Journal of Materials Research


An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

W.C. Olivera1 and G.M. Pharra2

a1 Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6116

a2 Department of Materials Science, Rice University, P. O. Box 1982, Houston, Texas 77251


The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

(Received December 23 1991)

(Accepted January 22 1992)