André Niclas

Lament Bourgeois

An inverse approach to determine the non-linear properties of induction heat-treated steels

The identification of the through-the-thickness variation of the non-linear properties of a steel structure due to a heat treatment by induction is considered. An inverse approach to that problem is proposed, which is based on a 4-point bending test of a heat-treated parallelepipedic bar. It includes a layer-removal method for measuring residual stresses. Precisely, two different inverse methods are described. For a medium carbon steel, an application based on experimental data is performed, which shows the efficiency of our approach and a good agreement between the two methods.

inverse problem / plasticity / X-ray diffraction / heat treatment / residual stresses

Introduction

The optimization of mass, volume and strength among others, constrains the engineer to design steel components with local reinforcement resulting from specific treatments. Superficial treatments such as induction hardening, shot-peening and nitriding are often practiced. These processes introduce residual stresses and gradients in mechanical properties within the material, precisely, gradients in plastic properties (for example the tensile yield strength and the strain hardening modulus). Various computational tools provide the designer with accurate residual stress predictions within the component. However, the gradient in the plastic properties is unknown and has to be identified.

In the framework of classical tensile tests, establishing the relationship between microstructural composition and plastic properties would necessitate the realization of homogeneous test bars composed of different types of microstructure. These tests would give uncertain results, first because homogeneous bars are very difficult to produce and, second, because of brittleness (test bars could fail before the tensile yield strength is reached).

This paper is concerned with a new methodology to determine the plastic constitutive parameters of heat treated material, with application to medium carbon steel. It is based on the analysis of a bending test by inverse methods. We first describe the heat treament and its consequences and, secondly, the bending test. Then, following a brief presentation of X-ray diffraction, which is used to calculate the stress fields in our test bars, two different inverse approaches are proposed based on the bending test to determine the gradient in plastic properties within the affected layer. The first one is based on measurements of the stress fields before and after the test. The second one consists of minimizing the discrepancy between the data obtained during the real test and those provided by a simulation of the test.

The heat treatment

The treatment which is studied here consists of a high-frequency induction hardening. The industry currently uses this process, which changes the microstructural composition within a layer of adjustable thickness. Its physical principles are summarized as follows (see for example [START_REF] Davies | Induction Heating Handbook[END_REF]) for details).

(i) A high frequency current passes through an inductor and creates a magnetic field.

(ii) Eddy currents are principally induced on the surface of the piece placed near the field coil.

(iii) These currents heat the piece, locally raising the temperature above the austenitization threshold (AC1 point). A transformation into austenite takes place within a depth of several millimetres. (iv) The specimen is finally quenched, resulting in austenite being transformed into martensite (the hardest phase of steel). The mechanical state after treatment is characterized by the presence of a residual stress field and a gradient in microstructural properties. Residual stresses have been created by variations in temperature and phase changes during treatment, which are both responsible for volume changes. Since the thermal and metallurgic evolutions at the surface and within the component are very different, internal strains develop to balance these volume variations. At the end of the treatment, the residual stress field can be measured by many destructive methods (removal of matter and X-ray diffraction, hole drilling, etc.).

Metallurgical transformations, which consist of a modification of the crystallographic structure, also occur during treatment: the arrangements of the atoms in grains and grain shapes change and generate many phases which have different microscopic aspects and different mechanical properties. The kinetics of thermal phenomena have a direct influence on the metallurgical transformation, which is described in TTT and CCT diagrams (see for example [START_REF] Barralis | Précis de Métallurgie[END_REF] for definitions) that are specific to each metal. The industrial processes such as induction hardening are intended to transform the initial material into a martensitic phase within a desired depth of the component. This transformation necessitates an increase in temperature above the AC1 point (often higher than 750 • C) to obtain austenitic phase, followed by a very fast quench (the quenching rate must be higher than 50 • C • s -1 ). The majority of austenite is then transformed into martensite with improved mechanical properties. A gradient in the metallurgical composition is often expected within the component because the metal has not been totally austenitized during heating or because the cooling rate has been insufficient to obtain 100% martensite. At the macroscopic scale, this phenomenon results in gradients in mechanical properties.

We postulate that the elastic properties of the metal are not affected by the heat treatment. This assumption lies in the fact that the crystalline structure of the different phases (martensite, ferrite and other) is the same (B.C.C. structure). Only the plastic properties may have been altered by the heat treatment.

The 4-point bending test

This section is dedicated to the description and the modelling of the 4-point bending test.

The objective

This paper addresses the identification of the tensile yield strength and the strain hardening modulus, which are assumed to fully characterize the plastic response of the material within the layer affected by heat treatment. This identification can only be done by introducing additional irreversible strain in this layer through a mechanical test, here a 4-point bending test, which has at least three advantages (see figure 1 for notation). (i) It is easy to perform. (ii) The applied bending moment is uniform in directions x and y, which motivates the assumption that total strains, plastic strains and stresses are only depending on z. (iii) During such a test, the outer layers are the most stressed (tensile stresses are created on one side, called side (l), compression stresses on the other side, called side (u)). It is an advantage here because the outer layers are precisely those in which the tensile yield strength are the largest.

The mechanical fields

The test bar is a parallelepided which occupies the domain h] in the Cartesian coordinates (x,y,z), 2h being much smaller than L 1 and L 2 . To simplify notations, variables (x,y,z) will often be designated by (1, 2, 3).

=[0,L 1 ]×[0,L 2 ]×[-h,
We assume that before and during the bending test, total strain, plastic strain and stress fields only depend on z. This assumption, partly motivated earlier, relies on the fact that:

(i) the heat treatment is uniform in directions x and y, (ii) the mechanical fields generated during bending between the two points B and C are also independent of x and y, provided we consider a region which is a not too close to these two points (according to Saint-Venant's principle). Denote by u, ε, ε p and σ displacement, total strain, plastic strain and stress, respectively. Since σ zz (x, y, ± h) = 0, equilibrium implies σ zz = 0in . Furthermore, we disregard shear stress

σ 1z = σ 2z = 0.
(1)

The assumed form for the stress field is therefore

σ =     σ 11 (z) σ 12 (z) 0 σ 12 (z) σ 22 (z) 0 00 0     .
(2)

The total strain tensor being a function of z, the only compatibility equations are

∂ 2 ε ij ∂z 2 = 0 (i, j = 1, 2),
which are satisfied by

ε ij = β ij -zγ ij , (3)
where the second-order tensors β and γ are constant. The tensor β defines the strain in the plane of equation z = 0. We also assume that

ε 1z = ε 2z = 0. ( 4
)
We now use the strain-displacement relationship to relate the tensor γ introduced in (3) to the displacements. Let u i (x,y,z) (i = 1, 2) and w(x,y,z) be the components of displacement in directions x, y and z.Using(3) and ( 4), one finds that

γ ij = ∂ 2 w ∂x i ∂x j ,
revealing that ∂ 2 w/∂x i ∂x j is constant and that γ is nothing but the curvature tensor of the plane of equation z = 0. Plastic strain, which satisfies tr ε p = 0, is assumed to have the expression

ε p =     α 11 (z) α 12 (z) 0 α 12 (z) α 22 (z) 0 00 -α 11 (z) -α 22 (z)     .

Description of the testing device

The testing device is presented in figure 1. The four contact points transmit, in the region of the test bar situated between points B and C, a moment per unit of length (in direction y) M 11 which is uniform in directions x and y and of value

M 11 =- 1 2 Fd L 2 =-M. ( 5
)
This loading is applied with the following kinematical conditions on curvature:

γ 12 = 0,γ 22 = 0.
Note that, since contact at B and C is not perfect, the moment is actually uniform only at a certain distance away from the two points.

A classical device provides the intensity of the force F and the displacement of its point of application. Furthermore, strain gauges situated on both sides of the test bar provide the strain at the boundary ε ij (h) and ε ij (-h). These data yield estimates of the mid-plane strain β ij and the curvature γ ij , by solving the system of equations

ε ij (h) = β ij -hγ ij , ε ij (-h) = β ij + hγ ij , (6)
and then estimates of the strain field.

During the test, the load F is first increased from 0 to F m , then decreased back to 0.

The constitutive law

The zero strain state for the total strain and plastic strain corresponds to the state of the test bar just after the heat treatment. This state will be designated as the "initial state". It is characterized by a residual stress field denoted by σ 0 which is self-equilibrated. We assume that the constitutive law is given by the classical Prager's model (see for example [START_REF] François | Elasticité et Plasticité[END_REF]), which corresponds to the following free energy:

W ε, ε p = σ 0 : ε -ε p + 1 2 ε -ε p : C : ε -ε p + 1 2 H ε p : ε p ,
where C is the linear elasticity Hooke's tensor and H is the modulus of strain hardening. We deduce the thermodynamical forces associated with the state variables ε and ε p respectively using

σ = ∂W ∂ε , A =- ∂W ∂ε p ,
resulting, more explicitely, in the Hooke's law

σ = σ 0 + C : ε -ε p (7)
and

A = σ -H ε p . (8)
Given the particular form of mechanical fields ε, ε p and σ defined in the previous paragraph, equation ( 7) is rewritten as

       σ 11 = σ 0 11 + E 1-ν 2 (ε 11 + νε 22 ) -(α 11 + να 22 ) , σ 22 = σ 0 22 + E 1-ν 2 (νε 11 + ε 22 ) -(να 11 + α 22 ) , σ 12 = σ 0 12 + E 1+ν (ε 12 -α 12 ), (9)
in which E and ν are Young's modulus and Poisson's ratio, respectively. The yield function which defines the Von Mises convex of plasticity is

F(A) = Q(A) -k, Q(A) = 3 2 A ′ : A ′ ,
where A ′ is the deviatoric part of A and k is the tensile yield strength. The loading and unloading conditions with the classical normality flow rule are

     F(A) 0, F(A)<0 → εp = 0, F(A) = 0 → εp =ωA ′ , ω 0.
The plastic behaviour of the material is thus characterized solely by the tensile yield strength k and the strain hardening modulus H .

