Determination of x-ray elastic constants using an in situ pressing device
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Determination of x-ray elastic constants using an in situ pressing device D. H. J. Teeuw and J. Th. M. De Hosson Department of Applied Physics, Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands (Received 27 March 1997; accepted 7 November 1997)
The experimental determination of x-ray elastic constants are performed by in situ measurements of the dependence of the strain state in selected crystallites for different applied external compressive stresses. The use of compressive applied stresses instead of tensile applied stresses is of interest for x-ray elastic constant determinations for materials which exhibit brittle crack-like behavior, which cannot be loaded to high tensile stresses in, for example, four-point bending devices. The x-ray elastic constants for h146j a –Al2 O3 are determined with the pressing device and compared to calculated as well as experimentally determined values which were tested in tensile loading devices.
X-ray residual stress measurements are based on the determination of elastic lattice strains in polycrystalline materials, which are to be converted to macroscopic stress states using linear elasticity theory.1 In this conversion, material elastic constants are required. For these material elastic constants often the macroscopic elastic constants, Young’s modulus, and Poisson’s ratio, are used. However, this procedure does not necessarily lead to accurate results for the determination of the absolute values of the residual stress state in the material, since the macroscopic elastic constants are an average of all the single-crystal elastic constants for different lattice planes in the material.2,3 For instance, if a specimen is textured, the macroscopic elastic constants do not correspond to the crystallographic plane specific x-ray elastic constants. Consequently, it is not possible to determine absolute values for the residual stress state in the material. More accurate values of the absolute residual stress state are determined when the crystallohhklj graphic plane specific x-ray elastic constants 1y2s2 hhklj and s1 are used instead. These x-ray elastic constants can be determined when a specimen is loaded in situ inside a diffractometer and the lattice spacing deviations are measured for different specimen orientations and applied loads. Uniaxial tensile loading or four-point bending are usually employed in x-ray elastic constant determination.4,5 In the determination of x-ray elastic constants of materials which exhibit brittle crack-like behavior, these techniques run into problems because of mechanical failure of the specimen. In compressive loading, in contrast to experiments which make use of four-point bending devices, there is no gradient in the applied stress as a function of depth from the surface. Especially for materials which have larger penetrations depths, like ceramics, the materials volume sampled by the x-rays should contain a J. Mater. Res., Vol. 13, No. 7, Jul 1998
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