable Isotope Facility laboratory (http://stableisotopefacility.ucdavis.edu/). One mg of the fish dry sample was used for δ 13 C and δ 15 N, while 3 mg of the sample was used for δ 34 S analyses. Lipids were not removed from our samples prior to analysis to avoid any protocol discrepancy among species and reduce δ 13 C, δ 15 C and δ 34 S dispersion (Post et al., 2007).

Measurement of dual 13 C: 12 C and 15 N: 14 N ratios in the samples was performed using a PDZ Europa ANCA-GSL elemental analyzer interfaced to a PDZ Europa 20-20 isotope ratio mass spectrometer ([IRMS] Sercon Ltd., Cheshire UK). Measurements of 34 S: 33 S were performed using an Elementar vario ISOTOPE cube interfaced to a SerCon 20-22 IRMS (Sercon Ltd., Cheshire UK). δ 13 C, δ 15 N and δ 34 S values were expressed relative to the international standards of Vienna PeeDee Belemnite, atmospheric N 2 and Vienna-Canyon Diablo Troilite, respectively. Multipoint calibrations were done based on commercial standards IAEA-N1, N2 and N3 and USGS 40 and 41 for δ 13 C and δ 15 N, and IAEA-S1, S2

and S3 for δ 34 S. The experimental precision was calculated as the mean of standard deviations for within-run internal standards replicates for each analysis: ± 0.09 for δ 13 C, ± 0.08 for δ 15 N and ± 0.22 for δ 34 S.

Data analysis

The occurrence (in %) of different prey items into fishes' non-empty stomachs was averaged across sampling periods for each species, allowing to characterize their general feeding regime. (ANOVA) was then used to test for significant differences (P<0.05) between seasons in mean δ 13 C, δ 15 N and δ 34 S (all species combined, d.f. = 1). The overall δ 13 C and δ 34 S variation range (i.e., maximum -minimum value) and variance characterizing fish communities at different periods were used to illustrate the global trophic niche utilized by the demersal fish community over time, i.e., the overall diversity of food resources used by fishes and their relative origins (benthic vs. pelagic, coastal vs. oceanic). The overall δ 15 N range values and variance were also calculated to infer the diversity of trophic levels potentially represented in the demersal fish community at the two sampling periods, assuming that different positions in the food web would result in a difference of at least 3.4 ‰ between two trophic levels (Post, 2002;Post et al., 2007). Additionally, the relationship between community-level fish size (all species combined) and δ 13 C, δ 15 N and δ 34 S were examined to test for a possible size structuration of trophic relationships within the demersal fish community, such as investigated in [START_REF] Al-Habsi | δ 13 C and δ 15 N elucidation of size-structured food webs in a Western Arabian Sea demersal trawl assemblage[END_REF]. Those relationships were tested using linear regression models, and considered significant if P < 0.05. The banded eagle ray Aetomylaeus nichofii was excluded from size vs. isotope ratios analyses as its size measurement method differed from other fish species.

Results

A total of 46 fish specimens representing 15 different species and 7 orders were collected over the two sampling periods (Table 1). This included 26 fish samples from 9 species in March 2014, 20 fish samples from 12 species in December 2014, and 6 species collected during both periods. Overall size range of the fish community was 7.5 to 55.0 cm SL (excluding the banded eagle ray Aetomylaeus nichofii) (Table 1). Among the 46 fish dissected for stomach content analyses, 12 (26 %) had empty stomachs, including two species for which only one specimen was collected, resulting in no available data for diet analysis. A total of 29 individual fish could be analyzed for dual carbon and nitrogen isotopes, and 27 for sulfur isotopes (Table 1).

All 13 species for which prey could be observed in the stomachs were characterized by a clear carnivorous diet, with variable contributions of fish and invertebrate prey (Table 2).

Only Fistularia petimba (species 15) had consumed exclusively fish prey, but fish prey were also observed in all stomachs of Saurida tumbil (species 1) and Ulua mentalis (species 4), and in one third (33 %) of the stomachs of Nemipterus bipunctatus (species 8) and Pelates quadrilineatus (species 11) ( Seasonal variations in mean δ 15 N were not significant (Table 3). However, δ 15 N levels characterizing the demersal fish community varied from 14.19 to 16.89 ‰ in March and from 14.85 to 16.88 ‰ in December, resulting in an overall δ 15 N variation range lower in December than in March (2.03 and 2.7 ‰, respectively), consistently with a lower variance in December (Table 3). A more contracted trophic structure with lower variations in trophic positions among species was therefore observed in December compared to March (Fig. 2).

