Gloriant

Y Zhou

Amélie Fillon
email: amelie.fillon@insa-rennes.fr

D Laillé

T Gloriant

Crystallographic anisotropy of the superelastic and mechanical properties of the Ti-20Zr-3Mo-3Sn alloy evidenced by nanoindentation at the grain scale

Keywords: Titanium alloys, Nanoindentation, Electron backscattered diffraction, superelasticity, mechanical anisotropy, martensitic transformation

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Introduction

Superelasticity and mechanical properties of Ti alloys significantly depends on the crystallographic orientation [START_REF] Inamura | Relationship between Texture and Macroscopic Transformation Strain in Severely Cold-Rolled Ti-Nb-Al Superelastic Alloy[END_REF][START_REF] Chai | Self-accommodation in Ti-Nb shape memory alloys[END_REF][START_REF] Kim | Martensitic transformation and superelastic properties of Ti-Nb base alloys[END_REF][START_REF] Kim | Texture and shape memory behavior of Ti-22Nb-6Ta alloy[END_REF]. Uniaxial tensile tests on single crystals oriented in <100> β , <110> β and <111> β for metastable β-Ti alloys were realized by Zhang et al. [START_REF] Zhang | Elastic properties of Ti-24Nb-4Zr-8Sn single crystals with bcc crystal structure[END_REF] and showed a clear crystallographic anisotropy of the superelasticity and mechanical responses.

Currently, compression pillars have also been used to investigate the local material properties at micron and submicron length scales which rely strongly upon miniaturized specimens [START_REF] Frick | Loss of pseudoelasticity in nickel-titanium sub-micron compression pillars[END_REF][START_REF] Frick | Orientation-independent pseudoelasticity in small-scale NiTi compression pillars[END_REF]. Knowledge of orientation-dependent behavior in superelastic Ti alloys is highly desirable in order to optimize the mechanical performances of functional devices to meet the requirements for any proposed applications. To broaden these experimental studies covering more crystallographic directions in the β-Ti crystals, a large number of differently oriented single crystals would be necessary. However, tremendous resources with regard to specimen preparations prohibit extensive testing programs [START_REF] Britton | The effect of crystal orientation on the indentation response of commercially pure titanium: experiments and simulations[END_REF]. On the other hand, nanoindentation, when combined with suitable analysis methods, has the potential to become an efficient tool to provide desired information on the anisotropic performances at significantly lower resources and cost at micrometer or nanometer scale [START_REF] Frick | Orientation-independent pseudoelasticity in small-scale NiTi compression pillars[END_REF][START_REF] Tromas | Hardness and elastic modulus gradients in plasma-nitrided 316L polycrystalline stainless steel investigated by nanoindentation tomography[END_REF][START_REF] Tromas | Hardness cartography to increase the nanoindentation resolution in heterogeneous materials: Application to a Ni-based single-crystal superalloy[END_REF][START_REF] Frick | Stress-induced martensitic transformations and shape memory at nanometer scales[END_REF][START_REF] Laplanche | Sudden stress-induced transformation events during nanoindentation of NiTi shape memory alloys[END_REF][START_REF] Pathak | Spherical nanoindentation stress-strain curves[END_REF].

Recently, nanoindentation has been also used to investigate the superelastic effect [START_REF] Kumar | Assessment of small-scale deformation characteristics and stress-strain behavior of NiTi based shape memory alloy using nanoindentation[END_REF][START_REF] Wood | Nanoindention response of superelastic materials[END_REF][START_REF] Zhang | Nanoscale pseudoelasticity of single-crystal Cu-Al-Ni shape-memory alloy induced by cyclic nanoindentation[END_REF][START_REF] Nien | Superelasticity of TiNi-based shape memory alloys at micro/nanoscale[END_REF][START_REF] Pfetzing | Nanoindentation of pseudoelastic NiTi shape memory alloys: thermomechanical and microstructural aspects[END_REF][START_REF] Pfetzing-Micklich | Nanoindentation of a pseudoelastic NiTiFe shape memory alloy[END_REF]. When the nanoindentation platform is coupled with optical microscopy, the targeted indent locations can be chosen visibly and precisely [START_REF] Tromas | Hardness cartography to increase the nanoindentation resolution in heterogeneous materials: Application to a Ni-based single-crystal superalloy[END_REF]. As such, a large number of nanoindentations can be performed on individual grains with a wide variety of crystal orientations in polycrystalline materials [START_REF] Tromas | Hardness and elastic modulus gradients in plasma-nitrided 316L polycrystalline stainless steel investigated by nanoindentation tomography[END_REF][START_REF] Jabir | Crystallographic orientation dependence of mechanical properties in the superelastic Ti-24Nb-4Zr-8Sn alloy[END_REF], which is particularly feasible to investigate the anisotropic properties of polycrystalline materials at grain scale. The information on anisotropy of the superelasticity, hardness and elastic modulus at grain scale can be of great interest to understand and predict the influences of texture on the macroscopic properties of engineering alloys. However, only a few concerned experimental studies exist in literature.

Polycrystalline β-metastable Ti-20Zr-3Mo-3Sn alloy (at.%; abbreviated as Ti2033) was investigated in the present work. According to the results in earlier work in our group [START_REF] Gao | Influence of texture and transformation strain on the superelastic performance of a new Ti-20Zr-3Mo-3Sn alloy[END_REF], Ti2033 alloys exhibited good superelasticity with a high strain recovery of 3.5% after solution-treated at 1123 K for 0.5 h, and the effect of texture on the superelasticity of Ti2033

Materials and methods

The Ti2033 alloy was elaborated using cold crucible levitation melting (CCLM) of pure raw materials. The synthesized button-shape ingots were then homogenized at 1223 K for 20 h, 90 % cold-rolled, recrystallized at 1073 K for 0.5 h, and water-quenched, so as to retain the β-metastable phase with appropriate grain size and random texture having all possible crystal orientations.

The phase composition was analyzed by x-ray diffraction (XRD) using a Bruker D8 Advance XRD system with Cu Kα radiation operated at 40 kV and 40 mA over the 2θ range of 36° -95° with a step size of 0.02° and a scanning speed of 0.2°/min. The morphology and grain size was observed by optical microscopy. The crystallographic orientations of individual grains were identified by electron back-scattered diffraction (EBSD) analyses on a JEOL JSM 6400 scanning electron microscope equipped with a TSL EBSD system using an accelerating voltage of 20 kV, a working distance of 15 mm, and a step size of 4 μm. Data were analyzed using CHANNEL 5 software package. The specimens were prepared by electrochemical polishing in an electrolyte composed of perchloric acid (4 vol. %) and methanol (96 vol. %) with a controlled temperature of -14 ~ -16 °C and a controlled electric current of 0.2 A for 45 s. Surface roughness (Ra) was measured by atomic force microscopy (AFM).

