MODES OF EQUILIBRIUM OF ELASTIC MICROSTRESSES IN TEXTURED MATERIALS

Yu.Perlovich¹, M.Isaenkova¹, H.J.Bunge², V.Fesenko¹

¹Moscow Engineering Physics Institute, Kashirskoe shosse 31, Moscow 115409, Russia
²Institut fur Metallkunde und Metallphysik, TU Clausthal, Grosser Bruch 23, Clausthal-Zellerfeld 38678, Germany

Keywords: rolling texture, pole figure, peak position, lattice elastic deformation.

Application of a position-sensitive detector by texture measurements allows to register the X-ray line profile for each point of a pole figure. The treatment of obtained data by use of «the fitting procedure» involves a search of the optimal Pseudo-Voigt approximating function, providing a minimal difference between integral intensities of measured and model profiles. According to the used procedure, the following parameters of the X-ray line are determined by taking into account an influence of instrumental factors: integral intensity, angular half-width, peak position, fractions of Gauss and Cauchy components, background level. Distributions of these parameters in the stereographic projection of the sample are constructed, so that along with the usual texture pole figure, that is the normalized distribution of integral intensity, pole figures of other parameters of X-ray line become attainable.

A pole figure of peak position 2q for the registered X-ray line (hkl) describes the distribution of lattice elastic deformation along crystallographic normals <hkl> depending on their orientation in the space of external coordinates. A value 2q(j,y) characterizes the local elastic deformation of crystalline lattice in grains (subgrains, blocks, coherent domains), whose normals <hkl> are parallel to the direction (j,y). In some cases values of peak position 2q were recalculated into values of interplanar spacing d_hkl and relative deviations Dd(j,y)/<d> of these values from the weighted average level <d> were determined. Depending on the type of local elastic deformation, that is extension or compression, the deviation has the sign «+» or «-» with reference to the average lattice condition.

The distribution Dd(j,y)/<d> reflects an actual equilibrium of elastic microstresses in the studied sample. Since microstresses by definition are equilibrated within a volume of several neighbouring grains, the volume irradiated in the course of X-ray texture measurement is sufficiently large to satisfy conditions for microstress equilibrium. Therefore, the texture pole figure is formed due to reflections from regions, whose crystalline lattice experiences alternatively elastic deformations of opposite signs, so that microstresses associated with these elastic deformations are mutually balanced within the reflecting volume. If along one of normals <hkl>, belonging to some crystallite, the lattice experiences elastic extension, along its other normals of the same type elastic compression takes place and, as a result, the volume of the crystallite remains unchangeable.

Pole figures of peak position for various rolled materials were constructed and the dependence of their features on the texture character was analyzed. Among studied materials there were steels, Cu, Nb, Zr alloys, Ti, Ti-Ni alloys. Rolling of Ti-Ni single crystals results in the development of various deformation textures, containing different number of components - one, two or more, depending on the initial orientation and the deformation degree. Thus, it was possible to study an evolution of the elastic stress distribution as the rolling texture complicates.

When the rolling texture contains a single component, as it takes place by rolling of a single crystal in the stable orientation, each maximum of this component divides into two halves, characterized alternatively by opposite signs of elastic deformation. In other words, the texture component, formed by blocks with close orientations, consists actually of two subcomponents, differing in types of elastic deformation along mutually corresponding normals. Each group of blocks, whose lattice is elastically extended along one of normals <001> and compressed along other normals <001>, has in the orientational space a neighbouring group of blocks with the lattice deformed in the opposite manner, that is compressed along the corresponding normal <001> and extended along other cubic normals.

When a texture of the rolled single crystal is formed by a pair of mutually equivalent components, these components equilibrate one another owing to predominant alternative action of extensive and compressive elastic stresses within the respective texture maxima. Unlike the case of one-component texture, the majority of substructure elements of each component are deformed elastically in a similar manner, so that each maximum of the first component shows the elastic deformation only of one type («+» or «-»), whereas the corresponding maximum of the second component shows the elastic deformation of the opposite type. Exceptions are maxima lying on diameters of the pole figure.

A regular distribution of elastic microstresses takes place in polycrystalline metal materials in consequence of cold rolling up to high deformation degrees, as a sharp texture with distinct features of axiality develops. Such an axiality consists in stretching of texture maxima along parallels of the stereographic projection, that is the developed rolling texture includes a continuous succession of components with the common RD. In this case elastic microstresses are distributed in the following manner: zones of extension and compression are aligned parallel with texture maxima at their opposite slopes and form a cross-wise pattern, so that diameters of the pole figure separate regions with opposite signs of elastic deformation.

In the most general case the rolling texture shows a significant scattering, so that the distribution of elastic microstresses looses its clearness and becomes more complicated. Such an effect, in particular, can be connected with coexistence of texture components, formed at successive stages of rolling due to operation of different mechanisms of plastic deformation. However, even in those cases, when the distribution of lattice elastic deformation seems to be rather random, a predominance of extensive or compressive stresses remains evident within alternating quadrants of the pole figure.

Only in some materials with developed twinning the distribution of lattice elastic deformation proves to be symmetric about both diameters of the pole figure, being almost identical within its four quadrants.