Gabrielle Tiphéne
email: gabrielle.tiphene@ec-lyon.fr

Paul Baral
email: paul.baral@uclouvain.be

Solène Comby-Dassonneville
email: solene.dassonneville@insa-lyon.fr

Gaylord Guillonneau
email: gaylord.guillonneau@ec-lyon.fr

Guillaume Kermouche
email: kermouche@emse.fr

Jean-Michel Bergheau
email: jean-michel.bergheau@enise.fr

Warren Oliver
email: warren.oliver@kla.com

Jean-Luc Loubet
email: jean-luc.loubet@ec-lyon.fr

Gabrielle Tiphéne -Corresponding Author

High-Temperature Scanning Indentation: A new method to investigate in situ metallurgical evolution along temperature ramps

Keywords: nanoindentation, annealing, microstructure

come

I. Introduction

Significant progress in high-temperature nanoindentation testing has been made over the last decade, opening the way to the investigation of thermally activated mechanisms at different length scales. Micron-scale measurements of the hardness, Young's modulus and even creep properties at temperatures up to 800°C and beyond now appear feasible 1- 4 . A recent paper of Baral et al. [START_REF] Baral | In situ characterization of AA1050 recrystallization kinetics using high temperature nanoindentation testing[END_REF] has also highlighted the ability of high-temperature nanoindentation to investigate in situ microstructural evolution, i.e., static recrystallization [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF] , in an aluminum alloy. High-temperature nanoindentation is clearly one of the most promising techniques to reveal new insights into the small-scale properties of materials. Among all the challenges that have been overcome to allow high-temperature measurements, one of the most critical is the development of a suitable tip and sample thermal regulation to eliminate/minimize thermal drift issues [START_REF] Wheeler | Elevated temperature, in situ indentation with calibrated contact temperatures[END_REF][START_REF] Wheeler | Indenter materials for high temperature nanoindentation[END_REF][START_REF] Wheeler | High temperature nanoindentation: The state of the art and future challenges[END_REF] . This development has led to various regulation strategies and procedures that are usually dependent on the setup [START_REF] Minnert | New ultra-high temperature nanoindentation system for operating at up to 1100 °C[END_REF][START_REF] Wheeler | Elevated temperature, in situ indentation with calibrated contact temperatures[END_REF][START_REF] Everitt | High temperature nanoindentation -the importance of isothermal contact[END_REF][START_REF] Wheeler | Elevated temperature, nano-mechanical testing in situ in the scanning electron microscope[END_REF] . It is worth noting that the use of such procedures takes time [START_REF] Baral | In situ characterization of AA1050 recrystallization kinetics using high temperature nanoindentation testing[END_REF][START_REF] Wheeler | High temperature nanoindentation: The state of the art and future challenges[END_REF][START_REF] Wheeler | Elevated temperature, nano-mechanical testing in situ in the scanning electron microscope[END_REF] . Unfortunately, during such a period of time, thermally dependent physical transformations in materials can occur [START_REF] Bozzolo | Fast in-situ annealing stage coupled with EBSD: A suitable tool to observe quick recrystallization mechanisms[END_REF][START_REF] Lauridsen | Non-destructive characterization of recrystallization kinetics using three-dimensional X-ray diffraction microscopy[END_REF][START_REF] Christien | A method for the monitoring of metal recrystallization based on the in-situ measurement of the elastic energy release using neutron diffraction[END_REF][START_REF] Lauridsen | Recrystallization kinetics of individual bulk grains in 90% cold-rolled aluminium[END_REF] . Therefore, important information can be missed. More precisely, this is a very important issue when investigating recrystallization mechanisms in polycrystalline materials 12- 15 or crystallization in amorphous materials [START_REF] Vasconcellos | Comparative study of isothermal and isochronal crystallisation of metallic glasses[END_REF][START_REF] Pelletier | Physical properties of bulk amorphous glasses: influence of physical aging and onset of crystallisation[END_REF][START_REF] Fukami | Crystal growth and time evolution in Zr-Al-Cu-Ni glassy metals in supercooled liquid[END_REF][START_REF] Nieh | Comparative studies of crystallization of a bulk Zr-Al-Ti-Cu-Ni amorphous alloy[END_REF][START_REF] Zhang | Influence of relaxation and crystallization on micro-hardness and deformation of bulk metallic glass[END_REF][START_REF] Apreutesei | Crystallization and hardening of Zr-40at.% Cu thin film metallic glass: Effects of isothermal annealing[END_REF][START_REF] Idriss | Evolution of the elastic modulus of Zr-Cu-Al BMGs during annealing treatment and crystallization: Role of Zr/Cu ratio[END_REF] . This issue can even affect the well-known indentation size effect, which has been deeply investigated during the past two decades [START_REF] Wang | Influences of Sample Preparation on the Indentation Size Effect and Nanoindentation Pop-in on Nickel[END_REF][START_REF] Nix | Size effects in crystalline : a law for strain gradient plasticity[END_REF][START_REF] Franke | Temperature dependence of the indentation size effect[END_REF] . Consequently, it is of crucial importance to develop robust nanoindentation methodologies to permit the measurement of mechanical properties at high temperature without the need to use time-consuming thermal stabilization procedures.

In the paper of Baral et al. [START_REF] Baral | In situ characterization of AA1050 recrystallization kinetics using high temperature nanoindentation testing[END_REF] , it is clearly stated that the strategy used is only relevant to characterize slow recrystallization kinetics because of both the stabilization time and the duration of an indentation test (approximately 8 min per test).