Nanoindentation tests were performed on grains with the size larger than 50 µm along the surface normal direction using two indenters: a spherical indenter with a radius of 50 μm (Sp50) and a Berkovich (Bkv) indenter. The two indenters have been calibrated on fused silica. Individual grains with defined orientations by EBSD were located by optical microscopy attached to the instrumented nanoindentation test system. To minimize the influence of grain boundaries and neighboring grains, nanoindentation tests were performed at approximately central area of each targeted grain. A large number of nanoindentation measurements were performed on individual grains to explore their superelastic responses (depth recovery ratio η h and work recovery ratio η w ) and mechanical properties (indentation hardness H IT and indentation modulus E IT ). Measured results were presented in the

Results and discussion

Microstructural characterizations

The XRD profile in Fig. 1a displays the (011), (002), ( 112

Nanoindentation load-displacement curves

Fig. 2 shows the normalized load-displacement (F-h) curves for grains oriented in <001> β , <101> β , and <111> β , respectively. The maximum indentation load was controlled respectively at F m = 60 mN for the Sp50 indenter and at F m = 10 mN for the Bkv indenter, so as to obtain an approximately equivalent maximum indentation depth h m for both indenters (h m ≈ 300 nm). Normalized nanoindentation curves were obtained from the raw load-displacement (F-h) curves by scaling the load and depth by their respective maximum load F m and maximum depth h m . Normalized F/F m -h/h m curves gives more sensitivity to unloading curves and enable a direct reading of η h values which correspond to the x-intercepts of unloading curves, as indicated in Fig. 2a. The depth recovery ratio η h is defined as the recoverable depth divided by the maximum depth h m. The work recovery ratio η w is defined as the ratio of recoverable work to the total work and is represented by the area enclosed between the normalized unloading curve, the y=1 vertical line and the x axis.

Normalized F-h curves allow to emphasize the orientation dependence of η h and η w ratios. When indenting with the Sp50 indenter, the recoverability is highly dependent on the crystallographic orientation of the indented grain: η h and η w for grains orientated in the <001> β direction, noted η h <001> and η w <001> , have the largest values of 82% and 83%, respectively, as compared to η h <101> and η w <101> that present intermediate values of 75% and 75%, and η h <111> and η w <111> that display the lowest values of 69% and 68%. For the Bkv indenter, recovery ratios are relatively low (~32%), with no significant orientation-dependence. The characteristic of unloading curves is closely associated with the recoverability and reflects the deformation mechanisms underneath the indenters. Bkv indenter produces sudden high stresses, leads to an immediate onset of plasticity, and subsequently causes extremely steep unloading curves [START_REF] Jabir | Crystallographic orientation dependence of mechanical properties in the superelastic Ti-24Nb-4Zr-8Sn alloy[END_REF], whereas spherical indentations exhibit gentle and soft unloading curves, suggesting the occurrence of strain accommodation by reversible phase transformation [START_REF] Zhou | Investigation of the superelastic behavior of a Ti-16Zr-13Nb-2Sn sputtered film by nanoindentation[END_REF]. It is noteworthy that measurements of recoverability (η h and η w ) by nanoindentation demonstrate high reproducibility. For instance, using Sp50 indenter, the means values of depth recovery ratio <η h > for each principal direction show very small mean standard deviations of 1.04 %, 0.93 %, and 1.38% for the <001> β , <101> β , and <111> β directions, respectively.

J o u r n a l P r e -p r o o f

Anisotropy of depth and work recovery ratios

To present the crystallographic anisotropy of the superelasticity, depth-and workrecovery ratios of Sp50 and Bkv indentations measured from individual grains were presented in standard stereographic triangles in Fig. 3. With this representation, it is clearly observed that η h and η w values are indeed influenced by the crystallographic orientations. For both indenters, grains orientated in the <001> β direction exhibit the largest η h and η w values, and followed by those of grains oriented in the <101> β and <111> β directions. Besides, the η h and η w values for Sp50 indenter are higher than those for the Bkv indenter in all directions.

J o u r n a l P r e -p r o o f

Specifically, the values of η h and η w for the Sp50 indenter vary in the ranges of 66% -85% and 67% -86%, respectively, for which the ranges are approximately twice of those for the Bkv indenter with η h varying from 29% to 40% and η w from 31% to 38%, respectively. The larger dispersion ranges (∆ (max-min)) of η h and η w values obtained with the Sp50 indenter suggest that spherical indentations are more sensitive to the crystallographic loading direction when compared to the Bkv indentations. It confirms that the spherical nanoindentation is capable of characterizing the crystallographic anisotropy of the depthand work-recoverability involving reversible stress-induced martensitic (SIM) transformation in superelastic alloys. The different nanoindentation behaviors probed using two different indenters is strongly related to the geometry of the indenter tips. Indenting with the Sp50 indenter clearly displays higher recoverability evidencing the superelasticity, whereas Bkv indentations result in more pronounced plastic deformation. The sharp Bkv indenter generates high strain which cannot be accommodated by elastic deformation and stress-induced martensitic transformation (superelastic deformation), so that plastic deformation through dislocation motions is the predominant deformation mechanism under Bkv indenter [START_REF] Pan | Different mechanical response of TiNi film induced by the shape of indenter during nanoindentation[END_REF][START_REF] Ni | Microscopic superelastic behavior of a nickel-titanium alloy under complex loading conditions[END_REF]. In the case of Bkv J o u r n a l P r e -p r o o f indentations, their η h and η w values vary narrowly with respect to crystal orientations. It could be argued that plastic deformation of β phase seems not sensitive to crystallographic direction. The SIM transformation competes with the dislocation motions. The generation of dislocations, on one hand, is not desirable for the occurrence of SIM transformation from β phase to α″ phase, and on the other hand, impedes the reverse transformation from α″ phase to the parent β phase, resulting in a low recoverability. In contrast, the strain field developed underneath the Sp50 indenter is more likely to favor larger martensitic transformation and facilitate the capture of the superelastic nature in metastable β Ti2033 alloy. Therefore, it can be concluded here that the indenters in different geometries generate different strain level, and reveal different amount of elastic, superelastic and plastic deformation, showing the characteristics of different magnitudes of indentation recovery ratios for spherical and Bkv indentations.

It is well established that the superelasticity nature in β-Ti alloys arises from the reversible martensitic transformation between the bcc structure of the parent β phase and the C-centered orthorhombic structure of the stress-induced α'' martensite [START_REF] Gao | Influence of texture and transformation strain on the superelastic performance of a new Ti-20Zr-3Mo-3Sn alloy[END_REF][START_REF] Yang | Texture investigation of the superelastic Ti-24Nb-4Zr-8Sn alloy[END_REF][START_REF] Yang | Characterization of the martensitic transformation in the superelastic Ti-24Nb-4Zr-8Sn alloy by in situ synchrotron X-ray diffraction and dynamic mechanical analysis[END_REF][START_REF] Yang | Plastic deformation via hierarchical nano-sized martensitic J o u r n a l P r e -p r o o f twinning in the metastable β Ti-24Nb-4Zr-8Sn alloy[END_REF]. The formation of α'' phase from a β crystal follows the orientation relationships [START_REF] Duerig | Formation and reversion of stress induced martensite in Ti-10V-2Fe-3Al[END_REF]: {100} β // (100) α″ , and <111> β // [110] α″ . Six lattice correspondence variants Vi (i = 1 to 6) can be defined from the orientation relationship, as shown in Fig. 4. It is commonly assumed that the variant that would accommodate maximum strain along the loading direction (compression or tension) would produce maximum driving force for the martensitic transformation and would thus be preferentially formed in each grain [START_REF] Inamura | Relationship between Texture and Macroscopic Transformation Strain in Severely Cold-Rolled Ti-Nb-Al Superelastic Alloy[END_REF][START_REF] Kim | Texture and shape memory behavior of Ti-22Nb-6Ta alloy[END_REF][START_REF] Tahara | Lattice modulation and superelasticity in oxygen-added β-Ti alloys[END_REF]. Thus, the formation of the favorable variants of stress-induced martensite is dependent on the loading direction. It also suggests that superelastic effect is orientation-dependent. The theoretical maximum value of transformation strain which can be obtained along a given crystallographic direction of the β phase is consisted with the maximum lattice deformation strain that can be obtained along this direction.

