Analysis of ball-indentation load-depth data: Part I. Determining elastic modulus
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Analysis of ball-indentation load-depth data: Part I. Determining elastic modulus B. Taljat, T. Zacharia, and F. M. Haggaga) Oak Ridge National Laboratory, Metals and Ceramics Division, Oak Ridge, Tennessee 37831-6140 (Received 8 August 1995; accepted 24 October 1996)
Analysis of ball-indentation process was made by the finite element (FE) method. A series of indentation FE analyses were made on materials with different elastic modulus (E), and a simple relationship between E and the load-depth (F-h) unloading data is presented. In order to check for the influence of other material properties, thorough research has been performed, introducing a combination of response surface (RS) and FE analysis. As a result, a relationship between the indentation unloading slope, E, and the strain hardening exponent was derived. Also, the indenter compliance effect has been investigated. The indenter compliance correction was calculated and applied to the experimentally measured F-h results. Experimental testing was made on three materials with essentially different elastic moduli. Comparison of the results obtained by newly developed equations with the results from other well-known equations is also presented.
I. INTRODUCTION
Deep indentations made by a hard spherical penetrator to a maximum depth of one half its diameter, causing permanent or predominately plastic deformation in the material beneath the indenter, are considered in this work. Even though a deep penetration of an indenter to a ductile material causes very high plastic deformation, the extent of plastic deformation observed in the unloading process (also called “reverse plastic flow”) is very small or negligible compared to the plastic deformation during loading, and defines the unloading process as an essentially elastic process. Analytical solutions dealing with any kind of indentation process have been derived within the theory of elasticity, considering very shallow or elastic indentations, which makes them derivable in closed form. Such expressions can basically be solved to determine the elastic properties of the material, considering the indentation unloading data as input. Analytical expressions describing contact between two elastic bodies were first developed by Hertz around 1890.1 They are, due to their simplicity, still often used for various calculations, such as calculating the elastic modulus of the bodies in contact. In his extensive work, Tabor2 presented many valuable applications of the indentation process for exploring various mechanical properties of indented materials. Important analytical relations for indentation force and depth were derived by Sneddon,3–5 which can also be used for calculating elastic modulus, E. Sneddon’s equations were devela)
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oped with the assumption of a rigid indenter and an elastic half-space. With the assumption that unloading is an elastic process and with an accurate m
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