Investigation of the relationship between elastic modulus and hardness based on depth-sensing indentation measurements

An analytical relationship between the reduced modulus E r and hardness H for solid materials is established based on the conventional depth-sensing indentation method of Oliver and Pharr. It is found that the two properties are related through a material parameter that is defined as the recovery resistance R s. This parameter is shown to represent the energy dissipation during indentation. Based on indentation measurements with the use of a Berkovich indenter, the relationship is given as E r = 0.6647 HR s . Also presented is a simple set of procedures to determine the area of indent. The procedures require three measured quantities, i.e., the peak load and corresponding displacements as well as the depth of residual indentation, but do not require complicated curve fitting process and regression analysis which themselves involve the specimen material. Nano-indentation tests were conducted using a Berkovich indenter on five materials spanning a wide range of hardness and plasticity. Experimental results revealed two important features: (a) the reduced modulus predicted by the new E r– H relationship is the same as that obtained by the conventional method; (b) the elastic modulus and hardness values determined by the simple set of procedures are comparable to those obtained by using the conventional method.