To shorten notations, we introduce the following scalars

E ′ = E 1 -ν 2 ,E ′′ = E 1 + ν ,E 1 = E 2 = E ′ ,E 3 = E ′′ ,
and simplified indices notation:

   σ 1 = σ 11 , σ 2 = σ 22 , σ 3 = σ 12 ,      ε 1 = ε 11 + νε 22 , ε 2 = νε 11 + ε 22 , ε 3 = ε 12 .
For i = 1, 2, 3, we define β i , γ i and α i from the components of tensors β, γ and ε p , respectively, exactly as the ε i 's are defined from the components of tensor ε just above. With this notation, relations (3) and ( 9) simply become

ε i = β i -zγ i (i = 1, 2, 3) (10)
and

σ i = σ 0 i + E i (ε i -α i )( i = 1, 2, 3). ( 11
)
The initial stress field σ 0 is assumed to depend only on z because heat treatment is uniform in directions x and y, as already mentioned. For the same reason, plastic parameters k and H are also assumed to depend only on z. Furthermore, the heat treatment being symmetrically applied on both faces of the test bar, one assumes that k, H and σ 0 are symmetrical with respect to the plane of equation z = 0.

Simulation of the bending test

To solve an inverse problem with the data obtained during the test, it is necessary to propose a modelling of this test (forward calculation). Total strain, plastic strain and stress fields are assumed to have the expressions previously indicated.

Generalized forces are defined by

N i = h -h σ i dz, M i = h -h zσ i dz( i = 1, 2, 3).
The initial stress field σ 0 is self-equilibrated and, by using (11), the generalized forces are written as

N i = E i S(β i -α i )( i = 1, 2, 3), M i =-E i Iγ i -E i S zα i (i = 1, 2, 3),
in which we define

S = 2h, I = 2 3 h 3 , • = 1 2h h -h • dz.
The kinematic and static conditions for the forward elastic-plastic calculation are respectively

γ 2 = 0,γ 3 = 0 and M 1 =-M, N i = 0 (i = 1, 2, 3).
The incremental algorithm of the forward calculation is classical (see for example [START_REF] Nguyen | On the elastic plastic initial-boundary value problem and its numerical integration[END_REF])); we just mention its two key steps.

(i) First step: compute the increment of total strain ε and the increment of stress σ corresponding to the rate of loading M, the increment of plastic strain ε p being kept constant. The expression of the rate of total strain is, according to kinematic and static conditions,

     γ 2 = 0, γ 3 = 0, β i = α i (i = 1, 2, 3), γ 1 = 1 E ′ I M -S I z α 1 .
(ii) Second step: compute the increment of plastic strain ε p such that the new thermodynamical force A + A remains in the convex of plasticity. We thus impose the consistency condition

F(A + A) = 0.
According to the flow rule, we furthermore impose that ε p is proportional to A ′ + A ′ . We deduce

ε p = A ′ + 2µ ε ′ ,
µ being the shear modulus, ε ′ being the deviatoric part of ε,and being defined by

= 1 2µ + H Q(A + 2µ ε) -k Q(A + 2µ ε) .
Since the total strain, plastic strain and stress fields depend only on z, the forward elastic-plastic computation needs only a discretization in the thickness direction. Subsequently, the mechanical fields are considered as mvectors (m: number of layers used in the thickness direction). The discretized parameters governing plastic behaviour (k, H ) are also m-vectors.

We point out that the component σ 0 12 of the initial stress field σ 0 is very close to 0 in comparison with the other components; this is due to the heat treatment procedure and inferred from X-ray diffraction measurements, discussed in the next section. Kinematic and static conditions for the 4-point bending test are such that the same conclusion applies to the component σ 12 at any step of the bending test.

Determination of the residual stress field

To apply our methodology, we need to measure the residual stress field within the treated test bars. It is determined by using X-ray diffraction. This method, detailed in [START_REF] Lebrun | Détermination des contraintes résiduelles par rayons X. Document de formation générale[END_REF], is based on the measurement of the interreticular distance between the crystallographic planes. The acquisition of the stress field within the piece necessitates the removal of the layers of material and successive diffraction measurements. Matter removal is accomplished by an electropolishing method, which does not perturbe the stress, to the contrary of, e.g., mechanical polishing. But the change in geometry induces a redistribution of the initial stress, which has to be recalculated from the successive diffraction measurements. Some reconstruction formulae for simple geometries are proposed in [START_REF] Moore | Mathematical correction for stress in removed layers in X-Ray diffraction residual stress analysis[END_REF], their extension to any geometry being solved in [START_REF] Ballard | On the inversion of subsurface residual stresses from surface stress measurements[END_REF]. For our particular geometry (stress field of form (2)) and if layers of constant thickness are removed from the whole surface, the following Moore and Evans formulae provide the stress field σ before matter removal as a function of stresses σ m measured on the successive surfaces (S = 2h being the total width of the piece):

σ i (z 1 ) = σ m i (z 1 ) + 2 S z 1 σ m i (z) z dz -6z 1 S z 1 σ m i (z) z 2 dz( i = 1, 2, 3). ( 12
)
For practical reasons, only a part of the surface has been removed in the framework of our study, precisely a square defined by [x 1 ,x 2 ]×[y 1 ,y 2 ] (see figures 2 and 3). In this configuration, the reconstruction formulae, determined in [START_REF] Bourgeois | Contrôle Optimal et Problèmes Inverses en Plasticité[END_REF], become:

σ i (z 1 ) = σ m i (z 1 ) + S z 1 f 1 (z)σ m i (z) dz -z 1 S z 1 g 1 (z)σ m i (z) dz( i = 1, 3) (13)
and

σ i (z 1 ) = σ m i (z 1 ) + S z 1 f 2 (z)σ m i (z) dz -z 1 S z 1 g 2 (z)σ m i (z) dz( i = 2, 3), (14)
where r 1 = L 1 /(y 2y 1 ) and r 2 = L 2 /(x 2x 1 ). The functions f 1 and g 1 introduced in ( 13) and ( 14) are

f 1 (z) = 6z(S 2 (r 1 -1) + z 2 ) -4(S 3 (r 1 -1) + z 3 ) 4(S 3 (r 1 -1) + z 3 )(S(r 1 -1) + z) -3(S 2 (r 1 -1) + z 2 ) 2 , g 1 (z) = 12z(S(r 1 -1) + z) -6(S 2 (r 1 -1) + z 2 ) 4(S 3 (r 1 -1) + z 3 )(S(r 1 -1) + z) -3(S 2 (r 1 -1) + z 2 ) 2 . ( 15
)
The functions f 2 and g 2 have the same expressions as f 1 and g 1 with r 1 replaced by r 2 . Setting r 1 and r 2 to 1 in (15), which corresponds to a removal of matter on the whole surface, ( 13)-( 14) degenerate into the classical Moore and Evans' formulae. One must bear in mind that the formulas ( 13)-( 14) are valid only for sufficiently small depths, say up to one fourth of the total width. Beyond that, geometry is too altered, so that the assumptions used to establish them are not valid.

Apart from the determination of the stress field, X-ray diffraction is also useful in determining the microstructural state within the piece at the end of treatment. Metallographic microsections give qualitative indications, microhardness measurements and analyses of X-ray diffraction peaks provide quantitative information. For a two-phase metal, the diffraction peak is the sum of the diffraction peak of each phase. It is possible to separate these two peaks. Since the metallurgical proportion and the relative peak area of one phase are proportional, X-ray diffraction provides the composition of the treated metal at a given point (see [START_REF] Lebrun | Détermination des contraintes résiduelles par rayons X. Document de formation générale[END_REF] for details). Figure 4 shows the variation of the metallurgical composition with depth for a particular test bar. The treated zone is a mixture of martensitic and ferritic phases. The proportion of martensite decreases with depth. These considerations are confirmed by microhardness measurements and observations of the microstructure. Figure 5 shows the variation of Vickers microhardness with depth. It has to be compared to the previous variation of the proportion of martensite. Figures 6 and8 respectively show the ferrito-perlitic and martensitic microstructures observed, figure 7 shows the mixed zone between these two microstructures. In fact, the martensitic phase is not pure but has a small proportion of ferrite which has not been austenitized during heat treatment.

In what follows, some of our assumptions will by justified thanks to these observations.

Identification of the plasticity model

We are now in a position to consider the main objective of this paper: the determination of the tensile yield strength k and the strain hardening modulus H for a steel test bar which was submitted to a heat treatment. These two parameters are function of coordinate z. Two different methods are considered to solve the problem.

(i) The first one is based on the difference between the stress fields measured before and after the 4-point bending test. (ii) The second one consists of an inversion of the data obtained during the test by using our forward model.

Method based on difference in stress fields

The stress field σ f which is present in the test bar after the bending test has been conducted, is, according to Hooke's law (7),

σ f = σ 0 + C : ε f -ε p ,
in which ε f is the final strain field. We observe that if the fields σ 0 , σ f and ε f are known, then the final plastic strain can be calculated using the equation above, which can also be written as:

α i = ε f i - σ f i -σ 0 i E i (i = 1, 2, 3).
Recall that the reference state for total strain and plastic strain is the state of the test bar before bending. The final strain field ε f is then calculated thanks to the indications given by the strain gauges located on the two sides z = h and z =-h during the test (see figure 1) by solving the system (6).

