PHYSICAL REVIE% 8 VOLUME 41, NUMBER 10 1 APRIL 1990 Dislocation dynamics. II. Applications to the formation of persistent slip bands, planar arrays, and dislocation cells R. J. Amodeo* and N. M. Ghoniem Mechanical, Aerospace and Nuclear Engineering Department, University of California, Los Angeles, Los Angeles, California 90024 (Received 10 July 1989) The dynamic organization of dislocations into spatially heterogeneous substructures is demon- strated by applying the principles of dislocation dynamics that were outlined in the preceding paper. Here it is shown that the formation of persistent slip bands is a consequence of the competition be- tween dipole formation and annihilation of dislocations of opposite Burgers vectors in the absence of temperature-enhanced climb recovery under cyclic stress conditions. Planar arrays, which are also uniaxial structures, are shown to arise from enhanced dislocation multiplication and the forma- tion of stable dipole configurations along a slip plane at lower temperatures where climb is unimpor- tant. Biaxial dislocation systems experience additional degrees of freedom compared with uniaxial systems because of available motion along additional slip systems. It is demonstrated that for a sys- tern of orthogonal slip directions at high temperatures in which climb and glide motion are competi- tive, dislocation cellular structures form as a result of immobile dipole and junction formation and by the internal elastic strain energy minimization caused by long-range self-shielding. It is shown that the internal elastic strain energy is reduced by the self-organization process. However, the short-range nonlinear processes (i.e. , dipole and junction formation) are shown not to allow absolute elastic energy minimization. I. INTRODUCTION Many different types of dislocation structures have been observed in metals. ' Recently, it was suggested that these structures form as a result of the reduction in free energy of the material systems. Dislocation pat- terns, called low-energy dislocation structures, are for- mally defined as any dislocation structure in which neigh- boring dislocations screen each other's stress field. ' How- ever, another school of thought suggests that dislocation structures form as a natural consequence of nonlinear in- teractions among specific dislocation elements within the grain. In general, dislocation structures consist of re- gions of high dislocation density separated by regions of almost dislocation-free material. The dislocation-rich re- gion is a soft region of facilitated deformation, and the dislocation-poor region is a hard region in which defor- mation processes do not occur. Even though Argon et al. have suggested that the steady-state existence of these structures has not been proved unambiguously, much experimental data verify the constancy of the dislocation density and characteristic dimensions of these structures. Dislocation structures [i. e. , persistent slip bands (PSB's), planar arrays, and cells and subgrains] are found to exist in deforming metals under a variety of experi- mental conditions. Persistent slip bands are formed un- der cyclic conditions of stress, and have been mostly ob- served in copper and copper alloys. ' " They are essen- tially uniaxial dislocation structures. They appear as sets of parallel walls, composed of dislocation dipoles which are separated by dislocation-free regions. The length di- mension of the wall is orthogonal to the direction of glide of the dislocation. Dislocation planar arrays are formed under monotonic stress deformation conditions. They are also parallel sets of walls which are composed of sets of dislocation di- poles. ' While PSB walls are found to be aligned in planes with the normal parallel to the direction of the critical resolved shear stress (CRSS), planar arrays are found to be aligned in planes with the normal perpendic- ular to the direction of the CRSS. The dislocation cell structure is a honeycomblike configuration in which there are regions of high disloca- tion density (the cell walls) and low dislocation density (the region between the walls). Cells can be formed under both monotonic' ' and cyclic conditions (the latter occurring after a large degree of cycling has occurred). Direct experimental observations of these structures have been reported for many materials. ' ' Both theoretical and computational models have been applied to study the formation of many types of dislocation structures. ' Current computational models do not accurately treat the dynamics of interaction of a system of dislocations. For example, only long-range forces are considered in the evaluation of dynamic dislocation motion. ' In recent cellular automata simulations, ' short-range interactions were included in addition to long-range forces, but a truly dynamical system is not accurately represented in the simulation. Information on the time scale for a sirnula- tion of this type is lacking. In Paper I we presented the fundamentals of the newly developed dislocation dynam- ics (DD) methodology. Here, we show that this meth- odology resolves some of the problems which exist today 41 6968 1990 The American Physical Society