Measurement of local mechanical properties using multiple indentations by a special conical indenter and error analysis
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Shogo Kashiwa Department of Mechanical Engineering, Graduate School of Engineering, Kyushu University, Fukuoka 819-0395, Japan
Hiroshi Noguchia) Department of Mechanical Engineering, Faculty of Engineering, Kyushu University, Fukuoka 819-0395, Japan (Received 10 July 2015; accepted 1 December 2015)
This paper proposes a method for determining the mechanical properties (Young’s modulus, Poisson’s ratio, yield strength, and work hardening factor) of a material at a specific point using an indentation technique that utilizes a specially designed indenter in conjunction with an inverse problem and finite element analyses. The specially designed indenter combines the characteristics of spherical and conical indenters and can be used to produce multiple indentations at a single point. The feasibility of the proposed method for determining the local mechanical properties of a material was confirmed by detailed precision verifications in the ideal case and the worst case.
I. INTRODUCTION
The mechanical properties of a material around highstress areas such as the tip of a fatigue crack vary with the movement of the solute atoms. For example, it has been reported that the mechanical properties change with strain aging around the tip of a non-propagating crack on the fatigue limit of carbon steel.1–3 Moreover, the mechanical properties around the tip of a fatigue crack in a hydrogen gas environment change with the hydrogen concentration.4,5 These changes in the mechanical properties are localized, and the authors considered that a nanoindentation technique6,7 can be used to measure them. A series of the authors’ studies is presently being conducted with the ultimate purpose of determining the mechanical property changes that occur with the movement of the solute atoms. As the first step, a method for determining the local mechanical properties (Young’s modulus E, Poisson’s ratio m, yield strength rY and work hardening factor n) by indentation is proposed in this study. The determination of the local mechanical properties of materials by indentation has been the subject of several previous studies.7–13 Oliver and Pharr,7 and Pharr et al.8 used the initial part of the unloading curve of the load–depth relation to determine E. Zorzi and Perottoni9 used Vickers hardness in addition to determine m. By their methods, only E and m could be determined. Although Bucaille et al.,10 and Akatsu et al.11 used multiple indenters that had different apex angles to determine the mechanical properties of Contributing Editor: George M. Pharr a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.383 J. Mater. Res., Vol. 31, No. 2, Jan 28, 2016
a material, the determination at a specific point of a material with its accuracy was not undertaken, because the mechanical properties could not be determined without changing the indenter and the measurement point. Bouzakis and Michailidis,12 and Kang et al.13 compared the relationship between stress–strain and load–depth relation by using finite element metho
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