D Locq

M Martin

F Fossard

' precipitation study of a Co-Ni-based alloy

A Co-Ni-based alloy strengthened by '-(L1 2 ) precipitates was utilized to investigate the precipitation evolution after various cooling rates and several aging conditions. In this study, the precipitate size and volume fraction have been studied via scanning electron microscopy and transmission electron microscopy. The influence of the precipitation evolution was measured via microhardness tests. The cooling rate study shows a more sluggish ' precipitation reaction compared with that observed in a Ni-based superalloy. Following a rapid cooling rate, the application of appropriate double aging treatments allows the increase of the ' volume fraction as well as the control of the size and distribution of the precipitates. The highest hardness values reach those measured on supersolvus cast and wrought Ni-based superalloys. The observed ' precipitation behavior should have implications for the production, the heat treatment, the welding or the additive manufacturing of this new class of high temperature materials.

I. Introduction

The mechanical properties and especially the tensile strength of /' superalloys strongly depend on the fraction, distribution and size of the ' phase precipitates. Regarding high ' fraction wrought Nibased superalloys, the ' precipitation is predominantly controlled by the cooling rate [1,[START_REF] Raisson | High Temperature Materials for Power Engineering 1990 Part II[END_REF][START_REF] Mao | [END_REF][START_REF] Gabb | Superalloys 2008[END_REF][START_REF] Guédou | Superalloys 1992[END_REF] after the solutioning heat treatment. Generally, one or two aging treatments are then applied to adjust the ' precipitate characteristics [START_REF] Locq | Superalloys 2000[END_REF][START_REF] Locq | Superalloys 2004[END_REF][START_REF] Devaux | 8th International Symposium on Superalloy 718 and Derivatives[END_REF] .

Recently, several research teams have found that Co-based alloys can possibly be strengthened by the precipitation of a L1 2 -' phase based on Co 3 (Al,W). This new phase is the subject of numerous studies since the article of Sato et al. [START_REF] Sato | [END_REF] . More recently, Indian researchers published a series of articles on Co-based alloys strengthened by the precipitation of the Co 3 (Al,Mo,X) phase (where X is Ta or Nb) [10,11,12,13,14] . Even more recently, a novel Co-Ti-Cr alloy was shown to be strengthened by ' precipitates [15] . All these results have attracted great attention of several research groups. Most of the studies on Co-Al-W alloys are dedicated to the improvement of their mechanical properties and environmental resistance by means of alloying in relation to the microstructure. Only few studies focused on the '-Co 3 (Al,W) phase precipitation and more precisely on the coarsening behavior [16,17,18,19,20,21] .

The present work was performed on a Co-Ni-based alloy, the composition of which was derived from that of a quaternary model alloy studied by Shinagawa et al [22] . The Ni substitution for Co promotes the widening of the /' domain, the increase of the ' solvus temperature and the decrease of the lattice parameter mismatch between the and ' phases.

The objective of the present study was to investigate the mechanism of the ' precipitation during various heat treatments. We firstly studied the influence of the cooling rate on the ' precipitation and the results were compared to those obtained jointly on a Ni-based superalloy. In a second time, we investigated the effect of three aging parameters to optimize the ' precipitation and consequently the strength of this Co-Ni-based alloy.

II. Experimental procedure

The Co-GP-1 Co-Ni-based alloy contains 30 at% of Ni, 7 at% of Al and 10 at% of W [22] . Minor elements (C, B and Si) were added to control the grain size and to improve the grain boundary properties (Table I). The alloy was melted from raw elements by vacuum induction melting and then poured into a metallic mold. A cylinder was machined from the ingot, encapsulated in a steel can, held at 1250°C for 3 hours (supersolvus homogenization heat treatment) and then extruded with a reduction ratio of 10:1. Once the steel was removed, cylindrical samples (10 mm diameter and 10 mm length) were machined from the extruded billet and solution heat-treated for cooling rate or aging studies.

A Ni-based alloy was used for the cooling rate study as a reference material. Alloy N18 (Table I) is a powder metallurgy Ni-based superalloy used for production of high pressure compressor and turbine disks of the M88 turbofan for the Dassault Rafale fighter [START_REF] Guédou | Superalloys 1992[END_REF] . Cylindrical samples (10 mm diameter and 10 mm length) were machined out of an isothermal forging disk provided by Safran Aircraft Engine. These N18 samples belong to the same disk studied by Boittin et al. [START_REF] Boittin | Superalloys 2012[END_REF] .