Observed δ 15 N variation ranges were also largely inferior to the threshold level of 3.4 ‰ characterizing a change in trophic position.

Seasonal variations in mean δ 13 C were not significant either (Table 3). However, δ 13 C varied from -17.24 to -15.11 ‰ in March and from -17.48 to -13.58 in December, corresponding to an overall δ 13 C variation range of 2.13 and 3.9 ‰, respectively. Similarly, δ 13 C variance was lower in March than in December (Table 3) Accordingly, the fish community trophic structure appeared more widely distributed along the δ 13 C axis in December (Figs. 2 and3), implying a larger variability in the nature and origin of food resources consumed by fishes during that month. This pattern was confirmed by observed variability in δ 34 S values, which varied from 13.56 ‰ to 10.23 ‰ in March and from 13.03 ‰ to 19.09 ‰ in December. The overall δ 34 S variation range was therefore slightly larger in December (6.06 %) than in March (5.67 ‰), consistently with variance values (Table 3), although difference between months in mean δ 34 S was not significant (Table 3).

The fish community trophic structure therefore appeared slightly more widely distributed along both the δ 13 C and δ 34 S axes in December compared to in March (Fig. 3), confirming the consumption by fishes of food resources from more diverse mixture and origin in December.

Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

Species-specific δ 13 C, δ 15 N and δ 34 S values differed little between the two periods (Figs. 2 and3). Regarding fish size, only δ 15 N values appeared to significantly (P < 0.05) vary according to the size structure of the fish community, with larger species having higher nitrogen isotope ratios (Fig. 4). However, this relationship was weak (r 2 = 0.36).

Discussion

Our study highlighted a clear carnivorous diet, with a heavy reliance on invertebrate and fish prey, for all fish species examined in Muscat coastal waters. Fish prey was found in relatively large proportions in stomachs of some species, such as redcornet fish (Fistularia petimba), greater lizardfish (Saurida tumbil), long raker trevally (Ulua mentalis), Delagoa threadfin bream (Nemipterus bipunctatus) and four lined terapon (Pelates quadrilineatus).

However, the δ 15 N values of these species largely overlapped with those ones in stomachs of which mostly invertebrate prey was found. Furthermore, the overall δ 15 N values obtained at the community level had relatively narrow range, lower than the 3.4 ‰ threshold value usually characterizing the difference in nitrogen isotope composition between two consecutive trophic levels (Post, 2002;Post et al., 2007). This suggests that all species analyzed in our study had a similar trophic position in the food web. Therefore, our results indicate a largely mixed fish-invertebrate diet for most of demersal fish species in the Sea of Oman. Our results therefore highlight how essential insights from stable isotope analysis had proven to complement stomach content data, in order to fully apprehend the variability in feeding habits of consumers. Similar conclusions have been presented by recent studies [START_REF] Carassou | Trophic dynamics of the Cape stumpnose (Rhabdosargus holubi, Sparidae) across three adjacent aquatic habitats[END_REF]2017;[START_REF] Keller | Combined stomach content and δ 13 C/δ 15 N analyses of oilfish, escolar, snake mackerel and lancetfish in the western North Atlantic[END_REF][START_REF] Olson | Feeding ecology and prey resource partitioning of lenok (Brachymystax lenok) and Baikal grayling (Thymallus arcticus baicalensis) in the Eg and Uur rivers, Mongolia[END_REF]. Stomach contents indeed only provide very short-term information on consumer's diet, while isotopic ratios in the tissues reflect dietary habits over longer time scales (Cortés, 1997;Hobson, 1999;Post, 2002;[START_REF] Olson | Feeding ecology and prey resource partitioning of lenok (Brachymystax lenok) and Baikal grayling (Thymallus arcticus baicalensis) in the Eg and Uur rivers, Mongolia[END_REF]. In our study in particular, the low number of specimens collected for each species, together with the occurrence of fish with empty stomachs, further limited the efficiency of stomach content analysis for capturing the full range and variability in prey diversity characterizing demersal fish feeding regimen.

