ELASTIC LOADING AND ELASTOPLASTIC UNLOADING FROM NANOMETER LEVEL INDENTATIONS FOR MODULUS DETERMINATIONS

A new method for evaluating modulus and hardness from nanoindentation load/displacement curves is presented. As a spherical indenter penetra tes an elastoplastic half-space, the elastic displacement above the co ntact line is presumed to diminish in proportion to the total elastic displacement under the indenter. Applying boundary conditions on the e lastic and plastic displacements for elastic and rigid plastic contact s leads to an expression that can be best fit to the entire unloading curve to determine E, the reduced modulus, Justification of the formu lation is presented, followed by the results of a preliminary survey c onducted on three predominantly isotropic materials: fused quartz, pol ycrystalline Al, and single crystal W. Diamond tips with radii ranging from 130 nm to 5 mu m were used in combination with three different n anoindentation devices. Results indicate that the method gives propert y values consistent with accepted values for modulus and hardness. The importance of surface roughness and indentation depth are also consid ered.