A method for interpreting the data from depth-sensing indentation instruments
TL;DR: In this paper, a method for obtaining hardness and Young's modulus from the data obtained from these types of instruments is described, where the elastic displacements are determined from data obtained during unloading of the indentation.
Abstract: Depth-sensing indentation instruments provide a means for studying the elastic and plastic properties of thin films. A method for obtaining hardness and Young’s modulus from the data obtained from these types of instruments is described. Elastic displacements are determined from the data obtained during unloading of the indentation. Young’s modulus can be calculated from these measurements. In addition, the elastic contribution to the total displacement can be removed in order to calculate hardness. Determination of the exact shape of the indenter at the tip is critical to the measurement of both hardness and elastic modulus for indentation depths less than a micron. Hardness is shown to depend on strain rate, especially when the hardness values are calculated from the data along the loading curves.
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TL;DR: In this paper, the authors used a Berkovich indenter to determine hardness and elastic modulus from indentation load-displacement data, and showed that the curve of the curve is not linear, even in the initial stages of the unloading process.
Abstract: The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.
22,557 citations
TL;DR: In this article, the authors review the current understanding of the mechanics governing elastic-plastic indentation as they pertain to load and depth-sensing indentation testing of monolithic materials and provide an update of how they now implement the method to make the most accurate mechanical property measurements.
Abstract: The method we introduced in 1992 for measuring hardness and elastic modulus by instrumented indentation techniques has widely been adopted and used in the characterization of small-scale mechanical behavior. Since its original development, the method has undergone numerous refinements and changes brought about by improvements to testing equipment and techniques as well as from advances in our understanding of the mechanics of elastic–plastic contact. Here, we review our current understanding of the mechanics governing elastic–plastic indentation as they pertain to load and depth-sensing indentation testing of monolithic materials and provide an update of how we now implement the method to make the most accurate mechanical property measurements. The limitations of the method are also discussed.
6,616 citations
TL;DR: In this paper, it is shown that very large stresses may be present in the thin films that comprise integrated circuits and magnetic disks and that these stresses can cause deformation and fracture to occur.
Abstract: The mechanical properties of thin films on substrates are described and studied. It is shown that very large stresses may be present in the thin films that comprise integrated circuits and magnetic disks and that these stresses can cause deformation and fracture to occur. It is argued that the approaches that have proven useful in the study of bulk structural materials can be used to understand the mechanical behavior of thin film materials. Understanding the mechanical properties of thin films on substrates requires an understanding of the stresses in thin film structures as well as a knowledge of the mechanisms by which thin films deform. The fundamentals of these processes are reviewed. For a crystalline film on a nondeformable substrate, a key problem involves the movement of dislocations in the film. An analysis of this problem provides insight into both the formation of misfit dislocations in epitaxial thin films and the high strengths of thin metal films on substrates. It is demonstrated that the kinetics of dislocation motion at high temperatures are expecially important to the understanding of the formation of misfit dislocations in heteroepitaxial structures. The experimental study of mechanical properties of thin films requires the development and use of nontraditional mechanical testing techniques. Some of the techniques that have been developed recently are described. The measurement of substrate curvature by laser scanning is shown to be an effective way of measuring the biaxial stresses in thin films and studying the biaxial deformation properties at elevated temperatures. Submicron indentation testing techniques, which make use of the Nanoindenter, are also reviewed. The mechanical properties that can be studied using this instrument are described, including hardness, elastic modulus, and time-dependent deformation properties. Finally, a new testing technique involving the deflection of microbeam samples of thin film materials made by integrated circuit manufacturing methods is described. It is shown that both elastic and plastic properties of thin film materials can be measured using this technique.
2,347 citations
TL;DR: In this article, the continuous stiffness measurement (CSM) technique was used for the characterization of layered materials and nonhomogeneous composites and applied to the measurement of contact stiffness, elastic modulus, hardness, creep resistance, and fatigue properties of the materials used in magnetic storage devices.
1,378 citations
Cites methods from "A method for interpreting the data ..."
...Oliver and Pharr [5] found that the unloading curve is usually not linear as suggested by Doerner and Nix [24], but is better described by a power law: P ¼ Bðh hf Þm ð4Þ where B and m are empirically determined fitting parameters....
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...unloading curve is usually not linear as suggested by Doerner and Nix [24], but is better described by a power law:...