The resulting lack of statistics may thus introduce an interpretation bias, mostly related to the inherent microstructure heterogeneity. Recrystallization is a thermally activated mechanism that involves nucleation of dislocation-free grains in a deformed microstructure. These nuclei grow at the extent of the former microstructure grains until the whole recrystallization process is achieved [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF][START_REF] Doherty | Current issues in recrystallization: a review[END_REF] . The dislocation-free grains are softer than the deformed grains, which allows us to discriminate them from the former grains by a simple hardness test. Therefore, the quantification of recrystallization kinetics through nanoindentation testing requires an extensive set of nanoindentation data to be independent of microstructural heterogeneity, which can be done using ultrafast indentation measurements (less than 1 s). One advantage of high-speed nanoindentation is that it should also diminish displacement drift issues. Thus, it should even be possible to obtain data during the heating and cooling phases. Hence, the aim of this paper is to investigate whether High Temperature Scanning Indentation, a technique based on high-speed nanoindentation, is able to overcome the difficulties induced by the thermal stabilization time in order to pave the way for robust in situ quantifications of thermally activated physical transformations of materials.

In this paper, the first part presents the new High Temperature Scanning Indentation technique. A specific indentation methodology with an unloading segment, named three-step unloading, is proposed to avoid unloading nose issues in time-dependent materials. This technique is then validated through high-temperature experiments on fused silica and pure aluminum. The last part investigates the ability of High Temperature Scanning Indentation to track the mechanical properties and microstructure evolution in pure aluminum upon heating and cooling.

II. Methodology

The main objective of this paper is to conduct nonisothermal nanoindentation (i.e., during heating and cooling) to investigate in situ physical transformations in materials within a dedicated nanoindentation setup. One of the most important issues with high-temperature nanoindentation is thermal drift, which is a consequence of thermal fluctuations, mainly attributed to the tip-sample temperature mismatch. This thermal drift must remain low relative to the loading rate to ensure quantitative measurement of displacement. Therefore, specific calibration procedures must be used, depending on the temperature range and the setup. Most of the time, these calibration procedures are performed to ensure the temperature balance between the tip and the sample surface [START_REF] Wheeler | Elevated temperature, in situ indentation with calibrated contact temperatures[END_REF][START_REF] Wheeler | Indenter materials for high temperature nanoindentation[END_REF][START_REF] Wheeler | High temperature nanoindentation: The state of the art and future challenges[END_REF] . In this paper, the setting calibration process described by Minnert et al. [START_REF] Minnert | New ultra-high temperature nanoindentation system for operating at up to 1100 °C[END_REF] is used to set the temperatures of the tip in regards of the one of the sample (in isothermal conditions). The principle consists of finding the right thermal setting to minimize the displacement drift. To do so, the tip temperature is tuned during multiple tip-sample contact steps. This procedure is applied at different temperatures in the temperature range of the experiment. Once that those settings are known, the thermal ramps of the tip and the sample could be determined. When performing experiments, the tip and sample are heated using those ramps. For instance, imagine that the tip temperature should be 5°C higher than the sample at 100°C and 10°C at 200°C. Saying that the sample is heated at 3°C/min, the tip ramp should be 3.15°C/min. This technique allows calibration of the settings for the whole thermal cycle. This procedure needs to be performed for each new tested material with a dedicated calibration sample.

High-speed indentation tests

To minimize the impact of the temperature variations on the displacement during heating and cooling, the indentation cycle has to be fast enough with regard to the temperature evolution during an indentation test. For instance, an increase of 0.05°C during an indentation test with a thermal ramp of 3°C/min corresponds to a test duration of 1 s.

a. Loading part

One strong interest of high-temperature indentation is the investigation of rate-dependent mechanical properties (creep). Therefore, including a holding time at constant load is appropriate here. To avoid any load overshoot at the beginning of the creep segment, it is necessary to design a loading part smoothing the transition between loading and creep segments. Clearly, the usual constant indentation strain rate segment, which is often used to satisfy the principle of geometric similarity [START_REF] Lucas | Indentation power-law creep of high-purity indium[END_REF][START_REF] Kermouche | Cone indentation of time-dependent materials: The effects of the indentation strain rate[END_REF] , does not fit such a requirement. Hence, it is proposed to use a quarter sinus function instead, as illustrated in the load-versus-time curve of FIG. 1(a):

P(t) = P 𝑚𝑚𝑚𝑚𝑚𝑚 sin 𝜋𝜋 2𝑡𝑡 𝑙𝑙𝑙𝑙𝑚𝑚𝑙𝑙 𝑡𝑡 Eq. 1
where 𝑃𝑃 is the load, 𝑡𝑡 is the time, P 𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum load, and 𝑡𝑡 𝑙𝑙𝑙𝑙𝑚𝑚𝑙𝑙 is the loading time. With such a loading procedure, the force deceleration is slow enough to permit better control of the applied force by the PID when starting the creep segment. It is worth noting that this loading function does not allow us to keep the indentation strain rate constant during the loading part. Due to device limitations, the loading time could not be faster than 0.5 s when using a quarter sinus function. However, the quarter sinus loading method can lead to artificial pop-in at the beginning of the loading part where a very high loading rate is applied at a shallow depth. This feature can be seen in FIG. 1(b) and (d)

for indentation in aluminum at 300. This artifact could be avoided by defining a sigmoidal loading function for which the loading rate tends to zero at both the beginning and end of loading. Such a development is not within the scope of this paper and will be part of a complementary investigation that will deal exclusively with the analysis of pop-in during fast indentation cycles.

b. Unloading part

A quick unloading part (Δ𝑡𝑡 ≤ 0.5 𝑠𝑠) is also necessary to precisely determine the contact stiffness needed to calculate the hardness and modulus of the materials. Contrary to the loading part, there are no conditions to fulfill at the end of the unloading part. Therefore, a linear evolution of the load with time was initially chosen as the unloading function (see FIG. 1(a)):

𝑃𝑃(𝑡𝑡) = 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 �1 - 𝑡𝑡-𝑡𝑡 ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑡𝑡 𝑢𝑢𝑜𝑜𝑜𝑜𝑜𝑜𝑢𝑢𝑜𝑜 � Eq. 2
where 𝑃𝑃 is the load, 𝑡𝑡 is the time, P 𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum load, 𝑡𝑡 𝑢𝑢𝑢𝑢𝑙𝑙𝑙𝑙𝑚𝑚𝑙𝑙 is the time of the unloading part and 𝑡𝑡 ℎ𝑙𝑙𝑙𝑙𝑙𝑙𝑜𝑜𝑢𝑢𝑜𝑜 is the time at the end of the creep segment.

