Multiscale Discrete Dislocation Dynamics Plasticity

Abstract

Deformation and strength of crystalline materials are determined to a large extent by underlying mechanisms involving various crystal defects, such as vacancies, interstitials and impurity atoms (point defects), dislocations (line defects), grain boundaries, heterogeneous interfaces and microcracks (planar defects), chemically heterogeneous precipitates, twins and other strain-inducing phase transformations (volume defects). Most often, dislocations define plastic yield and flow behavior, either as the dominant plasticity carriers or through their interactions with the other strain-producing defects. Dislocation as a line defect in a continuum space was first introduced as a mathematical concept in the early 20th century by Voltera (1907) andSomigliana (1914). They considered the elastic properties of a cut in a continuum, corresponding to slip, disclinations, and/or dislocations. But associating these geometric cuts to dislocations in crystalline materials was not made until the year 1934. In order to explain the less than ideal strength of crystalline materials, Orowan (1934), Polanyi (1934 and Taylor (1934) simultaneously hypothesized the existence of dislocation as a crystal defect. Later in the late 50's, the existence of dislocations was experimentally confirmed by Hirsch, et al. (1956) andDash (1957). Presently these crystal defects are routinely observed by various means of electron microscopy.

Currents and dislocations at the continuum scale

“…This phenomenon is enhanced if the crystal is considered at high temperature or subjected to high temperature gradients, since the constrained motion of dislocations on predefined glide planes only holds for moderate temperature ranges. In this paper, overlooking on purpose the specific inter-dislocation dynamics [28,31,32] which causes attraction/repulsion between dislocations and are responsible for their aggregation, we consider the cluster as a mathematical object which must be described in a geometrically unified way together and accordingly with any single dislocation loop.…”

Kröner's formula for dislocation loops revisited

“…We believe that this new formula can have an impact for crystal growth practice, since in the presence of dislocations, scale separation can hardly be done in any realistic thermodynamic model accounting for dislocation creation and/or movement (cf., e.g., Zbib et al, 2005) outside equilibrium. Therefore, even at the macroscale, dislocation loops may appear while interacting with any other defect types (such as point defects, see Van Goethem et al, 2008).…”

Dislocation Mechanics of Extremely High Rate Deformations in Iron and Tantalum

“…where F P−K is the Peach Koehler force, m e is the effective mass of the moving dislocations [25], v is the dislocation velocity, and d is the dislocation drag coefficient, which is a function of temperature T, velocity v and the dislocation character θ (i.e., the angle between the dislocation line sense and its Burgers vector) [26][27][28][29].…”