All the heat treatments were conducted in horizontal resistance furnaces. Microstructural investigations were carried out at the center of the specimens. Samples used for scanning electron microscopy (SEM) imaging were polished to a 0.25 µm diamond finish and to a 0.02 µm colloidal silica suspension in a vibratory polisher (Buehler VibroMet 2). Transmission electron microscopy (TEM) samples were prepared via mechanical grinding and polishing of 3 mm diameter disks. These samples were thinned by electropolishing in a Struers Tenupol-3 polishing unit. The solution used for Co-GP-01 thin foils is (5 % perchloric acid + 95 % methanol) at 243 K and 10-20 V and the one used for N18 thin foils is (45 % acetic acid + 45 % butylcellosolve + 10 % perchloric acid) at 273 K and 10-14 V. Observations were performed using a Zeiss DSM982 Gemini or a Zeiss MERLIN FEG-SEM and a FEI CM20 or a Zeiss Libra 200 FE TEM at 200 kV. The images used for the quantification of the precipitate size and their area fraction are either TEM dark field images with a ‹001› zone axis or SEM images acquired near a {100}-type plane. These images were converted to binary images via a combination of manual and automatic coloring techniques using the GIMP-2 and the ImageJ software packages. As the images used for the precipitate size measurement originate from different techniques (SEM secondary electron (SE) or back-scattered electron (BSE) and TEM micrographs) and as the precipitate morphology varies, the precipitate size is determined on a different sampling: from 100 area measurements for the study related to the effect of the cooling rate and up to 275 to 1800 area measurements for the study related to the effect of aging. The precipitate size is defined as the weighted mean equivalent particle diameter. The weight of each precipitate is the volume of the spherical particle of same equivalent diameter ( πd [START_REF] Mao | [END_REF]

6

).

This weighting technique is necessary to ensure the relevance of the size measurements in terms of contribution of the precipitates to the size distribution. Vickers microhardness tests were conducted at room temperature on a Buehler OmniMet MHT tester (4.9 or 9.8 N). The hardness value is the average of 48 measurements on about 6 mm 2 .

III. Results and discussions

A. Influence of the cooling rate on the ' precipitation

The cooling rate study was carried out on both alloys Co-GP-01 and N18 to directly compare the ' precipitation behavior of a Co-Ni-based alloy with that of a Ni-based superalloy. Alloy N18 was selected as a reference alloy because of its high ' volume fraction as a wrought Ni-based superalloy (55-60%) which approaches the one estimated for alloy Co-GP-01 (60-70%). As the supersolvus heat treatment window is narrow for alloy N18 (1195-1230°C [START_REF] Boittin | Superalloys 2012[END_REF] ) and wide for alloy Co-GP-01 (~ 1035-1440°C [22] ), samples of both alloys were solution heat treated for one hour at 1200°C. This supersolvus solution treatment was followed by ice water quenching, air cooling, furnace cooling or slow cooling to produce a wide range of cooling rates. As the samples were not instrumented, the precipitation model adapted by Boittin to the supersolvus N18 alloy [START_REF] Boittin | [END_REF] was used to estimate the various cooling rates from the mean size of the ' precipitates. As both N18 and Co-GP-01 samples were cooled together, we estimate the same value of cooling rate for both materials. These results are presented in Table II. The precipitation model is understood to be accurate in a range of cooling rates from 5 to 700 K/min [25] , so that it should not be surprising that the precipitate size resulting from a 0.33 K/min cooling rate has been calculated by the precipitation model as it was resulting from a 0.16 K/min rate. This factor 2 in terms of cooling rates corresponds to a factor 1.4 in precipitate size, which is quite satisfactory given the fact that the cooling rate is far beyond the accuracy range of the model. Therefore, the estimations concerning the other cooling rates can be regarded as relevant.

A.1 Microstructure

The mean grain size is in the range 40-50 µm for alloy N18 and is larger for alloy Co-GP-01 (200-250 µm). This difference is mainly due to the material processing. Alloy Co-GP-01 was cast and extruded whereas alloy N18 was powder metallurgy processed. This later process leads to limited grain size growth even after supersolvus solution heat treatment due to prior particle boundaries [26,27] . was used to characterize  precipitates in ice water quenched and air cooled samples of both alloys due to the fine size precipitation in Co-GP-01 alloy whereas the other microstructures were investigated using SEM. Examples of the  precipitate distribution in N18 and Co-GP-01 alloys are shown in Figure 1. The mean equivalent particle diameters of the  precipitates for both alloys and for the four cooling conditions are compared in Table III. In ice water quenched N18 (Figure 1a), three populations of  precipitates are observed. The largest population presents a low number density and a particle size of around 150 nm. A second burst of precipitation leads to a high fraction of a second population of finer precipitates (20-40 nm) and a third population of very fine precipitates is observed near the larger ones. In ice water quenched Co-GP-01 alloy (Figure 1b), only one very fine population of  precipitates is detected. For the air cooling condition, two populations of  precipitates are present N18: a larger population having a mean size of 218 nm and a high particle fraction, and a second population of very fine precipitates (around 10-20 nm). For that same cooling condition, the Co-GP-01 sample contains only one dense and fine population of precipitates. For the slower cooling rates, the same trend is noticed, i.e. the precipitate size is always significantly smaller in the Co-Ni-based alloy (Figure 2). No second population of  precipitates is observed for both alloys after the furnace cooling. On the other hand, sparse fine precipitates are observed in the large channels in N18 and numerous very fine precipitates are present in the narrow channels in Co-GP-01. As far as the precipitate morphology is concerned, the first population of precipitates (first burst) in N18 presents a cuboidal shape for the fastest cooling conditions (ice water and air cooling). When decreasing the cooling rate, the N18 precipitates evolve to octocubes (furnace cooling) and finally to complex irregular shapes (0.33 K/min cooling) (Figure 1). For the Co-GP-01 alloy, the precipitates are nearly spherical for the fast cooling conditions, and then tend to change to cuboidal shape for the furnace cooling condition and with a tendency for splitting from the slowest cooling rate.

