Volume 2, Issue 4 (April 2005)
Review of Deformation Mechanisms, Texture, and Mechanical Anisotropy in Zirconium and Zirconium Base Alloys
The deformation systems in hexagonal close-packed (hcp) metals are not as symmetrically distributed as in cubic ones. Furthermore, because the primary slip systems are not as numerous and are limited to deformations in the <a> direction, twinning competes with slip in plastic deformation and can, depending on the deformation conditions, play an essential role. In order to explain the conditions in Zirconium and Zircaloy, the well-established relationships of hcp metals are discussed and so are their dependencies on the metal-specific parameters of the hexagonal structure. The interactions between deformation mechanisms and texture formation on the one side and deformation mechanisms and mechanical anisotropy on the other can be likewise transferred to other hcp metals, if one takes into account the differences in dependence of the metal-specific parameters.
The low offer of slip systems, their asymmetrical distribution (prism slip in <a> directions and — under constraint — pyramidal slip in <c+a> directions) as well as the strict crystallographic orientation relationships of first and second order pyramidal twinning result in the formation of a strong deformation texture. By virtue of twinning, even small deformation rates lead to large lattice rotations, which change the orientation of the crystallites where all basal poles align in the direction of the compressive force. The fact that in Zirconium and Zirconium base alloys the preferred crystallographic orientation, which is spread in the transverse direction, is also retained as the final stable position is explained by <c + a> pyramidal slip.
The decisive factor in texture development is the material flow, the degree of freedom of which is lowest for tube reducing as compared to sheet rolling and wire drawing processes. Therefore tube reducing (characterized by reductions in cross-section RA, wall thickness RW, and diameter RD) permits the most precise predictions of the operative forces and the resulting deformation mechanisms. Systematic investigations on the influence of the reduction parameters on the resulting preferred crystallographic orientation in Zircaloy tubing have shown that the determining factor controlling the texture development is the ratio RW1RD. For RW1RD > 1, the basal poles align preferentially in the radial direction. For RW1RD = 1, the basal poles are randomly distributed in the radial-tangential plane. For RW1RD < 1, the basal poles preferentially align in the tangential direction. The sheet texture is identical to the tube texture for RW1RD > 1, because in both examples the material flow is characterized by a preponderance of wall thickness reduction. The fiber texture of wire is identical to the texture of tubes for RW/RD = 1. One can visualize the wire deformation as corresponding to that of concentric tubes with different diameters to comply with tube reduction rates RW1RD = 1 under the condition of constant volume. Independent of the fabrication method for the cold-worked semi finished products, a first order prism pole aligns itself parallel to the direction of elongation. (During recrystallization, the basal poles do not change significantly. The basal planes, however, rotate continuously with increasing annealing temperature by ± 30° around their pole, so that in the final stable position, instead of a first order prism pole [cold deformation texture], a second order prism pole becomes parallel to the axial or rolling direction, respectively.) Knowing these dependencies, it is possible to tailor the texture of Zirconium base alloys tubing within the given limits to the requirements in nuclear application.
For textured materials, on the other hand, the deformation mechanisms are also responsible for the strong anisotropy of the mechanical properties. This is discussed on the example of specially prepared Zircaloy tubes, which were machined out of a sufficiently thick Zircaloy plate with pronounced sheet texture. By this procedure, one obtains around the circumference of the tubing continuously changing preferred orientations of the basal poles with the extreme orientations possible in Zircaloy tubing. For the different uni- and multiaxial loading conditions applied, the theoretical predictions of the mechanical behavior agrees in any case with the experimental results.
In nuclear application, the anisotropic behavior of biaxial loading conditions is represented by yield loci, creep loci, or burst loci according to the respective criteria yield stress, creep rate, or fracture stress. Depending on the texture and the loading conditions, an attempt is made to correlate the shape of the loci to the operative deformation mechanism. In this way, it is possible to find selection criteria for the desirable texture in Zircaloy cladding tubes.