This method is very relevant for materials with limited time-dependent mechanical properties, such as fused silica.

However, for materials that exhibit significant time-dependent mechanical properties in the investigated temperature range, such as pure aluminum at 300°C, a nose can appear on the unloading curve (see FIG. 1(b)). This feature is a well-known consequence of creep [START_REF] Ngan | Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation[END_REF] . This nose is problematic regarding the fitting of the unloading curve and therefore leads to inaccurate values of the contact stiffness 𝑆𝑆, as defined by Oliver and Pharr [START_REF] Oliver | An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[END_REF] . Note that when determining the contact depth ℎ 𝑐𝑐 (see Eq. 3 -

𝑃𝑃 𝑚𝑚𝑢𝑢𝑚𝑚 𝑆𝑆 ≪ ℎ 𝑚𝑚𝑚𝑚𝑚𝑚
), the error in the stiffness calculation has a low impact on the contact depth determination of aluminum. In fact, unlike the elastic modulus, the hardness 𝐻𝐻 is not so much impacted here, even in the presence of a nose.

Consequently, the main issue related to such a creep-induced nose is an inaccurate measurement of elastic modulus values (see Eq. 7 and Eq. 8). Ngan correction [START_REF] Ngan | Correcting power-law viscoelastic effects in elastic modulus measurement using depth-sensing indentation[END_REF] was applied but did not lead to accurate stiffness measurements. (c) Modified high-speed indentation cycle. The loading part is again constructed from a quarter sinus function, and a holding segment is implemented to measure creep parameters. Unloading is performed as quickly as possible using the three-step unloading method, i.e., three unloading steps of 0.05 s. The whole cycle lasts less than 1 s. (d) Load-displacement curve measured on pure aluminum at 300°C, corresponding to the indentation cycle presented in (c). Owing to the modified unloading procedure (i.e., the three-step unloading method), the nose is no longer observed. The unloading part can now be fitted using a linear function.

To overcome this issue, it is proposed here to use a three-step method during the unloading part (see FIG. 1(c)). The idea of such unloading method is to unload as fast as possible while having enough data points to accurately determine the stiffness. It is done using load steps during unloading. More precisely, a first unloading step, from 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 to 75%𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 , is applied instantaneously. It is stabilized for 0.05 s before decreasing to 50%𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 . The same stabilization of 0.05 s is performed before decreasing to 25%𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 . After another 0.05 s time interval, a linear unloading part is applied. The resulting load-versus-depth curve, where the nose is no longer present, is shown in FIG. 1(d) for pure aluminum at 300°C. The unloading part of the load-displacement curve can then be fitted accurately using a linear regression with the slope corresponding to the contact stiffness 𝑆𝑆. It is worth noting that no creep occurs when the steps in load stabilize at 75%𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 , 50%𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 or 25%𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 .

Methodology for data analysis

The procedure for data analysis is based on the model of Loubet [START_REF] Loubet | Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures[END_REF] , for which further details are given in the appendix.

According to this model, the contact depth ℎ 𝑐𝑐 is given by

ℎ 𝑐𝑐 = 𝛼𝛼 �ℎ 𝑚𝑚𝑚𝑚𝑚𝑚 - 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 𝑆𝑆 𝑢𝑢 + ℎ 0 � Eq. 3
where ℎ 𝑚𝑚𝑚𝑚𝑚𝑚 and 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 are the maximum depth and load, respectively, at the end of the creep segment, ℎ 0 is the tip defect and 𝛼𝛼 = 1.2 is a constant.

The unloading contact stiffness 𝑆𝑆 𝑢𝑢 is then calculated from:

𝑆𝑆 𝑢𝑢 = 1 1 𝑆𝑆 - 1 𝑆𝑆 𝐿𝐿𝐿𝐿 Eq. 4
where 𝑆𝑆 𝐿𝐿𝐿𝐿 is the load frame stiffness calibrated at the ambient environment. The load frame stiffness is supposed to remain independent of the temperature in the range of our experiments [START_REF] Minnert | New ultra-high temperature nanoindentation system for operating at up to 1100 °C[END_REF] .

By considering the tip as perfect, the contact area 𝐴𝐴 𝑐𝑐 is given by

𝐴𝐴 𝑐𝑐 = 𝜋𝜋 tan 2 𝜃𝜃 ℎ 𝑐𝑐 2 Eq. 5
where 𝜃𝜃 = 70.32°, the equivalent conical angle for a Berkovich tip.

The hardness 𝐻𝐻 (𝐺𝐺𝑃𝑃𝐺𝐺) and reduced elastic modulus 𝐸𝐸 𝑅𝑅 (𝐺𝐺𝑃𝑃𝐺𝐺) are given by: 𝐻𝐻 = 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 𝐴𝐴 𝑐𝑐 Eq. 6

𝐸𝐸 𝑅𝑅 = 𝑆𝑆 𝑢𝑢 2 � 𝜋𝜋 𝐴𝐴 𝑐𝑐 Eq. 7
Finally, Young's modulus 𝐸𝐸 (𝐺𝐺𝑃𝑃𝐺𝐺) is computed through:

𝐸𝐸 = 1 -𝜈𝜈 2 1 𝐸𝐸 𝑅𝑅 - 1 -𝜈𝜈 𝑡𝑡𝑜𝑜𝑡𝑡 2 𝐸𝐸 𝑡𝑡𝑜𝑜𝑡𝑡
Eq. 8

knowing the Poisson ratio of the sample 𝜈𝜈 and the tip elastic constants 𝐸𝐸 𝑡𝑡𝑜𝑜𝑡𝑡 and 𝜈𝜈 𝑡𝑡𝑜𝑜𝑡𝑡 . Creep data are analyzed using the methodology presented by Baral et al. [START_REF] Baral | Indentation creep vs. indentation relaxation: A matter of strain rate definition[END_REF] . In uniaxial tests, the representative stress 𝜎𝜎 𝑟𝑟 could be related to the representative strain rate 𝜀𝜀̇𝑟𝑟 using a power-law relation:

𝜀𝜀̇𝑟𝑟 = 𝑐𝑐𝜎𝜎 𝑟𝑟 1/𝑚𝑚
Eq. 9

where 𝑐𝑐 is the strength coefficient and 𝑚𝑚 is the strain rate sensitivity, which are material constants.

