On the elastic effects in power-law indentation creep with sharp conical indenters
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e elastic deformation contribution can significantly affect the measurement of the strain-rate sensitivity (SRS) of the plastic flow stress by indentation methods. In this paper, the effect of such elastic contribution is critically analyzed using an extension of a previous treatment developed by the authors for the elastic effects on the indentation of strain-hardening materials [J. Alkorta et al., J. Mater. Res. 20, 432 (2005)]. The analytical model is calibrated and validated through finite element calculations. The results show that when the elastic contribution to the total deformation is not negligible then the measured SRS is significantly lower than the real one. A satisfactory correction factor for the apparent SRS exponent is proposed based on parameters directly accessible to instrumented indentation test results.
I. INTRODUCTION
The control and analysis of the contact between a rigid sharp conical indenter and a flat elastoplastic power-law creeping material is essential to extract dynamic mechanical properties such as the strain-rate sensitivity (SRS) of plastic strength1 from indentation creep experiments. Indentation creep is very useful now that instrumented indentation equipments are widespread and more and more versatile, making possible, among other things, the local testing of thin coatings and micro/nano objects. Traditionally, dynamic properties have been extracted from constant-load indentation-creep penetration-time curves by means of semiempirical expressions that describe hardness evolution with time on the basis that the effective stress is proportional to hardness, and the effective strain rate is related to the rate of growth of the imprinted area.2–7 From an analytical viewpoint, Bower et al.8 and Storakers and Larsson9 made a special effort to understand the contact problem in power-law creeping materials. They found that when elastic effects can be neglected the creep-indentation problem may be reduced to a form that is independent of the geometry of the punch and, moreover, that hardness is time history independent. More recently, Cheng and Cheng10 determined the scaling relationships for self-similar indenters indenting solids that exhibit power-law creep. Let us consider a power-law creeping material: a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2008.0011 182 J. Mater. Res., Vol. 23, No. 1, Jan 2008 http://journals.cambridge.org Downloaded: 12 Mar 2015
= K⑀˙ m
(1)
,
where is the uniaxial stress, ⑀˙ is the uniaxial strain rate, m is the SRS, and K is a material constant. Using Cheng and Cheng10 nomenclature, hardness can be related to the indentation depth, h, and penetration rate, h˙, as follows, if elastic effects are negligible: H = K⭈⌸共m,兲
冉冊 h˙ h
m
,
(2)
where ⌸(m,) is a dimensionless function that depends on the geometry of the indenter, , and on the SRS, see table of symbols (Table I). By analogy with Eq. (1), contact hardness H (also called Martens hardness11) and logarithmic penetrationrate h˙/h can be considered
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