Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line ...defects moving at constant velocity. Troubled by singularities at certain ‘critical’ velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago. A generalization to anisotropic crystals has been attempted for pure screw and edge dislocations only for some special cases. This work aims to fill the gap of deriving a general anisotropic solution for pure screw dislocations applicable to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Further generalizations to arbitrary mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.
It is well known that, under plastic deformation, dislocations are not only created but also move through the crystal, and their mobility is impeded by their interaction with the crystal structure. ...At high stress and temperature, this "drag" is dominated by phonon wind, i.e., phonons scattering off dislocations. Employing the semi-isotropic approach discussed in detail in a previous paper (
,
, 24⁻35), we discuss here the approximate functional dependence of dislocation drag
on dislocation velocity in various regimes between a few percent of transverse sound speed c T and c T (where c T is the effective average transverse sound speed of the polycrystal). In doing so, we find an effective functional form for dislocation drag B ( v ) for different slip systems and dislocation characters at fixed (room) temperature and low pressure.
In this paper we discuss the effect of a non-constant dislocation drag coefficient on the very high strain rate regime within an analytic model describing mobile-immobile dislocation intersections ...applicable to fcc polycrystals. Based on previous work on dislocation drag, we estimate its temperature and pressure dependence and its effects on stress–strain rate relations. In the high temperature regime, we show that drag can remain the dominating effect even down to intermediate strain rates. We also discuss the consequences of having a limiting dislocation velocity, a feature which is typically predicted by analytic models of dislocation drag, but which is somewhat under debate because a number of MD simulations predict supersonic dislocations.
•We discuss the effect of non-constant dislocation drag on very high strain rates.•We do so within an analytic model of dislocation intersections for polycrystals.•At high temperatures, drag can dominate even down to intermediate strain rates.•We also discuss the consequences of having a limiting dislocation velocity.
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical ...energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Plastic deformation is mediated by the creation and movement of dislocations, and at high stress the latter is dominated by dislocation drag from phonon wind. By simulating a 1-D shock impact problem ...we analyze the importance of accurately modeling dislocation drag and dislocation density evolution in the high stress regime. Dislocation drag is modeled according to a first-principles derivation as a function of stress and dislocation character, and its temperature and density dependence are approximated to the extent currently known. Much less is known about dislocation density evolution, leading to far greater uncertainty in these model parameters. In studying anisotropic fcc metals with character dependent dislocations, the present work generalizes similar earlier studies by other authors.
•We analyze the importance of accurately modeling dislocation drag and dislocation density evolution in high stress shock impact simulations.•Dislocation drag is modeled according to a first-principles derivation as a function of stress and dislocation character.•Temperature and density dependence of dislocation drag are approximated to the extent currently known.•We study anisotropic fcc metals with character dependent dislocations and accurate drag coefficient.
We address the Hamiltonian formulation of classical gauge field theories while putting forward results some of which are not entirely new, though they do not appear to be well known. We refer in ...particular to the fact that neither the canonical energy momentum vector (Pμ) nor the gauge invariant energy momentum vector (Pinvμ) do generate space-time translations of the gauge field by means of the Poisson brackets: In a general gauge, one has to consider the so-called kinematical energy momentum vector and, in a specific gauge (like the radiation gauge in electrodynamics), one has to consider the Dirac brackets rather than the Poisson brackets. Similar arguments apply to rotations and to Lorentz boosts and are of direct relevance to the “nucleon spin crisis” since the spin of the proton involves a contribution which is due to the angular momentum vector of gluons and thereby requires a proper treatment of the latter. We conclude with some comments on the relationships between the different approaches to quantization (canonical quantization based on the classical Hamiltonian formulation, Gupta-Bleuler, path integrals, BRST, covariant canonical approaches).
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