Accessing the elastic–plastic properties closure by rotation and lamination

A new theory for processing polycrystalline materials by rotation and lamination is presented. The processing is realized by ultrasonic consolidation that can achieve welded interfaces with minimal (and in some respects, negligible) disturbance of the microstructure due to plastic deformation. Evidence of minimal plastic disturbance is presented for ultrasonic consolidations of Ni 201 and Cu 10100 polycrystals using orientation imaging microscopy. A theory of rotation and lamination is presented in the Fourier space of orientation distribution functions (ODFs). Rotations of polycrystals define the orbit of the ODF, and convex combinations of the orbit describe the set of all ODFs that can be achieved by lamination. These orbits and their laminations are described primarily in the (yield strength vs. inverse Young’s modulus) properties closure. It is demonstrated that the orbit for a Ni 201 material, which exhibits weak texture with some {1 0 0} cube component, is relatively small compared to that of the strongly {1 0 0} cube-oriented Cu 10100 material. The principal conclusion is that rotation and lamination is capable of accessing a substantial subset of the complete properties closure when the initial polycrystal lamina possesses a strong crystallographic texture.