J o u r n a l P r e -p r o o f

Fig. 4 The six lattice correspondences between the bcc structure of the β phase and the orthorhombic structure of α″ martensite phase.

When a given vector X in the coordinates of the parent β phase is transformed to X′ in the coordinates of α" phase through martensitic transformation (Fig. 4), the transformation strain of each variant ε 𝛽→𝛼 ′′ (𝑉𝑖) is calculated by [START_REF] Kim | Martensitic transformation, shape memory effect and superelasticity of Ti-Nb binary alloys[END_REF][START_REF] Kim | Crystal structure, transformation strain, and superelastic property of Ti-Nb-Zr and Ti-Nb-Ta alloys[END_REF]:

ε β→α ′′ (Vi) = |𝑋 ′(𝑉𝑖) |-|𝑋| |𝑋| (1)
where 𝑋 ′(𝑉𝑖) = 𝑇 (𝑉𝑖) 𝑋, and T (Vi) represents the lattice distortion matrix expressed in the coordinates of the parent β phase for each martensitic variant. The superelastic recovery is related to the transformation strain which arises from geometric lattice distortions between the β and α″ crystals. Therefore, the transformation strain can be calculated using the lattice parameters of β and α" phases, and their lattice correspondences. Lattice parameters calculated using unit-cell refinement software with the data from the XRD pattern of magnetron-sputtered Ti2033 film elaborated in our lab (in press) were used for the transformation strain calculations of Ti2033 alloys: a β = 3.395 Å, a α″ = 3.219 Å, b α″ = 5.008 Å, and c α″ = 4.874 Å. It is noted that the lattice parameters of β and α″ phases in Ti2033 film were used, rather than those of Ti2033 bulk measured by synchrotron XRD during tensile test [START_REF] Gao | Influence of texture and transformation strain on the superelastic performance of a new Ti-20Zr-3Mo-3Sn alloy[END_REF]. The reason is that the formation of α″ phase in Ti2033 bulk during tensile test is J o u r n a l P r e -p r o o f activated in tension, whereas the α″ phase in Ti2033 film is compression-stress-induced since magnetron-sputtered films elaborated at low sputtering pressure generally exhibit compressive stress due to the atomic peening mechanism [START_REF] Thornton | Internal stresses in titanium, nickel, molybdenum, and tantalum films deposited by cylindrical magnetron sputtering[END_REF]. Nanoindentation closely tends to produce compression loading condition in some sense, so that the martensitic transformation is induced in compression, which makes it more reasonable to use the lattice parameters of Ti2033 film for the calculation of transformation strain in order to rationalize the nanoindentation responses in the present work. implies the strain states under which the β→α″ transformation occurs: positive values for tensile strain state and negative ones for compressive strain state. It is observed that there is a pronounced difference in the magnitude of transformation strain in tension and compression for a given loading direction, suggesting a strong tension-compression asymmetry in the strain response.

This asymmetry phenomenon was commonly observed during uniaxial tests in superelastic β titanium textured alloys [START_REF] Zhang | Elastic properties of Ti-24Nb-4Zr-8Sn single crystals with bcc crystal structure[END_REF][START_REF] Zhang | Fatigue behavior of ultrafine-grained Ti-24Nb-4Zr-8Sn multifunctional biomedical titanium alloy[END_REF] and in NiTi alloys [START_REF] Gall | Tension-compression asymmetry of the stressstrain response in aged single crystal and polycrystalline NiTi[END_REF][START_REF] Gall | The role of texture in tension-compression asymmetry in polycrystalline NiTi[END_REF][START_REF] Mao | EBSD studies of the stress-induced B2-B19′ martensitic transformation in NiTi tubes under uniaxial tension and compression[END_REF]. for a given direction, the one with the largest magnitute was recorded as the theoretical maximum transformation strain under compression for this considered direction and was presented correspondingly in the standard stereographic triangle in Fig. 6. It is shown that the grains oriented in <001> β direction exhibit the maximum transformation strain of 5.4%, and it decreases as the orientation changes from <001> β towards <101> β and <111> β directions, as indicated by the contour lines in Fig. 6. It is clearly observed that transformation strain calculations and experimental η h and η w measurements are in good qualitative agreement following the same trend. That is, the crystallographic anisotropy of the recoverability in η h -IPF and η w -IPF can be rationalized by the calculations of maximum transformation strain under compression on the basis of the crystallographic orientation relationship of the martensitic transformation in β -Ti alloys. Therefore, it is reasonable to accept that the η h -and η w -IPF distributions can capture and reflect the crystallographic anisotropy of the superelasticity. given orientation, the E IT value for Bkv indenter was observed to be lower than that for Sp50 indenter, which is consistent with the results reported for pure titanium [START_REF] Fizanne-Michel | Determination of hardness and elastic modulus inverse pole figures of a polycrystalline commercially pure titanium by coupling nanoindentation and EBSD techniques[END_REF] and Ti2448 alloy [START_REF] Jabir | Crystallographic orientation dependence of mechanical properties in the superelastic Ti-24Nb-4Zr-8Sn alloy[END_REF]. (2)

Anisotropy of the indentation modulus

It is worth noting that the Young's modulus corresponds to uniaxial testing conditions while the indentation modulus is obtained from rather more complex loading conditions with triaxial stress state. The neglect of the triaxial stress state under the indenter introduces some <111> β towards the <101> β and <001> β , which is in a good qualitative agreement with the nanoindentation measurements in Fig. 7. The observed orientation dependence in Ti2033 is consistent with that calculated from the measured elastic stiffness in Ti-29Nb-Ta-Zr and Ti-25Nb-Ta-Zr single crystals [START_REF] Tane | Peculiar elastic behavior of Ti-Nb-Ta-Zr single crystals[END_REF]. Indentation moduli measured by nanoindentation are likely to be overestimated compared to Young's moduli calculated with elastic constants, which is probably due to the overestimation of the true contact area [START_REF] Mirshams | Correlation of nanoindentation measurements of nickel made using geometrically different indenter tips[END_REF][START_REF] Viswanathan | Direct observations and analyses of dislocation substructures in the α phase of an α/β Ti-alloy formed by nanoindentation[END_REF]. Accurate determination of the rue contact area during post-experiment using imaging techniques can be employed only if elastic recovery is negligible, which is not the present case.

