; Shizhong

Wei ; Shiwei

Thierry Barriere

Gang Cheng

; Liujie

Fangnao Xiao

Qiang Miao
email: miaoqiang@nuaa.edu.cn

Shizhong Wei

Shiwei Zuo

Liujie Xu

Uniform nanosized oxide particles dispersion strengthened tungsten alloy fabricated involving hydrothermal method and hot isostatic pressing

Keywords: particles dispersion strengthened tungsten alloy fabricated involving hydrothermal method and hot isostatic Oxide particle strengthening, Liquid-liquid doping, Compressive strength, Constitutive equation, ODS-W alloy Oxide particle strengthening, Liquid-liquid doping, Compressive strength, Constitutive equation, ODS-W alloy

Uniform nanosized oxide

Introduction

Over the past years, oxide particle dispersed into the tungsten matrix (ODS-W), was expected to obtain excellent mechanical properties by improving densification, refining the grains, impeding dislocation motion [START_REF] Das | Thermo-mechanical processing, microstructure and tensile properties of a tungsten heavy alloy[END_REF][START_REF] Wei | Effect of low temperature rolling on the tensile behavior of commercially pure tungsten[END_REF][START_REF] Bolt | Materials for the plasma-facing components of fusion reactors[END_REF]. As tungsten is a refractory metal, conventionally, to achieve full densification, its sintering temperature would reach to 2000-2500 °C for a long holding time [START_REF] Kim | The effect of yttrium oxide on the sintering behavior and hardness of tungsten[END_REF]. However, high temperature sintering usually leads to tungsten grains growing rapidly, which causes deteriorative properties, such as high ductile-brittle transition temperature (DBTT>400 °C), recrystallization brittleness and poor mechanical properties at high temperature [START_REF] Barabash | Selection, Development and characterisation of plasma facing materials for ITER[END_REF][START_REF] Yar | Chemically produced nanostructured ODS-lanthanum oxide-tungsten composites sintered by spark plasma[END_REF][START_REF] Veleva | Investigation of microstructure and mechanical properties of W-Y and W-Y 2 O 3 materials fabricated by powder metallurgy method[END_REF].

However, the improvement of mechanical properties of ODS-W alloy is limited for the application at high temperature and the increase of strength is often accompanied with the decrease of ductility [START_REF] Liu | Nanostructured yttria dispersion-strengthened tungsten synthesized by sol-gel method[END_REF]. A significant reason is that, the coarse oxide particles are usually located at the grains boundaries of alloys and then act as stress concentration, weakening the cohesion of interface between oxide particle and matrix and then leading to intergranular fracture and low toughness [START_REF] Liu | Nanostructured yttria dispersion-strengthened tungsten synthesized by sol-gel method[END_REF][START_REF] Samaras | Computer Simulation of Displacement Cascades in Nanocrystalline Ni[END_REF][START_REF] Liu | Characterization of ODS-tungsten microwave-sintered from sol-gel prepared nano-powders[END_REF]. Thus, on the premise of ensuring high density and small grain size, reducing the oxide particle size becomes one of the research topics for ODS-W alloy. It was reported that ultrafine La 2 O 3 or Y 2 O 3 doping tungsten powders can be prepared by wet chemical techniques [START_REF] Yar | Spark plasma sintering of tungsten-yttrium oxide composites from chemically synthesized nanopowders and microstructural characterization[END_REF][START_REF] Yar | Chemically produced nanostructured ODS-lanthanum oxide-tungsten composites sintered by spark plasma[END_REF]. However, during high temperature environment, La 2 O 3 and Y 2 O 3 particles in W matrix appear to agglomerate and then form larger particles, which could deteriorate the alloys' mechanical properties [START_REF] Shen | Microstructure of a commercial W-1% La 2 O 3 alloy[END_REF][START_REF] Xiao | Preparation, microstructure, and properties of tungsten alloys reinforced by ZrO 2 particles[END_REF][START_REF] Qu | Effects of high magnetic field on the melting behavior of W-1wt%La2O3 under high heat flux[END_REF].

Considering the higher compatibility of ceramic oxide (ZrO 2 , Al 2 O 3 ) with W matrix than rare earth oxide [START_REF] Li | Flow behavior and processing map for hot deformation of W-1.5ZrO 2 alloy[END_REF], in our previous research, our group prepared W-ZrO 2 alloy by vertical sintering and hot swaging from ultrafine powder by the wet chemical method [START_REF] Xiao | A hybrid microstructure design strategy achieving W-ZrO 2 (Y) alloy with high compressive strength and critical failure strain[END_REF]. The average size of ZrO 2 particle in tungsten matrix is about 1.5 μm. Wang et al. [START_REF] Wang | Preparation, microstructure, and constitutive equation of W-0.25 wt% Al 2 O 3 alloy[END_REF] prepared W-Al 2 O 3 alloys through the hydrothermal method, followed by the H 2 reduction process and the conventional H 2 sintering. However, the Al 2 O 3 particles embedded in tungsten matrix still reach to 3 μm.

