Dynamics of texture evolution in face-centered cubic polycrystals
The paper considers the texturing of face-centered polycrystals as the flow of an orientation density over a fundamental region of orientation space. First, the polycrystal model is discussed based on an orientation distribution function. The single crystal model is employed, and properties of Rodrigues' space relevant to the analysis are discussed. Then, the authors investigate the dynamics of the velocity fields arising from imposed deformation modes looking for the presence or absence of equilibriums in the field to identify critical points. It is shown that the equilibria are connected with crystallographic fibers by associating the slip systems with crystal symmetries. In order to simplify the analysis, two tools are introduced, namely standardized linearized stability analysis to assess the behavior of equilibrium interactions, and a parametrization of lattice spin that enables collapse of reorientation velocities under arbitrary deformation to a one-parameter family superposed by the macroscopic spin. The macroscopic spin is shown to affect the positions of equilibria. The continuous flows are examined relative to the stability of equilibria of flows starting with the same normalized spin. Under sufficiently high spin, the annihilation of equilibria implies that stable texture components do not persist under continued monotonic deformation. The parametrization of the lattice spins facilitates the connection of the evolving texture to related flows having equilibria. As examples, three deformation modes are examined: plane strain compression, pure shear and simple shear under Taylor hypothesis for partitioning the straining among crystals within an aggregate. As pure shear is related to plane strain compression by a rotation of the deformation rate and does not involve a macroscopic spin, the existing equilibria and their stabilities are identical to the equilibria within the rotation. On the other hand, simple shear possesses sufficient macroscopic spin to annihilate all equilibria and does not exhibit stable texture component under monotonic loading. The authors also obtain interesting links between plane strain compression and simple shear textures.
scientific article; zbMATH DE number 5600184
scientific article