In some studies of the coarsening behavior of '-Co 3 (Al,W) precipitates, the observation of the ' precipitation was not carried out after the cooling following the solution heat treatment but rather after the aging treatment [16,20] . After water quenching, no ' precipitation was noticed by Sauza [19] in Co-8.8Al-7.3W and Co-9.7Al-7.1W-2.1Ru (at%) alloys and by Xue [28] in two Co-Al-W-Ti-Ta alloys, using a SEM. However, very fine ' precipitates were observed in a water quenched sample of Co-10Al-10W (at%) using TEM (2-10 nm) [17] and in a water quenched sample of Co-9.3Al-7.4W (at%) using TEM and atom probe tomography investigations (3-8 nm) [21] . The same result was also observed on quenched Co-10Al-5Mo-2Nb (at%) using TEM [11] . Our TEM investigation on Co-GP-01 ice water quenched sample confirms these observations (mean diameter of 10 nm). As for high ' fraction wrought Ni-based superalloys, a rapid cooling condition does not prevent the nucleation (and certainly the growth) of the '-Co 3 (Al,W) precipitates in these new alloys, even in very thin samples (300 µm thickness) [ 21 ]. However, this first study to examine the influence of cooling rate (in a wide cooling rate range), clearly shows that the '-Co 3 (Al,W) precipitation kinetics are sluggish and leads to a distribution of more dense and finer precipitates than those observed in the reference Ni-based superalloy at a given cooling rate. Indeed, the interdiffusion coefficients close to the precipitation onset temperature are lower for the Co-Ni-based alloy because of its lower ' solvus temperature. Other parameters such as /' interface energy or elastic strains in both phases (due to differences in misfit) could also affect the precipitation kinetics.

A.2 Hardness

Hardness tests were performed on samples of both alloys for the four cooling conditions. The results of these measurements are presented in Figure 3. Once again, it is worth mentioning that the Co-GP-01 alloy behaves differently to the Ni-based superalloy. For alloy N18, the hardness is superior to 400 HV for the highest cooling rates. Then, as the cooling rate decreases, the strengthening decreases. In contrast, for the Co-Ni-based alloy, the hardness value is very low for the fastest cooling condition (< 250 HV) and increases to a maximum of 390 HV for the furnace cooling condition. For the slowest cooling rate, the Co-GP-01 hardness drops close to 350 HV. It is worth noting that Co-GP-01 hardness is superior to that of N18 when the cooling rate is less than 10 K/min.

A.3 Discussion

The influence of the cooling rate on the ' precipitation and on the hardness of a Co-Ni-based alloy is presented for the first time. These results are directly compared to those jointly obtained for a Nibased superalloy.

For the N18 superalloy and high cooling rates, the  precipitation kinetics are fast enough to lead to a distribution of precipitates with appropriate sizes to reach high strengthening. As the cooling rate decreases, the hardness substantially drops. It may be assumed that this behavior is due to the observed precipitate coarsening and change of morphology. Their morphology changes from cubes to octocubes after the furnace cooling and to complex shapes after the slowest cooling rate. These changes lead to large matrix corridors containing few fine precipitates, which promote easier dislocation motion.

In contrast, for the Co-Ni-based alloy and high cooling rates, the  precipitation kinetics are sluggish and lead to a distribution of a high density of very fine precipitates. For the ice water quenching, the low hardness value can be attributed to the presence of precipitates with a mean diameter smaller than 10 nm, which are easily sheared by the matrix dislocations. It can be assumed that the  fraction at the end of the quenching is not at equilibrium as observed by Azzam [21] . As the cooling rate decreases, the  precipitates coarsen but their size is significantly smaller than the N18 ones (3 to 7 times smaller) and their morphology remains close to the cube even after the slowest cooling rate. It can be also assumed that the  fraction at the end of the slower cooling conditions is closer to the equilibrium fraction. The hardness level increases to reach its highest value after the furnace cooling. Up to that cooling rate, the precipitates shearing should become harder (due to the increase of  fraction and to the coarsening of the precipitates), whereas after this point, the dislocations should more easily bypass the coarse precipitates.

