Identification of the constitutive equation by the indentation technique using plural indenters with different apex angl
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Takashi Wakui and Yuji Tanabe Department of Mechanical Engineering, Niigata University, Ikarashi Ni-nocho, Niigata-shi, Niigata-ken, 950-2181, Japan
Ikuo Ioka Department of Nuclear Energy Systems, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibakaki-ken, 319-1195, Japan (Received 8 January 2001; accepted 24 May 2001)
This paper describes a novel technique for determining the constitutive equation of elastic–plastic materials by the indentation technique using plural indenters with different apex angles. Finite element method (FEM) analyses were carried out to evaluate the effects of yield stress, work hardening coefficient, work hardening exponent, and the apex angle of indenter on the load–depth curve obtained from the indentation test. As a result, the characterized curves describing the relationship among the yield stress, work hardening coefficient, and the work hardening exponent were established. Identification of the constants of a constitutive equation was made on the basis of the relationship between the characterized curves and the hardness given by the load–depth curve. This technique was validated through experiments on Inconel 600 and aluminum alloy. The determined constitutive equation was applied to the FEM analyses to simulate the deformation including necking behavior under uniaxial tension. The analytical results are in good agreement with experimental results.
I. INTRODUCTION
The indentation technique with a depth-sensing measuring system is very promising and convenient for evaluating mechanical properties of materials at the micro- or nanometer scale level: thin surface layers, coatings, ion implanted layers, corroded surface layers, etc. A lot of effort has been made so far to examine the relationship between the indentation load versus depth curve behavior and the various fundamental mechanical properties of very thin surface areas and/or films. Some analyses using finite element method (FEM), which can treat elastic and plastic deformations, have been carried out to examine effects of interaction between the thin film and the substrate on the load/depth curve.1–7 In particular, Bhattacharya et al. have developed semi-analytically functional equations of the thin film on the substrate through systematic finite element simulations to predict the hardness variation with depth under various conditions and to
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Address all correspondence to this author. e-mail: [email protected] J. Mater. Res., Vol. 16, No. 8, Aug 2001
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separate the elastic properties of the film from those of the substrate.2 Likewise, the present authors have applied the depth-sensing indentation technique to investigate the degradation of mechanical properties of corroded surface layers of some ceramic materials.8,9 Inverse analyses using FEM on the load/depth curve have been carried out to quantitatively evaluate the variation of mechanical properties of the corroded surface layers.9,10 Although various fundamental mechanical proper
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