# An Attempt to Assess Recovery/Recrystallization Kinetics in Tungsten at High Temperature Using Statistical Nanoindentation Analysis

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## Abstract

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## 1. Introduction

^{3}or even less [12,13]. Zayachuk et al. [14] clearly highlighted that nanoindentation helped to discriminate whether a tungsten grain is recrystallized or not. Hardness and pile-up heights are shown to be lower in recrystallized grains than in deformed ones. Such individual measurements are, however, time-consuming and poorly selective when determining whether a fraction is recrystallized. The statistical nanoindentation theory that replaces the analysis of individual indents with the analysis of a large set of indents might overcome this issue. It has been successfully used to measure fractions of phases in materials [15]. The main assumption is that hardness distribution of a given phase does not overlap hardness distributions of the others [16]. The variance of hardness distribution of a given phase is related to the self phase heterogeneity, i.e., crystal orientation, dislocation density, defects, etc. In this paper it is proposed to examine whether or not this kind of measurement can be done to measure the recrystallized or recovered fractions of rolled tungsten samples.

## 2. Theory

#### 2.1. Recrystallization/Recovery

#### 2.2. Statistical Nanoindentation Theory

## 3. Materials and Methods

## 4. Results and Discussion

## 5. Conclusions

- The statistical nanoindentation analysis can help to separate contributions of recovery/recrystallization mechanisms to macroscopic softening;
- Recovery/recrystallization mechanisms can be investigated even when they overlap;
- The restoration-induced softening fraction estimated from hardness measurements is always higher than the fraction recrystallized estimated from statistical nanoindentation analysis or EBSD measurements;
- The nanoindentation hardness standard deviation is maximal when the softening fraction approaches 50% and is minimal both for the initial state and for the fully recrystallized state;
- The statistical nanoindentation analysis is a complementary approach to EBSD measurements to investigate the effect of deformed structure upon the competition between thermally activated restoration processes, such as recovery/recrystallization mechanisms.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Nanoindentation grids. The space between indents was set to 50 µm. The print size was about 5–10 µm.

**Figure 2.**Comparison of the hardness probability density function for the initial state and the fully recrystallized (ReX) state. The ReX state was fitted using a Gaussian function.

**Figure 3.**Hardness distributions after annealing. (

**a**) The effect of the annealing time (T = 1550 °C). (

**b**) The effect of the annealing temperature (t ≈ 500 s).

**Figure 4.**Hardness standard deviation versus softening fraction. The standard deviation is maximum when the softening fraction approaches 50%.

**Figure 5.**Hardness probability density function of recovered grains compared to the full probability density function (T = 1550 °C, t = 3000 s). Softening fraction ${X}_{H}$ is about 65% here, whereas fraction recrystallized X computed through nanoindentation testing is about 30%.

**Figure 6.**EBSD maps representing the evolution of softening fraction at T = 1550 °C. The grain boundaries are in black, the sub-grain boundaries are in red and the recrystallized grains are colored according to (IPF Z—normal direction).

**Figure 7.**The effect of time on the fraction recrystallized (T = 1550 °C) as measured by nanoindentation and EBSD. Comparison with softening fraction ${X}_{H}$ computed using the mean hardness value.

**Figure 8.**Mean hardness versus time for the whole set of grains or restricted to the recovered grains.

**Figure 9.**Estimated dislocation density computed from mean hardness versus time at different annealing temperatures.

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**MDPI and ACS Style**

Karanja, L.; Lenci, M.; Piot, D.; Maurice, C.; Durif, A.; Richou, M.; Gallais, L.; Minissale, M.; Kermouche, G.
An Attempt to Assess Recovery/Recrystallization Kinetics in Tungsten at High Temperature Using Statistical Nanoindentation Analysis. *Crystals* **2021**, *11*, 37.
https://doi.org/10.3390/cryst11010037

**AMA Style**

Karanja L, Lenci M, Piot D, Maurice C, Durif A, Richou M, Gallais L, Minissale M, Kermouche G.
An Attempt to Assess Recovery/Recrystallization Kinetics in Tungsten at High Temperature Using Statistical Nanoindentation Analysis. *Crystals*. 2021; 11(1):37.
https://doi.org/10.3390/cryst11010037

**Chicago/Turabian Style**

Karanja, Liz, Matthieu Lenci, David Piot, Claire Maurice, Alan Durif, Marianne Richou, Laurent Gallais, Marco Minissale, and Guillaume Kermouche.
2021. "An Attempt to Assess Recovery/Recrystallization Kinetics in Tungsten at High Temperature Using Statistical Nanoindentation Analysis" *Crystals* 11, no. 1: 37.
https://doi.org/10.3390/cryst11010037