Spherical Indentation and Implementation of S³/P for yield stress determination of brittle materials

A mathematically transparent and robust experimental method has been developed to estimate the yield stress of brittle materials through the analysis of depth-sensing spherical indentation. Employing Hertzian contact mechanics, an elastically invariant ratio based on the simple equation S³/P=6RE_r², (where S and P are contact stiffness and indentation load, respectively) has been derived that enables more accurate and confident determination of the transition from elastic to inelastic deformation; a transition that the yield stress dictates and represents. Using two diamond spheres with radii of 3.2 and 8.6 μm, the indentation test method and analyses are applied to two vitreous silicates: Corning's HPFS 7980® fused silica and Vitro's Starphire® soda-lime silicate. The estimated yield strengths are 8.15 GPa ± 2.5 % for the fused silica and 6.1 GPa ± 3.3 % for the soda-lime silicate, and both were independent of indenter radius. Verification of this new experimental method is demonstrated with an as-drawn titanium by showing equivalence of measured yield stress by its spherical indentation and that from uniaxial compression testing. This method will enable easier and more confident estimation of yield stress in brittle materials - a property that historically has been elusive to measure for these materials using common laboratory mechanical test methods.