The measurements of the initial and final stress fields σ 0 and σ f are performed using matter removal and X-ray diffraction. This technique being destructive, the measurement of σ 0 cannot be done before bending. It has to be done on a second test bar, called a reference test bar, which is assumed to be identical to the first in terms of geometry and heat treatment.

Assuming a purely elastic unloading of the 4-point bending test, the final plastic strain field is the same as the plastic strain field induced by maximum loading. Furthermore, the stress field at the maximum loading

(M = M M ) satisfies σ M 1 (z) = σ f 1 (z) -z M M I ,σ M i = σ f i (i = 2, 3).
We have then obtained both stress σ M and plastic strain ε p at the maximum loading. In planes corresponding to the coordinate z in which plastic strains are non zero, the yield criterion is satisfied at the maximum loading and provides the relation

Q(σ M (z) -H(z)ε p (z)) -k(z) = 0. ( 16
)
The identification of k and H is found in the previous equation, and is only possible in planes which have sustained irreversible straining. It is then necessary to impose a large maximum force F M to yield all the layers which have been affected by the heat treatment. Furthermore, this treatment generates compressive stresses on both sides of the test bar but the bending test generates compressive stresses only on side (u), which ends up being the side on which it is more convenient to conduct the identification process.

For a given coordinate z, the only equation of use is ( 16), in which the two unknown profiles k(z) and H(z) are present. It is then found convenient to assume specific types of variations with depth for them. Among the various possibilities, one consists of dividing the thickness [-h, h] of the test bar into several intervals [z i ,z i+1 ], on which k(z) and H(z)have a constant value k i and H i respectively. For simplicity sake, the intervals [z i ,z i+1 ] may correspond to the step adopted during the measurement of the surface stresses. The pair (k i ,H i ) is obtained by enforcing (16) at z = z i and z = z i+1 and thus solves the system of two equations (j = i, i + 1)

3 2 σ M ′ (z j ) : σ M ′ (z j ) -3H i σ M ′ (z j ) : ε p (z j ) + 3 2 H 2 i ε p (z j ) : ε p (z j ) -k 2 i = 0.
We point out however that the determination of constants H i using this technique leads to scattered, and even negative, values of H . This can be explained by the strong sensitivity of the H i 's to the values of ε p (z i ) and ε p (z i+1 ). Accuracy on field ε p is less than the accuracy on field σ M , since the estimation of the former needs the measurement of the stresses before bending (σ 0 ), and not only the measurement of the stresses after bending (σ f ).

Another approach is to find H(z)by other means, e.g., using the second method to be presented, then evaluate the field k(z) from ( 16). In figure 11, we present the results concerning k(z) with given values H(z)obtained using the second method (see further). The two curves correspond to two different test bars, which are supposed to have been submitted to the same heat treatment but which have been bent differently (the maximum bending moments are respectively

M M • L 2 = 182 N•mandM M • L 2 = 190 N•m).

Method based on modelling of the bending test

The second identification method, which is more classical, relies on the modelling of the bending test discussed in Section 3.5.

Principle

The aim is to adjust the functions k(z) and H(z) in the affected layer so that the responses of the real and the simulated structures are the same for the same loading history. To apply this method, we first have to define which observations are used for the identification, and, secondly, to specify the search domain for the unknown functions k(z) and H(z).

As far as the first point is concerned, we study the evolution of the curvature γ 11 = γ of the test bar, which depends on the applied moment M 11 =-M. The curvature γ is measured by the strain gauges thanks to relation ( 6) and M is provided by relation (5). We only use the increasing part of the loading since the unloading is elastic. More precisely, n + 1 points (M j ,γ j ) of the experimental curve γ = f(M) are known, with (M 0 ,γ 0 ) = (0, 0).

The theoretical curve γ = f(M)is obtained by using the algorithm described in Section 3.5, and by applying n loading steps M j = M j +1 -M j from M = 0, resulting in n + 1 values of calculated curvature γ jc starting in terms of k and H . Concerning the domains in which k(z) and H(z) are searched, it should be mentioned that they have to be sufficiently large so that the experimental curve is correctly reproduced by the forward modelling, but sufficiently small so that this good accuracy does not happen for pairs (k(z), H (z)) that are very different from each other. We propose to base our forward modelling on simple variations of k and H , deduced from our previous observations on the microstructure (see the end of Section 4), which have revealed that the thickness is divided into three zones corresponding each to a particular microstructure (ferrito-perlitic, mixed and ferritomartensitic) and that microhardness is an increasing function of z. The chosen simplified shapes k(z) and H(z), represented in figures 12 and 13, are defined by parameters k 1 ,l 1 ,H 1 ,k 2 ,l 2 and H 2 .

To model the response of the test bar, we also have to make use of the stress field σ 0 , which is determined from the reference test bar. The components of σ 0 (σ 0 12 can be neglected with respect to σ 0 11 and σ 0 22 )a r e reconstructed by matter removal on both sides. Note again that they are obtained up to a certain depth and need to be extended to the whole depth. This extension should ensure that the stress field is statically (equilibrium) and plastically (yield criterion) admissible.

A key assumption of the second method is to assume that the two components σ 0 11 (z) and σ 0 22 (z) have the same profiles and can be appropriately described by a single function s 0 (z) defined in terms of the two parameters σ 0 h and l 0 (see figure 14). This function s 0 (z) is even and corresponds to a parabola in the interval [0,l 0 ], taking a zero value at l 0 . This function is then linear on [l 0 ,h] taking for value σ 0 h at h. The function s 0 (z) is compared to measurements in figure 15 in which the parameters l 0 and σ 0 h are set to 2.2 mm and -740 MPa, respectively.

The function s 0 respects the statical admissibility of the initial stress field σ 0 . This initial stress field must also be plastically admissible, this condition being dependent on the unknown shape k(z).

Before presenting the numerical application, let us summarize the different parameters involved in the modelling of the bending test (forward calculation):

(i) the elastic constants E and ν, (ii) the profiles of the tensile yield strength k(z) and of the modulus of strain hardening H(z), which are functions of k 1 ,k 2 ,H 1 ,H 2 ,l 1 and l 2 , (iii) the initial stress field σ 0 , which is a function of l 0 and σ 0 h . Among these parameters, we consider that E, ν, k 1 ,H 1 ,l 0 and σ 0 h are known. The first four concern the untreated material and are obtained by means of a classical tensile test, the last two are obtained from residual stress measurements on the reference test bar. Thus, the unknown parametres are k 2 , H 2 , l 1 and l 2 .

The cost function J (17) of fields k(z) and H(z)hence reduces to a function J s of vector p = (k 2 ,H 2 ,l 1 ,l 2 ):

J s (p) = 1 n n j =1 γ jc (p) -γ j γ j 2 , (18)
and a minimizer p of J s (p) is sought.

Numerical application

Let us now study the minimization of J s . The difficulties are: (i) the parameters p i have different physical meanings and dimensions, (ii) the values of γ jc (p)(j= 1,...,n) are obtained by performing a forward elastic-plastic calculation. The elastic-plastic law is not sufficiently smooth to allow an exact calculation of the gradient of the function J s by using an adjoint state. The first difficulty can be solved by normalizing the problem. We first define a search domain

[p 1 min ,p 1 max ]× ••• × [p N min ,p N max ]
of the N parameters, the average values of which are p 1 moy ,...,p N moy . We transform the parameter p into a dimensionless parameter p by setting p = D -1 p, D being the diagonal N × N matrix formed by the previous average values. A new cost function Js is then defined by setting

Js ( p) = J s (p),
the gradient of Js being

J ′ s ( p) = DJ ′ s (p).
For the second difficulty, since we do not know the exact expression of gradient J ′ s ,w eh a v ec h o s e nt o approximate it using finite differences.

A subsidiary difficulty is to take some constraints on parameters into account. First, l 1 and l 2 satisfy l 1 l 2 . Besides, the field k(z) must be such that the initial stress field σ 0 is plastically admissible, that's to say √ Q(σ 0 ) -k<0. This condition results in

k 1 - 3 4 h -l 0 l 0 σ 0 h ,k 2 -σ 0 h .
The first inequality concerns known parameters and has already been taken into account through the choice of σ 0 h . The second inequality has to be accounted by the optimization. Constraints l 1 l 2 and k 2 -σ 0 h are imposed by projections in the domain of admissible parameters.

The quasi-Newton algorithm with BFGS's updating formula has been used (see for example [START_REF] Gill | Practical Optimization[END_REF] or [START_REF] Bonnans | Optimisation Numérique[END_REF]. A numerical application of our procedure is now presented, the control parameters being k 2 ,H 2 ,andl 2 . We assume l 1 = l 0 , which means that the domain initially in compression corresponds to the domain in which the properties of the material have been altered by heat treatment. This assumption relies on the experimental estimations of l 0 , given by the measurement of σ 0 (z),andl 1 , given by the observations of the microstructure at different depths. The two parameters l 0 and l 1 are approximately the same. The dimensions of the test bars are L 1 = 220 mm, L 2 = 21 mm and h = 4 mm, the length between B and C is set to 110 mm (d = 45 mm). The elastic and plastic constants of the untreated material are E = 200 GPa, ν = 0.3, k 1 = 455 MPa and H 1 = 6.5 GPa. The two parameters which define the initial stress field, through the function s 0 ,a r e l 0 = 2.2mmandσ 0 h =-740 MPa (the same as the ones used to draw figure 15). The identification is based on the two bending tests which have already been exploited for the first method, enabling the results on the tensile yield strength k(z) to be compared. The values of optimal parameters k 2 ,H 2 and l 2 which have been obtained for the two bending tests are represented in table I.

