An elastic-plastic indentation model and its solutions
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An elastic-plastic indentation model and its solutions Weiping Yu and James P. Blanchard Department of Nuclear Engineering and Engineering Physics, The University of Wisconsin at Madison, 1500 Johnson Drive, Madison, Wisconsin 53706 (Received 27 December 1995; accepted 17 May 1996)
An analytical model of hardness has been developed. Four major indentation tests, namely indentation by cones, wedges, spheres, and flat-ended, axisymmetric cylinders have been analyzed based on the model. Analytical relationships among hardness, yield stress, elastic modulus, Poisson’s ratio, and indenter geometries have been found. These results enable hardness to be calculated in terms of uniaxial material properties and indenter geometries for a wide variety of elastic and plastic materials. These relationships can also be used for evaluating other mechanical properties through hardness measurements and for converting hardness from one type of hardness test into those of a different test. Comparison with experimental data and numerical calculations is excellent.
I. INTRODUCTION
An indentation test is one of the most widely used mechanical tests for materials. In an indentation test, a hard indenter of a specified geometry, such as a ball, cone, or pyramid, is pressed into the surface of a flat specimen with a prescribed load for a specified time interval. The primary purpose of the test is to measure hardness, the mean contact pressure between the indenter and the specimen. The indentation test has been attractive both because hardness represents a basic material property— resistance to indentation deformation—and because it also enables us to obtain, by simple and nondestructive means, the approximate uniaxial stressstrain behavior of a specimen. At present, with the development of ultra-low-load indentation techniques, the indentation test has become the most successful technique for studying the mechanical properties of thin films and thin coatings. Recently, the indentation technique has been used to study the creep and load relaxation properties of time and temperature dependent materials. In addition, it has also been considered as a method for determining near-surface residual stresses and the fracture toughness in brittle materials. Theoretical analysis of general indentation problems, with various idealizations of the physical model, has been conducted for about a century. Several models exist for predicting indentation hardness in terms of uniaxial material properties, but they do not adequately cover the material properties and indenter geometries of interest. The purpose of this paper is to develop a general model which is capable of predicting hardness for a wide variety of elastic and plastic materials and for several of indenter geometries. Four major types of indentation tests, namely indentations by a cone, wedge, sphere, and flat-ended cylinder, are analyzed in detail and analytical equations of hardness as a function of material 2358
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