Quantifying plasticity-independent creep compliance and relaxation of viscoelastoplastic materials under contact loading
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e A. Tweedie Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Georgios Constantinides Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, 3603 Lemesos, Cyprus
Franz-Josef Ulm Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Krystyn J. Van Vlietb) Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received 5 May 2011; accepted 22 August 2011)
Here we quantify the time-dependent mechanical properties of a linear viscoelastoplastic material under contact loading. For contact load relaxation, we showed that the relaxation modulus can be measured independently of concurrent plasticity exhibited during the loading phase. For indentation _ can be measured creep, we showed that the rate of change of the contact creep compliance LðtÞ _ _ ¼ 2aðtÞhðtÞ=P independently of any plastic deformation exhibited during loading through LðtÞ max , where a(t) is the contact radius, h(t) is the displacement of the contact probe, and Pmax is the constant applied load during the creep phase. These analytical relations were compared with numerical simulations of conical indentation creep for a viscoelastoplastic material and validated against sharp indentation creep experiments conducted on polystyrene. The derived relations enable extraction of viscoelastic material characteristics, even if sharp probes confer concurrent plasticity, applicable for a general axisymmetric contact probe geometry and a general time-independent plasticity.
I. INTRODUCTION
As instrumented indentation experiments can be conducted to apply constant indentation depth while monitoring a decreasing load, as well as constant applied load while monitoring an increasing indentation depth, it is reasonable to expect that one can extract from such data properties such as the relaxation modulus and creep compliance. For example, in the case of load relaxation, ~ ðtÞ of the inideally a step displacement hðt Þ ¼ hmax H ~ denter probe is applied (where H ðt Þ is the Heaviside function) and the resulting load P(t) is monitored. However, in practice it remains challenging to identify which relaxation properties can be obtained rigorously from such
a facile experiment, and specifically how the relaxation modulus can be best extracted from the experimental data. Several previous useful approaches have been developed, and here we focus specifically on how one may obtain the relaxation modulus or creep compliance of the material when it is likely that plastic deformation of the material occurs concurrently with this time-dependent deformation. For indentation by rigid axisymmetric punches on an elastic solid, Galin1 derived the following relation2: 2M0 n Cðn=2 þ 1=2Þ 1=n PðtÞ ¼ pffiffiffi 1=n hðtÞ1þ1=n ð p BÞ n þ 1 Cðn=2 þ 1Þ
; ð1Þ
Address all correspondence to these authors. a) e-mail: [email protected] b) e
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