To relate the representative strain rate from uniaxial tests 𝜀𝜀̇𝑟𝑟 to the indentation strain rate 𝜀𝜀̇𝑜𝑜 𝑢𝑢𝑙𝑙 = ℎ ̇/ℎ , the following expression is used, as proposed by Baral et al. [START_REF] Baral | Indentation creep vs. indentation relaxation: A matter of strain rate definition[END_REF] :

𝜀𝜀̇𝑟𝑟 = 0.44 cot 𝜃𝜃 exp � 0.2 𝑚𝑚 � ℎ ḣ Eq. 10
From the same way, 𝜎𝜎 𝑟𝑟 the representative stress is related to the hardness 𝐻𝐻:

𝜎𝜎 𝑟𝑟 = 𝐻𝐻 𝛾𝛾 Eq. 11
where 𝛾𝛾 is the constraint factor, defined by Kermouche et al. [START_REF] Kermouche | Extraction of stress-strain curves of elastic-viscoplastic solids using conical/pyramidal indentation testing with application to polymers[END_REF] :

𝛾𝛾 = 𝜉𝜉 1 cot 𝜃𝜃 -(1 -𝜉𝜉 2 )𝐻𝐻/𝐸𝐸 𝜉𝜉 3 cot 𝜃𝜃 Eq. 12
with the geometrical constants for a cone of half-induced angle 𝜃𝜃 = 70.32°, i.e., Berkovich indenter, 𝜉𝜉 1 = 0.66, 𝜉𝜉 2 = 0.216 and 𝜉𝜉 3 = 0.24.

Using Eq. 9 to Eq. 12, strength coefficient 𝑐𝑐 and strain rate sensitivity 𝑚𝑚 are determined through a linear fit of the plot ln ℎ ̇/ℎ -ln 𝜎𝜎 𝑟𝑟 .

The analysis of Sherby and Armstrong 34 is used to determine the apparent activation energy 𝑄𝑄:

𝐻𝐻 𝐸𝐸 = 𝐶𝐶 0 exp 𝑄𝑄 𝑛𝑛𝑛𝑛𝑛𝑛 Eq. 13
where 𝐶𝐶 0 is a pre-exponential constant, 𝑛𝑛 is the gas constant, and 𝑛𝑛 is the stress exponent, which is equal to 5 for consistency with previous studies [START_REF] Ludwik | Über die Änderung der inneren Reibung der Metalle mit der Temperatur[END_REF] .

III. Validation

The High Temperature Scanning Indentation technique was validated on fused silica and pure aluminum. The proposed indentation method with the 3-step unloading part was carried out during anisothermal high-temperature cycles.

Validation on fused silica

The Young's modulus and hardness of fused silica versus temperature are plotted in FIG. 2. The Young's modulus of fused silica was investigated by numerous authors [START_REF] Wheeler | Elevated temperature, nano-mechanical testing in situ in the scanning electron microscope[END_REF][START_REF] Marx | Temperature Dependence of the Elastic Moduli and Internal Friction of Silica and Glass[END_REF][START_REF] Spinner | Elastic Moduli of Glasses at Elevated Temperatures by a Dynamic Method[END_REF][START_REF] Spinner | Temperature Dependence of Young's Modulus of Vitreous Germania and Silica[END_REF][START_REF] Bucaro | High-temperature Brillouin scattering in fused quartz[END_REF][START_REF] Beake | High-Temperature Nanoindentation Testing of Fused Silica and Other Materials[END_REF][START_REF] Schuh | Nanoindentation and contact-mode imaging at high temperatures[END_REF] and is known to increase with temperature. The evolution of the Young's modulus during the heating phase is in excellent agreement with the model of Spinner et al. [START_REF] Spinner | Temperature Dependence of Young's Modulus of Vitreous Germania and Silica[END_REF] . However, the obtained hardness values are slightly lower than those from Schuh et al. [START_REF] Schuh | Nanoindentation and contact-mode imaging at high temperatures[END_REF] , but they remain correct when considering possible error sources during high-temperature nanoindentation (thermal drift, tip area function changes, load frame stiffness being a function of temperature, etc.) .

FIG. 2 Young's modulus and hardness versus temperature on fused silica during a slow thermal ramp (3°C/min). The Young's

modulus values are in good agreement with the model of Spinner et al. [START_REF] Spinner | Temperature Dependence of Young's Modulus of Vitreous Germania and Silica[END_REF] . The hardness values are also in quite good agreement compared to those of Schuh et al. [START_REF] Schuh | Nanoindentation and contact-mode imaging at high temperatures[END_REF]

Validation on aluminum up to 325°C

As shown in FIG. 3, the Young's modulus of aluminum decreases linearly with temperature. The trend is in agreement with the literature data [START_REF] Simmons | Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook[END_REF] , even if the values are slightly lower. This difference may arise from the model used for data analysis or from the assumption of constant load frame stiffness in temperature.

The hardness also decreases linearly with temperature, and the values are in agreement with literature data [START_REF] Ludwik | Über die Änderung der inneren Reibung der Metalle mit der Temperatur[END_REF][START_REF] Wheeler | Activation parameters for deformation of ultrafine-grained aluminium as determined by indentation strain rate jumps at elevated temperature[END_REF] . It is worth noting that care should be taken here when compared with the results of Wheeler et al. since these results are contact model dependent.

FIG. 3 Young's modulus and hardness versus temperature on pure aluminum during a slow thermal ramp (3°C/min). The reference data are from [START_REF] Simmons | Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook[END_REF] for the Young's modulus and from [START_REF] Ludwik | Über die Änderung der inneren Reibung der Metalle mit der Temperatur[END_REF][START_REF] Wheeler | Activation parameters for deformation of ultrafine-grained aluminium as determined by indentation strain rate jumps at elevated temperature[END_REF] for hardness.

