Metals are polycrystalline, with physical, mechanical and chemical properties that to a large extent depend on the structure of the grains and the topology of the grain boundaries. For instance, strength and ductility is a function of grain size, lattice orientation, and the structural relation between neighbouring grains. When deformed the individual grains have to change their shape and orientation to comply with the external forces. Hence, the topology of the polycrystal is altered in all aspects. To predict the properties of the processed material, it is therefore necessary to describe the plastic response of the grains. However, to date experiments have been confined to studies of the macroscopic evolution of texture (surface investigations are not representative due to strain relaxation). Such data are not very powerful in terms of distinguishing between models, and as a consequence present-day models of deformation are simplistic ones, formulated at the beginning of the 20th century [1]. Provision of better deformation models is vital in other fields, including geophysics, where the formation history of rocks is deduced from the grain morphology.


Fig 115: Experimental principle. All of the grains within the channel illuminated by the beam will give rise to diffracted spots during scanning of . During straining these diffraction spots rotate. By indexing the spots the orientation changes of the grains can be inferred.

Here we present a universal technique for in situ studies of the plastic deformation of the individual grains. It has been developed at the 3DXRD microscope at ID11, which provides focused hard X-rays in the energy range of 50-100 keV. Hence, millimetre to centimetre thick specimens can be investigated, as required by typical deformation processes. The experimental principle is sketched in Figure 115. Diffraction spots are produced by the rotation method using a monochromatic beam. They are sorted with respect to the grain of origin by the indexing program GRAINDEX [2,3], which can handle about 100 grains simultaneously. Knowing the orientation of the grains at each strain level, the rotations are found.


Fig 116: The rotation of four embedded Al grains during tensile deformation up to 11%. The experimental data (o) are shown as inverse pole-figures, that represent the position of the tensile axis in the reciprocal space of the grains. A comparison is performed with the evolution path from 0% to 11% (­­) as predicted by a Sachs model.

The first results for the tensile deformation of 4 deeply embedded grains in a pure Al sample is shown in Figure 116. Compared to predictions of the standard Sachs and Taylor models, the models are found to fail in terms of both the direction and the rate of the rotation. At the same time information on the sub-grain scale (grain sub-division) is provided from the width of the diffraction spots. The experiment was later repeated, providing a reference data set of 100 grain rotations. Likewise, the methodology was expanded to include the evolution of the elastic strain tensor of the embedded grains [3].

The method is universally applicable provided grains are larger than 1 micrometre. Furthermore, it can be combined with other 3DXRD methods to provide 3D maps of the grain boundaries and their dynamics during processing [3].

References
[1] G. Sachs, Z. Ver. Deu. Ing. 72-22, 734 (1928).
[2] E.M. Lauridsen, S. Schmidt, R.M. Suter and H.F. Poulsen. J. Appl. Cryst., 34, 744-750 (2001).
[3] H.F. Poulsen, S.F. Nielsen, E.M. Lauridsen, S. Schmidt, R.M. Suter, U. Lienert, L. Margulies, T. Lorentzen and D. Juul Jensen. J. Appl. Cryst., 34, 751-756 (2001).

Principal Publication and Authors
L. Margulies (a, b), G. Winther (a), and H.F. Poulsen (a), Science, 291, pp 2392-2394 (2001)
(a) Risø National Laboratory, Roskilde (Danemark)
(b) ESRF