Hardness trends in micron scale indentation

A continuum theory for elastic–plastic solids that accounts for the size-dependence of strain hardening is employed to analyze trends in the indentation hardness test. Strain gradient plasticity theory incorporates an elevation of flow stress when non-uniform plastic deformations occur at the micron scale. Extensive experimental data exists for size-dependence of indentation hardness in the micron range for conical (pyramidal) indenters, and recent data delineates trends for spherical indenters. Deformation induced by rigid conical and spherical indenters is analyzed in two ways: by exploiting an approximation based on spherically symmetric void expansion and by finite element computations. Trends are presented for hardness as a function of the most important variables in the indentation test, including the size of the indent relative to the material length parameters, the strain hardening exponent, the ratio of initial yield stress to Young's modulus, and the geometry of the indenter. The theory rationalizes seemingly different trends for conical and spherical indenters and accurately simulates hardness data presented recently for iridium, a low yield strain/high hardening material. The dominant role of one of the material length parameters is revealed, and it is suggested that the indentation test may the best means of measuring this parameter.