It implies that it is difficult to prepare nanosized ceramic oxide particle reinforced tungsten alloy through the liquid-liquid method. However, in view of mixing soluble raw materials in a molecular level, the liquid-liquid method is still a candidate method for preparing high quality doped powder [START_REF] Liu | Characterization of ODS-tungsten microwave-sintered from sol-gel prepared nano-powders[END_REF]. Moreover, it is determined that mechanical milling is usually adopted to obtain nanosized powders [START_REF] Kiran | High energy milling on tungsten powders[END_REF][START_REF] Han | The effects of ball-milling treatment on the densification behavior of ultra-fine tungsten powder[END_REF]. Therefore, the combining of the above two methods was expected to obtain high-quality doped tungsten powder with ultrafine and uniform ceramic oxide particles.

In the present experiment, through hydrothermal synthesis and mechanical alloying, the doped powders with different Zr(Y)O 2 contents were prepared. Then, hot isostatic pressing (HIP) was adopted for the fabrication of high density W-Zr(Y)O 2 alloy to reduce tungsten grains size [START_REF] Liu | Microwave synthesis and properties of fine-grained oxides dispersion strengthened tungsten[END_REF][START_REF] Kurishita | Development of ultra-fine grained W-(0.25-0.8) wt% TiC and its superior resistance to neutron and 3 MeV He-ion irradiations[END_REF][START_REF] Kurishita | Development of ultra-fine grained W-TiC and their mechanical properties for fusion applications[END_REF][START_REF] Xie | Achieving high strength/ductility in bulk W-Zr-Y2O3 alloy plate with hybrid microstructure[END_REF]. Through the above processes, Zr(Y)O 2 particle with average size of 410 nm are obtained in the tungsten matrix. Moreover, the effects of the Zr(Y)O 2 content on the microstructure and properties of the W-Zr(Y)O 2 alloys were analyzed. In addition, the deformation behavior of W-Zr(Y)O 2 alloy was investigated by hot compression deformation at different temperatures and strain rates and then the constitutive equation was established.

Experimental procedure

Composition and preparation processes of W-Zr(Y)O 2 alloys

In present work, we prepared the W-Zr(Y)O 2 alloys through the hydrothermal method, followed by mechanical alloying and hot isostatic pressing. The raw materials were commercial zirconium oxychloride octahydrate (ZrOCl 1b. After that, the milled powders were pressed by the cold isostatic pressing process at a pressure of 250 MPa. The green compacts were then sintered at 2400 °C for 4 h in a hydrogen atmosphere. Then the sintering samples were hot isostatic pressed at 1400 °C and 200 MPa for 1h.

Measurement, experimental procedures, and analysis

The microstructure, composition and crystal structure of alloys were analyzed by EGA-SBH Scanning Electron Microscope (SEM) equipped with EDX detector and the high-resolution electron microscope (HRTEM).

The fabricated alloy' density was determined based on the Archimedes principle.

The HVS-1000A tester was employed to analyze the Vickers hardness of alloys using a 200 g load for 10s. Compressive properties of alloy were tested using a AG-I250KN material machine at room temperature. The compression rate is 1.0 mm/min. Hot compression tests for alloy were carried out on a Gleeble-1500D test machine at 1100 °C, 1200 °C, 1300 °C, and 1400 °C for 3 min, respectively.

Results and analysis

Microstructure of alloy

Seen from SEM images in Fig. particles are homogeneously distributed within the grains. These particles can generate, hinder and then accumulate dislocations in the grains during the deformation process. According to our previous research [START_REF] Wang | Effect of ZrO 2 content on microstructure and mechanical properties of W alloys fabricated by spark plasma sintering[END_REF], owing to the addition of the tiny amount of Zr(Y)O 2 (the doping amount is less than 0.75%), no diffraction peaks of containing-Zr phases can be found in XRD patterns. However, the sintering tungsten alloys were composed of ZrO 2 and W phases from the doped tungsten powders as shown in Fig. 5e of the reference [START_REF] Xiao | Preparation, microstructure, and properties of tungsten alloys reinforced by ZrO 2 particles[END_REF]. As mentioned above, a large amount of black particles were uniformly distributed in the tungsten matrix. The composition of black particles were determined by EDS analysis, which are rich in Zr, Y and O elements.

