High-strain dislocation patterning, texture formation and shear banding of wavy glide materials in the LEDS theory

In the course of plastic deformation, dislocations are trapped into positions of mutual stress-screening, i.e. Low-Energy Dislocation Structures (LEDS's), in which their energy per unit line length is U-D congruent to [Gb(2)(1-v/2)/4 pi (1-v]ln(R(LEDS)/b) with R(LEDS) the near-neighbor dislocation distance. As a class, the most common LEDS's are dislocation rotation boundaries separating misoriented volume elements. They form the so widely observed mosaic block alias dislocation cell structures of ''wavy glide'' materials. However, because the glide paths of dislocations terminate where they are trapped, dislocation rotation walls are the locations of abrupt strain gradients whose associated stresses increase with their misorientation angle as well as angle of inclination against the averaged shearing direction, i.e. the slip lines in the sense of continuum plasticity theory. With increasing misorientation angle, therefore, the dislocation boundaries rotate towards the macroscopic slip planes, e.g. in sheet rolling initially to be inclined about +/-40 degrees to the rolling plane (10). They delineate irregular slabs which eventually may become homologous with the macroscopically imposed strain (5), i.e. in rolling nearly parallel to the rolling plane, in torsion normal to the torsion axis. As the 2nd law of thermodynamics favors the lowest possible U-D, and thus the lowest possible R(LEDS) and largest rotation angle, there is no limit to the dislocation density in the walls, but new low-angle walls, seen as cell walls roughly normal to the high angle walls, are continuously formed through bending strains in the slabs (8). On account of their relatively long link lengths, the fresh cell walls constantly provide an unlimited supply of glide dislocations at a relatively small now stress, assuring a low workhardening rate. However, as soon as they are formed, also the new cell walls trap dislocations, thereby increasing their rotation angle, and begin to rotate towards parallellity with the slip lines. In the process the average thickness, D, of the slabs progressively diminishes in line with the empirical formula D = KGb/(tau-tau(o)). Meanwhile the higher-angle walls channel the glide in the slabs between them which is the cause of metallographic slip bands and can lead to shear-banding. Thus latently shear-banding is always present without any mechanical instability. The mutually misoriented lattice orientations in the slabs comprise the texture components. Since the rotation boundaries are overwhelmingly composed of trapped glide dislocations, their morphology, and thus the resulting textures, depend on availability of slip systems, three-dimensional dislocation mobility and initial crystal orientation. It is presumed, but still requires proof, that on account of the 2nd law the actually realized textures embody the largest possible misorientation angles compatible with the boundary conditions.