Figure 16 shows the experimental and computed bending curves (bending moment versus curvature) for optimal parameters k 2 ,H 2 and l 2 , and for each bending test. Finally, figures 17 and 18 present the optimal shapes k(z) and H(z) corresponding to each bending test, the first shape being compared to the one obtained by the first method. We note that the optimization of three parameters enables simulation of the bending test with an excellent accuracy. Furthermore, the experimental bending curves are very close to each other, which suggests that the effects of heat treatment are approximately the same for all test bars. Finally, the agreement between the shapes k(z) obtained by the two methods is quite good.

A sensitivity test

To complete this study, the influence of the affected thickness, which corresponds to hl 1 = hl 0 = hl according to our model, on the accuracy of the identified parameters k 2 ,H 2 and l 2 , is now considered. The interest of this sensitivity analysis is to determine whether our method is still applicable in the case of superficial treatments leading to smaller thicknesses of the affected layer.

To that purpose, the following numerical test is performed. For given values of k 2 , H 2 and l 2 , we compute the bending test using the algorithm of Section 3.5 for increasing values of l and obtain bending curves defining equation γ = f l (M). We add a small perturbation to each curve by replacing the previous equation with the two equations γ = (1 ± δ)f l (M), δ being constant and much smaller than 1. This perturbation corresponds to experimental defects such as imperfectly known kinematical conditions or errors in the model itself. We consider these curves as experimental results, and calculate the optimal parameters k ± 2 (δ, l), H ± 2 (δ, l) and l ± 2 (δ, l) by using our optimization algorithm. The sensitivity of the second method can be quantified by the values of k 2 (δ, l)/k 2 , with

k 2 k 2 (δ, l) = |k + 2 (δ, l) -k - 2 (δ, l)| k 2 ,
H 2 (δ, l)/H 2 and l 2 (δ, l)/ l 2 . Numerical calculations are performed with the constant parameters k 1 = 435 MPa, H 1 = 6.5G P a ,σ 0 h = -710 MPa, k 2 = 750 MPa, H 2 = 60 GPa and l 2 = 3.8 mm. The increasing values of l are 2.2 mm, 2.55 mm, 29 mm, 32.5 mm and 36 mm. Figures 19, 20 and 21 present the values of k 2 /k 2 , H 2 /H 2 and l 2 /l 2 as functions of the proportion of affected material, (hl)/l, for the two different values of δ 0.01 and 0.02. Figure 22 presents the average cost function J s corresponding to the optimal parameters k + 2 ,H + 2 and l + 2 on the one hand, to the optimal parameters k - 2 ,H - 2 and l - 2 on the other hand, as a function of the proportion of affected material and for the two values of δ. We note from figures 19-21 that the stability of the different parameters (at least for k 2 and H 2 ) decreases as the proportion of the affected material decreases. This is quite logical since this proportion must be sufficiently large so that the influence of the plastic parameters which characterize the affected layer on the bending curve is sufficiently strong. The average cost function corresponding to the optimal parameters increases when the proportion of the affected material decreases, which is due to the projections of the parameters in the domain defined by the constraints k 2 -σ 0 h and l 2 h. If the proportion of affected material decreases, k - 2 and l + 2 tends to go out of this domain. Enforcing the previous inequalities increases the difference between the "experimental" and optimal curves.

Conclusions

In this paper, we have proposed an inverse approach to determine the variation with depth z of the tensile yield strength k(z) and of the strain hardening modulus H(z) within a layer of steel affected by induction hardening, using a bending test on a parallelepipedic bar.

The inverse problem has been solved by two methods, first by measuring the residual stresses after the bending test, second by modelling the bending test. The first method is simple from a theoretical point of view, but the technique of X-ray diffraction requires a long time of experimental work. The main drawback of this method is that the number of unknowns is too large compared to the number of measurements, whose accuracy are low. As a consequence, the fields of interest, in particular H(z), are not determined with a satisfactory accuracy.

The second method partly solves this problem, by relying on all experimental points of the bending curve and only a few parameters characterizing the general shapes of k(z) and H(z). The main drawback of this method is that these shapes have to be chosen a priori. Microstructural observations have been essential to guide these choices. Furthermore, this method needs the provision of the initial stress field in all the bar, and thus to extend the stress field measured in a certain outer layer to the rest of the bar. This extension also implies a priori choices.

Comparing the two methods, it turns out that the second gives better results than the first, especially for the hardening modulus H(z). It must be pointed out that the quality of the identification strongly depends on the accuracy within which the characteristics of the untreated material are known.

Our numerical sensitivity test shows the limitations of the method. The sensitivity of the identified profiles with respect to experimental errors increases as the thickness of the affected layer decreases, so that the identification is only possible if the proportion of affected material is sufficiently large, say at least 20%. Our approach can be adapted to other superficial treatments than induction hardening, such as, flame quenching, LASER quenching, shot-peening and deep rolling. However, our approach would probably be inadequate for techniques such as plasma-coating which generate too thin layers. As far as treatments like nitriding, carbonitriding and case hardening are concerned, our method would necessitate modifications, since such treatments not only alter the plastic properties of the material but also the elastic ones.

Figure 1 .

 1 Figure 1. The 4-point bending test.

Figure 2 .

 2 Figure 2. Partial removal of matter.

Figure 3 .

 3 Figure 3. Partial removal of matter.

Figure 4 .

 4 Figure 4. Proportion of martensite as a function of depth.

Figure 5 .

 5 Figure 5. Vickers microhardness as a function of depth.

Figure 6 .

 6 Figure 6. Ferrito-perlitic microstructure.Figure 7. Mixed zone. Figure 8. Ferrito-martensitic microstructure.

Figure 7 .

 7 Figure 6. Ferrito-perlitic microstructure.Figure 7. Mixed zone. Figure 8. Ferrito-martensitic microstructure.

Figure 9 .

 9 Figure 9. Component σ 11 as a function of depth for initial, final and maximum load conditions.

Figure 10 .

 10 Figure 10. Component σ 22 as a function of depth for initial, final and maximum load conditions.

Figure 11 .

 11 Figure 11. Shape of the tensile yield strength k(z).

Figure 13 .

 13 Figure 13. A priori shape of H(z).

Figure 14 .Figure 15 .

 1415 Figure 14. Function s 0 adopted to model the variation with depth of σ 0 11 and σ 0 22 .

Figure 16 .

 16 Figure 16. Experimental and computed bending curves.

Figure 17 .

 17 Figure 17. Identified profile k(z).Figure18. Identified profile H(z).

Figure 18 .

 18 Figure 17. Identified profile k(z).Figure18. Identified profile H(z).

Figure 19 .

 19 Figure 19. Influence of the proportion of affected material on the sensitivity of k 2 .

Figure 20 .

 20 Figure 20. Influence of the proportion of affected material on the sensitivity of H 2 .

Figure 21 .

 21 Figure 21. Influence of the proportion of affected material on the sensitivity of l 2 .

Figure 22 .

 22 Figure 22. Average cost function for optimal parameters.

Table I .

 I Computed values of k 2 , H 2 and l 2 in the second method.

		k 2 (MPa)	H 2 (GPa)	l 2 (mm)
	Test bar 1	749	60	3.88
	Test bar 2	741	53.5	3.89

Acknowledgements

We thank M. Bonnet and Y. Leroy for helpful discussions.


El Hassani

El Mouden

Large-scale geographic patterns of mercury contamination in Morocco revealed by freshwater turtles

Keywords: bio-monitoring, chelonian, Hg, keratinized tissues, Mauremys, rivers

Mercury (Hg) is a toxic contaminant present in most aquatic ecosystems. High concentrations pose serious threats to organisms and to human health. Because previous studies focused on few countries, environmental hazard due to Hg contamination remains obscure in many geographic areas, and for example limited information is available in North Africa. We examined total Hg contamination in 13 sites in Morocco (12 rivers and one lake) spread over a large area, 400 km northsouth and 350 km west-east, that encompasses different biogeographic zones separated by the Atlas Mountains. Due to their longevity and sedentary habits, we used freshwater turtles as biological probes to monitor Hg exposure. Keratinized tissues reflect long-term Hg exposure; thus, we assayed Hg concentration in the claws of > 200 individuals and supplemented these data with blood Hg concentrations of > 60 individuals (a tissue that provides shorter term Hg exposure integration). The results provide the first largescale picture of Hg contamination in the aquatic freshwater systems of Morocco. Comparisons with previous studies revealed that some of the sites were highly contaminated (e.g. mean Hg concentrations were above 5 μg g -1 , a very high level in keratinized tissues) whereas other sites presented moderate or baseline levels. Unexpectedly, all highly contaminated sites were found in less densely populated areas, while more densely urbanized northern sites, even the sewers of large cities, were not highly contaminated. We hypothesize that silver mining activities in the southern High Atlas and in the Anti-Atlas contaminate rivers of the catchment basins over long distances. These findings indicate that fish, water consumption and contamination levels in local people should be further scrutinized

