Lawrence Livermore National Laboratory

Plastic deformation of single crystals is carried out by large number of dislocations. Dislocation theory enhanced by experimental tools such as transmission electron microscopy (TEM) has made significant advancements in understanding the plastic behavior of crystalline materials. However, due to the multiplicity and complexity of the dislocation mechanisms involved, there exists a huge gap between the properties of individual dislocations and unit dislocation mechanisms at the microscopic scale and the material behavior at the macroscopic scale. To translate the fundamental understanding of dislocation mechanisms into a quantitative physical theory for crystal plasticity, a new means of tracking the dislocation motion and interaction over large time and space evolution is needed. Three dimensional dislocation-dynamics (DD) simulation is aimed at developing a numerical tool for crystal plasticity. It directly simulates the dynamic, collective behavior of individual dislocations and their interactions. It produces stress strain curves and other mechanical properties, and allow detailed analysis of the dislocation microstructure evolution. In a numerical implementation, dislocation lines are respresented by connected discrete line segments that move according to driving forces including dislocation line tension, dislocation interaction forces and external loading. The dislocation segments respond to these forces by making discrete movement according to a mobility function that is characteristic of the dislocation type and the specific material being simulated. The dislocation mobility can be extracted from experimental data, or calculated by atomisic simulations. And the mobility is one of the key inputs to a DD simulation. Another important consideration for DD simulations is dealing with close dislocation-dislocation interactions such as annihilation and junction formation and breaking. These close interactions can be very complex and usually require special treatment. An efficient way to deal with them is to use prescribed 'rules'. A bottleneck for DD simulation is the calculation of the elastic interactions between dislocations which is long range in nature. In order to perform DD simulations for realistic material plastic behavior, efficient algorithms must be developed to enable the simulation over reasonable time and space range with a large number of dislocations.

An example of the geometric representation of dislocation lines in a DD simulation based on the screw-edge model.

This figure shows an example of the geometric representation of dislocation lines in a DD simulation based on the screw-edge model. The simulated crystal is a sub-lattice of the atomistic lattice with the unit cell length (a) on the order of a few nanometers for bulk simulations. A unit screw (in red) or edge (in blue) segment is thus defined by the unit cell and the Burgers vector (cf. left picture). Any arbitrary dislocation lines are then represented by piece-wise connected screw and/or edge segments (cf. top picture). These segments move within discrete time steps under the driving forces of the local resolved shear stress and according to the given mobility rules. The plastic flow is thus carried out under certain applied loading conditions such as constant strain rates. In principle, there is no unique way to discretize the space and the dislocation lines. It is possible to represent smooth dislocation lines with any desired degree of realism given enough discretization resolution. In practice, it is necessary to have a balance between resolution and efficiency in order to perform the simulation for realistic material plastic deformation.

Selected Publications

  1. M. Tang, L. P. Kubin, G. R. Canova, "Dislocation mobility and the mechanical response of bcc (Ta) single crystals: a mesoscopic approach ," Acta Mater. 46, 3221 (1998).
  2. V. V. Bulatov, M. Tang, H. Zbib, "Crystal plasticity from dislocation dynamics ," MRS Bulletin 26, 191 (2001).
  3. L. P. Kubin, B. Devincre, M. Tang, "Mesoscopic Modeling and Simulation of Plasticity in FCC and BCC crystals: Dislocations Intersection and Mobility ," J. Computer-Aided Materials Design 5, 31-54 (1998).

Maintained by   Randolph Q. Hood