Comment on the determination of mechanical properties from the energy dissipated during indentation
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ased on a comparison of relationships between the energy dissipated during indentation and the ratio of hardness to elastic modulus, a procedure is outlined to determine hardness and elastic modulus from the ratio of the elastic to total energy dissipated during an indentation cycle for non-ideal indenters. The parameter −1 is given in Table I for cone angles of 60° 艋 艋 80°.6 Using a similar approach Ni et al. obtained for a spherical indenter −1 ⳱ 1.687(h/R)−0.62,8 where R is the radius of the indenter and h maximum indention depth. It has been proven in these studies that the relationships are valid for conical and spherical indenters independent of pileup and sink-in. A comparison of the parameter −1 as determined in different studies is given in Table I. In recent study Choi et al. reported a dependency of −1 on the ratio of hardness to elastic modulus for a cone angle of 70.3°.10 A value of 5.17 was given for We/Wt 艌 0.15 and 7.3 for We/Wt < 0.15. Another interesting study was reported by Ma et al. also for cone angle of 70.3°, where the effect of tip rounding was considered on the basis of finite element method (FEM) and analytical
Indentation testing has become a standard technique for assessing elastic modulus and hardness of materials.1 However, one aspect of concern remains the effects of pileup and sink-in.2 Recently, the relationship between energy dissipated during indentation and the ratio of hardness H to reduced elastic modulus, Er has received attention in a number of studies.2–14 This energy ratio appears to offer a method to determine hardness, elastic modulus, and contact area and to circumvent the effects of pileup and sink-in.3–9 On the basis of scaling relationships in combination with finite element simulations, Cheng et al. obtained the following equation for a conical indenter for the ratio of reversible We to total work Wt:6 We H = −1 Wt Er
(1)
.
TABLE I. Comparison of parameter −1 from literature. −1
Source
[(1.5 tan + 0.327)(1 + 0.27)] 5.74 5.17 7.3 5.04 ∼5 5 4.678 (2 tan )
冉 冋 冋
⑀ H  + 2 Er tan
冊
Cone angles of 60° 艋 艋 80°6 Cone angles of 70.3°6 We/Wt 艌 0.15, cone angle 70.3°10 We/Wt < 0.15, cone angle 70.3°10 Berkovich, fit to results of Dejun et al.12 Experimental data Max and Balke13 Vickers, Venkatesh, et al.14 Berkovich, Venkatesh, et al.14 Malzbender and de With3
−1
−1
Malzbender and de With3
冉 冊册 冉冊
We H H = 1−7 + 15.5 Wt Er Er
2
We H H = 1 − 9.39 + 159.75 Wt Er Er
Cone 70.3°, fit to results by Dao et al.15 2
− 2410.5
冉 冊册 H Er
1.687(Hr)−0.62
3
Cone 70.3°, fit to results by Ma et al.11 Sphere8
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0162 1090
J. Mater. Res., Vol. 20, No. 5, May 2005
© 2005 Materials Research Society
Rapid Communications
FIG. 1. Comparison of the results obtained by Cheng et al.6 with (a) Choi et al.,10 (b) Ma et al.,11 and (c) Dejun et al.12
relationships.11 The results by Choi et al.10 and a fit to the results by Ma et al.11 for the case of an ideal in
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