Introduction

Mercury (Hg) is a widespread contaminant that originates from various natural and anthropogenic sources [START_REF] Mason | The biogeochemical cycling of elemental mercury: anthropogenic influences[END_REF][START_REF] Selin | Global biogeochemical cycling of mercury: a review[END_REF]). It can be transported by atmospheric and water fluxes and it tends to concentrate in aquatic ecosystems, sometimes creating reservoirs that can release considerable amounts of Hg into the environment [START_REF] Morel | The Chemical cycle and bioaccumulation of mercury[END_REF][START_REF] Mason | Role of the ocean in the global mercury cycle[END_REF]. Hg is a toxic element that circulates rapidly across trophic levels, accumulates in animal tissues, and reaches deleterious concentrations especially in predators, including humans [START_REF] Jernelöv | Mercury accumulation in food chains[END_REF]Aschner & Aschner 1990;[START_REF] Boening | Ecological effects, transport, and fate of mercury: a general review[END_REF][START_REF] Bernhoft | Mercury toxicity and treatment: a review of the literature[END_REF][START_REF] Driscoll | Mercury as a global pollutant: sources, pathways, and effects[END_REF]. Complex physico-chemical and biochemical processes are involved in the global fluxes of Hg across ecosystems and organisms, including air transport (e.g. Hg vapor Hg0), precipitation, deposition, transformation (e.g. Hg is methylated by microorganisms to form methyl-Hg), as well as various degrees of assimilation and accumulation by plants and animals [START_REF] Miller | Estimation and mapping of wet and dry mercury deposition across northeastern North America[END_REF]. Although it is important to study the whole process in order to precisely track Hg and accurately address environmental and health issues, comprehensive assessment of Hg contamination in entire trophic webs is often logistically unfeasible. Consequently, vast geographic regions have been insufficiently investigated or not monitored at all. In this broad context, identifying reference organisms and using simple sampling techniques is a useful approach for large scale tracking of Hg accumulation in water ecosystem.

In North Africa, broad scale estimates of atmospheric Hg deposits suggest that such contamination represents a potential environmental threat [START_REF] Pirrone | Mercury emissions to the atmosphere from natural and anthropogenic sources in the Mediterranean region[END_REF][START_REF] Pacyna | Global emission of mercury to the atmosphere from anthropogenic sources in 2005 and projections to 2020[END_REF]). Yet, few local-scale studies are available, they provided contrasting results. In an Algerian site, elevated groundwater Hg concentrations have been reported and associated with worrying contamination levels of schoolchildren [START_REF] Benhamza | Contamination by mercury of groundwater of the North Numidian zone of Azzaba, North East Algéria. Effect of inorganic mercury contamination of population[END_REF]. In Morocco, low concentrations of Hg were found in commercialized fish and cephalopods [START_REF] Chahid | Contents of cadmium, mercury and lead in fish from the Atlantic sea (Morocco) determined by atomic absorption spectrometry[END_REF] and in humans that regularly consume these animals [START_REF] Elhamri | Hair mercury levels in relation to fish consumption in a community of the Moroccan Mediterranean coast[END_REF]; but relatively high levels were detected in the Mediterranean mussel Mytilus galloprovincialis [START_REF] Maanan | Biomonitoring of heavy metals using Mytilus galloprovincialis in Safi coastal waters, Morocco[END_REF]. Another study documented high metal contamination of a river mouth in a densely populated area, but confusing effects of the tide and water currents generated complex and fluctuating patterns [START_REF] Bennasser | Assessment of the metals contamination of the low Sebou sediments (Morocco)[END_REF]. Overall, to the best of our knowledge, published information regarding Hg concentrations of the environment in North Africa is restricted to a small number of sites and is partly blurred by ambivalent results and by the impact of confusing factors. Improving our knowledge is important for mapping the relative risk due to Hg contamination at large scale, especially in continental aquatic ecosystems where Hg tends to bioaccumulate in its most toxic form, i.e. methyl-Hg. Because substantial spatial and temporal variations of Hg water contamination further complicate assessments [START_REF] Bindler | Does within-bog spatial variability of mercury and lead constrain reconstructions of absolute deposition rates from single peat records? The example of Store Mosse, Sweden[END_REF][START_REF] Selin | Seasonal and spatial patterns of mercury wet deposition in the United States: Constraints on the contribution from North American anthropogenic sources[END_REF], reference values collected over a large spatial scale are needed.

In this study, freshwater turtles were used as bioindicators to monitor Hg contamination across a wide geographic gradient in Morocco, ranging from semiarid Mediterranean to highly arid sub-Saharan climatic zones. The gradient encompasses rivers situated in the plains of northern Morocco to the southern part of the Atlas Mountains. It also includes both highly urbanized and sparsely populated rural areas. Despite the complexity of the processes governing trace metal accumulation, Hg contamination generally tends to increase in urban and industrialized areas compared to rural areas [START_REF] Rutter | A comparison of speciated atmospheric mercury at an urban center and an upwind rural location[END_REF][START_REF] Wei | A review of heavy metal contaminations in urban soils, urban road dusts and agricultural soils from China[END_REF][START_REF] Azimi | Effect of mercury pollution on the urban environment and human health[END_REF]. Thus, rivers crossing large cities should be more contaminated compared to those running from the foothills of the Atlas in rural areas with low population density.

Freshwater turtles are useful biological probes for tracking Hg in the aquatic environment [START_REF] Bergeron | Influence of feeding ecology on blood mercury concentrations in four species of turtles[END_REF]Hopkins et al. 2013a;[START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF]. They feed on relatively high trophic levels and exhibit a high somatic conversion rate of the food: two features that explain their ability to integrate long-term Hg exposure into their tissues that express a slow turn over (e.g. dermis, bones). The most toxic form of Hg, MeHg, tends to bioaccumulate and to bind to keratin and hence is expected to be deposited in the keratin rich claws. Precisely, Hg concentrations recorded in the keratinized tissues of turtles offer a reliable way to monitor long-term Hg accumulation caused by environmental exposure in contaminated areas (Hopkins et al. 2013a). In contrast, monitoring Hg concentrations directly in waters and sediments is challenging due to the strong temporal fluctuations caused by events such as flooding and highly variable flow rates. Precisely Moroccan rivers are subjected to extremely strong flooding events (Zielhofer et al. 2010;Tramblay et al. 2012). Terrestrial and freshwater chelonians are long-lived organisms with limited capacity for long-distance migrations. Most individuals are philopatric and have a small home range in comparison to other widely sampled vertebrates (e.g. birds and mammals). The contamination levels of their tissues should reflect their local environment while migrating or wandering animals can be contaminated far from the place where they have been sampled. Therefore, sedentary species like turtles provide relatively spatially accurate information. Many freshwater turtles are easy to catch, tolerant to manipulation and they are abundant in many aquatic ecosystems.

Their claws provide suitable keratinized tissues for assays, allowing nonlethal monitoring of Hg concentrations (Hopkins et al. 2013a;[START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF]. In addition, blood can be easily retrieved via venipuncture; this provides a complementary tissue to assess short-term (e.g. days, weeks) exposure to Hg contamination (Hopkins et al. 2013a). Freshwater turtles are characterized by indeterminate growth (growth continues after sexual maturity), they display strong variations of growth trajectories and thus many populations contain a wide range of juvenile and adult body sizes (Rhen and Lang 1995). Most studies showed a positive relationship between body mass and Hg contamination, older and larger individuals accumulating contaminants over time [START_REF] Meyers-Schöne | Comparison of two freshwater turtle species as monitors of radionuclide and chemical contamination: DNA damage and residue analysis[END_REF][START_REF] Bergeron | Influence of feeding ecology on blood mercury concentrations in four species of turtles[END_REF]). Overall, freshwater turtles display a unique set of features that allow the surveillance of Hg in aquatic systems using cost-effective and minimally invasive field procedures.

We sampled more than 200 individuals of Mediterranean turtles (Mauremys leprosa), a freshwater species locally abundant and widely distributed over a very large area in the western Mediterranean region. Using non-destructive techniques, we collected blood and cut the tip of claws in order to assay Hg concentrations in these two tissues. Overall, we sampled 12 rivers and one artificial lake. Our main objectives were twofold. Firstly, we examined if the claws and the blood of a previously untested chelonian species in a previously untested area were effectively contaminated by Hg. This methodological objective aimed to test if M. leprosa can be used as a possible biological probe across its vast distribution range around Mediterranean areas and in North Africa. Secondly, providing that the first objective was fulfilled, we intended to perform the first large-scale assessment of Hg contamination of Morocco using a uniform methodology. Indeed, continental waters of the Maghreb region are seriously threatened by climatic changes (Schilling et al. 2012). They are overexploited and polluted to supply agricultural, industrial and touristic activities. Preserving water resources in Morocco is urgent and of paramount importance. Thus, assessing Hg concentrations, one of the most widespread water pollutants, represents a key environmental and health issue.

In practice, we addressed three main successive questions:

1) Do Mediterranean turtles exhibit significant Hg concentrations in their claws and in their blood as observed in several other species?

2) Is there a significant relationship between body mass and Hg concentration levels?

3) Are Hg burdens related to the putative sources of Hg in a broad geographical context? For example, are Hg concentrations measured in turtles proportional to the density of industrial or municipal sources across Morocco?

Material and methods

Study sites

From 2012 to 2016, we sampled 13 aquatic sites (12 rivers and 1 lake) spread across a wide area of Morocco (Table 1; supplementary material Table A; Fig. 1), ~ 400 km north-south versus ~ 350 km west-east that includes very large and small cities, i.e.

