Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach

A theoretical framework is proposed to derive a dynamic equation motion for rectilinear dislocations within isotropic continuum elastodynamics. The theory relies on a recent dynamic extension of the Peierls-Nabarro equation, so as to account for core-width generalized stacking-fault energy effects. The degrees of freedom of the solution of the latter equation are reduced by means of the collective-variable method, well known in soliton theory, which we reformulate in a way suitable to the problem at hand. Through these means, two coupled governing equations for the dislocation position and core width are obtained, which are combined into one single complex-valued equation of motion, of compact form. The latter equation embodies the history dependence of dislocation inertia. It is employed to investigate the motion of an edge dislocation under uniform time-dependent loading, with focus on the subsonic/transonic transition. Except in the steady-state supersonic range of velocities---which the equation does not address---our results are in good agreement with atomistic simulations on tungsten. In particular, we provide an explanation for the transition, showing that it is governed by a loading-dependent dynamic critical stress. The transition has the character of a delayed bifurcation. Moreover, various quantitative predictions are made, that could be tested in atomistic simulations. Overall, this work demonstrates the crucial role played by core-width variations in dynamic dislocation motion.Comment: v1: 11 pages, 4 figures. v2: title changed, extensive rewriting, and new material added; 19 pages, 12 figures (content as published

Dislocations and cracks in generalized continua

Dislocations play a key role in the understanding of many phenomena in solid state physics, materials science, crystallography and engineering. Dislocations are line defects producing distortions and self-stresses in an otherwise perfect crystal lattice. In particular, dislocations are the primary carrier of crystal plasticity and in dislocation based fracture mechanics.Comment: arXiv admin note: text overlap with arXiv:1708.0529

Critical Dynamics of Burst Instabilities in the Portevin-Le Chatelier Effect

We investigate the Portevin-Le Chatelier effect (PLC), by compressing Al-Mg alloys in a very large deformation range, and interpret the results from the viewpoint of phase transitions and critical phenomena. The system undergoes two dynamical phase transitions between intermittent (or "jerky") and "laminar" plastic dynamic phases. Near these two dynamic critical points, the order parameter 1/\tau of the PLC effect exhibits large fluctuations, and "critical slowing down" (i.e., the number $\tau$ of bursts, or plastic instabilities, per unit time slows down considerably).Comment: the published 4-page version is in the PRL web sit

A dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: Chaos,turbulence and band propagation

Experimental time series obtained from single and poly-crystals subjected to a constant strain rate tests report an intriguing dynamical crossover from a low dimensional chaotic state at medium strain rates to an infinite dimensional power law state of stress drops at high strain rates. We present results of an extensive study of all aspects of the PLC effect within the context a model that reproduces this crossover. A study of the distribution of the Lyapunov exponents as a function of strain rate shows that it changes from a small set of positive exponents in the chaotic regime to a dense set of null exponents in the scaling regime. As the latter feature is similar to the GOY shell model for turbulence, we compare our results with the GOY model. Interestingly, the null exponents in our model themselves obey a power law. The configuration of dislocations is visualized through the slow manifold analysis. This shows that while a large proportion of dislocations are in the pinned state in the chaotic regime, most of them are at the threshold of unpinning in the scaling regime. The model qualitatively reproduces the different types of deformation bands seen in experiments. At high strain rates where propagating bands are seen, the model equations are reduced to the Fisher-Kolmogorov equation for propagative fronts. This shows that the velocity of the bands varies linearly with the strain rate and inversely with the dislocation density, consistent with the known experimental results. Thus, this simple dynamical model captures the complex spatio-temporal features of the PLC effect.Comment: 17 pages, 18 figure

Microhardness and elastic modulus of nanocrystalline Al-Zr

An investigation of the mechanical properties of nanocrystalline Al-Zr alloy composites has been conducted via nanoindentation and Vickers microhardness experiments. The microhardness of the samples exhibits a four-fold increase over the concentration range of 0-30 wt.% Zr, from {approximately}0.7 GPa to nearly 3 GPa. The aluminum grain size is found to be strongly correlated with the level of zirconium present in the samples, suggesting that the observed hardness increase can be attributed to the combined effects of alloying and grain size reduction. The elastic moduli of the nanocrystalline Al-Zr samples are determined to be similar to the modulus of coarse-grained aluminum and independent of zirconium content

Thermal convection with non-Newtonian plates

The coupling between plate motions and mantle convection is investigated using a fully dynamic numerical model consisting of a thin non-Newtonian layer which is dynamically coupled to a thick Newtonian viscous layer. The non-Newtonian layer has a simple power-law rheology characterized by power-law index n and stiffness constant Μ p. A systematic investigation of steady, single cell configurations demonstrates that under certain conditions ( n > 7 being one of them) the non-Newtonian layer behaves like a mobile tectonic plate. Time-dependent calculations with multicellular configurations show the ability of the plate-mantle coupling model to adjust the number of plates and their sizes in accordance with the flow in the Newtonian layer. These calculations show that the geometry and number of plates do not necessarily resemble the planform of convection below.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72550/1/j.1365-246X.1992.tb02109.x.pd

Lattice Resistance and Peierls Stress in Finite-size Atomistic Dislocation Simulations

Atomistic computations of the Peierls stress in fcc metals are relatively scarce. By way of contrast, there are many more atomistic computations for bcc metals, as well as mixed discrete-continuum computations of the Peierls-Nabarro type for fcc metals. One of the reasons for this is the low Peierls stresses in fcc metals. Because atomistic computations of the Peierls stress take place in finite simulation cells, image forces caused by boundaries must either be relaxed or corrected for if system size independent results are to be obtained. One of the approaches that has been developed for treating such boundary forces is by computing them directly and subsequently subtracting their effects, as developed by V. B. Shenoy and R. Phillips [Phil. Mag. A, 76 (1997) 367]. That work was primarily analytic, and limited to screw dislocations and special symmetric geometries. We extend that work to edge and mixed dislocations, and to arbitrary two-dimensional geometries, through a numerical finite element computation. We also describe a method for estimating the boundary forces directly on the basis of atomistic calculations. We apply these methods to the numerical measurement of the Peierls stress and lattice resistance curves for a model aluminum (fcc) system using an embedded-atom potential.Comment: LaTeX 47 pages including 20 figure

The gauge theory of dislocations: a uniformly moving screw dislocation

In this paper we present the equations of motion of a moving screw dislocation in the framework of the translation gauge theory of dislocations. In the gauge field theoretical formulation, a dislocation is a massive gauge field. We calculate the gauge field theoretical solutions of a uniformly moving screw dislocation. We give the subsonic and supersonic solutions. Thus, supersonic dislocations are not forbidden from the field theoretical point of view. We show that the elastic divergences at the dislocation core are removed. We also discuss the Mach cones produced by supersonic screw dislocations.Comment: 16 pages, 5 figure