Papers by Keyword: Geometrically Necessary Dislocation

Abstract: Misorientation can be calculated over large datasets and a theme of this paper is the usefulness of examining the results statistically. Comparing the statistics of misorientations calculated from neighbouring pixels (or grains) with those calculated from pairs of pixels (or grains) selected at random helps to indicate deformation and recrystallisation mechanisms. Taking boundary length into account provides a link to grain boundary energy, and boundary length versus misorientation data should be used to examine how boundaries with different misorientations evolve through time. Time lapse misorientation maps indicate how orientation changes through time at particular points in a microstructure during in situ experiments. The size of areas which have changed orientation by particular amounts can be linked to boundary length and boundary migration velocities. When dealing with different phases, the statistics of angular relationships, akin to intraphase misorientation analysis, can indicate orientation relationships in the absence of prior knowledge, which is advantageous in investigating the plethora of minerals that make up the Earth.

Abstract: The Weighted Burgers Vector (WBV) is defined as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) x (Burgers vector)]. It can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has five advantages over other measures of local lattice distortion. 1. It is a vector and hence carries more information than any scalar measure of local misorientation. 2. It has an explicit mathematical link to the individual Burgers vectors of dislocations. 3. Since it is derived via tensor calculus, it is not dependent on the map coordinate system, in contrast to existing measures of local misorientation which are not only scalar but dependent on the coordinate system used. 4. Calculation involves no assumptions about energy minimisation. 5. The numerical differentiation involved in calculating the WBV may introduce errors, but there is a direct mathematical link to a contour integral. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations. Errors in orientation measurement will have a much smaller effect here, and dislocations can be detected which are otherwise lost in the noise of any local calculation.

Abstract: The work hardening behavior was investigated in ferritic steels containing hard particles or soft Cu particles with various volume fractions and particle diameters, and then the effect of plastically deformable soft particles on the work hardening was evaluated in terms of the accumulation of GN dislocations. The amount of work hardening and dislocation density increased with an increase of volume fraction of dispersion particles and a decrease of particle diameter in hard particle dispersion steel. On the other hand, in soft Cu particle dispersion steel, the effect of volume fraction and particle diameter on work hardening behavior was relatively small. TEM observation suggested that stress relaxation around particle takes place by plastic deformation of Cu particle itself. In order to consider the effect of plastic deformation of Cu particles on accumulation of GN dislocations, "particle plastic accommodation parameter" was proposed to modify the Ashby's work hardening theory. As a result, the amount of work hardening was successfully predicted for both the hard and soft particle dispersion steels

Abstract: Microstructure and texture formation in DP steels obtained by thermal treatment at temperatures of 780 °C i.e. between Ac1 and Ac3 and at 900 °C, i.e. above Ac3 and following different cooling techniques were studied by means of X-ray and electron diffraction techniques. The formation of the different structure constituents as well as substructure parameters such as blocks size and misorientation between them induced by thermal treatment was detailed analyzed. Various methods – conventional X-ray methods, high-energy synchrotron radiation and EBSD measuring – the texture of the bcc phase were applied in order to investigate their influence on the results. Beside texture heredity, a softening of the initial texture components induced by cold rolling and of related anisotropy of steels due to thermal treatment was estimated.

Abstract: Initiation of intragranular cracks during low cycle fatigue is governed by complex microstructural phenomena. Depending on the loading amplitude, number of cycles, lattice structure and/or chemical composition, different dislocation structures (veins, cells or Persistent Slip Bands) develop and induce heterogeneous localization of strain and stress in the material. For a better comprehension of crack initiation in 316LN stainless steel, low cycle fatigue tests and numerical simulations were performed. Specimens of 316LN steel with polished shallow notch were cycled with constant loading amplitude and Persistant Slip Bands were identified by SEM observations. In parallel, numerical studies were carried out with the model of cristalline plasticity CristalECP. Simulations were performed on 3D polycristalline aggregates of 316LN steel with the finite elements code Abaqus® and Cast3m®. The results show a heterogeneous localization of strain in bands. For a more precise computation of the mechanical fields and to introdruce a grain size effect, Geometrically Necessary Dislocations were introduced in CristalECP. The GNDs are directly related and computed with the lattice curvature.

Abstract: The paper is devoted to research of an influence of average grains size on scalar dislocation density, fraction of geometrically necessary dislocations, internal stresses and bending- torsion of crystal lattice. Polycrystals of submicrocrystalline copper produced by torsion under hydrostatic pressure were investigated by TEM method.

Abstract: In this study, we develop a multiscale crystal plasticity model that represents evolution of dislocation structure on formation process of ultrafine-grained metal based both on dislocation patterning and geometrically necessary dislocation accumulation. A computation on the processes of ultrafine-graining, i.e., generation of dislocation cell and subgrain patterns, evolution of dense dislocation walls, its transition to micro-bands and lamellar dislocation structure and formation of subdivision surrounded by high angle boundaries, is performed by use of the present model. Dislocation patterning depending on activity of slip systems is reproduced introducing slip rate of each slip system into reaction-diffusion equations governing self-organization of dislocation structure and increasing immobilizing rate of dislocation with activation of the secondary slip system. In addition, we investigate the effect of active slip systems to the processes of fine-graining by using the pseudo-three-dimensional model with twelve slip systems of FCC metal.

Abstract: In this study, the conventional Bailey-Hirsch’s relationship is extended in order to express the increase of critical resolved shear stress due to the lack of dislocation lines in a grain. This model is introduced into a triple-scale crystal plasticity model based on geometrically necessary crystal defects and the homogenization method. A FE simulation is carried out based on the proposed model for FCC polycrystals with different grain sizes. It is numerically predicted that yield behavior of fine-grained metals depends on the initial dislocation density and the initial grain size. Furthermore, yield point drop that is observed in annealed FCC fine-grained metal can be reproduced.

Abstract: A sliding wear test was conducted in a copper single crystal having (001) surface. Microstructures induced by the sliding wear were investigated by means of the electron channelling contrast (ECC) imaging and electron backscattered diffraction (EBSD) analysis. The microstructures below the worn surface consisted of the stack of dislocation cell structure, layered structure and equiaxed fine-grained structure. At the dislocation cell structure, there was no significant change in crystallographic orientation. On the other hand, the crystal at the layered structure rotated continuously around the axis which was perpendicular to sliding wear direction. In the fine-grained structure, preferential orientations no longer existed. The authors attempted to explain grain boundary formation in terms of a rotation angle gradient which is proportional to density of geometrically-necessary dislocations.

Abstract: The relationship between grain subdivision mechanisms of a crystalline metal and the strain gradient under severe plastic deformation is studied by using molecular dynamics simulations in quasi two dimensions. Two problems are simulated for single crystal models: (a) uniaxial tensile and compressive deformation and (b) localized shear deformation. In the case of uniaxial deformation, a large number of dislocation pairs with opposite Burgers vectors are generated under deformation, but most dislocations are vanished due to pair annihilation under relaxation. Therefore, no dislocation boundary can be formed. On the other hand, in case of localized shear deformation with large strain gradient, dislocation boundaries are formed between undeformed and deformed regions. These dislocations can be regarded as geometrically necessary dislocations. Consequently, the importance of the strain gradient to make grain boundaries under plastic deformation can be confirmed by atomic simulations.