Representative strain of indentation analysis
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Norimasa Chiba Department of Mechanical Engineering, National Defense Academy, Hashirimizu, Yokosuka 239, Japan
Xi Chena) Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027-6699 (Received 25 March 2005; accepted 19 May 2005)
Indentation analysis based on the concept of representative strain offers an effective way of obtaining mechanical properties, especially work-hardening behavior of metals, from reverse analysis of indentation load–displacement data, and does not require measuring of the projected contact area. The definition of representative strain adopted in previous studies [e.g., Dao et al., Acta Mater. 49, 3899 (2001)] has a weak physical basis, and it works only for a limited range in some sense of engineering materials. A new indentation stress-state based formulation of representation is proposed in this study, which is defined as the plastic strain during equi-biaxial loading. Extensive numerical analysis based on the finite element method has shown that with the new formulation of representative strain and representative stress, the critical normalized relationship between load and material parameters is essentially independent of the work-hardening exponent for all engineering materials, and the results also hold for three distinct indenter angles. The new technique is used for four materials with mechanical properties outside the applicable regime of previous studies, and the reverse analysis has validated the present analysis. The new formulation based on indentation stress-state based definition of representative strain has the potential to quickly and effectively measure the mechanical properties of essentially all engineering materials as long as their constitutive behavior can be approximated into a power-law form.
I. INTRODUCTION A. Brief review of indentation mechanics
Instrumented indentation is widely used to probe the constitutive relationships of engineering materials. During the experiment, a sharp rigid indenter (with a half apex angle ␣) is penetrating normally into a homogeneous solid, where the indentation load P and displacement ␦ are continuously recorded during loading and unloading [Figs. 1(a) and 1(b)]. For an elastic-perfectly plastic and stress-free bulk material, by neglecting friction and the finite compliance of the measuring system and the indenter tip, the constitutive properties (Young’s modulus E, Poisson’s ratio , and yield strength y) can
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0280 J. Mater. Res., Vol. 20, No. 8, Aug 2005
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be approximately related with the indentation hardness H and indentation modulus M by classic formulae1–4 H = P Ⲑ A = cby
(1)
,
and S = ␥
2
公
M公A
(2)
.
Here, the hardness H is the ratio between load P and projected contact area A. The indentation modulus M is given by the plane-strain modulus E¯ ≡ E/(1 − 2), for isotropic materials and by a more complicated
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