Fes (34° 02′ 16″ N-5° 00′ 12″ W), Marrakech (31° 37′ 40″ N-7° 59′ 05″ W), Agdez (30° 40′ 31″ N-6° 24′ 25″ W) and Meski (31° 51′ 15″ N-4° 16′ 49″ W). A large mountainous formation represented by the High Atlas (> 4100 altitude max) and the Middle Atlas (> 3350 altitude max) divides the study area into four major biogeographical zones. A typical Mediterranean semi-arid climate occurs in the plains of the most northern sites (e.g. Moulay Driss site). A more arid and hot climate prevails in the north foothills of the High Atlas (e.g. Marrakech site). A sub-Saharan arid and hot climate characterize the sites situated in the southern parts (e.g. Ouarzazate, Agdez), and a semi-arid continental (cold in winter and hot in summer) climate occurs in the area between the High Atlas and the Middle Atlas (Zaïda site). Importantly, the main mountain chains separated major large catchment basins. For instance, the rivers sampled at the sites 1, 2 and 3 belong to the same aquatic system; similarly, the river sampled at the site 5 is an affluent of the river of the site 6. The rivers sampled at the sites 9, 10 and 13 converge to the lake (site 12) which in turn supplies the river sampled at the site 11. Therefore, the 13 sites sampled could be assigned to three main geographic areas (Fig. 1): rivers running from the North slopes of the Atlas (sites 1-6), rivers running from the region situated between the High Atlas and the Middle Atlas toward the east (sites 7 and 8) and rivers (+ one lake) running from the south slopes of the High Atlas toward the west and/or the south (sites 9-13). In analysis, we considered these three main catchment basins rather than the four major biogeographical zones.

Within these main catchment basins, we sampled a variety of sites, considering the origin of each river, flow rate, continuity of the aquatic system and degree of anthropogenic pressure. Some sampling sites were situated upstream or downstream of cities with highly variable population sizes, from less than 1000 people to more than one million inhabitants (supplementary material Table A). Several rivers are interrupted most of the year, except during infrequent flooding events. Several sites were situated at the sewers of the cities (e.g. Fes), while other rivers ran directly from the mountains without crossing any urbanized area except very small villages (e.g.

Ouaoumana) (Table 1; supplementary material Table A).

Study species

We captured, by hand or using traps baited with fish and/or meat, 262 individuals of the Mediterranean turtle Mauremys leprosa. This species is widespread in Morocco and it often occurs in large numbers. This turtle inhabits various types of freshwater and brackish water bodies and rivers [START_REF] Meek | Aspects of the population ecology of Mauremys caspica in North West Africa[END_REF]. It is a medium size chelonian; females being larger than males [START_REF] Bonnet | Is sexual body shape dimorphism consistent in aquatic and terrestrial chelonians?[END_REF]. In Spain, body size (straight shell length) ranges approximately between 25 and 95 mm in juveniles; the mean body size is 165 mm (max 205 mm) and 145 mm (max 175 mm) respectively in females and males (Muñoz and Nicolau 2006). Measurements recorded in the Moroccan population studied suggest that individuals are slightly larger; the smallest turtles was 34 mm long, the mean body size was 169 mm (max 257 mm) and 154 mm (max 203 mm) respectively in females and in males [START_REF] Bonnet | Blood mixtures: impact of puncture site on blood parameters[END_REF]. In most individuals (> 80%, N = 211), following capture we cut off the extremity of 3 to 5 claws per turtle and kept the samples in Eppendorf tubes filled up with 100% ethanol. We also blood sampled approximately 30% of the individuals (N = 66) and retrieved 0.1 to 0.9 ml of blood (see [START_REF] Bonnet | Blood mixtures: impact of puncture site on blood parameters[END_REF] for puncture details). The blood was immediately centrifuged (at 10,000×g for 3 min) to separate plasma from blood cells (essentially erythrocytes; hereafter referred as 'RBC' for red blood cells).

Absolute ethanol was then added to RBC for preservation. We recorded sex, body size (straight shell length, SSL with a calliper) and body mass (± 1 g measured with an electronic scale). Body condition was expressed as log-body mass scaled by logbody size [START_REF] Bonnet | Sexual dimorphism in steppe tortoises (Testudo horsfieldii): influence of the environment and sexual selection on body shape and mobility[END_REF]. It is an integrative index of the health and trophic status of individuals that accounts for body reserves (lipidic, proteic, glucid reserves), gut content and clutch mass notably [START_REF] Bonnet | Is sexual body shape dimorphism consistent in aquatic and terrestrial chelonians?[END_REF]). Individual body condition was calculated as the residual value from the linear regression of body size length against body mass [START_REF] Bonnet | Sexual dimorphism in steppe tortoises (Testudo horsfieldii): influence of the environment and sexual selection on body shape and mobility[END_REF]. Each turtle was permanently marked (shell notches) and rapidly released at the site of capture.

Two subspecies of the Mediterranean turtle have been identified, M. l. leprosa and Mauremys leprosa saharica. The ridge of the High Atlas separates their respective distribution range (M. l. leprosa in the north and M. l. saharica in the south; [START_REF] Fritz | Impact of mountain chains, sea straits and peripheral populations on genetic and taxonomic structure of a freshwater turtle, Mauremys leprosa (Reptilia, Testudines, Geoemydidae)[END_REF]). Only M. l. saharica occurs in the southern sites sampled (sites 7 to 13; Fig. 1). In this subspecies, individuals were either moderately or highly contaminated (see the Results section). Thus, the geographical differences in contamination levels we observed were not blurred by this taxonomic issue.

Mercury analysis

Total Hg concentration measurements were performed on dried tissue aliquots ranging from 2 to 10 mg using an Advanced Mercury Analyzer (AMA-254, Altec) as described in [START_REF] Blévin | Wide range of mercury contamination in chicks of Southern Ocean seabirds[END_REF]. The analytical process consists of a drying period prior to a combustion phase at 750 °C which leads to the release of Hg from the samples. Subsequently, the Hg vapor produced is carried by an oxygen flow to a gold amalgamator and trapped on its surface. Thereafter, the collected Hg is liberated from the amalgamator by a short heat-up and then detected by atomic absorption spectrophotometry.

All analyses were repeated two to three times until reaching a relative standard deviation below 5%. Accuracy was checked using TORT-2 Lobster Hepatopancreas (NRC, Canada) as certified reference material (0.27 ± 0.06 μg g -1 dwt), and results were in good agreement with the certified values (0.24 ± 0.04 μg g -1 dwt, N = 6).

Blanks (control samples) were analysed at the beginning of each set of samples and the detection limit of the method was 0.05 ng. All Hg concentrations are expressed as micrograms per gram dry weight (dw).

Statistical analyses

Not all measurements were recorded on each individual and it was often impossible to determine the sex of small individuals. Therefore, sample size varied from 66 for Hg concentration assayed in the RBC, to 213 for claw sampling, and to 262 for SSL. In several individuals, sampling was incomplete (e.g. two body masses not available), generating modest fluctuations in the final sample size used for analyses.

The relationship between the Hg concentrations respectively assayed in the claws and in the RBC was assessed using a linear regression on 34 individuals where both tissues were analysed. In this subsample, the normal probability plot of the residuals (that exhibited a normal distribution) was approximately linear. This indicates that the error terms were normally distributed in this analysis. Further, a careful inspection of the data set revealed that it was free from outliers (see the Results for the correlation between Hg concentrations measured in the RBC and in the claws r = 0.92 and r = 0.94 using respectively untransformed and Box-Cox transformed data; nonparametric tests were not affected). In addition to site (the main factor), sex (categorical factor) and body mass (continuous covariate) were implemented in the analyses because these factors can influence contamination levels in some turtle species [START_REF] Meyers-Schöne | Comparison of two freshwater turtle species as monitors of radionuclide and chemical contamination: DNA damage and residue analysis[END_REF][START_REF] Bergeron | Influence of feeding ecology on blood mercury concentrations in four species of turtles[END_REF] albeit not in others (Hopkins et al. 2013b). Body size and body mass were highly correlated (R2 = 0.98, F1, 258 = 10,986, P < 0.001). Each individual was represented only once. Analyses were performed with STATISTICA.12 (StatSoft France 2013, www.statsoft.fr.)

Results

Hg concentrations varied across a wide range of values, from 0.030 to 13.956 μg g -1 in the claws (mean 1.756 ± 2.308 μg g -1 , n = 211) and from 0.011 to 2.114 μg g -1 in the RBC (mean 0.260 ± 0.394 μg g -1 , n = 66). This wide spectrum of variation among individuals shows that in certain cases, the targeted tissues were able to concentrate appreciable amounts of Hg in M. leprosa.

Comparison between RBC and claw Hg concentrations

The Hg concentrations measured in the RBC and in the claws were highly correlated (r = 0.92, F1, 32 = 187.67, P < 0.001, N = 34 individuals with both RBC and claws sampled, Fig. 2). The values recorded in the claws were significantly higher (Wilcoxon test for paired samples, Z = 5.069, P < 0.001).

Relationship between body mass and Hg concentrations

We found significant negative correlations between body mass and Hg concentrations measured in the claws (r = -0.33, F1, 207 = 25.71, P < 0.001, N = 209) and in the RBC (r = -0.75, F1, 56 = 75.41, P < 0.001, N = 58) (Fig. 3). A small proportion of the variance was explained in the first correlation (R² = 11%), but this proportion was elevated in the second (R² = 56%). Considering each of the three main catchment basins separately, negative correlations were found only in the turtles sampled in the south slope rivers (r = -0.433, P < 0.001 and r = -0.611, P < 0.002 for Hg concentrations measured in the claws and in the RBC, respectively); in the two other basins, we found no significant correlation (Fig. 3).

