Numerical Derivative Analysis of Load-Displacement Curves in DepthSensing Indentation
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Numerical Derivative Analysis of Load-Displacement Curves in DepthSensing Indentation Tom Juliano1, Vladislav Domnich1, Tom Buchheit2, and Yury Gogotsi1 1 Department of Materials Science and Engineering Drexel University, Philadelphia, PA 19104, USA 2 Department of Microsystems, Materials, Tribology and Technology - Sandia National Laboratories, Albuquerque, NM 87185, USA ABSTRACT The use of load-displacement derivative behavior and power-law curve fitting is applied to find the location of events for a number of different materials during depth-sensing indentation. Load-displacement curves for Berkovich indentations on fused silica, fullerene thin film on sapphire, CdTe thin film on silicon, single crystal silicon, carbide derived carbon, and a polymethylmethacrylate/hydroxyapatite (PMMA/HA) particle composite are examined. The analysis is applied to quantify the location of different events that occur during material loading and unloading. INTRODUCTION Depth-sensing indentation is a technique used to characterize local mechanical properties of small volumes for many types of solid materials and thin films. Load and displacement data is collected throughout a typical indentation experiment and standard techniques such as the Oliver and Pharr method [1] are used to extract hardness and modulus properties for isotropic solids. Recent improvements in load-displacement data analysis have led to accurate property measurements on thin films [2]. In such cases, the Oliver and Pharr method must be modified to allow for substrate effects. For many materials, discrete phenomena such as phase transformation, dislocation nucleation, or cracking take place during indentation testing, showing up as transient events in the resultant load-displacement curve. Sapphire has been shown to exhibit a significant “pop-in” displacement feature in its loading curve, due to dislocation nucleation, when spherical indenter tips are used [3]. For silicon indentation with spherical tools, the pop-in feature upon loading, which is proposed to be due to phase transformation from cubic-diamond Si-I to β-tin Si-II, has been found [4,5]. In the silicon unloading curve, elbowing (continual decrease in slope of unloading curve) and pop-out features have been observed for both sharp and spherical tools [5,6]. Both events were shown to be due to different phase transformations [6]. Phasetransformation-induced features in unloading curves of germanium and some other materials have also been found [7]. The presence or nature of a particular event shape can depend on crystal orientation, loading or unloading rate, number of loading cycles, indentation depth, or indenter geometry. However, these discrete events cannot be analyzed by conventional techniques that require load-displacement data to form continuous curves during loading and unloading portions of the experiment. For this reason, it is necessary to develop quantitative methods to determine the point where the event, whatever mechanism it is due to, begins.
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