Weidner, Donald J.1; Li Li1, Jiuhua Chen1, Michael T. Vaughan1, Shenghua Mei2, and William Durham2
1Department of Geosciences, State University of New York, 11794-2100
2L-206, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA
dweidner@sunysb.edu
NSLS-X17B (MAP)
The Reuss state of uniform stress and the Voigt state of uniform strain have long been considered as the bounds for the stress-strain state of an aggregate. In the case where plastic flow can occur within the material, and where the strength of the individual grains varies with orientation or state of the grains, the situation becomes more complex. Even in the Voigt state, where strain is uniform, the partition of strain between elastic and plastic may vary from grain to grain and the partitioning will depend on the properties of the individual grains. Thus, the elastic strain will not be governed by the Reuss-Voigt bound. Synchrotron diffraction is capable of probing the elastic strain-state of different populations of grains within an aggregate of a specimen under differential stress. We present here the elastic strain for a magnesium oxide sample for the population of grains that have the (1,0,0) axis parallel to the maximum stress and those that have the (1,1,1) axis parallel to this stress. These data are collected as the specimen is deformed by several per cent at a constant strain rate. The stress is calculated using the elastic moduli of MgO for the P,T conditions of the experiment. While the elastic strain for the two populations is fairly similar, the inferred stress is very different. We conclude that the Reuss-Voigt bounds would not properly represent the elastic state of this aggregate. These results give interesting insights into the nature of aggregates. They suggests that Singh et al., 1998's analysis is incomplete as he uses the Reuss and Voigt models as bounds for the elastic state. Furthermore, we conclude that orientation dependent strength may produce incorrect results when inferring elastic properties from static high-pressure x-ray experiments.
Reference:
Singh, A.K., C. Balasingh, H.K. Mao, J. Shu, and R.J. Hemley, Rev. High Pressure Sci. Technol., edited by M. Nakahara, pp. 205-210, 1998.