A stepwise backward multiple regression suggested that the body condition of the individuals was best explained when the Hg contamination level was taken into account (Table 2). Indeed, the model was slightly, albeit significantly, improved when Hg concentration was included in addition to body size (straight shell length, SSL). Importantly, the coefficient for Hg concentrations was negative (Table 2).

Geographic differences

The mean body size of the turtles varied among sites (ANOVA using SSL as the dependent variable, F12, 198 = 5.325, P < 0.001 or using BM, F12, 196 = 5.065, P < 0.001). Therefore, we considered body mass (BM) in subsequent analyses. The Hg concentrations measured in the claws differed markedly among the aquatic sites sampled (Table 3; Figs. 3 and4a). As sex has no significant effect on Hg concentrations, analyses were performed again without this factor; this allowed us to include 15 small unsexed individuals (Table 3). Because the effect of body mass was significant, we also presented mean values adjusted to body mass (Fig. 4b). The site main effect remained very strong (Table 3), with significant differences among most sites (Table 4). Considering the three main catchment basins, a GLM analysis revealed strong effects on Hg concentrations in claws (see grey patterns in Fig. 3 and Table 5). The minimal Hg concentration (an index of the background level) varied among these three main areas: 0.03, 0.24 and 0.78 μg g -1 respectively in the north-, east-and south-oriented slopes of the mountains.

The smaller sample size based on RBC did not include the two sites situated in the most eastern part of the studied geographic area (i.e. Zaïda and Meski). It was nonetheless possible to compare the rivers downstream of the North versus South slopes of the Atlas. We found a strong differences between these broad areas (Kruskal-Wallis test, H1 = 42.862, P < 0.001, N = 66). The mean values were 0.052 ± 0.042 μg g -1 (N = 43) in the north and in the south and 0.650 ± 0.057 μg g -1 (N = 23), and thus, they were approximately one order of magnitude higher in the southern aquatic systems.

Discussion

The current survey performed over a large geographic scale on a large sample size of Mediterranean turtles revealed very strong differences of Hg contamination across the freshwater systems of Morocco. The mean concentrations recorded suggest that some sites were highly contaminated whereas others presented moderate or low contamination levels. The variation across sites was not random. Instead, all the sites sampled that are supplied by waters running from the south slopes of the High Atlas were highly contaminated whereas contamination remained moderate or low in the other sites. Below we discuss methodological issues regarding the use of freshwater turtles to investigate Hg contamination in the environment; next, we consider the strong contrasts observed among the sites. sentinels of marine environments, Hg concentrations recorded in feathers (a keratinized tissue) above a mean value of 2 μg g -1 induce deleterious population effects (Goutte et al. 2014). In general, a mean value of 5 μg g -1 is considered as a threshold above which negative effects are expected in birds (Eisler 1987;Fig. 5 in Burger and Gochfeld 2004). Thus, our data clearly reveal high contamination levels specifically in the aquatic systems downstream of the south slopes of the High Atlas (yet the proportion of methyl-Hg should be investigated for a more accurate assessment; Blanvillain et al. 2007).

Usefulness of M. leprosa to track Hg contamination

Rivers are rapidly changing systems, especially in arid countries like Morocco where sudden flooding events can quickly strip sediments, reshape banks and modify the delimitation of the main and secondary beds (Zielhofer et al. 2010). In this everchanging context, assessing chronic environmental exposure to contaminants can be particularly difficult. Long-lived sedentary organisms that can be sampled individually offer a valuable way to circumvent this difficulty and to integrate temporal variations of Hg exposure, providing that they accumulate and retain Hg in their tissues. Our results precisely show that M. leprosa fulfils this criterion. Such capacity of accumulation is particularly valuable in the context of rapid and seasonal changes of water flows combined with possible time variations of Hg release from the sources toward rivers.

Hg shows an affinity for keratinized tissues due to their high sulphur content. Thus, Hg tends to accumulate in the claws of reptiles. Sampling this tissue is particularly useful because the tip of the claws can be easily taken without damaging individuals (Hopkins et al. 2013a;[START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF]. The wide range of variation of Hg concentrations among individuals with the elevated maximal values we found in this study revealed that M. leprosa is an appropriate species to monitor Hg. The strong correlation we found between Hg concentrations measured in claws and RBC, with higher concentrations in the former, has been previously documented in other species (Hopkins et al. 2013b;[START_REF] Schneider | Mercury contamination in reptiles: an emerging problem with consequences for wild life and human health. Mercury: Sources, Applications and Health Impacts[END_REF]. The most accurate contamination signal to survey a polluted river was obtained from claws due to their higher accumulating potential (Hopkins et al. 2013a). However, the differences we observed between claw and RBC concentrations in the most contaminated catchment basin, along with the strong negative relationship between body mass and RBC Hg concentrations (this relationship was weaker with claws), suggest that these tissues offer complementary measures for Hg exposure (Fig. 3). Claws grow slowly and provide long-term accumulation assessment while relatively rapidly renewed blood cells rather reflects short-term exposure and likely provides more dynamic results.

The steep and strong negative correlation between body mass and Hg concentration is likely associated to an ontogenic shift in foraging ecology. This relationship can be used as a correcting factor to calibrate environmental monitoring of Hg exposure, at least in areas where Hg contamination is substantial.

Large-scale geographic variations

Our most salient results regarding Hg concentrations were the clear geographical pattern and the negative effect of body mass (Table 4; Fig. 3). The significant influence of body mass on Hg concentrations was negative, but significant only in the most contaminated area and thus of secondary importance compared to the dominant effect of site. Exploring underlying physiological or behavioural mechanisms that explain why small turtles tended to accumulate more Hg than larger ones was out of scope of the current study. This significant effect was taken into account during the analyses, however. Thus, possible differences among populations regarding mean body size or sex ratio could not account for the strong geographic differences we observed. Moreover, the assays performed in the claws and in the blood provided parallel outcomes: the rivers downstream the south slopes of the Atlas were highly contaminated, exhibiting mean concentrations ten times higher than in other sites. Thus, both long-term integration of claws measurements (i.e. months; Hopkins et al. 2013b) and short-term integration of blood assays (i.e. days-weeks; Hopkins et al. 2013a, b) converged to show that all rivers (and one lake) connected to the catchment basins of the southern slopes of the Atlas were highly contaminated by Hg.

The rivers we sampled in the valleys down the southern slopes of the Atlas also receive the waters from the northern slopes of the Anti-Atlas chain (Fig. 1). In the Anti-Atlas (> 3300 altitude max), mining industries (e.g. Imiter Mine, Jbel Saghro) exploit a peculiar silver ore, Ag2HgS2, named imiterite [START_REF] Guillou | L'imitérite, Ag2HgS2, nouvelle espèce minérale; propriétés et structure cristalline[END_REF]. This mineral contains appreciable amounts of Hg 2+ [START_REF] Guillou | L'imitérite, Ag2HgS2, nouvelle espèce minérale; propriétés et structure cristalline[END_REF] that can be released in the environment during the extraction of silver. Other mineral deposits precisely situated upstream of the sites we sampled present similarities with the Imiter type deposit; several have been exploited previously or are currently exploited [START_REF] Marcoux | The Ag Hg Zgounder ore deposit (Jebel Siroua, Anti-Atlas, Morocco): a Neoproterozoic epithermal mineralization of the Imiter type[END_REF]. Overall, in the Anti-Atlas, the extraction of mercuriferous native silver (2 to 30 wt% Hg; Marcoux andWadjinny 2005) may explain the high level of Hg contamination of the rivers and lakes situated downstream. The Anti-Atlas region of Morocco is considered as a silver metallogenic province [START_REF] Marcoux | The Ag Hg Zgounder ore deposit (Jebel Siroua, Anti-Atlas, Morocco): a Neoproterozoic epithermal mineralization of the Imiter type[END_REF]. Although our sampling strategy was not designed to assess this issue, our data fit well with this scenario. The rivers situated in the valleys that collect the water from the Anti-Atlas were the most contaminated; they all converge to the Ouarzazate artificial lake. Accumulating sediments may favour the fixation and methylation of Hg where the turtles forage or shelter (M. leprosa is a riverbed dweller). One site (11, Oued Drâa; Fig. 1) does not receive waters directly exposed to mine activities, but it is approximately 60 km downstream of the lake and it is also highly contaminated (the water of Oued Drâa is supplied by the dam).

Further investigations are required to better understand if the high Hg contamination of the rivers that run between the southern slopes of the Atlas and the northern slopes of the Anti-Atlas is caused by silver deposit exploitations (e.g. using discriminant isotopic signatures of Hg). Moreover, other types of mining, industrial and urban activities that can release various trace metals in the environment (e.g. Cd, Cu, Pb and Zn) should be considered to obtain a more comprehensive view of water contamination by trace metals in Morocco [START_REF] Sedki | Toxic and essential trace metals in muscle, liver and kidney of bovines from a polluted area of Morocco[END_REF][START_REF] Barkouch | Well water contamination at a mining extract zone near Marrakech city in Morocco[END_REF]. Due to complex and often very ancient geological structures, ore deposits and mine exploitations are abundant and very diverse, and they are spread across most of the country [START_REF] Mouttaqi | Les principales mines du Maroc[END_REF]). Yet, they mostly concentrate in the northern slopes of the old formations (> 400 MA) of the Anti-Atlas (Figs. 1 and 2 in [START_REF] Mouttaqi | Les principales mines du Maroc[END_REF].