In comparison with Ni-based superalloys, alloy Co-GP-01 shows after quenching a more sluggish phase precipitation reaction associated with low hardness. There are benefits of such behavior during the production, the heat treatment, the welding or the additive manufacturing of this new class of high temperature materials to be considered. Firstly, in high ' fraction wrought Ni-based superalloys, the application of a rapid cooling, in particular in massive components supersolvus heat treated, could result in quench-cracking or severe shape distortion phenomena [29,30] . These issues are partly attributed in these alloys to the impossibility to avoid or to limit the strengthening ' phase precipitation during the severe quench. The nucleation and growth of extensive cooling ' precipitates result in high strengthening and, depending on the part geometry, can act as tensile stresses responsible for quench cracking. Such quench cracks were observed in N18 specimens after oil or water quenching [25] . Secondly, Ni-based superalloys with high contents of Al and Ti are regarded as non-weldable materials [START_REF] Chester | Superalloys II[END_REF][START_REF] Henderson | [END_REF] . As the additive manufacturing can be assimilated to a multilayer welding process, its applicability to high precipitation hardened Ni-based superalloys is deemed to be very challenging [33,34] . In particular, the susceptibility to strain-age cracking during post-welding heat treatments, is promoted by high content of ' forming elements (such as Al, Ti, Ta and Nb) [START_REF] Chester | Superalloys II[END_REF][START_REF] Rowe | Welding Research[END_REF] which results in high ' fraction. In such alloys, as IN738LC [36] or N18, the precipitation kinetics is fast, and as a consequence high cooling rates cannot prevent the nucleation and the growth of a significant percentage of precipitates. The resulting high precipitation hardening can then lead to strain-age cracking. In contrast, alloy 718 is considered to be less prone to this phenomenon due to the more sluggish precipitation kinetics of the strengthening '' phase [START_REF] Chester | Superalloys II[END_REF][START_REF] Lingenfelter | Superalloy 718: metallurgy and applications[END_REF][START_REF] Thamburaj | [END_REF] . This sluggish precipitation in alloy Co-GP-01 can be partly explained by a higher /' interface energy than in Ni-based superalloys. The /' interface energy evaluated in model Ni-Al-Cr alloys is generally in the 10-20 mJ•m -2 range [21] , whereas the /'' interfacial energy was evaluated at 95 mJ•m -2 in alloy 718 [39] . This value was found equal to 48 mJ•m -2 in a low supersaturated Co-Al-W alloy [21] . Moreover, the interface energy increases as the -' lattice parameter misfit becomes larger. Reported lattice misfit values in Co-Al-W alloys are generally larger than in Ni-based superalloys. This allows the high ' coarsening rate to be explained [17] . But as previously mentioned, the equilibrium ' fraction is not attained at the end of the quenching, so the alloy will still undergo nucleation and growth processes during initial stage of aging. A high interface energy will inhibit the increase of /' interface surface and thus impede the ' nucleation and growth processes [18] .

B. Influence of the aging step on the  precipitation

From the first part of the present study, it appears that the  precipitation in the Co-Ni-based alloy Co-GP-01 is more sluggish than in the Ni-based superalloy N18. The second part of this work focuses on the influence of the aging conditions on the  precipitation in the Co-Ni-based alloy. As the  precipitation in the Co-Ni-based alloy is less dependent on the cooling rate than in N18, the aging conditions become more deciding for the adjustment of the mechanical properties. Hardness tests and microstructural observations were conducted to investigate the effect of aging temperature and duration or of the application of a double aging treatment.

The aging study was carried out only on the Co-Ni -based alloy Co-GP-01. For this reason, it is no longer necessary to conduct the solution heat treatment at 1200°C which leads to a large grain size (200-250 µm). For the aging study, all the samples were solution heat treated at 1050°C for four hours and ice water quenched. All the aging treatments were also followed by an ice water quenching. A recrystallized microstructure with a mean grain size close to 50 µm was thereby obtained. The same sample geometry was used as in the cooling rate study and as no ' precipitation was observed after quenching using SEM investigation, it is expected that the ' precipitates are very fine (close to 10 nm).

B.1 Effect of the aging temperature

After solution heat treatment, a single aging treatment was carried out in the 650-1000°C range for 24 hours. The strengthening of the material was assessed by Vickers hardness testing with a 1 kg load (Figure 4). These results show that the hardness peak is reached at 800°C for an aging duration of 24 hours. These hardness data were completed with TEM and SEM observations of the ' precipitation (Figure 5). It appears that the ' precipitates undergo an extensive range in terms of particle size, shape and fraction. For the lowest aging temperatures (650-750°C), the ' precipitates present a size of few dozen of nanometers with a spherical morphology and a high fraction. Beyond 900°C, the ' fraction begins to diminish and the precipitates coarsen to several hundreds of nanometers with rounded cube shape. In the 800-900°C range, the ' fraction is still high but the precipitate size increases to few hundreds of nanometers. The precipitates have generally a cuboidal shape but lower order of symmetry morphologies are observed like "L" or more complex "Tetris-like" shapes (Figures 5b and5c). The ' area fraction and precipitate size were measured on samples aged between 800 and 1000°C for 24 hours (Figure 6). The precipitate size (mean diameter) increases from 112 nm at 800°C to 545 nm at 1000°C whereas the ' area fraction decreases from 63% to 31%.

