Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics (original) (raw)
2004, Modelling and Simulation in Materials Science and Engineering
Constitutive rules are developed to include three-dimensional dislocation mechanisms, such as line tension and dynamic junction formation, within a two-dimensional dislocation dynamics formulation. Some of the junctions that form dynamically can operate as Frank-Read sources. Boundary value problems are solved by using superposition to represent the solution in terms of the infinite medium fields for discrete dislocations and non-singular complementary fields that enforce the boundary conditions. This framework is used to analyse the plane strain tension of a single crystal. Calculations are carried out to strains of 3-8%, and the transition from stage I to II hardening is exhibited. The dependence of this transition and of the stage II hardening on constitutive parameters is explored. A variety of stress-strain responses are obtained and compared with available experimental results. The emergence of dislocation cells is seen and the structure of the cells is described.
Related papers
Crystal Plasticity and Hardening: A Dislocation Dynamics Study
Procedia Engineering, 2009
Following the publication of several seminal studies, discrete dislocation dynamics has become well-established as a means of analysing the response of ductile crystals and polycrystals to mechanical loading. Developments undertaken by different authors have followed two principal directions: (i) the use of simple 2D formulations that do not seek to capture correctly the details of slip geometry, but allow some insight to be developed into the trends and relationships, and (ii) large scale 3D simulations seeking to represent correctly the geometry of dislocation segments, and their spatial distribution and interaction. The former is computationally inexpensive and fast, but fails to capture the effects of grain orientation. The latter is associated with large overheads in terms of the computational effort. The purpose of the present study is to propose and develop an intermediate level approach, whereby the geometry of the crystal slip is captured to a greater degree, while computational difficulty is kept to a minimum. The results are analysed in terms of the dependence of yield stress and cyclic hardening on the crystal orientation and dislocation interaction with each other and with the grain boundaries.
Dislocation Mean Free Paths and Strain Hardening of Crystals
Science, 2008
Predicting the strain hardening properties of crystals constitutes a long-standing challenge for dislocation theory. The main difficulty resides in the integration of dislocation processes through a wide range of time and length scales, up to macroscopic dimensions. In the present multiscale approach, dislocation dynamics simulations are used to establish a dislocation-based continuum model incorporating discrete and intermittent aspects of plastic flow. This is performed through the modeling of a key quantity, the mean free path of dislocations. The model is then integrated at the scale of bulk crystals, which allows for the detailed reproduction of the complex deformation curves of face-centered cubic crystals. Because of its predictive ability, the proposed framework has a large potential for further applications.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.