Thus, these black particles with spherical appearance probably are Zr(Y)O 2 particles. Some oxide dispersion-strengthened tungsten alloys prepared through the hydrothermal method and mechanical alloying were listed in Table 3, respectively.

Wang et al. [START_REF] Wang | Preparation, microstructure, and constitutive equation of W-0.25 wt% Al 2 O 3 alloy[END_REF][START_REF] Wang | Microstructure and preparation of an ultra-fine-grained W-Al 2 O 3 composite via hydrothermal synthesis and spark plasma sintering[END_REF] prepared the W-Al 2 O 3 powders by hydrothermal method. After SPS and conventional H 2 sintering, respectively, the average size of Al 2 O 3 particles existed in their alloys reach to 1.5 μm and 2.0 μm, as shown in Fig. 3d. Moreover, with the increasing of the doping amount, these Al 2 O 3 particles agglomerate together and have bad bonding interface with their tungsten matrix, leading to high porosity and bad mechanical properties of the alloys. Li et al. [START_REF] Li | Fabrication and mechanical properties of tungsten alloys reinforced with c-ZrO2 particles[END_REF] prepared W-2wt%ZrO 2 by vertical sintering (2700 °C) combined with the hot swaging process. Though the high sintering temperature closing to the melting point of ZrO 2 and extremely short duration contribute to obtain the ZrO 2 particle size, the dispersive ZrO 2 particles still reach to 1.5 μm in size and the tungsten grains grow up to 80-150 μm. For mechanical alloying of ODS-W powders, the refinement effect on oxide particle size is also limited even through doping nanosized oxide particles. Angel Muñoz et al. [START_REF] Muñoz | La 2 O 3 -reinforced W and W-V alloys produced by hot isostatic pressing[END_REF] prepared the W-La 2 O 3 powder using nanosized La 2 O 3 particles ranging from 10 to 50 nm in size as raw material. However, the large adsorption effect of nanosized oxide particles leads to forming particle aggregations even after ball-milling for 30 hours [START_REF] Zhao | Thermal shock behavior of fine grained W-Y 2 O 3 materials fabricated via two different manufacturing technologies[END_REF]. Similar cases can be found in references [START_REF] Liu | Mechanical properties and microstructures of W-1%Y 2 O 3 microalloyed with Zr[END_REF][START_REF] Aguirre | Mechanical properties of Y 2 O 3 -doped W-Ti alloys[END_REF][START_REF] Ki | Fabrication of high temperature oxides dispersion strengthened tungsten composites by spark plasma sintering process[END_REF]. In this work, the uniformed-size and ultrafine particles in the tungsten alloy were obtained, indicating the combining of adopted liquid-liquid doping and mechanical alloying is the appropriate to reduce the particles size. TEM was performed to characterize the microstructures of the prepared W-Zr(Y)O 2 alloy. As shown in Fig. 4(a,b), lots of nanosized oxide particles ( marked by orange arrows ) are in range of 25-100 nm under TEM observation. Some nanosized particles tend to aggregate (Fig. 4b). The selected area electron diffraction pattern (SAEDP) reveals that the Zr(Y)O 2 particle exhibits a face-centered cubic (fcc) structure with a zone axis of [-112]. HRTEM images show the lattice spacing of 2.9646 Å and 1.8152 Å in cubic ZrO 2 phase. As ZrO 2 phase without stabilizer is monoclinic structure at room temperature [START_REF] Yu | Precipitation mechanism and microstructural evolution of Al 2 O 3 /ZrO 2 (CeO 2 ) solid solution powders consolidated by spark plasma sintering[END_REF], the detection of cubic phase ZrO 2 confirms the Y 2 O 3 has a stabilizing effect on ZrO 2 phase. The existence of stabilized cubic phase Zr(Y)O 2 also indicates that the formation of micro-cracks caused by volume change due to ZrO 2 phase transitions would be avoided during the alloy cooling to room temperature. SADP image from selected area ( black box in Fig. 4b) was identified as cubic α-W phase with a zone axis of [-113]. Moreover, dislocation lines and loops pointed by white arrows were also observed in tungsten grains or around oxide particles. Fig. 4c shows that the particles exhibit a good bonding with the tungsten phase. Meanwhile, the HRTEM image also shows the presence of amorphous structure area in the interfaces with about 2 nm wide, which may be caused by diffusion of containing-Zr phase into the W phase during high temperature sintering. The inset in Fig. 4d shows the magnified images of interface, from which, it can be seen that there are not coherent relation between tungsten phase and oxide phase.

