The ideal strength of tungsten

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%.

Depth-sensing indentation instruments provide a means for studying the elastic and plastic properties of thin films. A method for obtaining hardness and Young's modulus from the data obtained from these types of instruments is described. Elastic displacements are determined from the data obtained during unloading of the indentation. Young's modulus can be calculated from these measurements. In addition, the elastic contribution to the total displacement can be removed in order to calculate hardness. Determination of the exact shape of the indenter at the tip is critical to the measurement of both hardness and elastic modulus for indentation depths less than a micron. Hardness is shown to depend on strain rate, especially when the hardness values are calculated from the data along the loading curves.