The apparent activation energy was then determined by studying the evolution of the modulus-compensated hardness 𝐻𝐻/𝐸𝐸 against 𝑛𝑛 𝑚𝑚 /𝑛𝑛, where 𝑛𝑛 is the absolute testing temperature and 𝑛𝑛 𝑚𝑚 is the absolute melting temperature (see FIG.

4 and Eq. 13). Young's modulus data in temperature were taken from [START_REF] Simmons | Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook[END_REF] . Another approach would be to fit the obtained 13

Young's modulus data on all the interesting temperature scale to use them. However, it does not impact the following results. 𝐻𝐻/𝐸𝐸 decreases as the temperature increases. The slope of the curve gives the apparent activation energy and changes two times (at approximately 125°𝐶𝐶 and 250°𝐶𝐶). The values are consistent with the reference data [START_REF] Wheeler | Activation parameters for deformation of ultrafine-grained aluminium as determined by indentation strain rate jumps at elevated temperature[END_REF] .

FIG. 4 Modulus-compensated hardness versus the inverse of temperature over melting temperature. The literature data are from [START_REF] Ludwik | Über die Änderung der inneren Reibung der Metalle mit der Temperatur[END_REF][START_REF] Wheeler | Activation parameters for deformation of ultrafine-grained aluminium as determined by indentation strain rate jumps at elevated temperature[END_REF] .

The temperature-compensated indentation strain rate versus modulus-compensated hardness is plotted in FIG. 5 In conclusion, the proposed High Temperature Scanning Indentation technique allows quick and precise indentation measurements to be performed during a nonisotherm thermal cycle with a quasi-continuous resolution in temperature (i.e., one data point per 1°C). By comparison with literature models and experimental data, strong validation has been performed on fused silica and aluminum for the hardness and modulus, as well as for the activation energy.

IV. Application of High Temperature Scanning Indentation to the monitoring of thermally activated mechanisms 1. Results

The proposed High Temperature Scanning Indentation technique is applied to study the in situ evolution of the mechanical properties of pure aluminum during nonisothermal temperature cycles (heating at 3°C/min, holding at 300°C or 325°C before cooling at 3°C/min). Further details on the material and thermal cycles are given in the Materials and methods section. Hardness versus temperature curves are plotted in FIG. 6(a) and (b) for the two investigated thermal cycles. The results are well reproducible during the heating phase. The hardness appears to decrease linearly with temperature. However, a slight change in the slope can be noticed for a temperature of approximately 250°C. For both samples, a decrease in hardness occurs during the hold temperature step. During the cooling phase, the hardness increases linearly. The hardness versus temperature curves during the cooling phase are not superimposed. As shown in FIG. 9, the temperature holding segment was prescribed to occur at a higher temperature for the second experiment (holding at 325°C). Therefore, the hardness at the beginning of the cooling step for the second experiment was expected to be lower than that with the first experiment (holding at 300°C). However, the slope appears to be relatively similar.

It is worth noting that this slope (in absolute value) is lower than that observed during the heating phase. The variation in the strain rate sensitivity m with temperature is given in FIG. 7 for the 300°C thermal cycle. Similar results are obtained for the 325°C thermal cycle. Unlike hardness, there is almost no difference between heating and cooling, even though a slightly lower value might be noticed for the cooling phase. Some recrystallized grains are clearly visible on the sample heated up to 300°C. Initial grains can be identified through the presence of LABs. The recrystallization fraction is approximately 20%. In comparison, the recrystallization process was much more advanced on the sample heated up to 325°C. There are many fewer subgrain boundaries, and the recrystallized grains are relatively larger. The recrystallization fraction is closer to 50% for this thermal cycle, which is consistent with a lower hardness after the 325°C thermal cycle.

Discussion

The temperature dependence of the hardness can be explained through various mechanisms. Thermal activation of viscoplasticity mechanisms (activation of dislocation movements: dislocation glide, dislocation climb, etc.) that have been extensively studied for aluminum [START_REF] Ludwik | Über die Änderung der inneren Reibung der Metalle mit der Temperatur[END_REF][START_REF] Shen | Low-Temperature Creep at Ultra-Low Strain Rates in Pure Aluminum Studied by a Helicoid Spring Specimen Technique[END_REF] are clearly the most important mechanisms, as pointed out in the previous section. Nonetheless, the differences observed between heating and cooling require the consideration of other mechanisms such as static recovery and recrystallization.

The hardness of metals is known to depend upon the dislocation density [START_REF] Tabor | The hardness of solids[END_REF][START_REF] Tumbajoy-Spinel | Microstructural and micromechanical investigations of surface strengthening mechanisms induced by repeated impacts on pure iron[END_REF] . The higher the dislocation density is, the higher the hardness. Cold work increases the amount of dislocations in metals; aluminum hardness is thus dependent on the amount of cold work. When the temperature increases, dislocation annihilation is eased due to dislocation climb and cross-slip (thermally activated viscoplasticity mechanisms), which lead to a decrease in the dislocation density (i.e., hardness). This mechanism is known as static recovery [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF] .

A change in the slope of the curves of hardness versus temperature (heating) -see FIG. 6 -is observed at approximately 250°C. This result might be attributed to a change in the static recovery mechanism or to the occurrence of a second metallurgical mechanism, i.e., recrystallization [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF] . Such variation is also observed in FIG. 4: the apparent activation energy increases drastically at 250°C.

Recrystallization 6 is characterized by the birth and growth of new grains at the extent of the initial microstructure. The driving force of this mechanism is the stored energy (i.e., dislocation density). Recrystallized grains are characterized by a low dislocation density that is often considered null. Therefore, the hardness of recrystallized grains is significantly lower than that of a cold-rolled microstructure. So, during heating, because static recovery and recrystallization occur, the dislocation density decreases drastically, as does the hardness.