Density and microhardness

The density, microhardness and compressive properties at room and high temperatures are listed in Table 2. Although the theoretical densities decrease due to lower density of Zr(Y)O 2 existed in the alloy, three W-Zr(Y)O 2 alloys all have higher densities compared to pure tungsten and their densities increase slightly with the increase in the Zr(Y)O 2 mass fraction. On the one hand, the improvement of sinterability would be caused by abundant surface energy and grain boundary energy of ultrafine milled powder [START_REF] Wesemann | Fracture strength and microstructure of ODS tungsten alloys[END_REF][START_REF] Liu | Eliminating bimodal structures of W-Y 2 O 3 composite nanopowders synthesized by wet chemical method via controlling reaction conditions[END_REF][START_REF] Dong | Preparation of ultra-fine grain W-Y 2 O 3 , alloy by an improved wet chemical method and two-step spark plasma sintering[END_REF]. On the other hand, the dispersion of oxide particles can effectively inhibit pores and cracks, and greatly refine compactness [START_REF] Cui | Microstructure and high temperature deformation behavior of the Mo-ZrO 2 alloys[END_REF].

However, alloys still exhibit lower relative densities, which are all below 97%, owing to the existence of sintered defects in the alloys.

For the microhardness, the addition of Zr(Y)O 2 increases the microhardness compared to pure tungsten. The microhardness of the W-Zr(Y)O 2 alloys increases with increasing of Zr(Y)O 2 mass fraction. The higher microhardness may be due to the following reasons: On the one hand, the higher alloy' density and the smaller grain size mean the higher microhardness [START_REF] Xiao | Microstructure and mechanical properties of W-ZrO 2 alloys by different preparation techniques[END_REF]; On the other hand, the dispersive nanosized Zr(Y)O 2 particles, increase the dislocation density of the tungsten matrix and then strengthen the tungsten matrix, which contribute to the increase in hardness as well [START_REF] Xu | Microstructure and high-temperature frictional Wear property of Mo-based composites reinforced by aluminum and lanthanum oxides[END_REF].

Compressive properties of tungsten alloys

The stress-strain curves of tungsten alloys during compressive deformation were shown in Fig. 5. Obviously, pure tungsten lacking strengthening phase has the lowest ultimate strength and fracture strain [START_REF] Xiao | Microstructure and mechanical properties of W-ZrO 2 alloys by different preparation techniques[END_REF]. However, due to the lower porosity resulted from pressing sintering, the compressive strength and fracture strain of pure W in current research are 14.5% and 32.1%, respectively, which are higher compared to the reported conventional sintering and SPSed pure W [START_REF] Wang | Effect of ZrO 2 content on microstructure and mechanical properties of W alloys fabricated by spark plasma sintering[END_REF]. With the increase in the Zr(Y)O 2 content, the strength and fracture strain continue to decrease. In W-0.75wt%Zr(Y)O 2 alloy, the compressive strength and fracture strain decrease to 1350 MPa and 0.215, respectively. However, these alloys still exhibit high compressive properties. As shown in Fig. 5b andc, the transparent black areas show the compressive strength and fracture strain of W-Zr(Y)O 2 alloys in current research. It is obvious that the prepared alloys exhibit the higher compressive properties compared to the SPSed sintering and conventional sintering alloys reported in references [START_REF] Wang | Preparation, microstructure, and constitutive equation of W-0.25 wt% Al 2 O 3 alloy[END_REF][START_REF] Wang | Effect of ZrO 2 content on microstructure and mechanical properties of W alloys fabricated by spark plasma sintering[END_REF], respectively. For SPSed sintering alloy, generally, the smaller grains contribute to the improvement of properties. However, the lower quality powder results in the larger ZrO 2 particles (Table 3) among tungsten alloys, leading to the poor microstructure and mechanical properties. It is easy to understand that, due to the pressureless sintering, the conventional sintering alloys exhibit lower compressive strength and fracture strain. Compared to the swaged W-(0-1.5%) ZrO 2 alloys [START_REF] Li | Fabrication and mechanical properties of tungsten alloys reinforced with c-ZrO2 particles[END_REF],