As our study is the first one to address diet of demersal fish from soft-bottom habitats with stable isotopes in the Sea of Oman, comparisons with similar studies in the region is difficult. The study of [START_REF] Mill | Stable isotope data as reef food-web descriptors in a dynamic tropical environment[END_REF] was focused on coral-reef associated fish species and it did not include any species common with our study. Only one fish species, Argyrops spinifer, which was collected in our study, was also analyzed by [START_REF] Al-Habsi | δ 13 C and δ 15 N elucidation of size-structured food webs in a Western Arabian Sea demersal trawl assemblage[END_REF] was not apparent at the level of species. In our study in the Sea of Oman, no significant relationship between fish size and isotope ratios were evident at the demersal fish community level, except for δ 15 N which increased with fish size but with a low regression coefficient (r 2 < 0.4). Rastgoo and Navarro (2017) also reported a positive correlation between trophic levels estimated from stomach content data in the literature, and fish size in the Sea of Oman. Based on a restricted number of samples, those relationships could however not be tested at the species level in our study. This aspect should therefore be the focus of more future studies in the Sea of Oman, in order to explicit the size-related variability in demersal fish diet in this particular region. Issues of size-related structuration in ecological traits characterizing fish communities indeed have crucial implications in terms of fisheries management locally, since, as emphasized in [START_REF] Al-Habsi | δ 13 C and δ 15 N elucidation of size-structured food webs in a Western Arabian Sea demersal trawl assemblage[END_REF], size-based metrics are increasingly promoted to assess fishing impacts on natural communities at an ecosystem scale.

Analysis of stable isotope data conducted herein also suggest a possible seasonal change in the range of diversity and origin of prey consumed by demersal fish in the studied area, reflected by a larger range and variance of δ 13 C (and δ 34 S to a lesser degree) values in December compared to March. Indeed, carbon and sulfur isotopic ratios depends not only on the nature of prey contributing to consumers' diet, but also on their origin such as benthic vs.

pelagic or coastal vs. marine (Hobson, 1999;[START_REF] Layman | Applying stable isotopes to examine food-web structure: an overview of analytical tools[END_REF]. Accordingly, along the δ 13 C and δ 34 S gradients, the trophic structure of demersal fish community appeared relatively 'relaxed' in December, and more 'contracted' in March (although variations in mean values between seasons were not significant for any isotope). . This apparent change in the trophic

Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008 structure may logically reflect seasonal changes in oceanographic conditions in our study area, in particular variations in water temperature, water column mixing and primary productivity related to the seasonal monsoon [START_REF] Piontkovski | Seasonal and interannual variability of chlorophyll a in the Gulf of Oman compared to the open Arabian Sea regions[END_REF]. Stronger winds occurring during the monsoon season, extending from March/April to September/October, result in a stronger mixing of the water column, as highlighted by highly variable patterns of water temperature during this period [START_REF] Al-Hashmi | Seasonal changes of Chlorophyll a and environmental characteristics in the Sea of Oman[END_REF]. Stable isotope composition in fish muscles reflects food assimilation along periods ranging from weeks to months, depending on species and life stages [START_REF] Buchheister | Turnover and fractionation of carbon and nitrogen stable isotopes in tissues of a migratory coastal predator, summer flounder (Paralichthys dentatus)[END_REF]. Therefore, it is likely that fish collected at the end of the monsoon period, i.e., in December, have been feeding in a

marine environment with increased re-suspension of material from the bottom (e.g., sediments) to the middle and surface layers of the water column, and enhanced exchanges between coastal and offshore water masses. Such resuspension and mixing processes potentially resulted into a larger set of prey origin available for fish in December (mixture of surface, bottom and/or coastal, marine fueled prey), as compared to fish collected at the beginning of the monsoon, i.e., in March, which have likely been feeding upon prey relying on basal resources from a more restricted range of environmental conditions. This hypothesis should be tested in future studies, as the low number of analyzed samples in our study precludes any clear conclusion to be drawn in this regards.

