Mesoscale theory of grains and cells: crystal plasticity and coarsening

Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures, polycrystalline grains form from the melt and coarsen with time: the dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we hitherto have had no simple, continuum explanation for the evolution of dislocations into sharp walls. We present here a mesoscale theory of dislocation motion. It provides a quantitative description of deformation and rotation, grounded in a microscopic order parameter field exhibiting the topologically conserved quantities. The topological current of the Nye dislocation density tensor is derived from a microscopic theory of glide driven by Peach-Koehler forces between dislocations using a simple closure approximation. The resulting theory is shown to form sharp dislocation walls in finite time, both with and without dislocation climb.Comment: 5 pages, 3 figure

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.Comment: 9 pages, 3 figure

Micro-plasticity and intermittent dislocation activity in a simplified micro structural model

Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The latter, defined by a periodic length and a shear-stress amplitude, represents a pre-existing micro-structure. These model parameters, along with the mobile dislocation density, are found to admit a diversity of micro-plastic behaviour involving intermittent plasticity in the form of a scale-free avalanche phenomenon, with an exponent for the strain burst magnitude distribution similar to those seen in experiment and more complex dislocation dynamics simulations.Comment: 30 pages, 12 figures, to appear in "Modelling and Simulation in Materials Science and Engineering

"Cold Melting" of Invar Alloys

An anomalously strong volume magnetostriction in Invars may lead to a situation when at low temperatures the dislocation free energy becomes negative and a multiple generation of dislocations becomes possible. This generation induces a first order phase transition from the FCC crystalline to an amorphous state, and may be called "cold melting". The possibility of the cold melting in Invars is connected with the fact that the exchange energy contribution into the dislocation self energy in Invars is strongly enhanced, as compared to conventional ferromagnetics, due to anomalously strong volume magnetostriction. The possible candidate, where this effect can be observed, is a FePt disordered Invar alloy in which the volume magnetostriction is especially large

The Hall-Petch effect as a manifestation of the general size effect

The experimental evidence for the Hall-Petch dependence of strength on the inverse square-root of grain size is reviewed critically. Both the classic data and more recent results are considered. While the data can be fitted to the inverse square-root dependence excellently (but using two free fitting parameters for each dataset), it is also consistent with a dependence on the simple inverse of grain size (with one free fitting parameter for each dataset). There have been difficulties, recognised for half-a-century, in explaining the inverse square-root expression. A Bayesian analysis shows that the data strongly supports the simple inverse expression proposed. Since this expression derives from underlying theory, it is also more readily explicable. It is concluded that the Hall-Petch effect is not to be explained by the variety of theories found in the literature, but is a manifestation of, or underlain by, the general size effect observed throughout micromechanics, due to the inverse relationship between the stress required and the space available for dislocation sources to operate.Comment: Paper presented at Plasticity 2014, The Bahama

Melting as a String-Mediated Phase Transition

We present a theory of the melting of elemental solids as a dislocation-mediated phase transition. We model dislocations near melt as non-interacting closed strings on a lattice. In this framework we derive simple expressions for the melting temperature and latent heat of fusion that depend on the dislocation density at melt. We use experimental data for more than half the elements in the Periodic Table to determine the dislocation density from both relations. Melting temperatures yield a dislocation density of (0.61\pm 0.20) b^{-2}, in good agreement with the density obtained from latent heats, (0.66\pm 0.11) b^{-2}, where b is the length of the smallest perfect-dislocation Burgers vector. Melting corresponds to the situation where, on average, half of the atoms are within a dislocation core.Comment: 18 pages, LaTeX, 3 eps figures, to appear in Phys. Rev.

Influence of head size on the development of metallic wear and on the characteristics of carbon layers in metal-on-metal hip joints

Background and purpose Particles originating from the articulating surfaces of hip endoprostheses often induce an inflammatory response, which can be related to implant failure. We therefore analyzed the metal content in capsular tissue from 44 McKee-Farrar metal-on-metal hip prostheses (with 3 different head sizes) and we also analyzed the morphological structure of layers located on articulating surfaces