although hot swaging slightly improve the compressive properties, the large grains (50-120 μm) and oxide particles (about 1.5 μm) resulted from high temperature sintering (nearly 2700 °C), lead to the limited reinforcement effect on tungsten grains and lower fracture strain. transgranular failure in tungsten grains. In our previous research [START_REF] Xiao | A hybrid microstructure design strategy achieving W-ZrO 2 (Y) alloy with high compressive strength and critical failure strain[END_REF], though the W-1.5wt%ZrO 2 alloy was also fabricated through HIP sintering, coarse oxide particles at GBs induce stress/strain concentration and cause interfacial decohesion at weaker GBs, resulting in the main intergranular pattern in alloys' fractures surface (Fig. 14a in ref. [START_REF] Xiao | Microstructure and mechanical properties of W-ZrO 2 alloys by different preparation techniques[END_REF]). In present research, the ultrafine oxide particles evenly distributed in tungsten matrix (marked by the black particle in inset) may be the main reason obtaining the changed fracture pattern, through improving the fracture strength of the tungsten grains and GBs. In fact, during deforming, the fabricated alloy involves more plastic deformation, such as significant W grain tearing and grain deformations as shown in Fig. 6c andd. The strengthening effect of oxide particle on the fabricated alloy can be also evidenced by the presence of slip lines (Fig. 6b) as well as microdimples (Fig. 6d).

The stress-strain curves of tungsten alloy tested under different conditions were shown in Fig. 7. It was found that the flow stress increases with the increase of strain rate, while it decreases with the increase of deformation temperature. It indicates that the stress strongly depends on the strain rate and the deformation temperature. When tested at 1100 °C with strain rate of 0.1 s -1 , the peak stress is 533.5 MPa. When the strain rate increases to 1 s -1 , the peak stress increases to 577.4 MPa.Firstly, the heating time is not enough for material softening due to a relatively high deformation rate [START_REF] Lin | A critical review of experimental results and constitutive descriptions for metals and alloys in hot working[END_REF]. Secondly, the higher strain rate enhances the density of dislocations and the degree of work hardening. During deformation at a high strain rate, the work hardening cannot be completely eliminated [START_REF] He | A physically-based constitutive model for a nitrogen alloyed ultralow carbon stainless steel[END_REF][START_REF] Zhang | Hot workability and constitutive model of the Cu-Zr-Nd alloy[END_REF]. At a fixed strain rate, for example, when the strain rate is 0.1 s -1 and the temperature is 1200 °C (Table 2), the peak stress is 492.5 MPa. When the temperature increases to 1400 °C, the peak value of stress is reduced to 437.7 MPa. At high temperature, the tungsten alloy contains a higher layer of stacking fault energy and the cross-slip easily occurs in the process of deformation, which makes it easier to soft for material and then reduces the resistance to deformation [START_REF] Wang | A comparative study of several constitutive models for powder metallurgy tungsten at elevated temperature[END_REF][START_REF] Galiyev | Correlation of plastic deformation and dynamic recrystallization in magnesium alloy ZK60[END_REF].

In our previous research [START_REF] Li | Flow behavior and processing map for hot deformation of W-1.5ZrO 2 alloy[END_REF], due to the occurrence of dynamic recrystallization during hot working, the stress-strain curves of tungsten alloy after deformation at 1400 °C with a strain rate of 0.01 s -1 firstly increased to a peak value rapidly, and then decreased until it reached a relatively steady value. However, from Fig. 7, it can be seen that all the curves show the steady-state flow stress characteristics. In the given temperature and strain rate, the stress-strain curve seems to reach a horizontal line.

This may be due to the presence of ultrafine Zr(Y)O 2 particles in alloys. The homogeneous dispersion of oxide nano-particles in tungsten alloy could pin dislocations and grain boundaries, and thus inhibit the grain growth, enhancing the high temperature strength and improving the recrystallization temperature [START_REF] Setyawan | Effects of transition metals on the grain boundary cohesion in tungsten[END_REF]. In this model, the relationship among the strain rate ( /s -1 ), flow stress (σ/ MPa for a given strain of 0.55) and temperature (K), was established through the Arrhenius model [START_REF] Cai | Constitutive equations for elevated temperature flow stress of Tie6Ale4V alloy considering the effect of strain[END_REF], as it usually is employed to predict the deformation behavior of alloys under different deformation conditions [START_REF] Lu | Constitutive modeling of two-phase metallic composites with application to tungsten-based composite 93W-4.9Ni-2.1Fe[END_REF]. The establishment of the Arrhenius model is based on the following equations (Eqs:1-3).

for all ασ (1) ασ<0.8

(d) (c) (b) (2) ασ>1.2 (3) (a)
Where, R is the universal gas constant (8.314 J mol -1 K -1 ); Q is the activation energy of hot deformation (KJ mol -1 ); A, A 1 , A 2 , n, n 1 , β and α are all the correlative materials constant and α= β/n 1 .