J o u r n a l P r e -p r o o f

Indentation hardness

Conclusion

In the present study, the superelastic Ti2033 alloy was investigated by nanoindentation and EBSD in order to shed lights on the crystallographic anisotropy of indentation responses.

The main conclusions were made as follows:

(1) The crystallographic anisotropy of the superelasticity revealed in η h -IPF and η w -IPF can be rationalized by the calculations of maximum transformation strain under compression on the basis of the crystallographic orientation relationship of the martensitic transformation in β-Ti alloys. Therefore, it is reasonable to accept that the nanoindentation η h -and η w -IPF distributions can capture and reflect the crystallographic anisotropy of the superelasticity.

(2) Indentation modulus E IT exhibited orientation dependence for both Sp50 and Bkv indenters. The IPF distributions of the indentation modulus were qualitatively similar to the one predicted by calculations of Young's modulus from the measured elastic constants. No crystallographic anisotropy of indentation hardness was detected, due to multiple slip systems activated in the bcc β crystal.

(3) Indentation responses were strongly determined by the indenter geometry. Spherical nanoindentation is more appropriate to capture the superelastic nature of materials and probe crystallographic anisotropy of the indentation responses, due to the strain distribution field generated under the Sp50 indenter which is smoothly distributed and more favorable for the martensitic transformation (superelastic deformation), as compared to the case of sharp Bkv indenter.

  were studied by macroscale tensile test experiments. In the present study, nanoindentation was employed to characterize the local mechanical properties within individual grains for which orientations were known from prior electron backscattered diffraction (EBSD) mapping. The strategy of coupling nanoindentation with EBSD was to explore the crystallographic anisotropy of the indentation responses in individual grains of β Ti2033 J o u r n a l P r e -p r o o f polycrystalline alloy.

[

  001]-[101]-[111] standard stereographic triangles based on the inverse pole figure (IPF) in surface normal direction (ND, parallel to the indentation direction), in order to build the distribution maps (η h -, η w -, E IT -and H IT -IPF), which could correlate the mechanical properties with the crystallographic orientation of a given individual grain. Note that the points in η h -, η w -, E IT -and H IT -IPFs were positioned according to the orientation J o u r n a l P r e -p r o o f positions of measured grains in the EBSD IPF in ND, and their colors were scaled according to the measured values. Each colored point was related to an average value of at least five measurements.

  Fig. 1 (a) XRD pattern, (b) optical microscope image, (c) EBSD orientation map and (d) inverse pole figure (IPF) in surface normal direction (ND) obtained from the same area in Ti2033 alloy.

Fig. 2

 2 Fig. 2 Normalized F/F m -h/h m nanoindentation curves of Sp50 (continuous curves) and Bkv (dotted curves) indentations applied on: (a) <001> crystals, (b) <101> crystals, and (c) <111> crystals.

Fig. 3

 3 Fig. 3 ηh -IPF and ηw -IPF measured with: (a, b) Sp50 indenter and (c, d) Bkv indenter.

Fig. 5a shows

  Fig.5ashows the coordinate system employed for calculations of transformation strain

Fig. 5 (

 5 Fig. 5 (a) Schematic illustration of the coordinate system employed for calculations of transformation strain. The angle θ denotes the angle between the loading direction and [001] β direction in the considered β grain oriented in [11 ̅ 0] β . (b) Transformation strain ε 𝛽→𝛼 ′′ (𝑉𝑖) of each variant as a function of θ angle.

Fig. 6

 6 Fig. 6 Orientation dependence of the calculated maximum transformation strain associated with the

Fig. 7

 7 Fig. 7 shows the distribution of the indentation modulus, E IT -IPF, for the Sp50 and Bkv indenters. According to color scales, the IPFs were scaled into 3 sections with the dashed lines. The colored points distributed within the IPF triangles for the two indenters follow the same trend: the grains orientated in <001> β and <111> β crystallographic directions exhibit the lowest and largest values, respectively, and grains orientated in <101> β direction fall in the intermediate, which suggests the orientation dependence of E IT . For a

Fig. 7

 7 Fig. 7 Indentation modulus inverse pole figures (E IT -IPF) measured with: (a) the Sp50 indenter and (b) the Bkv indenter.

  difficulties to clearly determine the real local Young's modulus. Nevertheless, the objective of this work was focused on evolution tendency of elastic modulus with respect to the crystallographic orientations, rather than the determination of the absolute value of this local elastic property. Comparison of the values of the Young's and indentation moduli deserves further research. Thus, indentation modulus evolution could be roughly correlated with the evolution of Young's modulus. For a grain orientated in <h k l> direction aligned with the loading axis, the Young's modulus E hkl can be deduced from Eq. 2. The elastic constants of Ti-22Zr alloy, c 11 = 109.2 GPa, c 12 = 98.9 GPa and c 44 = 14.3 GPa[START_REF] Salvador | Discovery of Low-Modulus Ti-Nb-Zr Alloys Based on Machine Learning and First-Principles Calculations[END_REF], were used for the calculation of theoretical Young's modulus and were considered for discussion and comparison with indentation moduli measured in our Ti2033 alloy.

Fig. 8

 8 Fig. 8 shows the inverse pole figure distribution of calculated Young's modulus for Ti-22Zr β crystal. The crystallographic orientation dependence is obviously demonstrated as indicated by the ranges bounded by dashed lines. The IPF distribution of calculated Young's modulus shows a decreasing trend as the crystallographic orientation of grains changes from

Fig. 8

 8 Fig. 8 Orientation dependence of Young's modulus calculated from elastic constants of Ti-22Zr alloy.

Fig. 9 Fig. 9

 99 Fig.9shows the indentation hardness inverse pole figure (H IT -IPF) measured with the Sp50 and Bkv indenters. In contrast to the inverse pole figure distributions of η h, η w E IT , no significant trend was found for H IT values as a function of the crystallographic orientation for both indenters, suggesting that H IT is orientation-independent. Similar result has been reported in polycrystalline β Ti-Al alloys where no obvious change was identified for indentation hardness of β grains[START_REF] Lei | Microtexture and nanoindentation of α and β Phases in Ti-6Al-1.5 Cr-2.5 Mo-0.5 Fe-0.3 Si titanium alloy[END_REF]. It is related to the bcc structure of the β grains which can contain 48 possible slip systems. In β-Ti alloys, slip planes are observed to be {110}, {112} or {123} planes and several slip systems are frequently observed to operate simultaneously in the same grain[START_REF] Castany | Dislocation mobility in gum metal β-titanium alloy studied via in situ transmission electron microscopy[END_REF][START_REF] Castany | In situ TEM study of dislocation slip in a metastable β titanium alloy[END_REF]. Thus, the isotropic distribution of H IT values of the Ti2033 alloy can be ascribed to the active dislocation activity in bcc crystals. It is different from the observations in pure α-Ti with hexagonal structure that indentation hardness varied significantly with crystal orientation: indentation hardness for individual grains orientated in [0001] direction exhibited the highest value, then decreased as the orientations deviated from the [0001] direction[START_REF] Britton | The effect of crystal orientation on the indentation response of commercially pure titanium: experiments and simulations[END_REF][START_REF] Fizanne-Michel | Determination of hardness and elastic modulus inverse pole figures of a polycrystalline commercially pure titanium by coupling nanoindentation and EBSD techniques[END_REF][START_REF] Zambaldi | Orientation informed nanoindentation of α-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip[END_REF]. This is due to a strong anisotropy of slip systems in hcp α-Ti structure.J o u r n a l P r e -p r o o f