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TL;DR: In this paper, Sneddon's analysis for the elastic contact between a rigid, axisymmetric punch and an elastic half space is used to show that a simple relationship exists between the contact stiffness, the contact area, and the elastic modulus that is not dependent on the geometry of the punch.
Abstract: Results of Sneddon's analysis for the elastic contact between a rigid, axisymmetric punch and an elastic half space are used to show that a simple relationship exists between the contact stiffness, the contact area, and the elastic modulus that is not dependent on the geometry of the punch. The generality of the relationship has important implications for the measurement of mechanical properties using load and depth sensing indentation techniques and in the measurement of small contact areas such as those encountered in atomic force microscopy.
1,363 citations
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TL;DR: In this article, a solution of the axisymmetric Boussinesq problem is derived from which are deduced simple formulae for the depth of penetration of the tip of a punch of arbitrary profile and for the total load which must be applied to the punch to achieve this penetration.
3,959 citations
TL;DR: In this paper, the authors investigated the properties of indentation hardness on the sub-micrometre scale in nickel, gold and silicon and showed that indent areas and therefore hardness can be determined from penetration depth with reasonable accuracy, and that elastic relaxation can be quantitatively understood.
Abstract: In this paper we investigate the properties of indentation hardness on the sub-micrometre scale in nickel, gold and silicon. Indenter penetration depths as low as 20 nm are used. The area of the indents is determined by electron microscopy, and thus the Meyer hardness calculated. The indenter penetration is monitored continuously during loading and unloading. We show that indent areas, and therefore hardness, may be determined from penetration depth with reasonable accuracy, and that elastic relaxation can be quantitatively understood. We discuss the marked increase of indentation hardness with decreasing indent size on the sub-micrometre scale. Small indents in silicon showed no evidence of cracking, but did show unusual deformation characteristics.
883 citations
TL;DR: The physical meaning of Vickers hardness, determined by use of residual indentation measurements, is analyzed in this article, where the roles played by the plasticity and elasticity are discussed.
Abstract: Studies of Vickers hardness of magnesium oxide are presented in the literature for three purposes. They give information about relations between hardness and brittleness, (plasticity and toughness behavior); they show the anisotropical effect of the structure of the material and they are a tool to study the chemomechanical effects (Rebinder effects). Generally, the Vickers hardness is evaluated by measurements of the diagonals of residual indentation. Equipment was built which gives a record of the applied depression depth (h) as a function of the carried load P (in the range 10−1 N to 10+1 N). Investigation of the curves P(h) during loading and unloading and microscopical observations of residual indentation show that phenomena are complex. The contact is elastoplastic. The roles played by the plasticity and elasticity are discussed. The physical meaning of Vickers hardness, determined by use of residual indentation measurements, is analyzed.
384 citations
TL;DR: The third-order elastic constants of germanium, magnesium oxide, and fused silica have been measured using the pulse superposition method for determining the ultrasonic velocity as a function of both uniaxial and hydrostatic pressure as mentioned in this paper.
Abstract: The third‐order elastic constants of germanium, magnesium oxide, and fused silica have been measured using the pulse superposition method for determining the ultrasonic velocity as a function of both uniaxial and hydrostatic pressure. From these measurements all six third‐order elastic constants were calculated by using the equations of Thurston and Brugger for MgO and Ge, and the three independent isotropic third‐order constants were calculated for fused SiO2.The results for Ge are in good agreement with the most recent data of McSkimin and Andreatch. The results for MgO agree in part quite well with theoretical data calculated from a Born‐Mayer potential. Drastic failure of the three Cauchy relations indicates the presence of many body forces. For fused silica, the remaining Cauchy relation is, as may be expected, not well fulfilled.
286 citations
01 Aug 1961
TL;DR: In this article, it was shown that there is little change in the diameter of the indentation during withdrawal but a decrease in its depth, which was expressed analytically in terms of the elastic constants of the metal and there is reasonable agreement between the theoretical and observed changes in depth.
Abstract: This paper discusses the changes in shape which occur when a hard conical indenter is pressed into a metal (to form a plastic indentation) and then withdrawn. It is shown that there is little change in the diameter of the indentation during withdrawal but a decrease in its depth. This may be expressed analytically in terms of the elastic constants of the metal and there is reasonable agreement between the theoretical and observed changes in depth. The elastic energy released when the indenter is withdrawn may be calculated and it is shown that this accounts quantitatively for the elastic rebound observed when a conical indenter strikes an elasto-plastic metal. The analysis is also applied to the experimental results given by Davis and Hunter in 1959.
281 citations