As the deformation temperature and strain rate both affect the deformation behavior [START_REF] Meng | Flow behavior and processing map for hot deformation of ati 425 titanium alloy[END_REF], the Zener-Hollomon parameter (Z), which means the deformation rate factor of temperature compensation, was used to reveal the coupling effects of strain rate and temperature on flow stress [START_REF] Dummer | Effect of strain rate on plastic flow and failure in polycrystalline tungsten[END_REF]: [START_REF] Kim | The effect of yttrium oxide on the sintering behavior and hardness of tungsten[END_REF].

When deformation temperature is fixed, after introducing Eq. ( 4) into Eqs.

(1)-( 3), we can obtain the following equations (5-8):

(5)

(6) (7) (8)
Where the n 1 and β can be calculated from the slope of ln(σ)-ln( ) plot and σ-ln( ) plot, respectively, as shown in Fig. 8. These lines are almost parallel, indicating that the slopes of the lines vary in a very small range. The slight variation in the slopes of these lines may be attributed to scattering in the hot compression experimental data.

The calculated mean values of n 1 and β are 26.79518 and 0.0588, respectively. Then, the α values can be determined to be 0.002194. The values of n and b, is the slopes of ln -ln[sinh(ασ)] and 1000/T-ln[sinh(ασ)] plots as shown in Fig. 9, which are 21.42387667, and 1.98223, respectively. Thus the value of Q (activation energy) is Rnb =353.0710624 kJ/mol. The Eq.( 9) can be obtained from taking the logarithm of Eq. ( 4): [START_REF] Samaras | Computer Simulation of Displacement Cascades in Nanocrystalline Ni[END_REF] The values of ln A and n could be obtained from the intercept and line slope of the ln[sinh(ασ)]-lnZ as shown in Fig. 10, which is 20.54226 and 20.78805, respectively.

By substituting the values of the material constants A, n, Q and α into equations [START_REF] Das | Thermo-mechanical processing, microstructure and tensile properties of a tungsten heavy alloy[END_REF], the relationship between strain rate and temperature of the W-0.25wt%Zr(Y)O 2 alloy at a strain of 0.55 can be expressed as:

Compensation for strain

It was reported that the strain obviously affected greatly the material constants (a, n, Q, lnA) at evaluated temperature [START_REF] He | A physically-based constitutive model for a nitrogen alloyed ultralow carbon stainless steel[END_REF][START_REF] Cai | Constitutive equations for elevated temperature flow stress of Tie6Ale4V alloy considering the effect of strain[END_REF]. Therefore, compensation of strain should be taken into account in order to establish constitutive equations to predict the flow stress more accurately. In this study, the material constant values under different strains were calculated within the range of 0.05-0.55 and the interval of 0.05. The different material constants at different strains were plotted in Fig. 11. The sixth order polynomial fitting Eq. ( 11) was employed to describe the relationship between material parameters and strain. The calculated coefficients are listed in Table 4 By rearranging Eq. ( 4), the predicted flow stress can be calculated by a function of the Zener-Hollomon parameter as shown in Eq. ( 12).

(

) 12
The comparison of the experimental and predicted flow stress datas in all test deformation conditions is shown in Fig. 5. The results show a good agreement between the calculated datas and the experimental datas. Only in some deformation conditions (i.e. at 1100 °C in 1 s -1 and 1300 °C in 0.1 s -1 ), a remarkable variation between experimental and computed flow stress datas could be observed in Fig. 5a and c, respectively.

To further assess the prediction accuracy of the developed model, we introduced the average relative error (AARE):

σ σ σ ( 13
)
Where is the experimental value, is the predicted value, and N is the total number of data. The value of AARE is 3.6%, which indicates a good prediction accuracy of the developed model. fabricated through the hydrothermal method and mechanical alloying, followed by hot isostatic pressure. 2. The average particle size is about 410 nm. Through TEM observation, lots of nanosized oxide particles less than 50 nm exists in the tungsten matrix.

Conflicts of interest

There are no conflicts to declare.

Fig. 1 .

 1 Fig. 1. SEM images of W-0.75wt%Zr(Y)O 2 powders prepared through different methods: (a) Hydrothermal method; (b) Hydrothermal method, followed by mechanical alloying.