(

  𝑐 11 -𝑐 12 )(𝑐 11 +2𝑐 12 ) + ( 𝑘 2 +ℎ 2 𝑙 2 +𝑘 2 𝑙 2 ) (ℎ 2 +𝑘 2 +𝑙 2 ) 2 }

	1 𝑐 44	-	2 𝑐 11 -𝑐 12	)	(ℎ 2

-1

Acknowledgements

Y. Zhou acknowledges the China Scholarship Council (CSC) for her Ph.D financial support (No. 201701810085). The authors also acknowledge the SCANMAT platform of the University of Rennes for providing access to SEM facilities.

Declaration of Competing Interest

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

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:


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Rheological Characterizations of Dispersions of Clay Particles in Viscoelastic Polymer Solutions

Kaouther Ben Azouz clay can lead to great improvement in many properties, such as mechanical, barrier or fire resistance of the polymer [START_REF] Zhang | Fire properties of styrenic polymereclay nanocomposites based on an oligomerically modified clay[END_REF]. In recent developments, nanofibers and nanocomposites are obtained by electrospinning from polymer solutions with clay nanoparticles as fillers [START_REF] Fong | Generation of electrospun fibers of nylon 6 and nylon 6montmorillonite nanocomposite[END_REF].

The characterization of the mechanical properties of clay/polymer nanocomposites is generally performed through linear viscoelastic oscillatory flow measurements [7 -8]. The shape of the mechanical spectra may provide useful information on the global exfoliation of the particles and on the percolation threshold as it has been shown for clay/polystyrene nanocomposites [START_REF] Zhao | Rheological characterization of polystyrene-clay nanocomposites to compare the degree of exfoliation and dispersion[END_REF]. In clay/polymer systems, the structures of the associations of particles are related to the clay/monomer interactions. Weak or stronger gels may be formed, depending on the degree of swelling of the clay galleries by the monomers. Under shear, these associations may break down and different mechanisms have been proposed to understand the rheological properties of such systems [START_REF] Zhao | Rheological characterization of polystyrene-clay nanocomposites to compare the degree of exfoliation and dispersion[END_REF]. In polymer melts, the solid-like behaviour with no solid-liquid transition observed beyond a critical clay content, is attributed to an incomplete relaxation due to physical jamming or percolation [10 -11].

The specific plate-like microstructure of clay is at the origin of different types of particle associations referred as face-to-face (FF), edge-toface (EF) or edge-to-edge (EE) ones [START_REF] Luckham | The colloidal and rheological properties of bentonite suspensions[END_REF]. It depends on pH conditions. For sodium-montmorillonite/water dispersions, the calculation of the total energy of interaction shows a decrease of EF attraction at basic pH while FF associations seem to be predominant. Then, the gel-like structures are less stiff than in acid conditions [START_REF] Durán | Rheological and electrokinetic properties of sodium montmorillonite suspensions. I. Rheological properties and interparticle energy of interaction[END_REF].

Recently, the shear orientation of viscoelastic clay/polymer solutions (laponite/PEO-water solutions) was investigated by coupling classical rheological measurements with the birefringence techniques. This method shows that, when shear rate increases, firstly, particles orient in the flow, and then the polymeric chains are stretched and their anisotropy contributes also to the total birefringence [START_REF] Schmidt | Rheology and flow-birefringence from viscoelastic polymerclay solutions[END_REF]. These laponite/PEO-water solution model systems have been widely studied by different groups and provide useful elements for the comprehension of the microstructures depending on particle-particle and particle-polymer interactions. Daga et al. [START_REF] Daga | Linear viscoelastic master curves of neat and laponite filled poly(ethylene oxide) -water solutions[END_REF] obtained master curves for G' and G'' by means of time-temperature and time-concentration superpositions. The competi-tion between the PEO adsorption on laponite removing polymer from the solution and formation of bridging network may explain the results. Ageing effects are observed: the presence of PEO retards the gelation kinetics of laponite dispersions. The study of transient response to simple shear coupled with light scattering experiments [START_REF] De Bruyn | Micron-scale origin of the shear-induced structure in Laponite-poly(ethylene oxide) dispersions[END_REF] shows that, above a critical shear rate, there is rupture of the particles aggregates, inducing the formation of polymer-clay bonds. At high shear rates, the hydrodynamic forces are sufficient to break the network.

Baghdadi and Sardinha [START_REF] Baghdadi | Rheology and gelation kinetics in laponite dispersions containing poly(ethylene oxide)[END_REF] discuss the microstructure depending on the pH and on the polymer length at a given ionic force. Different scenarios are proposed. At pH7, FE associations between particles lead to aggregates and/or percolated structure. With low molecular weight PEO, adsorbed polymer chains form like steric barrier, then breakdown of the structure. Long chains allow bridging between particles. The free chains remaining in the fluid cause a depletion attraction. At pH 10, without polymer, FF aggregates dominate. During aging, diffusion of the particles is at the origin of rupture of the aggregates, leading to a higher effective volume fraction; if it is high enough, one observes an elastic behaviour similar to a colloidal glass one. Free chains in the fluid give a depletion force opposing to the homogenisation of the system which behaves like a viscoelastic liquid because of a lower effective volume fraction. High molecular weight polymers allow a gel structure caused by interparticle bridges. In oscillatory flow, in the linear viscoelastic (LVE) regime, the effect of long-term aging (up to 1000 days) has been examined for controlled pH and chain length [START_REF] Baghdadi | Long-term aging effects on the rheology of neat laponite and laponite-PEO dispersions[END_REF]. The neat laponite dispersions (1 -3 %w/w concentration) forms soft solids as aging and the mechanical spectra are in good agreement with the Soft Glass Rheology model [START_REF] Sollich | Rheological constitutive equation for a model of soft glassy materials[END_REF]. At low polymer concentration, the response of the clay dominates while at high polymer concentrations, the response of the system is governed by the polymer one at high frequencies. This is due to the free chains in solution.

The elasticity of a fluid can be measured through the first normal stress difference N 1 or from rod climbing. Contrary to dispersions in polymer melts, in polymer solutions, the increase of particle concentration leads to an increase of N 1 . This effect, observed with dispersions of kaolinite in a Boger fluid (polyisobutylene-polybutene solution) is due to a screening effect of solvent on particles [START_REF] Choi | Rheological properties of particle suspensions in a polymeric liquid[END_REF].