B.2 Effect of the aging duration

The influence of the hold time of aging was studied at 800, 900 and 1000°C on samples previously solution heat treated (1050°C for four hours and ice water quench). The aging duration was 24, 96 and 192 hours. The evolution of the hardness for these different aging states is presented in Figure 7. The microstructure essentially consists of ' precipitates embedded in the matrix and some fine precipitates (bright in BSE imaging) are noticed in grain boundaries. A preliminary analysis of these intergranular particles (in a Zeiss Libra® 200 FE equipped with energy-dispersive X-ray spectroscopy and electron energy loss spectroscopy) points out a W-rich phase with boron. No new phase was detected after 96 or 192 hours compared with the 24 hour aging. At an aging temperature of 800°C, the precipitate size and the ' fraction both slightly increase with time. The influences of these two phenomena balance each other out and lead to a stable hardness level. At 900°C, the precipitate coarsening is accelerated but here the ' fraction increase is not sufficient to avoid the hardness decline. For the highest aging temperature, both the decreaseof the' fraction and the rapid rise of the precipitate size are observed. However, the hardness value is unchanged on this time range. It seems that for these severe conditions, the precipitation hardening is no more effective and that this hardness level matches with the matrix strengthening.

B.3 Effect of a double aging

For the great majority of studies on Co-based /' alloys, a single aging treatment is applied after the solution heat treatment. A double aging treatment was identified in only one article [40] but without studying its influence on the microstructure or on the strengthening. For polycrystalline Ni-based superalloys, up to four aging treatments are industrially carried out [START_REF] Novotnak | Superalloys 2008[END_REF] . Generally, two aging sequences are applied with the second aging treatment temperature below or above the first one. In order to further increase the strength of alloy Co-GP-01, we applied double aging treatments with the second aging treatment temperature 100°C or 150°C below the first one (Table IV).The first aging temperature is in the range 800-1000°C. The aging duration of each aging treatment is of 24 hours. The hardness data for these different double aging treatments are presented in Figure 10. The application of a double aging treatment systematically leads to an increase of the hardness compared with the related single aging treatment (Figure 10). When the second aging is carried out 100°C below the temperature of the first aging treatment, the hardness increase is in the range 10-20%, this benefit goes up to 10-30% when the second aging treatment is applied at -150°C (especially for the high temperature first aging treatment). The double aging treatment "850°C/24h + 700°C/24h" gives the highest hardness value of 427 HV which is close to those measured on supersolvus C&W (cast and wrought) Ni-based superalloys. SEM-FEG or TEM observations of the ' precipitation were performed on some double aging specimens (Figure 11). The ' fraction and precipitate size were measured on samples double aged "800°C/24h + 700°C/24h", "950°C/24h + 800°C/24h" and "1000°C/24h + 850°C/24h" (Figure 12). For the low temperature aging treatment, the ' precipitate morphology is unmodified (Figures 11a and11b) and their size and fraction slightly increase compared with the microstructure observed after a single aging treatment (Figure 12 -800°C first aging temperature). Fine ' precipitates were detected by means of TEM observations only for treatment with a first aging at 900°C and higher (not presented). At 900°C and 950°C, very few and fine precipitates were observed in the largest matrix channels. After a first aging treatment at 950°C, the coarse ' precipitates are rounded cuboidal shaped (Figure 11c). The application of a second aging treatment at lower temperature leads to notable differences: first, the ' fraction increases significantly and the precipitates present a more aligned and regular distribution (Figure 11d). A slight decrease of their mean size is measured (Figure 12).

A more dramatic evolution is noticed between the single aging treatment at 1000°C and the related double aging treatment (second aging at 850°C) (Figures 11e and11f). The area fraction of coarse precipitates evolves from 31% for the 1000°C/24h aging treatment to 46% for the 1000°C/24h + 850°C/24h aging treatment. Moreover, the application of the second aging at 850°C produced a microstructure with a ' bimodal precipitation. This second population in the large  channels has a mean size of 120 nm and an area fraction of 16%. The coarse and fine precipitates have a total ' area fraction of 62%. This is equal to that obtained after a single aging treatment at 850°C for 24 hours. And this is twice the area fraction measured after a single aging treatment at 1000°C for 24 hours. Again, the coarse precipitate population exhibits a more aligned and regular distribution after the application of the second aging treatment.

