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M. V. Swain CSIRO Division of Applied Physics, Lindfield, New South Wales, 2070, Australia (Received 13 July 1992; accepted 28 September 1992)

A simple model is described with which the entire force versus penetration behavior of indentation with a sphere, during loading and unloading, may be simulated from knowledge of the four test material parameters, Young's modulus, Poisson's ratio, flow stress at the onset of full plastic flow and strain hardening index, and the elastic properties of the indenter. The underlying mechanisms are discussed and the predictions of the model are compared with data produced by an ultra low load, penetration measuring instrument.

I. INTRODUCTION Load cycle indentation, which produces plots similar to that typical for steel shown in Fig. l(a), is being used increasingly to investigate the mechanical properties of material where the depth of penetration must be small. The plots basically reflect the interaction of the indenting process with the four test material properties, Young's modulus, Poisson's ratio, initial flow stress and strain hardening, and the elastic properties of the indenter. Indentation may be wholly elastic, elastic/plastic, or wholly plastic, and the mix of these responses is subtly reflected in the shape of the plots. Consequently, understanding their significance and estimating materials properties from them require a suitable model of the indentation process. The expressions developed in this paper model load cycle indentation with a spherical indenter and are applicable to any mix of elastic /plastic behavior. The model is limited only by the requirement that the radius of the circle of indenter contact must be less than the spherical radius of the indenter. Loads are increased and decreased in discrete steps and force equilibrium is assumed at each step. Load cycle plots are generated by an implementation of the model on an ordinary IBM compatible PC. Modeled load cycles plots may be compared with ones produced by a UMIS-2000 ultra-micro-indentation system developed by the Division of Applied Physics of CSIRO in Australia.1 The UMIS-2000 also allows indentation with multiple partial unloading, producing plots similar to Fig. l(b), also typical of steel. This technique permits the elastic and plastic components of indentation to be separated and hardness and elastic modulus to be calculated at each step as a function of penetration. This technique is also included and modeled. Multiple partially unloaded data plots may also be compared with ones produced by J. Mater. Res., Vol. 8, No. 2, Feb 1993

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Penetration FIG. 1. (a) Load cycle plot typical of an elastic/plastic material such as steel, (b) Multiple partial unloading plot typical of an elastic/plastic material such as steel.

the UMIS-2000 and with examples of a hardness and modulus plot derived from them. 1993 Materials Research Society

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