EXPERIMENTAL 2.1 COMPOSITION OF THE DISPERSIONS

Carboxymethyl cellulose (CMC) is a polymer derived from natural cellulose. CMC is a white granular substance soluble both in hot and cold water [21 -22]. One of the most important properties of CMC is its ability to act as a thickener [START_REF] Edali | Rheological properties of high concentrations of carboxymethyl cellulose solutions[END_REF]. Characteristics which make it useful are: high viscosity at low concentrations, surfactant, and bulking abilities. They are not toxic and do not promote allergic reactions in humans [START_REF] Baker | Methylcellulose & Sodium Carboxymethylcellulose: Uses in Paper Conservation, The Book and Paper Group Annual[END_REF]. CMC is used in textile manufacturing as a coating or a sizing agent. It is used in water-based drilling fluids [START_REF] Benchabane | Rheological properties of carboxymethyl cellulose (CMC) solutions[END_REF]. CMC is also found in detergents, soaps, food products, thickeners, pharmaceuticals, and cosmetics.

Bentonite is a montmorillonite clay of the smectite group. Among its significant properties is its high swelling capacity [START_REF] Bekkour | Rheological characterization of bentonite suspensions and oil-in-water emulsions loaded with bentonite[END_REF], its ability to adsorb significant amounts of polymer on its surfaces, and the formation of a gel structure with yield stress and viscoelastic properties at low clay concentrations [START_REF] Luckham | The colloidal and rheological properties of bentonite suspensions[END_REF]. It is widely used as thickening agent and as key component in various industrial fluid formulations. Among its uses in civil engineering is the soil boring, or the control of the pollutants transport in the environment, and other industrial applications which include cosmetics, chemical, food products, or petroleum [26 -27].

In water-based drilling fluids, where bentonite is a major component, CMC is appropriate to increase the stability of mud for drilling purposes and the viscosity of mud fluid as it stabilizes the aqueous suspensions of clay due to its high water retention. It maintains adequate flow properties at high temperature and salinity [START_REF] Edali | Rheological properties of high concentrations of carboxymethyl cellulose solutions[END_REF][START_REF] Baker | Methylcellulose & Sodium Carboxymethylcellulose: Uses in Paper Conservation, The Book and Paper Group Annual[END_REF][START_REF] Benchabane | Rheological properties of carboxymethyl cellulose (CMC) solutions[END_REF][START_REF] Bekkour | Rheological characterization of bentonite suspensions and oil-in-water emulsions loaded with bentonite[END_REF][START_REF] Benchabane | Effects of anionic additives on the rheological behaviour of aqueous calcium montmorillonite suspensions[END_REF]. Montmorillonite is a layered silicate presenting a multiscale organization as shown on Figure 1 according to [START_REF] Zhao | Rheological characterization of polystyrene-clay nanocomposites to compare the degree of exfoliation and dispersion[END_REF]. The interactions between various polymers and smectite layers have been investigated in detail in several studies. Nowadays, it is well established that, when a polymer is mixed with a clay suspension, the interactions lead to the adsorption of the polymer on the clay surfaces. This adsorption depends on the dimensions and the flexibility of the polymer molecule, which are closely related to its length. It may lead to desorption of solvent molecules from the surface [START_REF] Luckham | The colloidal and rheological properties of bentonite suspensions[END_REF].

PREPARATION OF THE SAMPLES

All the products used in this work are provided by VWR Prolabo France. For each mixture, the base CMC powder is firstly, dissolved in 100 g of deminirelized water. The mass concentrations of the CMC aqueous solution range from 0.1 to 2.5 %w/w. Three different grades of CMC have been used, respectively named LV (Low Viscosity), MV (Medium Viscosity) and HV (High Viscosity) and corresponding to different molecular weights (90000, 250000 and 700000). After 24 h stirring of the CMC aqueous solution, bentonite powder is dispersed in the solution with a 5 %w/w fixed concentration. These bentonite/CMC solution mixtures are submitted to a continuous agitation during 48 h using magnetic stirrers. After that, the samples are kept at 20°C.

EXPERIMENTAL RESULTS

Rheological properties of dispersions of clay particles in aqueous solutions of carboxymethyl cellulose are measured in both permanent and oscillatory shear flows.

PERMANENT SHEAR FLOW: AGING STUDY

Experimental results presented in this part, are obtained for polymer concentrations upper or equal to 1 %. Since the stress history of the sample is of great importance [START_REF] Coussot | Viscosity bifurcation in thixotropic, yielding fluids[END_REF], experimental procedures have been precisely defined. Measurement protocol is determined in the following way: a pre-shear at 10 s -1 constant shear rate, during 2 min to homogenize the fluid is followed by a rest of 10 min. After that, a rising continuous ramp with a 0.033 Pa/s slope is applied to the sample. The purpose of this study is to determine the equilibrium of fluids. During aging study of the dispersions the fluid is kept at rest throughout 24 h at constant temperature 20°C and then is gently stirred, each day during 1 hour before measurements [START_REF] Bekkour | Linear Viscoelastic Behaviour of Bentonite-Water Suspensions[END_REF]. The equilibrium is reached when the rheological properties of the fluid become identical, therefore, when the rheograms become overlaid. Required time to reach the equilibrium state for all concentrations seems to be 15 days. The pH is measured every day. It ranges between 9 and 10 for all the samples and slightly decreases with aging.

Figure 2 shows the rheograms obtained on dispersion in an aqueous solution of CMC1HV. It displays, in the first day, the existence of an identified yield stress which tends to disappear as the dispersion in polymer solution is growing older. The same tendency is observed for the other concentrations and molecular weights of the polymer. The dispersions are shear-thinning. The ratio shear stress/shear rate defines the shear viscosity for fluid systems. It is plotted vs. the shear stress on Figure 3. The initial increase of the curve corresponds to stresses below the yield stress. A slope of the straight line equal to 1 is associated to a constant shear rate i.e. to a strain proportional to the time. Since the applied stress is a ramp, this leads to a strain proportional to the stress. This behaviour characterizes an elastic solid. In fact, the system behaves as an elastic network, like a gel. Above the yield stress, the systems flow and are shearthinning. The viscosity decreases as the suspension is older. The shape of the curves reveals that different mechanisms occur during the flow. They involve changes of the conformation of macromolecules, rupture of the network crosslinks, rupture of the aggregates and orientation of particles in the flow [START_REF] Schmidt | Rheology and flow-birefringence from viscoelastic polymerclay solutions[END_REF][START_REF] De Bruyn | Micron-scale origin of the shear-induced structure in Laponite-poly(ethylene oxide) dispersions[END_REF][START_REF] Barnes | An Introduction to Rheology[END_REF]. The suspension in water is a shear-thinning fluid, but the existence of a yield stress is not as clear as in the previous case (Figure 4). Nevertheless, from a log-log plot, it appears that the established flow occurs only above a critical stress whose value increases when the system is older. Contrary to the dispersion in the polymer solution, the general tendency is an increase of the viscosity of bentonite suspension in water by getting old as shown in figure 5.