B.4 Discussion

In this second part of this work, the influences of the temperature and duration of a single aging treatment were investigated as well as that of a double aging treatment. Hardness measurements were collected and, when possible, correlated to microstructural investigations. The ' area fraction and precipitate size were quantified. High ' fraction and fine precipitate size are required for high mechanical strength. It is assumed that the mobility of the dislocations is governed by the width of the matrix  channels [START_REF] Locq | Superalloys 2004[END_REF][START_REF] Pollock | [END_REF]. When this dimension is large, dislocations can move easily by glide through the matrix channels resulting in poor mechanical properties. In contrast, when the channel width becomes smaller, dislocations have to propagate by ' shearing processes which are more energy requiring processes. In order to quantify the effect of the width of the matrix channels on hardness, this dimension was calculated through a basic assumption. A two-dimension pattern of perfect cube-shaped ' particles was used to calculate the mean channel width for each aging treatment (only microstructure without fine second precipitation observed). With this geometrical arrangement, the channel width L is defined as

𝐿 = 𝑒(𝑓 -1 2 -1)
Where e is the average edge length of the ' precipitates (calculated from the particle area) and f is the ' area fraction. Despite this basic approach, the link between hardness and the channel width is clearly established (Figure 13). A rapid decrease is noted between channel width of 10 and 100 nm which is experimentally observed in the aging temperature and in the double aging studies. For the aging duration study, the steady hardness level noticed at 800°C can be directly linked to the slight variation of the channel width (17 to 26 nm). At 900°C, the channel width almost doubles and the hardness moderately decreases (8 %). At 1000°C, the channel widening is even more marked, but the hardness level remains relatively constant. As the ' solvus temperature of Co-GP-01 is 1035°C, it is assumed that at 1000°C, the precipitation strengthening is no more effective and only the matrix hardness is measured. The ' fraction was extracted from the calculated phase diagram of Co-GP-01 alloy without minor elements, using Thermo-Calc software with TCNI8 database. As this new family of materials seems not well-documented in the database, it was necessary to consider only  and ' as possible stable solid phases for the calculation. The temperature was also shifted of 65°C to fit the experimental ' solvus temperature (Figure 14). Finally, this calculation shows that the equilibrium ' fraction between 750 and 850°C is 65-67%. This computed value is close to the area ' fraction measured after a single aging treatment applied in this temperature range (Table V) or after a double aging treatment with the second step in this temperature range.

IV. Conclusions

The ' precipitation evolution and hardness behavior of the Co-Ni-based alloy Co-GP-01 after different heat treatments have been examined. Regarding the cooling rate and the aging parameters, the following conclusions can be drawn based on the obtained results:

1/ In comparison with a high ' fraction wrought Ni-based superalloy, the application of a high cooling rate to a Co-Ni-based results in much finer ' precipitates. This more sluggish precipitation reaction is related to a low hardening. This precipitation behavior should give benefits during the production, the heat treatment, the welding or the additive manufacturing of this new class of high temperature materials.

2/ After a rapid cooling rate, high hardness can be reached through appropriate single or double aging treatments. These hardness values are similar to those measured on supersolvus C&W (cast and wrought) Ni-based superalloys. A monomodal or a bimodal ' population can be achieved according to the aging parameters. In the same way, the total area ' fraction can reach 60 to 70 %. The channel width can be then adapted to reach the target mechanical properties. These results show that the microstructure and so the hardness can be adjusted through the aging parameters. It is easier to control the microstructure, in particular for large components, because the Co-Ni-based alloy is much less sensitive to the cooling rate.

list of figure captions

Fig. 1 -

 1 Fig. 1 -Typical /' microstructure in Ni-based N18 (on the left) and in Co-Ni-based Co-GP-01 (on the right) after: an ice water quenching (a,b), an air cooling (c,d), a furnace cooling (e,f) or a 0.33 K/min cooling (g,h). TEM images (dark field-‹001› zone axis (a-d) and BSE SEM images (eh)).

Fig. 2 -

 2 Fig. 2 -Effect of cooling rate from solution heat treatment (1200°C) on Ni-based N18 and Co-Nibased Co-GP-01 precipitate mean size.

Fig. 3 -

 3 Fig. 3 -Effect of cooling rate from solution heat treatment (1200°C) on Ni-based N18 and Co-Nibased Co-GP-01 room temperature hardness.

Fig. 4 -

 4 Fig. 4 -Influence of the aging temperature on Co-GP-01 room temperature hardness (24 hours aging treatment).

Fig. 5 -

 5 Fig. 5 -Typical /' microstructure in Co-GP-01 after 1050°C/4h /ice water quench solution treatment and: 700°C/24h (a), 800°C/24h (b), 900°C/24h (c) or 1000°C/24h (d) aging treatment. TEM image (dark field-‹001› zone axis) (a) and BSE SEM images (b-d)).

Fig. 6 -

 6 Fig. 6 -Influence of the aging temperature on Co-GP-01 ' area fraction and precipitate size (24 hours aging treatment).

Fig. 7 -

 7 Fig. 7 -Influence of the aging time and duration on Co-GP-01 room temperature hardness.

Fig. 8 -

 8 Fig. 8 -Influence of the aging duration on Co-GP-01 ' area fraction.

Fig. 9 -

 9 Fig. 9 -Influence of the aging duration on Co-GP-01 precipitate size.

Fig. 10 -

 10 Fig. 10 -Influence of a single aging treatment and of double aging treatments on Co-GP-01 room temperature hardness.

Fig. 11 -

 11 Fig. 11 -Typical /' microstructure in Co-GP-01 after 1050°C/4h /ice water quench solution treatment and: 800°C/24h (a), 800°C/24h + 700°C/24h (b), 950°C/24h (c), 950°C/24h + 800°C/24h (d), 1000°C/24h (e) or 1000°C/24h + 850°C/24h (f) aging treatment. BSE SEM images.