When recrystallization starts, a strong increase in the hardness standard deviation might be expected since some grains are recrystallized and other grains are not. In the current work, the volume affected by indentation is larger than the recrystallized grain size. The maximum penetration depth is approximately 3 µm (ranging from 1 µm to 3 µm depending on the temperature and recrystallization state), which corresponds to an average contact radius of 10 µm.

Considering that the length of the indentation-affected volume is approximately 3 times the contact radius, it leads to a value of 30 µm when the average recrystallized grain size is approximately 5 µm (extracted from FIG. 8 for the 300°C thermal cycle). Consequently, the hardness value can be assumed to be the mixed value of the recrystallized grain and the recovered grain hardness through the recrystallization fraction. The increase in the recrystallization fraction leads to a global hardness decrease. This approach is the usual way to measure recrystallization kinetics through hardness measurements [START_REF] Richou | Recrystallization at high temperature of two tungsten materials complying with the ITER specifications[END_REF] , even though it neglects the effects of static recovery that also influence hardness.

Note that such a methodology has been applied previously in the framework of in situ high-temperature nanoindentation by Baral et al [START_REF] Baral | In situ characterization of AA1050 recrystallization kinetics using high temperature nanoindentation testing[END_REF] . The decrease in hardness during the hold temperature segment might be seen as the signature of recrystallization despite ongoing competition with static recovery. FIG. 8 indicates that for the sample heated to 325°C, the recrystallization fraction is much higher, which is in agreement with the thermal activation of recrystallization mechanisms. It can also be observed that the density of subgrain boundaries (i.e., dislocation density) is much lower, which means that static recovery continues parallel to recrystallization.

At the end of the high-temperature holding phase, the microstructure of the samples changed. In recrystallized grains, the density of dislocations is low compared to that of the cold-rolled sample. Therefore, during cooling, the decrease in hardness with temperature is expected to be much lower. Indeed, the temperature dependence of hardness would be mainly governed by thermal activation of viscoplasticity (in contrast to cold-rolled grains). Recovery and recrystallization become negligible.

When studying FIG. 6, hardness' decrease during holding at 300°C is higher than during holding at 325°C. However, the reverse effect would be expected since recovery and recrystallisation kinetics increases with increasing temperature.

In fact, those phenomena are temperature and time-dependent. The microstructural evolution (linked to hardness variations) is the same for the two cycles up to 300°C. From this point, while the sample 1 is hold at 300°C, a linear increase of temperature (3°C/min up to 325°C) is performed. This sample experiences recovery and recrystallisation during the 8min needed to increase temperature up to 325 °C, which leads to significant hardness decrease. When starting the holding period at 325°C, recrystallisation of this sample is almost achieved: hardness will not change a lot.

It must be noted that strain rate at the end of loading is not constant as a function of temperature. This could impact the measured hardness values [START_REF] Leitner | Dynamic nanoindentation testing: is there an influence on a material's hardness[END_REF] . However, aluminum has a relatively low strain rate sensitivity, as shown in Fig. 7. When doing the experiments, an increase of strain rate at the end of the holding segment is evidenced when increasing temperature: it goes from 0.05 s -1 at the ambient to 0.2 s -1 at 325°C. To quantify the impact of such an increase on hardness values, strain rate sensitivity could be linked to hardness using [START_REF] Wheeler | Activation parameters for deformation of ultrafine-grained aluminium as determined by indentation strain rate jumps at elevated temperature[END_REF] :

𝑚𝑚 = 𝜕𝜕 ln(𝐻𝐻) 𝜕𝜕 ln(𝜖𝜖)
Eq. 14

Saying that

Δ ln(𝐻𝐻) = 𝑚𝑚Δ ln(𝜀𝜀) Eq. 15 the impact of strain rate variation on hardness could be estimated.

The increase of strain-rate with temperature (from 0.05s -1 at 25°C to 0.2s -1 at 300°C) should induce an increase of 7% to 23% of hardness (m=0.05-0.15 -see FIG. 7). However, a decrease in hardness is observed during the tests (due to viscoplasticity, static recovery and recrystallization). The decrease that is observed would be a little higher if the measurement were carried out at the exact same strain rate for all the temperatures Regarding the recrystallization mechanism, Baral et al. [START_REF] Baral | In situ characterization of AA1050 recrystallization kinetics using high temperature nanoindentation testing[END_REF] proposed taking advantage of pop-in phenomena that are more likely on recrystallized grains than on deformed grains. Unfortunately, an artifact is observed on the load-displacement curve due to the quarter of the sinus load segment (see FIG. 1). One way to solve the problem without changing the loading function would be to use a spherical tip to postpone the load needed for the appearance of the first pop-in.

However, this approach would introduce another bias in hardness evolution interpretation since self-similarity would be intrinsically lost with such a geometry.

Conclusion

This paper presents the High Temperature Scanning Indentation technique, a nanoindentation methodology, to track the evolution of in situ mechanical properties during a ramp of a tempering profile. The main points are as follows:

• Thermal drift are overcome through the use of high-speed nanoindentation;

• The loading profile using a quarter sinus segment allows measurements of hardness and creep properties;

• The Young's can be measured owing to the use of the three-step unloading method, a specific unloading profile that limits the occurrence of an unloading nose (for time-dependent materials);

• The hardness, Young's modulus and creep properties can now be measured quasi-continuously as a function of temperature (i.e., one data point per 1°C);

• The methodology is validated on fused silica and aluminum.

This High Temperature Scanning Indentation methodology has been applied to cold-rolled pure aluminum that undergoes recrystallization during the tempering ramp:

• During heating, the hardness measured on similar samples is well reproducible;

• Hardness upon heating and cooling varies in a different manner, pointing out the occurrence of static recovery upon heating;

• A hardness drop is observed during the constant temperature segment. This effect is related to recrystallization, which has been assessed by postmortem EBSD microstructural characterizations;

• Creep, recovery and recrystallization mechanisms can be measured through high-speed nanoindentation testing using a suitable tempering ramp.

