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An apparatus was constructed that measured hardness under load. The instrument measured hardness using a strain-gauge load cell and a linear voltage displacement transducer. Loading rates were less than 1 yu,m/s. Results were similar to the results of other electronic hardness measurement devices, in that the hardness fell with increasing load. Glasses measured have Meyers indexes from 1.6 to 1.75, while polycrystalline materials showed much more complex behaviors. A model was formulated to explain the data for glasses based on expansion of shear planes.

I. INTRODUCTION Hardness is a simple way to probe the deformation behavior of materials. It is sensitive to small changes in materials such as hard surface layers, solid solutions, crystal alignment, and dispersion hardening.1 It is, therefore, a useful characteristic for quality control and materials comparison. Hardness theory is best developed for metals, but hardness of glasses can also be measured. There are theoretical problems, however, since many glasses are classically brittle materials, and therefore should not deform plastically. Another difficulty is a load dependence, which occurs even in diamond-pyramid hardness measurements. The hardness of brittle materials tends to fall with increasing load.1 The load dependence is difficult to understand, however, because the shape of the indentation does not change as the indentation proceeds. This principle of shape invariance eliminates effects from work hardening or softening.1 In this paper indentation hardness is defined traditionally, as the load divided by the area. An attempt was made to separate elastic from plastic deformation, but the word hardness as used in this paper retains its original meaning. Bemhardt19 developed the idea that the load dependence of hardness is due to a surface energy term, for as the volume of the indentation increases, a surface is produced in the indentation. This surface energy term has a second-power dependence on a linear dimension of the deformation, while the volume energy term has a thirdpower dependence. As the deformation becomes larger, the relative importance of the surface lessens, lowering the hardness. The difficulty with the theory was that the surface energy required to effect the deformation was far too large. Bernhardt19 tried to solve this problem by including all surfaces, such as cracks and fault lines, in his surface-energy terms. The most common explanation for load dependence is Tate's theory of elastic recovery of the indentations.3 He assumed that the shape invariance does not apply to the ends of the diagonals. The ends of the diagonals 3112 http://journals.cambridge.org

J. Mater. Res., Vol. 7, No. 11, Nov 1992 Downloaded: 18 Mar 2015

retreat a fixed amount, no matter what the load. If this explanation is true for glasses, the hardness taken under load will be load independent. Results of Kranich and Scholze4 support this idea. They measured the size of indentations in silicate glasses, while the diamond was under load. They used an interferometer