Fig. 12 -

 12 Fig. 12 -Influence of double aging treatments on Co-GP-01 ' area fraction and precipitate size.

Fig. 13 -

 13 Fig. 13 -Influence of the channel width on the hardness of Co-GP-01 alloy.

Fig. 14 -

 14 Fig. 14 -Experimental (192 hours aging treatments) and calculated ' fraction vs temperature for Co-GP-01and N18 alloys.

Fig. 1 -

 1 Fig. 1 -Typical /' microstructure in Ni-based N18 (on the left) and in Co-Ni-based Co-GP-01 (on the right) after: an ice water quenching (a,b), an air cooling (c,d), a furnace cooling (e,f) or a 0.33 K/min cooling (g,h). TEM images (dark field-‹001› zone axis (a-d) and BSE SEM images (e-h)).

Fig. 2 -Fig. 3 -

 23 Fig. 2 -Effect of cooling rate from solution heat treatment (1200°C) on Ni-based N18 and Co-Nibased Co-GP-01 precipitate mean size. Fig. 3 -Effect of cooling rate from solution heat treatment (1200°C) on Ni-based N18 and Co-Nibased Co-GP-01 room temperature hardness.

Fig. 4 -

 4 Fig. 4 -Influence of the aging temperature on Co-GP-01 room temperature hardness (24 hours aging treatment).

Fig. 5 -

 5 Fig. 5 -Typical /' microstructure in Co-GP-01 after 1050°C/4h /ice water quench solution treatment and: 700°C/24h (a), 800°C/24h (b), 900°C/24h (c) or 1000°C/24h (d) aging treatment. TEM image (dark field-‹001› zone axis) (a) and BSE SEM images (b-d)).

Fig. 6 -

 6 Fig. 6 -Influence of the aging temperature on Co-GP-01 ' area fraction and precipitate size (24 hours aging treatment).

Fig. 7 -Fig. 8 -Fig. 9 -Fig. 10 -

 78910 Fig. 7 -Influence of the aging time and duration on Co-GP-01 room temperature hardness. Fig. 8 -Influence of the aging duration on Co-GP-01 ' area fraction. Fig. 9 -Influence of the aging duration on Co-GP-01 precipitate size. Fig. 10 -Influence of a single aging treatment and of double aging treatments on Co-GP-01 room temperature hardness.

Fig. 11 -

 11 Fig. 11 -Typical /' microstructure in Co-GP-01 after 1050°C/4h /ice water quench solution treatment and: 800°C/24h (a), 800°C/24h + 700°C/24h (b), 950°C/24h (c), 950°C/24h + 800°C/24h (d), 1000°C/24h (e) or 1000°C/24h + 850°C/24h (f) aging treatment. BSE SEM images.

Fig. 12 -

 12 Fig. 12 -Influence of double aging treatments on Co-GP-01 ' area fraction and precipitate size.

Fig. 13 -

 13 Fig. 13 -Influence of the channel width on the hardness of Co-GP-01 alloy.

Fig. 14 -

 14 Fig. 14 -Experimental (192 hours aging treatments) and calculated ' fraction vs temperature for Co-GP-01and N18 alloys.

Acknowledgements -Thanks are due to our colleagues Théo Guérin, Agnès Bachelier-Locq, Nicolas Horezan and Denis Boivin for their great experimental help.


Catherine Fouchier
email: catherine.fouchier@cemagref.fr

Pierre Javelle

Patrick Arnaud

Dimitri Defrance

Looking at catchments in colors: why not? But what if we can not even look at them?

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Constant routing function

 We want to assess the ability of a simple conceptual and parsimonious rainfall-runoff model to deliver flood alerts on ungauged catchments. To do so, we applied a proxybasin scheme using several sets of nested catchments.

 We want to know if allowing spatial variability in our model improves its performances. To answer this question, we tested different levels of spatial variability into our model.

Studied catchments in southern France. The downstream catchment are drawn with a green border, the upstream ones are drawn with a blue border.

Lumped rainfall

For each B and C cases distributed rainfall distributed production function

-Q outlet = Σ Q i

Data Calibration and validation

 The distributed version performs slightly better than the lumped version.

 Fully distributing the routing parameters results in better alerts than using uniform routing parameters in the distributed version.

 To fully assess the performance of the model, further evaluation should be carried out in an operational mode, i.e. using an initialisation procedure to determine the value of the production parameter at the beginning of each event instead of using a calibrated value (see Javelle et al, 2010). However, the R² coefficients calculated between the calibrated initial level of the production store (S 0 /A) and a daily moisture index gives an indication about the "ability" to initialise the model in a operational use. The R² values obtained at the downstream calibration indicate that the distributed version of the model seems the most promising for an operational use.

