A new loading history for identification of viscoplastic properties by spherical indentation
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In this paper a new loading history for extracting the stress–strain curve as well as the viscosity and creep behavior from indentation experiments is developed. It is based on a simple model describing the viscoplastic spherical indentation with a power-law hardening rule and a velocity-dependent overstress. Using this model, patterns were generated consisting of load-depth data and corresponding material parameters. The loading history for the simulation of the patterns was considered as a variable combination of loading and creep processes. To compare the identification potential of different loading histories, the inverse problem of determining the viscoplastic material parameters was solved by using neural networks. The emerging loading history uses a multiple-creep process with equidistant load steps and allows an identification of material parameters with much higher accuracy than with single creep. It will be used for further work, where the identification method is generalized using more realistic finite element simulations for a finite deformation elastic–viscoplastic material behavior.
I. INTRODUCTION
The indentation technique is a popular method for the investigation of mechanical properties of materials. The advantages of indentation experiments include that only small amounts of material are needed. Because of its nondestructive nature, the experiment is multirepeatable with the same specimen. Tabor1,2 has demonstrated that either a spherical indenter or several pyramidal indenters with different tip angles have to be used when the stress–strain relation of a bulk material is to be investigated. For example, it is possible to determine Young’s modulus,1,3–7 the hardening behavior according to monotonic loading,1,5,6,8 viscosity effects,9,10 and the parameters governing the response of nonlinear isotropic and kinematic hardening of the Armstrong–Frederick type.11,12 Raman and Berriche10 carried out extensive experimental investigations on bulk Sn and thin Al films. Different loading histories were considered: Creep at different loads and abrupt load change. The simple model used is given by ⑀˙ = kncr
,
(1)
where the strain rate and the stress are defined by ⑀˙ ⳱ (1/hp)(dhp/dt) and ⳱ P/A, respectively. In these relations, hp is the current indenter plastic depth, P is the applied load on the indenter, and A the projected contact area.3 The stress exponent ncr can be determined from a J. Mater. Res., Vol. 19, No. 1, Jan 2004
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double-logarithmic diagram, where the strain rate is plotted versus the stress. From Eq. (1), an unlimited creep follows, because the stress will never become zero. Therefore, this model can only describe the short-term creep behavior of soft materials like Sn and Al. Spherical indentation of viscoplastic material was investigated earlier by means of the finite element method.13 The viscoplasticity model used is similar to the well-known Chaboche model and based on an equilibrium hardening behavior with an additional vel
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