Although limited in sampling effort and lack of spatial replication, this study highlights the utility of detailed dietary studies to improve our understanding on demersal fish community structure in a data poor region. Even based on a small data set, this study emphasized some clear and interesting features characterizing the trophic structure of demersal fish communities, demonstrating the utility of the approach to inform fishery management in the Sea of Oman. The use of stable isotopes to address fish dietary requirements and relationships also remains novel for the entire country, as highlighted by the scarcity of studies addressing this issue in our region. We therefore strongly advocate for complementary investigations to be implemented based on this methodology, in order to not only improve knowledge on the trophic ecology of the highly diverse fish assemblages characterizing the coastal environment of Oman [START_REF] Al-Jufaily | Oman fish biodiversity[END_REF], but also to contribute to the development of ecosystem-based approaches to the management of local fisheries, which have a crucial economic and cultural importance in the region (Sideek et al., 1999;Valinassab et al., 2006). Such future studies should rely on an appropriately designed and intensive sampling of both fish and their potential prey at contrasted seasons and locations, so as to: 1) provide necessary data for the calculation of consumer trophic positions

Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

based on precise stable isotope data, as mean trophic level of commercial species are an important parameter from a fisheries management perspective (see for example Abd El-Rahman, 2014 for a case study in Oman), and 2) incorporation of stable isotope data into mixing models for estimating food resource contribution in supporting demersal fish community diet across time and space. Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008 95,0 0,0 0,0 0,0 25,0 0,0 0,0 0,0 100,0 0,0 Aetomylaeus nichofii (2) 45,0 50,0 0,0 0,0 50,0 0,0 0,0 0,0 0,0 50,0 Taeniamia fucata (3) 35,0 0,0 50,0 0,0 50,0 0,0 0,0 0,0 0,0 0,0 Ulua mentalis (4) 30,0 0,0 0,0 0,0 100,0 0,0 0,0 0,0 100,0 0,0 Gerres filamentosus (5) 13,3 33,3 33,3 0,0 0,0 0,0 0,0 0,0 0,0 66,7 Plectorhynchus pictus (6) 30,0 0,0 0,0 100,0 100,0 0,0 100,0 0,0 0,0 100,0 46,7 0,0 0,0 66,7 100,0 0,0 33,3 0,0 0,0 33,3 Argyrops spinifer (10) 26,7 0,0 0,0 100,0 66,7 0,0 33,3 0,0 0,0 0,0 Pelates quadrilineatus (11) 38,4 0,0 0,0 0,0 66,7 0,0 0,0 0,0 33,3 33,3 Pseudorhombus arsius (12) 26,3 0,0 25,0 50,0 25,0 0,0 0,0 0,0 0,0 0,0 Grammoplites suppositus (13) NA NA NA NA NA NA NA NA NA NA Arius thalassinus (14) 5,0 0,0 0,0 100,0 0,0 0,0 0,0 0,0 0,0 0,0 Fistularia petimba (15) 50,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 100,0 0,0

Figure captions

Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

Fig. 1 :

 1 Fig.1: Location of the sampling site (red star) in the coastal area of Muscat, Sea of Oman.

  Author-produced version of the article published in Regional Studies in MarineScience, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

Stable isotope data were plotted separately for each sampling season in two dimensional-spaces, i.e., δ 13 C vs. δ 15 N and δ 13 C vs. δ 34 S. One-way analysis of variance

Table 2

 2 Author-produced version of the article published in Regional Studies in MarineScience, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008(species 14). At least half of analyzed stomachs of N. bipunctatus, Nemipterus japonicus (species 9), and Pseudorhombus arsius (species 12) contained crabs as well (Table2).Shrimps (Dendrobranchiata, Crustacea) were found in all stomachs of U. mentalis, P. pictus and N. japonicus and in at least half of the stomachs analyzed for Aetomylaeus nichofii (species 2), Taeniamia fucata (species 3), N. bipunctatus, A. spinifer, and P. quadrilineatus.At least a quarter of analyzed stomachs for S. tumbil and P. arsius were also filled with shrimps. Manta shrimps (Stomatopoda, Crustacea) were observed in the stomach of one individual N. bipunctatus. Mollusks (Gastropoda) were also abundant prey items (Table2).Gastropods occurred in P. pictus stomachs, and in one third of N. japonicus and A. spinifer stomachs. Annelida (Polychaetes) were only observed in stomachs of N. bipunctatus. Other prey items recorded included unidentified crustaceans and particulate organic matter (detritus)

). Crabs

(Brachyura, Crustacea)

occurred in all stomachs of Plectorhynchus pictus (species 6), Argyrops spinifer (species 10) and Arius thalassinus (Table

2

).