The nanoindentation methodology developed in this paper should allow the design of a set of experiments to measure thermally activated physical transformations in metals in a cost-and time-effective way.

Materials and methods

Materials

To validate the developed High Temperature Scanning Indentation technique, experiments were carried out on different materials. The validation was started on a fused silica sample of 2 mm thickness and 12.5 mm diameter, provided by Edmund Optics. This material was chosen as a reference material for nanoindentation measurement. Its temperature properties are also well known [START_REF] Everitt | High temperature nanoindentation -the importance of isothermal contact[END_REF][START_REF] Wheeler | Elevated temperature, nano-mechanical testing in situ in the scanning electron microscope[END_REF][START_REF] Marx | Temperature Dependence of the Elastic Moduli and Internal Friction of Silica and Glass[END_REF][START_REF] Spinner | Elastic Moduli of Glasses at Elevated Temperatures by a Dynamic Method[END_REF][START_REF] Spinner | Temperature Dependence of Young's Modulus of Vitreous Germania and Silica[END_REF][START_REF] Bucaro | High-temperature Brillouin scattering in fused quartz[END_REF][START_REF] Beake | High-Temperature Nanoindentation Testing of Fused Silica and Other Materials[END_REF][START_REF] Schuh | Nanoindentation and contact-mode imaging at high temperatures[END_REF][START_REF] Trenkle | Hot nanoindentation in inert environments[END_REF] .

In the second part of the validation process, two samples of pure aluminum are studied. They were also used to investigate the microstructure evolution of pure aluminum upon heating and cooling. Samples are cold laminated with a reduction of 80% of their thickness. They are 3 mm thick and 11.5 mm in diameter. These samples are mechanically polished by hand up to 1 µm (diamond solution). After indentation measurements, the two samples were electropolished to characterize the microstructural state using Electron Back-Scattering Diffraction in a JEOL FEG 6500F Scanning Electron Microscope. Postprocessing was performed using the MTEX MATLAB ToolBox 51 . The step size was set between 0.36 µm and 0.4 µm to obtain an indexation higher than 80%.

Experimental apparatus

The indentation measurements were performed using an InSEM HT nanoindentation system (KLA Nanomechanics).

A doped diamond Berkovich tip was set up on the apparatus. Tip calibration was performed at ambient conditions on fused silica. Because the stiffness of the indenter is approximately 5 10 5 -1 10 6 𝑁𝑁/𝑚𝑚, when testing aluminum, the load frame stiffness was calibrated on the aluminum samples at ambient conditions prior to experiments [START_REF] Roudet | Propriétés mécaniques par indentation multi-échelles des matériaux bio-sourcés aux céramiques[END_REF] . Note that indents in aluminum are higher and deeper than in fused silica, so indentation in aluminum is very stiff compared to indentation in fused silica.

Samples were mounted the same way as in Minnert et al. [START_REF] Minnert | New ultra-high temperature nanoindentation system for operating at up to 1100 °C[END_REF] . All indentation tests were performed under vacuum (< 9 10 -3 𝑃𝑃𝐺𝐺), and the nanoindentation system was installed in a SEM VEGA3 system (Tescan). The distance between each indents was at least 10ℎ 𝑐𝑐 [START_REF] Phani | A critical assessment of the effect of indentation spacing on the measurement of hardness and modulus using instrumented indentation testing[END_REF] . The acquisition frequency was 1 kHz.

The tip and the sample were heated apart by conduction, and the heating process was controlled by specific PID loops.

The settings calibrated using the procedure presented in Section II.

Thermal cycles

On fused silica, the heating ramp was set at 3°C/min up to 350°C. On aluminum samples, the heating and cooling rates were also at 3°C/min. The holding temperatures were 300°C for 35 min and 325°C for 70 min (see FIG. 9). The cycle with holding at 325°C was used for the validation process of the new proposed methodology. On the thermal cycle with holding at 300°C, the performed indentation cycle was that with the linear unloading part (see FIG. 1(a)).

Plastic depth 𝒉𝒉 𝒓𝒓 ′

Loubet's model is based on indentation measurements made on an elastic, perfectly plastic material. specifically, he considers that the depth underneath the tip is purely plastic. Consequently, he relates the indentation depth to a plastic depth, named ℎ 𝑟𝑟 ′ , with the following expression:

ℎ 𝑟𝑟 ′ = ℎ - 𝑃𝑃 𝑆𝑆
Eq. 17

The plastic depth is presented in FIG. 10 and FIG. 11. FIG. 11 shows the intersection between the displacement axis and the linear fit with the S slope.

Tip defect

When carrying out real experiments, the tip is never perfect. Therefore, the real contact area is underestimated if considering a perfect tip (see FIG. 10). The hatched purple area is a perfect tip contact area without defects. Because the real tip is slightly round, the purple zone should be added to the perfect contact area to obtain the real contact area.

Therefore, to solve this issue, a tip defect term ℎ 0 is added in the contact depth expression when calculating the tip contact.

ℎ 𝑟𝑟 ′ = ℎ -𝑃𝑃 𝑆𝑆 + ℎ 0 Eq. 18

This term could be easily determined when plotting stiffness against depth changes for a homogeneous material such as fused silica during calibration of the system with CSM measurements. For a perfect tip, this term should be 𝑆𝑆(ℎ) = 𝑏𝑏ℎ. When there is a tip defect, the equation becomes 𝑆𝑆(ℎ) = 𝑏𝑏(ℎ -ℎ 0 ), and ℎ 0 be determined. Let us note that the obtained value of ℎ 0 depends on the load frame stiffness determined by calibration.

FIG.

12 Determination of the tip defect from the stiffness-displacement curve made on fused silica using CSM mode.

At low depth, the term ℎ 0 allows us to be more precise in the calculation of the contact area. At large depths, the error between the ideal contact area and the real contact area becomes negligible.

