Contact-area-based FEA study on conical indentation problems for elastoplastic and viscoelastic-plastic bodies
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The authors discuss the contact-area-based indentation contact mechanics instead of the conventional penetration-depth-based analysis. In time-independent elastoplastic regime, the indentation load P versus contact area A relationship for a cone indentation is linear both for the loading and the unloading paths. The slope of the loading path directly yields the Meyer hardness HM, and the slope of the unloading path, i.e., the unloading modulus M, is related to the elastic modulus E9 through the relation of M 5 E9tan b/2. The relation of the total contact area A to the purely elastic and the purely plastic contact areas of Ae and Ap are theoretically as well as numerically examined. The normalized relationship between Ap/A versus Ap/Ae is equivalent to the Johnson’s hardness plot of HM/Y versus E9tan b/Y. By extending the concept of Ae and Ap to time-dependent viscoelasticplastic regime, a detailed discussion is made how to eliminate the plastic deformation/flow from the total contact area A(t) to yield the viscoelastic contact area Ave(t) prior to determining the linearviscoelastic parameters and functions. I. INTRODUCTION
At the onset of a cone indentation contact, due to the tip acuity and its stress/strain concentration beneath the tip of indenter, the contact may cause a finite amount of plastic yield even at small-scale indentation loading. Accordingly, the plastic flow would play an important role not only in elastoplastic but also in viscoelasticplastic cone indentation contact problems. In elastoplastic regime, the Meyer’s contact hardness HM is uniquely described in terms of the so-called plasticity index of E9tan b/Y that is defined as the indentation strain (tan b) divided by the strain at the elastic limit (Y/E9) using the elastic modulus E9 (5 E/(1m2); E is Young’s modulus and m is Poisson’s ratio), inclined face angle b of a cone indenter, and the plastic yield stress Y.1 The Meyer hardness HM equals HM (elastic) 5 E9tan b/2 in the elastic extreme of the plasticity index less than 1 and reaches HM (plastic) 5 CY (C: the constraint factor), when the index exceeds about 50, where the contact behavior becomes very plastic and ductile. Strain hardening (work hardening) adds a further complication to the elastoplastic contact problems, requiring the concept of the representative yield stress YR at the representative strain eR to uniquely describe the normalized hardness HM/YR as a function of E9tan b/YR.1,2 Such complication associated with straina)
Address all correspondence to this author. e-mail: [email protected] This author was an editor of this focus issue during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs. org/jmr-editor-manuscripts/ DOI: 10.1557/jmr.2011.343 256
J. Mater. Res., Vol. 27, No. 1, Jan 14, 2012
hardening makes it difficult to determine the yield stress Y from the contact hardness observed in experiments, though the elastic modulus E9 is successfully determined from the unloading stif
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