Theoretical and experimental analysis of indentation relaxation test
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Guillaume Kermouche Ecole des Mines de Saint Etienne, Centre SMS, Laboratoire LGF UMR 5307, Saint Etienne, France
Jean-Michel Bergheau Université de Lyon, Ecole Nationale d’Ingénieurs de Saint Etienne, LTDS UMR CNRS 5513, Saint Etienne, France
Jean-Luc Loubet Université de Lyon, Ecole Centrale de Lyon, LTDS UMR CNRS 5513, Ecully, France (Received 3 February 2017; accepted 8 May 2017)
Indentation relaxation test is investigated from theoretical and experimental points of view. Analytical expressions are derived based on the conical indentation of a homogeneous linear viscoelastic half space. Two loading kinetics prior to the hold displacement segment are studied—i.e., constant displacement rate and constant strain rate. Effects of loading procedure on measured relaxation behavior are considered. It is pointed out that a constant strain rate loading is required to perform depth-independent relaxation measurements and the strain rate affects the relaxation spectrum up to a critical time constant. Few experiments on poly(methyl methacrylate) are then performed to check the consistency of the analytical results. Some experimental limitations are also discussed. Good agreement is found between analytical calculations and experimental measurement trends, especially for the constant strain rate loading effect on the measured relaxation behavior.
I. INTRODUCTION
Measuring time-dependent mechanical properties of materials at small scale and elevated temperature is one of the current challenges for nanoindentation testing.1–3 Progress in technologies to perform high temperature nanoindentation is now reaching a critical point and most related challenges are on the way to being elucidated.1 Successful small scale mechanical characterization up to 600 °C and more have already been published.1,4 However it is worth noticing that experimental data at high temperature are much more limited than those measured using room temperature indentation.2,4 Hence there is a need to develop accurate methodologies to extract creep and/or relaxation parameters of materials with a limited set of data, which is the aim of this paper. Several methods have been developed successfully to relate uniaxial creep parameters to indentation tests using constant load and hold (CLH) creep tests.2,5–13 Indeed, this loading procedure is well adapted to most nanoindenters, which are load-controlled. Moreover, recent progress in feedback loop rapidity allows the characterization of the first tenths of second. All this precludes the apparition of an extended field of characterization for Contributing Editor: Linda S. Schadler a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2017.203
nanoindentation tests. However, such tests present some limits which are more or less sensitive as a function of the material mechanical behavior. During the hold load segment, the indentation-affected volume increases continuously. This makes more and more material enter primary creep. For this reason, Goodall et al.20 claime
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