Fig. 3c shows

  Fig.3cshows the the particle size distribution, with Gaussian Fit on the histogram, are in a state of normal distribution based on 200 particles. Over 90% of particles range from 100 nm to 650 nm in diameter without the coarse particle of more than 1 μm. The average particle size is about 410 nm. In fact, lots of nanosized oxide particles less than 50 nm cannot easily be observed through SEM observation.Ultrafine and uniformed-size Zr(Y)O 2 particles uniformly dispersed in the tungsten matrix may be due to the powder preparation process. As shown in Fig.1a, the surfaces of the powder particles are covered with white substances. EDS analysis reveals that these white substances are rich in Zr and Y elements, belonging to the containing-(Zr, Y) substance. By high-energy ball-milling technique, the white containing-(Zr, Y) substances and tungsten powder particles not only were refined, but also would be dispersed into smaller particles. After sintering, these containing-(Zr, Y) substances would transform into the dispersive and ultrafine Zr(Y)O 2 particles.

Fig. 2 .

 2 Fig. 2. Microstructure of alloys: (a) Pure W; (b) W-0.25wt%Zr(Y)O 2 ; (c) W-0.5wt%Zr(Y)O 2 ; (d) W-0.75wt%Zr(Y)O 2 .

Fig. 3 .

 3 Fig. 3. (a) BSE image of tungsten alloys with 0.5wt%Zr(Y)O 2 alloy; (b) EDS spectrum on the white arrow A in Fig. 3a; (c) Particle size distribution of Zr(Y)O 2 in W-0.5wt%Zr(Y)O 2 alloy and (d) Particle size VS W alloys reinforced different

Fig. 4 (

 4 Fig. 4(a, b) TEM images of tungsten alloy showing Zr(Y)O 2 particles; (c) HREM image of tungsten alloy; (d) HREM image of Zr(Y)O 2 /W interface

  For W-Zr(Y)O 2 alloys, the influence of Zr(Y)O 2 on the compressive properties is complicated. The W-0.25wt%Zr(Y)O 2 alloy exhibits the highest strength of 1577 MPa and fracture strain of 0.262, approximately 25.2% and 40.5% higher than those of the pure W, respectively.

Fig. 5 .Fig. 6 ,

 56 Fig. 5. (a) Compressive stress-strain curves of W alloys with different Zr(Y)O

Fig. 6 .

 6 Fig. 6. Fracture surface of W-0.25%Zr(Y)O 2 alloy

Fig. 7 .4 Deformation constitutive model 4 . 1

 741 Fig. 7. True stress-strain curves of the W-0.25wt%Zr(Y)O 2 alloy under different deformation conditions: (a) 1100 °C; (b) 1200 °C; (c) 1300 °C; (d) 1400 °C. 4 Deformation constitutive model 4.1 Establishment of the constitutive model

Fig. 8 .Fig. 9 .

 89 Fig. 8. Relationships between: (a) lnσ-ln ; (b) σ-ln .

Fig. 10

 10 Fig. 10 Relationship between ln[sinh(ασ)] and lnZ.

Fig. 11 . 1 .

 111 Fig. 11. Relationship between the strain and material constants: (a) a; (b) n; (c) Q; (d) lnA.

3 .

 3 The W-0.25wt% Zr(Y)O 2 alloy possesses the highest ultimate compressive strength of 1577 MPa and the fracture strain of 0.262, which are approximately 25.2% and 40.5% higher than those of the pure tungsten, respectively. Moreover, the fabricated W-Zr(Y)O 2 alloys exhibit better microstructure and compressive properties compared to some published experimental results.

4 .

 4 The relationship between flow stress, strain rate, and deformation temperature was investigated through establishing the constitutive equation and strain compensation model. The values o AARE is 3.6% respectively, which indicates that the developed constitutive equation could predict the flow stress with good correlation.

Founding:

  This work is supported by National Natural Science Foundation of China [No. 51672070], National Natural Science Foundation of China [No. 51874185], Henan province science and technology innovation talent plan, China [No. 2017JQ0012] and Graduate Research and Innovation Projects in Jiangsu Province [ No. KYCX19_0182].

  [START_REF] Wei | Effect of low temperature rolling on the tensile behavior of commercially pure tungsten[END_REF]

Table 1

 1 •8H 2 O; grade AR), yttrium nitrate [Y(NO 3 ) 3 •6H 2 O; grade AR] and ammonium metatungstate [(NH 4 ) 6 H 2 W 12 O 40 •5H 2 O; grade AR; AMT]. The five W-Zr(Y)O 2 alloys containing 0%, 0.25wt%, 0.5wt%, 0.75wt% and 5.0wt% Zr(Y)O 2 , were denoted as H 0 , H 0.25 , H 0.5 , H 0.75 and H 5.0 , respectively, as listed in Table 1. Chemical composition of W-Zr(Y)O 2 alloys.