OSCILLATORY SHEAR FLOW

An alternative procedure for investigating the stability or the flocculation of dispersions is through viscoelastic measurement [START_REF] Luckham | The colloidal and rheological properties of bentonite suspensions[END_REF][START_REF] Tadros | Use of viscoelastic measurements for investigating the stability/flocculation of concentrated dispersions[END_REF]. Measurements of the elastic and viscous moduli G' and G'' of the CMC aqueous solutions, bentonite/water suspensions and bentonite/CMCwater dispersions were made under oscillatory shear stress. Oscillatory experiments measure the response of viscoelastic materials to smallamplitude oscillatory shear at frequency w (rad/s). In oscillatory shear, the complex shear modulus G* is defined as the ratio of the shear stress to the strain. The real and imaginary part of G*, respectively G' and G'' are respectively called the elastic modulus and loss modulus. The elastic modulus G' represents the elasticity of the material, and hence the solid-like behaviour. While, the loss modulus G'' represents the viscous character, and consequently the liquid-like behaviour of the system. The phase angle shift (loss angle) d is defined by tand = G''/G'.

Stress sweep at a given frequency: determination of the linear regime

In oscillatory shear flow, a stress sweep at a given frequency gives information on the extend of the linear response domain of the material and also, on the degradation of its mechanical properties when the stress level exceeds some critical value. The determination of the linear region is done at frequencies 0.1, 1, and 10 Hz. The protocol used for sweeping, consists of pre-shear as similar as in permanent flow followed by a sweep versus shear stress in an interval of 0.01 to 20 Pa.

Figure 6 gives the result of the stress sweep for CMC aqueous solution for CMC1HV and CMC1LV, at 0.1Hz frequency. At this frequency, G'' is larger than G'. The elastic modulus is negligible for the lower molecular weights. For the larger one (HV), the two moduli decrease for a shear stress of about 1 Pa. Figure 7 shows the behaviour of bentonite dispersion in water. At low shear stress, G' and G'' are independent of the shear stress and G' is larger than G'' that means a predominant elastic behaviour. Then, one observes a slight decrease of G' while G'' increases. Beyond a critical value of the shear stress (about 1.5 Pa), the two moduli sharply decrease and G'' becomes larger than G'.

Figure 8 presents the comparison between a dispersion in a CMC solution and its continuous phase at the same concentration and the same molecular weight of polymer (CMC 1HV). For the dispersion, in the linear domain, G' is upper than from top to bottom: Beyond of this critical value of shear stress, the sample start to flow. Both moduli downfall; the viscous one predominates, and the elastic one becomes negligible. This is in good agreement with the flow curve (Figure 2).

A classification of the different possible large amplitude oscillatory behaviours has been proposed on the basis of a network model involving two parameters a and b defining respectively the creation and loss rates of junctions as the shear strain increases [START_REF] Sim | Large amplitude oscillatory shear behaviour of complex fluids investigated by a network model: a guide line for classification[END_REF]. Four types of behaviours can be distinguished. Among of them, Type I corresponds to a < 0 and b > 0 i.e. the creation term decreases while the loss term increases. In this case, the two moduli G' and G'' decrease when the shear strain exceeds a critical value. Type III is associated to a > 0, b > 0 and a < b: the creation and loss terms increase with the shear strain but the destruction rate is faster than the creation one. Then, above a critical value of the shear strain, a strain hardening of G'' is observed, followed by a strain thinning while G' is strain thinning. According to this classification, the curves related to the polymer solutions, with concentrations in the semi-diluted or concentrated regimes correspond to Type I network. The weak overshoot of G'' observed in Figures 7 and8 corresponds to Type III and can be explained by the balance between formation and destruction of the junctions [START_REF] Sim | Large amplitude oscillatory shear behaviour of complex fluids investigated by a network model: a guide line for classification[END_REF].

Frequency sweep in the linear domain

The protocol used for frequency sweep consists of pre-shear as similar as permanent flow followed by a frequency sweep from 10 -3 to 10 Hz. Shear stress amplitude is fixed at 0.02 Pa. The elastic modulus G' and the viscous modulus G'' are reported in Figures 9 and 10 as functions of frequency, for CMC and bentonite. The polymer solution displays a classical behaviour of a viscoelastic fluid with a terminal region (G' ≈ w 2 and G'' ≈ w) in the low frequency range and an intersection point at a crossover frequency w c (Figure 9). The moduli and the maximum relaxation time (given by 1/w c ) increases when the polymer concentration c p increases. Then, the terminal region is shifted towards the lower frequencies which cannot be explored with the rheometer. For the lower concentrations i. e. in the dilute regime, the fluid behaves as a viscous one with G'' ≈ w and G' negligible.

The dispersion B5 exhibit an elastic behaviour with a quasi-plateau modulus G' which is ten to twenty fold G'' (Figure 10). This gel-like behaviour is modified when the clay particles are dispersed in the polymer solutions. Figure 11, obtained for the dispersions in CMC0.1MV and CMC1.5MV, shows that G' > G'' except at low and high frequencies. G' slowly increases with the frequency and with the polymer concentration (Figure 11). One can conjecture from Figure 11 that there are two intersection points of G' and G'' curves for two characteristic frequencies w c1 and w c2 related to two relaxation times t 1 and t 2 . As c p increases, these intersection points are shifted towards lower frequencies, resulting in an increase of the relaxation times. The comparison between Figures 9 and12 shows that the viscoelastic character of the suspending medium is modified by the addition of particles and the material tends to act as an elastic gel when the polymer concentration increases. In the interval [w c1 , w c2 ] G' becomes predominant even for the lower polymer concentrations. For 0.1HVB5, the evolution of G' and G'' with the frequency is quasi parallel with a slow increase like G' μ w a and a = 0.2. When c p increases, the exponent a decreases and G' tends to a plateau while a minimum of G'' appears. That means a stronger gel.

Comparing to B5 system, as c p increases, the moduli increase and become larger than for B5, due to the contribution of the polymer. But the elastic character of the fluids is less marked as in the plateau region, G' is approximately 25G'' for B5, 2.5G'' for 0.1HVB5 and 10G'' for 2.5HVB5. The influence of the molecular weight of the polymer depends on the polymer concentration. Figure 13 represents G' for c p = 0.1 %. One can observe that the elastic modulus is larger for the lower molecular weight. It is the contrary for c p = 1 %: in this case, HV corresponds to higher values of G' (Figure 14). This gives information on the different natures of the networks involved.

