Nonuniform Substructure of Textured Metal Materials:
Experimental Study and New-Discovered Regularities

Yuriy Perlovich, Margarita Isaenkova and Vladimir Fesenko

Moscow Engineering Physics Institute, Kashirskoe shosse 31, Moscow 115409, Russia

Most data on the structure of metal materials, accessible by use of the standard X-ray methods, relate only to grains of some orientations, being in the reflecting position by X-ray measurements. Meantime, almost all technological treatments of metal materials lead to formation of specific crystallographic textures, so that metal becomes similar to a composite, whose components consist of grains with different orientations. Prehistories of these grains differ in plastic deformation mechanisms, trajectories of reorientation, strain hardening and, as a result, the substructure of textured material proves to be sharply inhomogeneous. In order to describe real metal materials from such point of view, a new efficient X-ray method of Generalized Pole Figures (GPF) was developed /1/. The method allows to obtain information about grains of all possible orientations and consists in diffractometric registration of the X-ray line profile by each successive position of the sample in the course of texture measurement, so that for planes {hkl} of all orientations (y,j) diffraction or substructure parameters are measured.

Obtained results are presented as GPF, that is distributions of measured and calculated X-ray diffraction or substructure parameters in the stereographic projection of the sample depending on the orientation of reflecting crystallographic planes {hkl}. Among main diffraction parameters there are integral intensity I of the registered X-ray line (hkl), its angular position 2q and the physical half-width b, fraction of the Gauss function in the approximated line profile; among substructure parameters, which can be calculated by X-ray data, – size of coherent domains D, interplanar spacing d_hkl, lattice distortion e, dislocation density r and some others. The normalized GPF I_hkl(y,j) is the usual texture pole figure {hkl}. The distribution of peak position GPF 2q_hkl(y,j) can be recalculated into the distribution of lattice elastic deformation GPF Dd(y,j)/d_av along crystallographic axes <hkl>, where d_av - average weighted interplanar spacing and Dd(y,j)=d(y,j)-d_av with signs “+” or “-“ for cases of local elastic extension or contraction, respectively.

Since the physical half-width b_hkl depends on fragmentation of grains / distortion of their crystalline lattice and the peak position is determined by interplanar spacing along the normal to reflecting planes, GPF b_hkl and GPF 2q_hkl give the fullest accessible description of substructure, formed in textured metal materials. Application of this method resulted in discovery of new, formerly unknown regularities, controlling the substructure nonuniformity in metal materials both after plastic deformation and thermal treatment /2-5/.

It was found that, depending on the orientation of reflecting planes, the physical half-width b of the registered X-ray line can vary from 10¸15 angular minutes up to 1.5¸2 degrees and even higher. The actual upper limit of line broadening is beyond reach for detection, since usually the wider is the X-ray line the lower are both its intensity and the measurement accuracy. Hence, in the same sample the substructure condition of crystallites varies within a very wide range: side by side with large blocks, having the relatively perfect lattice, there is a fraction, characterized by extremely small coherent domains and/or the utmost lattice distortion. When comparing positions of maxima and minima in GPF I_hkl and GPF b_hkl, it becomes evident that minima of line broadening coincide with texture maxima, whereas maxima of line broadening are localized within texture minima. In other words, the dispersity of coherent domains and the lattice distortion are minimal in texture maxima and increase up to highest values by passing to texture minima. This is the most general rule, controlling the substructure inhomogeneity of textured materials. Substructure differences between texture maxima and texture minima are explained on the basis of texture formation models by use of the concepts of orientation stability, successive retardation and activation of slip systems, fragmentation of grains due to fluctuations of their orientation about the stable position.

It becomes evident by consideration of GPF 2q_hkl (or GPF Dd_hkl/d_av) for deformed materials, that the interplanar spacing d_hkl changes continuously, when passing from one region of GPF to another, differing in the orientation of reflecting planes. Hence, the concept of interplanar spacing as applied to textured samples has a sense only on condition that it is determined as a distribution. Moreover, an inhomogeneous distribution of d_hkl has place not only in deformed polycrystals, but even in rolled single crystals with the sharp one-component texture. As a result of rolling, within the single crystal two subcomponents prove to be formed, close by orientations and differing in types of elastic deformation (extension or compression) along the same cubic axes.

A common feature of GPF 2q_hkl (or GPF Dd_hkl/d_av) is the cross-wise pattern, consisting in alternation of quadrants with opposite predominant signs of elastic deformation. . It is seen that zones of extension and compression tend to be aligned parallel with texture maxima at their opposite slopes. When the rolling texture is multi-component and shows significant scattering, the distribution of lattice elastic deformation looses partially its clearness and becomes more complicated. But even in these cases a predominance of extensive or compressive microstrains remains evident within alternating quadrants of GPF. The revealed regularity of inhomogeneous microstrain distribution provides the equilibrium of residual microstresses in rolled textured materials and can not be predicted by mental models.

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5. Yu. Perlovich, M.Isaenkova, Mat. Sci. Forum, 443-444 (2004), 255-258.