	Samples	W(wt.%)	ZrO 2 (wt.%)	Y 2 O 3 (wt.%)
	H 0	100.000	0.000	0.000
	H 0.25	99.718	0.250	0.032
	H 0.50	99.437	0.500	0.063
	H 0.75	99.154	0.750	0.096
	H 5.0	94.370	5.000	0.630
	The procedures for fabricating alloy comprise the following steps: Firstly,
	ZrOCl 2 •8H

2 O, Y(NO 3 ) 3 •6H 2 O and (NH 4 ) 6 H 2 W 12 O 40 •5H 2 O were dissolved in distilled water, respectively. Subsequently, a certain amount of ZrOCl 2 •8H 2 O and Y(NO 3 ) 3 •6H 2 O were homogeneously mixed. Then, the mixture was added slowly to the (NH 4 ) 6 H 2 W 12 O 40 •5H 2 O solution with stirring. HNO 3 was adopt to decrease the solution's pH value to lower than 1.0. Finally, the mixed solution was put into a

stainless-steel autoclave with a PTFE lining. The autoclave was sealed and then heated at 276.5K min -1 until the reaction temperature was reached to 120 °C. The holding time of the hydrothermal reaction was 17 h. After that, the product was stirred for 120 min using an electric mixer with some distilled water. Through drying at 90 °C, the precursor powder was obtained. The obtained powder was calcined at

Table 2

 2 Microstructure and mechanical properties of alloys.

		Grain /oxide	Density	Vickers	Compressive strength (MPa)/ fracture strain
	Sam.	particle	size	(g/cm 3 )/	hardness
		(μm)		(%RD) a*	/HV	25°C	1200°C
	Pure W	10.5/-		18.238/94.5	378	1260/0.185	438.6/-
	W 0.25	6.5/0.31		18.281/95.3	456	1577/0.262	492.5/-
	W 0. 50	5.6/0.41		18.291/95.9	467	1420/0.223	533.7/-
	W 0.75	4.3/0.38		18.311/96.5	486	1350/0.215	516.1/-

a* Relative density

[START_REF] Xiao | Preparation, microstructure, and properties of tungsten alloys reinforced by ZrO 2 particles[END_REF]

.

Table 3

 3 Microstructures and properties of ODS-W alloys.

						Density
	Methods	Alloy	Process	W grain	Oxide particle	(g/cm 3 )/ (%	Microhardness	Refs.
				size (μm)	size (μm)		/HV
						RD)
		W-1%La 2 O 3	HIP	-	>5	18.9/90.6	-	[30]
	mechanically	W-1%Y 2 O 3	Sintering	4	1.4	-/<18.5	412.7	[31]
	alloyed	W-Ti-0.5%Y 2 O 3	HIP	2-5	>1	-	-	[32]
		W-1%Y 2 O 3 (0.2%Zr) Swaging	4.7	0.1-2	-/99.3	467	[33]

Table . 4

 . . Fitting values of parameters of the Arrhenius equation.

					(11)
		α/10 -3	n	Q	lnA
	A 0	4.38 B 0	-397.059 C 0	61.83677 D 0	11.85768
	A 1	-11.4 B 1	4639.339 C 1	780.7316 D 1	-233.666
	A 2	-41.67 B 2	-23722.6 C 2	52798.31 D 2	6874.381
	A 3	497.23 B 3	61010.93 C 3	-472133 D 3	-49872.5
	A 4	-1594.39 B 4	-77576.4 C 4	1608510 D 4	158141.4
	A 5	2225.9 B 5	38869.61 C 5	-2461810 D 5	-233247
	A 6	-1161.89 B 6	-397.059 C 6	1414360 D 6	130896.2

Acknowledgements

We would like to thank all the researchers who participated in our works discussed in the paper and whose names appear in references.

Strain/%

Declaration of interests

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.

*Declaration of Interest Statement


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Health-related quality of life correlates with time in therapeutic range in children on anticoagulants with International Normalised Ratio self-monitoring

Hamouda Abassi, Fanny Bajolle, Oscar Werner, Annie Auer, Amandine Marquina, Thibault Mura, Kathleen Lavastre, Sophie Guillaumont, Federico Manna, Pascal Auquier, et al.

To cite this version:

Hamouda

  Abassi, Fanny Bajolle, Oscar Werner, Annie Auer, Amandine Marquina, et al.. Healthrelated quality of life correlates with time in therapeutic range in children on anticoagulants with International Normalised Ratio self-monitoring. Archives of cardiovascular diseases, 2020, 10.1016/j.acvd.2020.05.022. hal-02977377