Elastic analysis of some punch problems for a layered medium
IBM1
01 Jan 1987-International Journal of Solids and Structures (Pergamon)-Vol. 23, Iss: 12, pp 1657-1664
TL;DR: In this article, the problem of flat-ended cylindrical, quadrilateral, and triangular punches indenting a layered isotropic elastic half-space is considered, and solutions are obtained numerically.
About: This article is published in International Journal of Solids and Structures.The article was published on 1987-01-01. It has received 816 citations till now. The article focuses on the topics: Isotropy.
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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
Book•
02 Feb 2004TL;DR: The role of stress in mass transport is discussed in this article, where the authors consider anisotropic and patterned films, buckling, bulging, peeling and fracture.
Abstract: 1. Introduction and overview 2. Film stress and substrate curvature 3. Stress in anisotropic and patterned films 4. Delamination and fracture 5. Film buckling, bulging and peeling 6. Dislocation formation in epitaxial systems 7. Dislocation interactions and strain relaxation 8. Equilibrium and stability of surfaces 9. The role of stress in mass transport.
1,562 citations
Cites background or methods from "Elastic analysis of some punch prob..."
...Micro-Raman spectroscopy has evolved as a possible experimental method for estimating local stress in nonplanar, submicron scale structures of interest in very large scale integration (VLSI) devices and MEMS; see, for example, Kobayashi et al. (1990) and DeWolf et al....
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...where E∗ is the reduced elastic modulus of the indenter{material system, E and o represent, as before, the elastic modulus and Poisson ratio, respectively, with the subscripts `s' and `in' denoting the specimen and the indenter, respectively, Ac is the projected contact area of the impression produced on the indented surface at the maximum load Pm, and the non-dimensional constant ®∗, which is on the order of unity, represents a correction factor which accounts for the shape of the indenter tip (King 1987); (Doerner and Nix 1988); (Oliver and Pharr 1992); (Dao et al....
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TL;DR: In this paper, the effects of the substrate on the determination of mechanical properties of thin films by nanoindentation were examined, and the properties of aluminum and tungsten films on the following substrates: aluminum, glass, silicon and sapphire.
1,410 citations
References
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01 Jan 1989
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: methodes : numeriques ; fonction de forme Reference Record created on 2005-11-18, modified on 2016-08-08
17,327 citations
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.
2,653 citations
TL;DR: In this article, a general theory of stresses and displacements in a two-layer system is developed in order to provide the engineer with a useful tool which is more directly applicable to the analysis of actual conditions encountered in soil deposits.
Abstract: The problems of airport and foundation engineering have become increasingly important in the war construction program. These problems frequently involve the consideration of stresses and settlements in layered soil deposits. The well‐known Boussinesq equations apply strictly only to homogeneous soil deposits. The general theory of stresses and displacements in a twolayer system is developed in order to provide the engineer with a useful tool which is more directly applicable to the analysis of actual conditions encountered in soil deposits. The basic equations of stresses and settlements are derived. The numerical evaluation of the surface settlement equation for the simplest case of Poisson's ratio equal to one‐half has been completed as the first of a series, and is presented in the form of influence curves for the analysis of practical problems.
508 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