Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests

Abstract A method has been proposed to determine the stress-strain curve of hard materials from ultra-low-load indentation tests using geometrically similar indenters. The hardness-flow stress, and characteristic plastic strain-cone angle correlations, for conical indenters, were obtained from a number of calculations with different stress-strain curves using the finite element code ABAQUS. The flow stress values thus obtained, lie between that predicted by the slip line field theory and the spherical cavity expansion model. These correlations do not assume any deformation mode, and are thus valid for a wide range of hardness to elastic modulus ratio. The validity of the proposed method was checked by determining the monotonic stress-strain curve of 1070 steel from ultra-low-load indentation tests performed in the present study. Also, the stress-strain curves of copper and steel were obtained from macroscopic hardness values reported by Atkins and Tabor (Atkins, A.G. and Tabor, D. (1965) Plastic indentation in metals with cones. Journal of the Mechanics and Physics of Solids 13 , 149–164.). The predicted stress-strain curves agree well with the known properties of these materials. These correlations were then used to determine the monotonic stress-strain curve of silicon nitride.