A thermodynamics-based variational method is developed to establish the equations of motion for threedimensional ͑3D͒ interacting dislocation loops. The approach is appropriate for investigations of plastic deformation at the mesoscopic scale by direct numerical simulations. A fast sum technique for determination of elastic field variables of dislocation ensembles is utilized to calculate forces acting on generalized coordinates of arbitrarily curved loop segments. Each dislocation segment is represented by a parametric space curve of specified shape functions and associated degrees of freedom. Kinetic equations for the time evolution of generalized coordinates are derived for general 3D climb/glide motion of curved dislocation loops. It is shown that the evolution equations for the position (P), tangent (T), and normal (N) vectors at segment nodes are sufficient to describe general 3D dislocation motion. When crystal structure constraints are invoked, only two degrees of freedom per node are adequate for constrained glide motion. A selected number of applications are given for: ͑1͒ adaptive node generation on interacting segments, ͑2͒ variable time-step determination for integration of the equations of motion, ͑3͒ dislocation generation by the Frank-Read mechanism in fcc, bcc, and dc crystals, ͑4͒ loop-loop deformation and interaction, and ͑5͒ formation of dislocation junctions.

This study, called APEX, is exploring novel concepts for fusion chamber technology that can substantially improve the attractiveness of fusion energy systems. The emphasis of the study is on fundamental understanding and advancing the underlying engineering sciences, integration of the physics and engineering requirements, and enhancing innovation for the chamber technology components surrounding the plasma. The chamber technology goals in APEX include: (1) high power density capability with neutron wall load \ 10 MW/m 2 and surface heat flux \ 2 MW/m 2 , (2) high power conversion efficiency ( \ 40%), (3) high availability, and (4) simple technological and material constraints. Two classes of innovative concepts have emerged that offer great promise and deserve further (2001) 181-247 182 research and development. The first class seeks to eliminate the solid ''bare'' first wall by flowing liquids facing the plasma. This liquid wall idea evolved during the APEX study into a number of concepts based on: (a) using liquid metals (Li or Sn-Li) or a molten salt (Flibe) as the working liquid, (b) utilizing electromagnetic, inertial and/or other types of forces to restrain the liquid against a backing wall and control the hydrodynamic flow configurations, and (c) employing a thin ( 2 cm) or thick ( 40 cm) liquid layer to remove the surface heat flux and attenuate the neutrons. These liquid wall concepts have some common features but also have widely different issues and merits. Some of the attractive features of liquid walls include the potential for: (1) high power density capability; (2) higher plasma b and stable physics regimes if liquid metals are used; (3) increased disruption survivability; (4) reduced volume of radioactive waste; (5) reduced radiation damage in structural materials; and (6) higher availability. Analyses show that not all of these potential advantages may be realized simultaneously in a single concept. However, the realization of only a subset of these advantages will result in remarkable progress toward attractive fusion energy systems. Of the many scientific and engineering issues for liquid walls, the most important are: (1) plasma-liquid interactions including both plasma-liquid surface and liquid wall-bulk plasma interactions; (2) hydrodynamic flow configuration control in complex geometries including penetrations; and (3) heat transfer at free surface and temperature control. The second class of concepts focuses on ideas for extending the capabilities, particularly the power density and operating temperature limits, of solid first walls. The most promising idea, called EVOLVE, is based on the use of a high-temperature refractory alloy (e.g. W -5% Re) with an innovative cooling scheme based on the use of the heat of vaporization of lithium. Calculations show that an evaporative system with Li at 1 200°C can remove the goal heat loads and result in a high power conversion efficiency. The vapor operating pressure is low, resulting in a very low operating stress in the structure. In ad...

The elastic field of complex shape ensembles of dislocation loops is developed as an essential ingredient in the dislocation dynamics method for computer simulation of mesoscopic plastic deformation. Dislocation ensembles are sorted into individual loops, which are then divided into segments represented as parametrized space curves. Numerical solutions are presented as fast numerical sums for relevant elastic field variables ͑i.e., displacement, strain, stress, force, self-energy, and interaction energy͒. Gaussian numerical quadratures are utilized to solve for field equations of linear elasticity in an infinite isotropic elastic medium. The accuracy of the method is verified by comparison of numerical results to analytical solutions for typical prismatic and slip dislocation loops. The method is shown to be highly accurate, computationally efficient, and numerically convergent as the number of segments and quadrature points are increased on each loop. Several examples of method applications to calculations of the elastic field of simple and complex loop geometries are given in infinite crystals. The effect of crystal surfaces on the redistribution of the elastic field is demonstrated by superposition of a finite-element image force field on the computed results. ͓S0163-1829͑99͒02625-9͔

A new methodology in computational micromechanics, dislocation dynamics (DD), is introduced.Dislocation dynamics is developed for examining the dynamic behavior of dislocation distributions in solid materials. Under conditions of externally applied stress, dislocations exhibit glide with a velocity proportional to a power of the applied stress 0. and climb motion with a velocity that is a function of the applied stress and temperature. These motions result from long-range force fields, comprising both externally applied stress and long-range interactions between individual dislocations. Short-range reactions are represented as discrete events. The DD methodology is to be differentiated from particle methods in statistical mechanics (e.g. , molecular dynamics and the Monte Carlo method) in two respects. First, DD is developed to study the dynamical behavior of "defects" in the solid. Generally, the density of defects is less than that of the particles that make up the solid. Second, the small number of dislocations allows for a complete dynamical representation of the evolution of dislocations in the material medium without the requirement of statistical averaging. The purpose of the DD methodology is to bridge the gap between experimentally observed phenomena and theoretical descriptions of dislocation aggregates, particularly the evolution of self-organized dislocation structures under temperature, stress, and irradiation conditions.

a b s t r a c tDislocation motion in body centered cubic (bcc) metals displays a number of specific features that result in a strong temperature dependence of the flow stress, and in shear deformation asymmetries relative to the loading direction as well as crystal orientation. Here we develop a generalized dislocation mobility law in bcc metals, and demonstrate its use in discrete Dislocation Dynamics (DD) simulations of plastic flow in tungsten (W) micro pillars. We present the theoretical background for dislocation mobility as a motivating basis for the developed law. Analytical theory, molecular dynamics (MD) simulations, and experimental data are used to construct a general phenomenological description. The usefulness of the mobility law is demonstrated through its application to modeling the plastic deformation of W micro pillars. The model is consistent with experimental observations of temperature and orientation dependence of the flow stress and the corresponding dislocation microstructure.