  Author-produced version of the article published in Regional Studies in MarineScience, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008 Oman has very close values of δ 13 C (mean ± standard deviation of -15.91 ± 0.10 and -15.99 ± 0.04, respectively) and δ 15 N (17.10 ± 032 and 15.18 ± 0.82, respectively). This suggests little variation in A. spinifer diet across different coastal regions in Oman waters, although no stomach content records or isotope data on the fish potential food resources were available for comparison in Al-Habsi et al. (2008). In a recent study, Rastgoo and Navarro (2017) reviewed stomach content data available from 21 finfish species of the Sea of Oman to infer their respective trophic levels. Only two species were common to our study: Nemipterus japonicus and Saurida tumbil, with both being characterized by a trophic level ≥ to 4, indicating a carnivorous diet dominated by the consumption of fish prey or high-order invertebrate consumers. Our study highlighted a similar result, although stable isotope data highlighted a probable mixture of fish and invertebrate prey for both species. Al-Habsi et al. (2008) found an apparent size-related structuration in δ 15 N and δ 13 C values at the demersal fish community level in the Arabian Sea, although such size structure

in the Arabian Sea. Comparison of the data suggested that A. spinifer from the Arabian Sea and the Sea of

Table 1 .

 1 Fig. 3: Mean (circles) and standard deviation (error bars) of δ 13 C (x-axis) and δ 34 S (y-axis) values measured in dorsal muscle of demersal fishes collected by trawling in Muscat coastal area. Numbers within circles indicate species codes, which are depicted in Table 1.Fig. 4: Relationships between fish size (x-axis) and a) δ 13 C, b) δ 15 N and c) δ 34 S values characterizing demersal fish community sampled in Muscat coastal area. Regression line and coefficient are only shown if the tested relationship is significant (P < 0.05). -produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008 Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008 Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008 Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

	Author

Table 2 :

 2 Average stomach fullness (%) and occurrence of various prey items (% of fish with non-empty stomachs) in stomachs of fishes collected off Muscat coastal area in December 2013 and March 2014. Refer to number of individuals and fish size ranges. With NA: not available due to empty stomach (refer to Table 1 and text).

	Fish species (code)	Stomach fullness	Unidentified	Unidentified	CRUSTACEANS Decapods Brachyura Dendrobranchiata	Stomatopoda	MOLLUSCS Gastropods	ANNELIDS Polychaetes	TELEOSTEI (bony fish remains)	Particulate Organic Matter
	Saurida tumbil (1)

Table 3 :

 3 Mean and variance (var.) of δ 13 C, δ 15 N and δ 34 S measured in fish muscle tissues in December 2013 and March 2014 in the Sea of Oman, all species combined. No significant differences were found between months for any isotopic ratio (P>0.05 for all analyses).Author-produced version of the article published in Regional Studies in MarineScience, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

		δ 13 C	δ 15 N	δ 34 S
	Month	Mean Var. Mean Var. Mean Var.
	December -15.94 0.96 16.03 0.24 17.13 3.84
	March	-15.90 0.33 15.72 0.72 16.57 3.68

Acknowledgements

This study was supported by the funds from College of Agricultural and Marine Sciences, Sultan Qaboos University -Dean's discretionary funds (IG/AGR/Dean/14/01). We thank all students from cohorts Fall 2014, Spring 2015 and Fall 2015 of the Introduction to Marine Science and Fisheries course (MASF2003) for participation in field sampling. We are also grateful to Mr. Khamis Al-Riyami, Mr. Farid Al-Abdali, captain Mr. Saleh Al-Maashari, and boat engineer Mr. Manolito Barate. From the UC Davis Stable Isotope facility, we thank Dr Joy Matthews and Dr Chris Yarnes for carbon/nitrogen and sulfur analyses, respectively, and Ms. Emily Schick for administrative and accounting support.

Author-produced version of the article published in Regional Studies in Marine Science, 2017, 16, 145-151 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.rsma.2017.08.008

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