Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics (original) (raw)
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Discrete Dislocation Plasticity
Handbook of Materials Modeling, 2005
Plastic deformation of crystalline solids is of both scientific and technological interest. Over a wide temperature range, the principal mechanism of plastic deformation in crystalline solids involves the glide of large numbers of dislocations. As a consequence, since the 1930s, when dislocations were identified as carriers of plastic deformation in crystalline solids, there has been considerable interest in elucidating the physics of individual dislocations and of dislocation structures. Major effort has also been devoted to developing tools to solve boundary value problems based on phenomenological continuum descriptions in order to predict the plastic deformations that result in structures and components from some imposed loading. Since the 1980s these two approaches have grown toward each other, driven by, for instance, miniaturization and the need for more accurate models in engineering design. The approaches meet at a scale where the collective behavior of individual dislocations controls phenomena. This encounter, together with continuously increasing computing power, has fostered the development of an approach where boundary value problems are solved with plastic flow modeled in terms of the collective motion of discrete dislocations represented as line defects in a linear elastic continuum . This is the field of discrete dislocation plasticity.
Modelling and Simulation in Materials Science and Engineering, 2008
In this paper, the main characteristics of Frank-Read (F-R) sources used in a mechanism-based discrete dislocation plasticity (M-DDP) analysis are estimated by employing a recently developed non-singular continuum elastic theory of dislocations. The critical nucleation stress, τ nuc , is determined more accurately because the dislocation core effects are considered precisely by atomistically-informing the dislocation dynamics simulations. The nucleation time is calculated and compared with the previous predictions. The dependence of the drag coefficient of dislocations on dislocation line orientation, which affects the nucleation time and also the shape of the emitted dislocation loop, is considered. In M-DDP simulations, τ nuc used for sources is calculated based on the assumption of an infinite domain. In reality, however, the critical nucleation stress is affected by other F-R sources. It is proposed in this paper that the critical nucleation stress should be modified by considering the effects of other dislocation sources. To this end, τ nuc should be determined for an F-R source in a finite cell with periodic boundary conditions. of the core region, indirectly accounting for the effects of the dislocation core, must be added. Useful discussions about the core cut-off parameters can be found in and .
On the consideration of climb in discrete dislocation dynamics
Philosophical Magazine A, 1998
A concept is outlined to incorporate dislocation climb in a discrete three-dimensional model of dislocation dynamics. Each dislocation line consists of a sequence of interconnected piecewise straight segments which are embedded in a homogeneous linear elastic medium. The dynamics are described by solving Newton's equation of motion for each portion of dislocation. Non-conservative dislocation motion is introduced by considering the osmotic force that arises from emitting or adsorbing point defects at the ...
Continuum modeling of dislocation interactions: Why discreteness matters?
Materials Science and Engineering: A, 2008
Continuum frameworks of dislocation-based plasticity theories are gaining prominence in the research community. In these theories, the underlying discrete lattice defects are represented by an averaged continuous description of a signed dislocation density. The long-range stress fields are accurately characterized but the short-range interactions are modeled phenomenologically. In this paper, we demonstrate by a rigorous analysis that short-range interactions resulting from certain aspects of the underlying discreteness cannot be neglected. An idealized problem of dislocation pile-ups against a hard obstacle is used to illustrate this observation. It is also demonstrated that the modeling of short-range interactions by a local gradient of dislocation distribution has limitations. It is realized that even though the stress contribution for distant dislocations is relatively small, it is the accumulation of these stress contributions from numerous such dislocations which culminates in substantial contributions. It would be inaccurate to neglect these effects. Our benchmark problem can be used for calibration of current and future theories of plasticity that attempt to accurately model short-range interactions.
Dislocation–obstacle interactions: Dynamic experiments to continuum modeling
Materials Science and Engineering: A, 2005
Incorporating the interaction of dislocations with obstacles remains a challenge in the development of predictive large-scale plasticity models. The need is particularly important in the elastic-plastic transition region where these interactions can dominate the behavior. By combining post-mortem analysis with dynamic straining in the transmission electron microscope, the atomic processes governing glissile dislocation reactions and interactions with obstacles has been determined. This information has been incorporated at least phenomenologically in models to assess the macroscopic stress-strain response. Two examples will be presented to demonstrate the methodology. The first example considers the interaction of dislocations with small vacancy Frank loops and the formation of defect-free channels in copper, and the second with the influence of imperfect annealing twin boundaries on the macroscopic stress-strain response in silver. In both examples, the importance of grain and twin boundaries as dislocation sources will be demonstrated. (I.M. Robertson).
On the formation and stability of dislocation patterns—I: One-dimensional considerations
International Journal of Engineering Science, 1985
distinguishing among mobile and immobile dislocations and operating within the framework of continuum mechanics it is possible to derive a set of partial differential equations of the diffusion-reaction type for the evolution of dislocation species. On examining the competition between gradient dependent terms modelling the motion of dislocations and nonlinear terms modelling their interactions, it is shown that stable solutions are possible. The wavelength turns out to be a material property in agreement with observations. The discussion is limited to one dimension, that is to glide of straight dislocations in the slip direction, and the model corresponds physically to the ladder-like structure of persistent slip bands.