Indentation creep vs. indentation relaxation: A matter of strain rate definition?
Introduction
Current developments in high temperature nanoindentation testing allow the measurements of material mechanical properties up to 1000 °C and certainly more in the near-future [1], [2], [3], [4], [5]. This opens a new research area dedicated to the characterization of material creep and relaxation properties at a very small scale. Indeed, the increasing developments of engineering surfaces such as layered coatings and tribo-films able to withstand extreme contact conditions bring a particular interest to high temperature nanoindentation.
However, the measurement of intrinsic creep properties using nanoindentation is still at stake. Some pioneering works highlighted the ability of instrumented indentation to measure strain rate sensitivity and activation energy from hardness versus time – or strain rate – measurements [6], [7]. All these works aim to relate uniaxial stress and strain rate to indentation measurements such as hardness, stiffness and penetration depth. However, those developments are only approximations based on restrictive assumptions [6], [8]. Yet, constant strain rate or indentation creep tests were scrutinized by many authors to eventually conclude that they were reliable [9], [10], [11], [12], [13], [14].
Indentation relaxation tests were less explored due to technical difficulties — i.e. thermal drift and displacement control overshoot [15], [16]. Therefore, only a few comparisons between indentation creep and indentation relaxation have been published. Nonetheless, indentation relaxation may present some advantages compared to indentation creep when indenting thin films or materials exhibiting size effects. Actually, the plastic – or viscoplastic – volume barely changes during the relaxation – constant contact area – segment whereas it can significantly increase during a creep – constant load – segment. Besides, as the plastic volume increases, more and more material is subjected to primary creep which could lead to erroneous measurements of the stationary creep parameters [15]. As a result, indentation creep is more prone to measurement artifacts arising from the variation of probed volume during the hold segment. Recently, Baral et al. [17] found an original way to overcome most of the indentation relaxation related issues so benchmarking indentation creep against relaxation is possible now. It is worth noting that extraction of creep data from these two kinds of loadings strongly differs. On one hand the computation of strain rate is directly related to hardness – for relaxation – and on the other hand it is related to penetration depth or contact stiffness — for creep. Therefore, the strain rate definition might be under discussion.
In this paper, it is proposed to challenge the ability of indentation creep and indentation relaxation to measure creep properties of a widely investigated model material that exhibits significant creep at room temperature — amorphous selenium. First, the basic theoretical features of constant strain rate, indentation creep and indentation relaxation are presented. Then the experimental methodology is developed. Results are presented in terms of strain rate versus hardness curves. The observed shift between indentation creep and indentation relaxation is discussed, questioning the strain rate definition in indentation creep. In the end, a new strain rate definition is proposed.
Section snippets
Creep tests
The indentation creep test is defined by a constant load hold segment while the displacement [7] or, more recently, contact stiffness [18], [19] is monitored as shown on the graph in Fig. 1a. During the test, the contact radius continuously grows as the material creeps. The hardness also referred as mean contact pressure is defined by the load divided by the projected contact area (Eq. (1)). The latter can be related to a uniaxial representative stress , with the reduced
Materials and methods
The selenium used in this study is chemical grade 5 nines pure and was purchased in the form of crystallized blocks. The blocks were melted in a beaker on a hot plate and then quenched into copper molds in order to get amorphous selenium. The as-cast sample was 31.75 mm in diameter and around 5 mm in thickness with a mirror-like surface. Nanoindentation tests were performed using a KLA Nanomechanics iNano® equipped with a Berkovich diamond tip. The whole apparatus was placed into a
Results and discussion
The creep behavior derived from indentation experiments is described by the evolution of indentation strain rate with hardness. Fig. 3 displays those graphs for the four temperatures tested. All the types of tests are compared and four to six curves by test are represented to assess the repeatability of the different methods. All the curves are onto the same master curve for temperature below 30 °C but a shift appears for higher temperatures between the relaxation tests on one side and the
Conclusion
In this paper, indentation relaxation and indentation creep tests are compared on a model material which is amorphous selenium. The main conclusions are:
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A shift in the strain rate vs. hardness curves is observed between indentation creep and indentation relaxation results when strain rate sensitivity is higher than .
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This shift is a matter of strain rate definition used to plot the curves.
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Several authors already pointed out that representative strain rate in indentation depends on strain
CRediT authorship contribution statement
Paul Baral: Data curation, Writing - original draft. Guillaume Kermouche: Writing - original draft, Supervision. Gaylord Guillonneau: Funding acquisition, Writing - review & editing. Gabrielle Tiphene: Writing - review & editing. Jean-Michel Bergheau: Writing - review & editing. Warren C. Oliver: Conceptualization, Methodology, Software. Jean-Luc Loubet: Conceptualization, Project administration.
Acknowledgments
This work was supported by the LABEX MANUTECH-SISE (ANR-10-LABX-0075) of Université de Lyon within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Agency (ANR). The authors thank also the financial support from Institut Carnot Ingénierie@Lyon, France and Institut Carnot M.I.N.E.S, France .
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