Consideration of pile-up

Pile-up [START_REF] Tabor | The hardness of solids[END_REF] can occur when performing indentation measurements. This effect increases the real contact area, so if not considered, the Young's modulus and hardness will be overestimated. Therefore, Loubet defined the contact depth using:

ℎ 𝑐𝑐 = 𝛼𝛼ℎ 𝑟𝑟 ′ Eq. 19
with 𝛼𝛼 = 1.2 from experimental results [START_REF] Demmou | Nanoindentation, Viscoplasticité & Piézo-Mécanique de Films de Dithio-Phosphate de Zinc Triboformés[END_REF][START_REF] Bec | Improvements in the indentation method with a surface force apparatus[END_REF] . This value was experimentally determined on gold by Bec et al. [START_REF] Bec | Improvements in the indentation method with a surface force apparatus[END_REF] . It was also validated theoretically for perfectly elastic materials [START_REF] Guillonneau | Nouvelles Techniques de Nano-Indentation Pour Des Conditions Expérimentales Difficiles : Très Faibles Enfoncements, Surfaces Rugueuses, Température, These[END_REF] and numerically for perfectly plastic materials [START_REF] Guillonneau | Nouvelles Techniques de Nano-Indentation Pour Des Conditions Expérimentales Difficiles : Très Faibles Enfoncements, Surfaces Rugueuses, Température, These[END_REF] in the case of a conical indenter. It is worth noting that when pile-up occurs, ℎ 𝑐𝑐 could be higher than the maximum depth.

Looking to Eq. 19, the condition for sink-in is not forbidden. Loubet's model could also been applied to materials that presents sink-in. Guillonneau et al. [START_REF] Guillonneau | Determination of the true projected contact area by in situ indentation testing[END_REF] shows that Oliver and Pharr's model and Loubet's model give the same results on fused silica, which presents sink-in.

Independence to the load frame stiffness 𝑺𝑺 𝑳𝑳𝑳𝑳

Eq. 18 can be rewritten using the raw displacement of the tip instead of ℎ, and the displacement corrected from the load frame stiffness when performing a nanoindentation experiment: we can deduce from this expression that even if an error is made in the frame stiffness calculation, it will not change the plastic depth value because the elastic part of the displacement 𝑃𝑃/𝑆𝑆 (where 𝑆𝑆 is not well calculated if 𝑆𝑆 𝐿𝐿𝐿𝐿 is not well estimated) is removed from u to calculate ℎ 𝑟𝑟 ′ . Therefore, with the use of Loubet's model, ℎ 𝑟𝑟 ′ , ℎ 𝑐𝑐 and hardness 𝐻𝐻 are independent of the load frame stiffness. This point is particularly interesting when performing experiments at low penetration depths for materials with high 𝐸𝐸/𝐻𝐻 ratios.

ℎ 𝑟𝑟 ′ =

8 FIG. 1

 81 FIG. 1 (a) High-speed indentation cycle applied during initial tests. The loading part is constructed from a quarter sinus function, a holding segment is implemented to measure creep parameters, and unloading is linear over time. The whole cycle duration is less than 1.2 s. (b) Load-displacement curve measured on pure aluminum at 300°C, corresponding to the indentation cycle presented in (a). The nose on the unloading part is an issue regarding the measurement of the initial contact stiffness and thus elastic modulus.

14 FIG. 5

 145 FIG. 5 Temperature-compensated indentation strain rate versus modulus-compensated hardness. The apparent activation energyis equal to 130 𝑘𝑘𝑘𝑘/𝑚𝑚𝑚𝑚𝑚𝑚. The literature data come from Phani and Oliver[START_REF] Phani | A direct comparison of high temperature nanoindentation creep and uniaxial creep measurements for commercial purity aluminum[END_REF] .

FIG. 6

 6 FIG. 6 (a) and (b): Hardness versus temperature for tested aluminum samples during the thermal cycles previously described, (a) during the whole thermal cycle, (b) magnified view of T>200°C. The hardness clearly changes considerably between the heating and cooling phases. The dashed lines underline the slope change during the heating phase. (c) and (d): Hardness versus time for tested aluminum samples during the thermal cycles previously described ((c) whole cycle, (d) zoom during holding phases). A

FIG. 7 FIG. 8

 78 FIG. 7 Strain rate sensitivity m of an aluminum sample versus temperature during the first thermal cycle previously described.

  It is clearly demonstrated here that the High Temperature Scanning Indentation technique, based on high-speed nanoindentation during thermal cycles, should allow the investigation of microstructural evolution mechanisms and viscoplasticity. The design of a set of experiments might be envisioned to access a limited number of experiments on the physical parameters governing viscoplasticity, recovery and recrystallization in metals in relation to the initial microstructural state.

FIG. 9

 9 FIG. 9 Temperature versus time during two thermal cycles on pure aluminum samples: one of the aluminum samples was heated to 300°C at 3°C/min and held for 35 min before being cooled to ambient conditions (first cycle). The other was heated to 325°C at3°C/min and held for 70 min before being cooled to ambient conditions (second cycle).

FIG. 10

 10 FIG. 10 Schematic representation of the contact geometry between a conical indenter and some material, defined in Loubet's model.ℎ is the measured indentation depth, ℎ 𝑟𝑟 ′ is the plastic depth, ℎ 0 is the tip defect and ℎ 𝑐𝑐 is the contact depth.

Availability of data and material

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

Not applicable

Declarations Funding

The authors acknowledge support from the CPER MANUTECH which financed the experimental system. work was supported by the French National Research Agency (ANR) under contract ANR-20-CE08-0022

Competing Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Appendix -The model of Loubet 1. Contact depth 𝒉𝒉 𝒄𝒄 versus contact area relation

The hardness of a material is defined as the ratio of the applied load 𝑃𝑃 divided by the projected contact area 𝐴𝐴 𝑐𝑐 (see Eq. 6).

The contact area can be geometrically determined from the contact depth. For a perfect conical indenter,

With 𝐶𝐶 0 a geometrical constant. For a Berkovich indenter, 𝐶𝐶 0 = 24.56. However, the contact depth is not directly measured and has to be calculated from the tip displacement measurement. This measurement does not account for pile-up or sink-in phenomena.