Influence of Hg concentration on body condition

We found a negative correlation between Hg concentration and turtle body condition (Table 2). Although this effect was weak, it was highly significant (Table 2). Perhaps high levels of Hg contamination perturb the physiology of the turtles as shown in other organisms [START_REF] Tan | The endocrine effects of mercury in humans and wildlife[END_REF]. Mean Hg concentrations measured in the dermis of the turtles sampled down the southern slopes of the Atlas were above a critical threshold of 5 μg g -1 , a value not yet tested/validated in chelonians or in other nonavian reptiles, however (Burger and Gochfeld 2004). Considering RBC concentrations, mean values ranging between 0.6 and 1 μg g -1 are however sufficient to perturb the hormonal physiology of turtles [START_REF] Meyer | Mercury exposure associated with altered plasma thyroid hormones in the declining western pond turtle (Emys marmorata) from California Mountain Streams[END_REF]; our results fall exactly within this range of variation. Alternatively, other environmental factors of the sites sampled may have influenced individual body condition independently from a possible impact of Hg contamination. For example, turtles sampled in sewers of the large cities may benefit from abundant food resources and permanent water availability. All these sites were situated in catchment basins not exposed to mining activity and thus poorly contaminated by Hg. Experimental and more focused field studies are needed to tease apart these yet fragile hypotheses.

Conclusions

Our results raise serious concerns about possible chronic exposure to Hg in the populations that live in vast areas of Morocco [START_REF] Tan | The endocrine effects of mercury in humans and wildlife[END_REF][START_REF] Green | Mercury contamination in turtles and implications for human health[END_REF].

Consumption of fish taken in the most contaminated rivers, combined with the use of highly contaminated water for irrigation, domestic needs, and for livestock consumption, may contaminate human populations. It would be informative to measure the concentrations of Hg in the most exposed populations, for example in the hairs. Different Mauremys species are spread over an immense geographic area that extends from southern Europe, North Africa and China. This taxon might be useful to track Hg exposure risks at a very large scale; museum collection might be used to investigate long-term trends.

Table 1. Broad characteristics of the 13 study sites sampled. The name of each river (+ one lake) and of the nearest city (in brackets) are provided. Site number (1 -13) and locations are also indicated in the Figure 1. Climatic characteristics were derived from [START_REF] Mokhtari | Spatialisation des bioclimats, de l'aridité et des étages de végétation du Maroc[END_REF]. Further hydraulic information regarding each site is provided column 4 and 5. The last column (N) provides the number of turtle sampled per site.

Table 4: Parameter estimates using GLM analysis to explore the effect of geographic site on Hg concentrations measured in the claws of freshwater turtles; body mass was implemented as a covariate. Site number is indicated in brackets (see Figure 1 for locations). Although 13 sites were sampled, one (Zaïda, site #6) was retained as a reference and thus results are provided for 12 sites.

Figure 1. Location of the 13 aquatic sites sampled along a wide geographical gradient in Morocco. Each site is referred to a number for simplicity, the name of the river, and the name of the nearest city in brackets. The rivers 1 -6 situated north to the high Atlas and middle Atlas chains run toward the west. The river 7 situated between these two chains runs toward the east. The rivers 7 -13 (+ one lake) situated south of the High Atlas and north to the Anti-Atlas (except # 8) run to the south. 1) Sebou (Fes), 2) Sebou (Moulay Driss), 3) Sebou ( Meknes), 4) Ouaoumana (Ouaoumana), 5) Zat (Ait Ourir), 6), Tensift (Marrakech), 7) Moulouya (Zaïda), 8) Ziz (Meski), 9) M'Goun (Kelaat M'Gouna), 10) Dades (Skoura), 11) Draa (Agdez), 12) Lake (Ouarzazate), 13) Iriri (Amerzagan). Map obtained from Ginkgomaps Projet, http://www.ginkgomaps.com/cartes_maroc.html 1). Details and location of each site are provided in Table 1. White, grey and black bars denote respectively sites from the north (siteS 1-6), east (sites 7 and 8) and south catchments basins (sites 9-13). The top graph (a) provides uncorrected mean values; the lower graph (b) provides mean values scaled by body mass

  section).The other analyses were based on larger sample sizes (e.g. N = 211 claw samples), and small individuals were included. The dependent variables were not normally distributed; they were generally skewed toward low values (especially Hg concentrations) or toward high values (SSL), even after log or Box-Cox transformations (all Shapiro-Wilk W < 0.975, P < 0.001); nonetheless, the seconds provided distribution close to normality. Therefore, the effect of geographic sites (the main issue addressed) on contamination levels was modelled with a Poisson distribution of untransformed Hg values and a log link in a generalized linear model (GLM); dispersion parameter was estimated by Pearson's chi-square statistic divided by its degrees of freedom. Analyses were performed again using Box-Cox transformed concentrations and none of the outcome was significantly changed (e.g.

Figure 2 .

 2 Figure 2. Relationship between Hg concentrations assayed in the claws versus blood in 34 Mediterranean turtles.

Figure 3 .

 3 Figure 3. Relationship between body mass and Hg concentration measured in the claw (a) and in the red blood cells (RBC) (b) of Mediterranean turtles. The parameters of the equation were respectively for the claw and for the RBC: R² = -0.110, F1, 207 = 25.710, log [Hg] claw = -0.33 log.BM + 1.09; R² = -0.564, F1, 56 = 72.413, log [Hg] RBC = -0.75 log.BM + 2.56. White, grey and black circles denote respectively sites from the north (sites 1-6), east (sites 7 and 8) and south catchments basins (sites 9-13); see text for further analyses and details

Figure 4 .

 4 Figure 4. Mean Hg concentrations (± SD) measured in the claws of Mediterranean turtles sampled in 13 aquatic sites (site number in X-axis as in Fig. 1). Details and location of each site are provided in Table 1. White, grey and black bars denote respectively sites from the north (siteS 1-6), east (sites 7 and 8) and south catchments basins (sites 9-13). The top graph (a) provides uncorrected mean values; the lower graph (b) provides mean values scaled by body mass

Acknowledgments

The authors thank T. Lechevalier, S. Lecq, and C.L. Michel for assistance during fieldwork. The authors are grateful to C. Churlaud from the Plateforme Analyses Elémentaires of the LIENSs laboratory for her technical support during Hg analyses.

The IUF (Institut Universitaire de France) is acknowledged for its support to PB.

Funding This work was supported by the Hassan II Academy of Sciences and Technics -Morocco (ICGVSA project).

Aschner, M., & Aschner, J. L. (1990). Mercury neurotoxicity: mechanisms of bloodbrain barrier transport. Neuroscience and Biobehavioral Reviews, 14,[169][170][171][172][173][174][175][176]

Comparison with published data

The scientific literature regarding Hg contamination in reptiles, including non-avian and avian taxa, provides abundant data and thus robust references [START_REF] Wayland | Biomarker responses in nesting, common eiders in the Canadian arctic in relation to tissue cadmium, mercury and selenium concentrations[END_REF]Burger and Gochfeld 2004;[START_REF] Turnquist | Mercury concentrations in snapping turtles (Chelydra serpentina) correlate with environmental and landscape characteristics[END_REF][START_REF] Schneider | Mercury contamination in reptiles: an emerging problem with consequences for wild life and human health. Mercury: Sources, Applications and Health Impacts[END_REF][START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF]. In a recent review [START_REF] Schneider | Mercury contamination in reptiles: an emerging problem with consequences for wild life and human health. Mercury: Sources, Applications and Health Impacts[END_REF] summarized, almost all assessments of Hg concentrations recorded in keratinized tissues including 23 chelonian species (N > 29 mean values). The average mean value was 0.717 ± 0.858 μg g -1 with a 95% CI of 0.681 to 1.161, a median of 0.324 and extreme values ranging from 0.002 to 2.851 (derived from the Table 1 in [START_REF] Schneider | Mercury contamination in reptiles: an emerging problem with consequences for wild life and human health. Mercury: Sources, Applications and Health Impacts[END_REF], one extreme outlier excluded). The mean values we observed in the south-eastern sites were all above 2 μg g -1 and reached mean values above 5.5 μg g -1 (Fig. 3). A recent study (Hopkins et al. 2013b) carried out in different sites upstream and downstream of a highly polluted spot in the Holston River (USA) offers a straightforward comparison with the 13 sites we investigated: moderate Hg concentrations were observed in three turtle species living upstream of a former chloralkali plant, but Hg concentrations rose to very high values immediately downstream of the contamination source, and remained elevated more than 100 km downstream. Our results are relatively close regarding the range of mean concentrations across sites (0.196 ± 0.490 to 5.887 ± 3.352 μg g -1 in Morocco versus 2.464 ± 0.339 to ~ 21.000 μg g -1 in the Holston River) and considering maximal values (13.956 in Morocco versus 42.250 μg g -1 in the Holston River). Overall, the high concentrations we found are closer to those recorded in a river classified as highly polluted in the USA (Hopkins et al. 2013b) compared to other systems investigated [START_REF] Schneider | Mercury contamination in reptiles: an emerging problem with consequences for wild life and human health. Mercury: Sources, Applications and Health Impacts[END_REF][START_REF] Schneider | An evaluation of the use of reptile dermal scutes as a non-invasive method to monitor mercury concentrations in the environment[END_REF]. In seabirds that are considered as major Table 2. Results of a backward stepwise regression analysis to examine the influence of Hg contamination on the body condition of the turtles. Log-body mass was implemented as the dependent variable, log-body size (SSL), and Hg concentrations measured in the claw were the explanatory variables. The final model retained both explanatory variables (r = 0.99, adjusted-R² = 0.98, F2, 206 = 5256.37, P < 0.001