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TECHNICAL PAPERS

Indentation Analysis of Elastic-Plastic Homogeneous and Layered Media: Criteria for Determining the Real Material Hardness

[+] Author and Article Information
N. Ye, K. Komvopoulos

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Tribol 125(4), 685-691 (Sep 25, 2003) (7 pages) doi:10.1115/1.1572515 History: Received July 10, 2002; Revised December 30, 2002; Online September 25, 2003
Copyright © 2003 by ASME
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References

Pharr,  G. M., 1998, “Measurement of Mechanical Properties by Ultra-Low Load Indentation,” Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process., 253, pp. 151–159.
Loubet,  J. L., Georges,  J. M., Marchesini,  O., and Meille,  G., 1984, “Vickers Indentation Curves of Magnesium Oxide (MgO),” ASME J. Tribol., 106, pp. 43–48.
Doerner,  M. F., and Nix,  W. D., 1986, “A Method for Interpreting the Data From Depth-Sensing Indentation Instruments,” J. Mater. Res., 1, pp. 601–609.
Oliver,  W. C., and Pharr,  G. M., 1992, “An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments,” J. Mater. Res., 7, pp. 1564–1583.
Lichinchi,  M., Lenardi,  C., Haupt,  J., and Vitali,  R., 1998, “Simulation of Berkovich Nanoindentation Experiments on Thin Films Using Finite Element Method,” Thin Solid Films, 312, pp. 240–248.
Pelletier,  H., Krier,  J., Cornet,  A., and Mille,  P., 2000, “Limits of Using Bilinear Stress-Strain Curve for Finite Element Modeling of Nanoindentation Response on Bulk Materials,” Thin Solid Films, 379, pp. 147–155.
Chen,  X., and Vlassak,  J. J., 2001, “Numerical Study on the Measurement of Thin Film Mechanical Properties by Means of Nanoindentation,” J. Mater. Res., 16, pp. 2974–2982.
Martinez,  E., and Esteve,  J., 2001, “Nanoindentation Hardness Measurements Using Real-Shape Indenters: Application to Extremely Hard and Elastic Materials,” Appl. Phys. A: Mater. Sci. Process., 72, pp. 319–324.
Bhattacharya,  A. K., and Nix,  W. D., 1988, “Analysis of Elastic and Plastic Deformation Associated With Indentation Testing of Thin Films on Substrates,” Int. J. Solids Struct., 24, pp. 1287–1298.
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Komvopoulos,  K., and Ye,  N., 2001, “Three-Dimensional Contact Analysis of Elastic-Plastic Layered Media With Fractal Surface Topographies,” ASME J. Tribol., 123, pp. 632–640.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
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Figures

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Axisymmetric finite element mesh used in indentation simulations of elastic-plastic homogeneous and layered media. (The inset at the top of the figure shows the refinement of the mesh adjacent to the contact interface.)
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Comparison of finite element results (FEM) and analytical solution 12 for the normalized mean contact pressure versus normalized interference distance for homogeneous elastic half-space compressed by a rigid spherical indenter
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Normalized mean contact pressure versus representative strain for different material properties of elastic-plastic homogeneous media indented by a rigid sphere
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Plastic zone evolution in elastic-plastic homogeneous medium with E*Y=10 indented by a rigid sphere: (a) δ/R=0.072, (b) δ/R=0.1, (c) δ/R=0.2, and (d) δ/R=0.4
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Plastic zone evolution in elastic-plastic homogeneous medium with E*Y=100 indented by a rigid sphere: (a) δ/R=0.005, (b) δ/R=0.007, (c) δ/R=0.04, and (d) δ/R=0.059
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Comparison of finite element results (FEM) and experimental data obtained by Marsh 14 of normalized hardness versus effective elastic modulus-to-yield strength ratio
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Comparison of finite element data obtained from Fig. 3 and solution given by Eq. (10) for the normalized interference distance corresponding to the material hardness versus yield strength-to-effective elastic modulus ratio
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Indentation load versus interference distance for elastic-plastic layered medium with El/(1−νl2)/σY,l=10 indented by a rigid sphere
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(a) Equivalent hardness of elastic-plastic layered medium normalized by the substrate hardness and (b) calculated layer hardness and yield strength normalized by corresponding real material property values versus normalized interference distance
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Plastic zone evolution in elastic-plastic layered medium with El/(1−νl2)/σY,l=10 indented by a rigid sphere: (a) δ/R=0.072, (b) δ/R=0.1, (c) δ/R=0.2, (d) δ/R=0.243, (e) δ/R=0.3, and (f ) δ/R=0.4

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