DISCUSSION AND CONCLUSION

This work allows the comparison of rheological properties of suspensions of solid particles in water and in viscoelastic aqueous polymer solutions. Clay particles have a particular structure since they are constituted of platelets, layered to form primary particles, aggregated together (Figure 1). During the study of aging, the value of pH, for all the suspensions, is in the range 9 -10. The pH only slightly decreases in the course of aging. These values indicate predominant Face to Face type associations with a great ability to trap more water between layers [12 -14]. Previous works from the laboratory [START_REF] Benchabane | Etude du comportement rhéologique de mélanges argiles -polymères[END_REF], showed that when CMC is mixed to montmorillonite suspensions, the polymer coats the clay particles and prevents the reorganization of the agglomerates by the usual mechanisms (face-to-face connections). In this case, the rheological behaviour of the CMC/bentonite suspensions depends on the structural state of the polymer. Clearly, the effect of aging is not the same for dispersions in water and in polymer solutions. In water, there is probably a dissociation of the aggregates and perhaps a partial exfoliation of the clay particles leading to the formation of an open tri-dimensional structure with an elastic behaviour as it can be seen from oscillatory measurements. In the polymer solution, at the beginning of the aging process, a yield stress can be determined especially in the case of high polymer concentration and/or molecular weight. Along aging, this yield stress tends to disappear and the system becomes more fluid. Initially, large aggregates are present in the dispersion. The stirring of the sample every day would lead to the rupture of the aggregates in smaller ones while the penetration of the macromolecules within these aggregates becomes easier together with their adsorption on the clay particles. For a young system, the shape of the curve of Figure 3 means that different mechanisms successively occur to explain the sharp decrease of the viscosity [START_REF] Barnes | An Introduction to Rheology[END_REF][START_REF] Walls | Yield stress and wall slip phenomena in colloidal silica gels[END_REF]. There is probably formation of a thin depletion layer in the vicinity of the solid surfaces of the rheometer geometry which acts as a lubrication layer. As the shear stress increases, the rupture of the large aggregates induces a further fall of the viscosity. Then, the orientation of the particles and the conformation change of the macromolecules in the flow takes place leading to a shearthinning behaviour.

Rossi et al. [START_REF] Luckham | The colloidal and rheological properties of bentonite suspensions[END_REF] explain that, a consequence of the adsorption of polymer on the particles is the desorption of solvent molecules from the surface of particles and water molecules may be transferred from the surface to the bulk. In the equilibrium state, the system does not consist of large bentonite aggregates dispersed in a polymer solution but of small aggregates coated by polymer in a less concentrated polymer solution. This argument combined with the existence of the depletion layer could explain the Figure 15 where the viscosity of CMC1HVB5 is smaller than CMC1HV.

The oscillatory measurement in the linear domain (i.e. in the limit of low shear stresses) characterizes the structure not perturbed by the flow. The addition of particles in a low polymer concentrated solution leads to a rise of the moduli (Figure 12) by two order of magnitude for c p = 0.1 %. While for c p = 2.5 %, the order of magnitude of the moduli is the same than for the polymer solution but the shape of the mechanical spectra is different. In the first case c p = 0.1 %), corresponding to a dilute/semi-dilute regime, the polymer chains connect the particles and aggregates and an elas-tic network is formed. For low molecular weight chains (LV on Figure 13) G' is much larger than for HV. The exfoliation is not cancelled by the presence of polymer and there is probably a combination of the effect observed for B5 and the crosslinks formation due to the presence of the polymer. When c p increases, in the semi dilute/concentrated regime, the mechanical properties of the network is mainly controlled by the macromolecular chains and the elastic modulus increases with the molecular weight (Figure 14).

In some systems in polymer melts, the absence of terminal zone is related to incomplete relaxation due to physical jamming with a solidlike behaviour, because of the mesoscopic structure of highly anisotropic clay tactoids [START_REF] Hyun | Rheology of Poly(ethylene oxide)/Organoclay nanocomposites[END_REF][START_REF] Ren | Linear viscoelasticity of disordered polystyrene-polyisoprene block copolymers based layered-silicate nanocomposites[END_REF]. From our mechanical spectra, the behaviour appears to be that of physical viscoelastic gels, with a terminal zone shifted towards lower frequencies as polymer concentration increases, corresponding to longer lifetimes of network junctions. The mechanical behaviour of the systems bentonite/aqueous polymer solutions considered here is the result of a competition between different mechanisms: ■ Association-dissociation of aggregates of particles ■ Adsorption of polymer on the particles and desorption of solvent molecules from the particles ■ Bridging of the particles by long polymer chains Then, different kinds of elastic networks may be formed which are destroyed when the shear stress exceeds some critical value, leading to the flow of the systems.

  Tests are performed with two constant stress rheometers, AR2000 from TA Instrument and Rheoscope 1 from ThermoHaake equipped with cone-and-plate geometries (AR 2000: acrylic cone, 40 mm diameter, 2° angle; Rheoscope: steel cone, 35 mm diameter, 2° angle). Results obtained from both rheometers are equivalent. The temperature is kept to 20°C. Sample preparation and other parameters like temperature were controlled, because of their influence on the final state of suspensions, and thus on the rheological behaviour. All tests were carefully carried out under the same conditions to allow comparison of the results. The different samples will be named as it follows: ■ Bn: Bentonite dispersion in water; concentration = n %w/w ■ CMCnXV: Aqueous solution of CMC; concentration = n %w/w, XV = LV, MV, or HV ■ CMCnXVB5: Bentonite dispersion B5 in an aqueous CMC solution CMCnXV (For instance, CMC1HVB5 means a 5% bentonite dispersion in a 1 % CMC HV aqueous solution).

Figure 1 :

 1 Figure 1: Schematic representation of montmorillonite multiscale organization [28].

Figure 2 (

 2 Figure 2 (left above):Rheograms for CMC1HVB5 : from top to bottom: 1 st , 3 rd , 5 th , 7 th , 9 th , 13 th , and 15 th day. In the insert, linear scale plot for 1 st and 15 th h day.

Figure 3 (

 3 Figure 3 (right above): Viscosity versus shear stress for CMC1HVB5.

Figure 4 (

 4 Figure 4 (left below): Rheograms for B5.

Figure 5 (

 5 Figure 5 (right below): Viscosity versus shear stress for B5.

Figure 6 :

 6 G' and G'' versus shear stress for CMC1LV and CMC1HV at 0.1 Hz.

Figure 7 :

 7 Figure 7: G' and G'' versus shear stress for B5 at 1 Hz.

Figure 8 :

 8 Figure 8: G' and G'' versus shear stress for CMC 1HV and CMC 1HVB5 at 0.1 Hz.

Figure 9 (

 9 Figure 9 (left above): G' and G'' versus angular frequency for CMC0.1HV, CMC1HV and CMC2.5HV.

Figure 10 (

 10 Figure 10 (right above): G' and G'' versus angular frequency for B5.

Figure 11 (

 11 Figure 11 (left below): G' and G'' versus angular frequency for CMC0.1MVB5 and CMC1.5MVB5.

Figure 12 (

 12 Figure 12 (right below): G' and G'' versus angular frequency for CMC HV B5 at different polymer concentrations.

  from top to bottom: Figure13:G' and G'' versus angular frequency for CMC HV, MV, LV B5 (c p = 0.1 %).

Figure 14 :

 14 Figure 14: G' and G'' versus angular frequency for CMC 1HVB5, 1MVB5, 1LVB5.

Figure 15 :

 15 Figure 15: Viscosity versus shear stress for CMC1HV and CMC1HVB5 at 1 st and 15 th day.

  1, 2 , Dominique Dupuis* 1 , Karim Bekkour 2 1 Laboratoire de Physique et Mécanique Textiles, EAC 7189 CNRS-UHA, 11 rue A. Werner, 68093 Mulhouse Cedex, France 2 Institut de Mécanique des Fluides et des Solides, CNRS-UDS, 2 rue Boussingault, 67000 Strasbourg, France