EGU Leonardo Topical

  B and C identical for each cell within a given catchment Lumped routing function with two parameters: -a shape parameter B -a lag parameter C Distributed routing function B i and C i parameters values in pixel i are functions of the d i distance to the outlet: B i = B 0 (pB.d i + 1) C i =C 0 + pC.d i



  Calibration at the 20 downstream outlets: calibration of the initial level of the production store (S 0 /A) for each flood calibration of the routing parameters for each watershed optimisation of the bounded Nash and Sutcliff criteria (C 2M , sea Mathevet et al., 2006) with optimal lag  Validation at inner points transferring parameters and initial production condition calibrated downstream  Multi-criteria evaluation in order to assess: how well the upstream calculated floods fit the observed ones (C1 to C2 criteria); how well the calibrated production parameters correlate to the moisture index of a continuous daily soil moisture accounting model (R² criteria, for the downstream catchments only); if the model delivers correct alerts (CSI index).



  Conference on the hydrological cycle "Looking at Catchments in Colors", 10-12 November 2010, Luxembourg Javelle, P., Fouchier, C., Arnaud, P., Lavabre, J., Flash flood warning at ungauged locations using radar rainfall and antecedent soil moisture estimations, Journal of Hydrology (2010), doi: 10.1016/j.jhydrol. 2010.03.032 Mathevet T., Michel C., Andréassian V. et Perrin C. (2006). A bounded version of the Nash-Sutcliffe criterion for better model assessment on large sets of basins. IAHS-AISH Publication, n° 307, 211-219. This work was supported by the Ecology, Energy, Sustainable Development and Sea French Ministry, Service Central d'Hydrométéorologie et d'Appui à la prévision des inondations (SCHAPI). Meteo-France is also acknowledged for having provided the rainfall data used in this study. Case A : lumped Case B : semi-distributed Case C : distributed (pC=0.1; pB=0.1) Performance criteria: (BNS: Bounded Nash and Stucliff criteria) C1: median flood BNS R²: correlation with continuous init. index C2: mean flood relative peak error CSI: critical success index for all criteria: the closer to 1, the better Runoff data from 67 watersheds in southern France: -20 "downstream" catchments ranging from 150 to 2170 km² -47 "upstream" catchments, considered as ungauged, nested within the "downstream" ones  Rainfall radar data (provided by a radar network) for 15 events between 2005 and 2008  Time step: 1h; spatial resolution: 1 km²


Pierre Javelle
email: pierre.javelle@cemagref.fr

Dimitri Defrance

Yoann Aubert

Stéphanie Diss

Philippe Cantet

Mathieu Tolsa

Catherine Fouchier

Patrick Arnaud

Jacques Lavabre

Dominique Breil

Application of the AIGA flash flood warning method to the 15th of June 2010 event on the Nartuby and Argens rivers (South of France)

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

> Comparison with observed damages

Flash flood forecasting at ungauged sites is one of the most difficult tasks in operational hydrology. The post-event analysis of catastrophic events offers the possibility to really appreciate the usefulness of warnings emitted during the crisis. This poster presents results obtained by the operational AIGA warning method during the dramatic 15th of June 2010 flood on the Nartuby and Argens rivers (South of France, 25 human losses).

The method correctly identifies the rivers where the most damages were reported: Nartuby, Florieye, Réal, downstream Argens (Fig. 4). However, due to quick basins response, the anticipation is quite short: only half an hour between the "red" warning emitted at Trans-en-provence near Draguignan on the Nartuby river, and the entrance of the water into the village (Fig. 5).

> Further investigations

An extensive post-event campaign coordinated by the French central flood forecast service (SCHAPI) was carried out in order to estimate peak discharges at different locations. This information will be compared with discharges calculated by the model. The same procedure must be applied to future events, in order to validate the method at ungauged locations.

> Description of the event

During the 15th and 16th of June 2010, an exceptional rainfall event occurred in South of France, with more than 300 mm recorded in 24 hours on a wide area. The downstream part of the Argens catchment was the most affected (Fig. 1a and1b). Rainfall return periods were locally greater than 100years (Fig. 1c). The AIGA method (Fig. 2) combines rainfall radar measurements, a simple distributed hydrological model, and references quantiles (flood and rainfall). It provides in real time maps characterizing the ongoing situation according to its return period, and dedicated to operational services (Fig. 3).

+ +

Fig. 5 :

 5 Fig. 5: Comparison between the AIGA warnings and the observed situation at the flooded village Trans-en-Provence on the Nartuby river (local time)

FigFig. 2 :

 2 Fig. 1a: The Argens catchment (2 760 km²) and some of its sub-catchments 1-Florieye (91 km²) 2-Nartuby (234 km²) 3-Réal (37 km²) 4-Endre (193 km²) 5-Aille (278 km²)

Fig. 3 :

 3 Fig. 3: AIGA rivers characterization during the 15 th -16 th of June event (loc. time)