Dislocation Walls in Finite Media: The Case of an Infinite Slab
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Dislocation Walls in Finite Media: The Case of an Infinite Slab M. Surh and W. G. Wolfer, Lawrence Livermore National Laboratory, Livermore, CA 94550 ABSTRACT The dislocation microstructure observed in solids exhibits cellular patterns. The interiors of these cells are depleted of dislocations while the walls contain dense bundles including the geometrically necessary dislocations leading to misorientations of the crystal lattice on either side. This clustering is the result of short-range interactions which favor the formation of dislocation dipoles or multipoles and tilt and twist boundaries. While this short-range ordering of dislocations is readily understood, the long-range pattern formation is still being studied. We examine finite tilt boundaries in an infinite medium, a model grain, and a free slab to investigate the conditions for longrange stress interactions. We find that finite tilt walls in a larger medium generally possess a long-range stress field because the local bending at the tilt wall is constrained by the surrounding material. 1) INTRODUCTION The nature of dislocation cell patterning in solids remains a topic of active research. What determines the cell size or the spacing of dislocation walls? Why do the misorientation angles of the subgrains alternate in sign as one scans across a dislocation microstructure? A partial answer to these questions can be found in earlier studies of Li [1,2] and in subsequent work by others [3-10]. While a tilt boundary of infinite extent has only a short-ranged stress field, it was shown by Li [2] a finite wall has an additional long-range stress field. This force-field can trap dislocations at a distance of about 0.4 D from the dislocation wall, where D is the height of the wall. In polycrystalline materials, the height of a dislocation wall or cell boundary is presumably on the order of the grain diameter. Upon further deformation, the geometrically necessary cell walls become the new grain boundaries, setting a new, and smaller length scale for further dislocation cells. This process of subgrain refinement should be self-similar, and may lead to the scaling laws discovered by Hughes and Chrzan [11,12,13]. However, there is a flaw in this explanation. As Li [2] has also shown, the finite dislocation wall should effectively trap more dislocations below and above the wall (leading to polygonization), thereby increasing its height or continuing the wall into adjacent grains if they are favorably oriented. We offer in this paper an alternate explanation. The stress field that emanates from the ends of a finite dislocation wall into adjacent grains is altered by the boundary conditions on the grain. While normal stresses to the grain boundary can always be readily transmitted into the adjacent grain, shear stresses can not. Computer simulations on the elastic behavior of grain boundaries by Adam et al. [14] and by Wolf [15] have shown that the layer shear modulus drops by an order of magnitude in twist grain boundaries compared to its value in the perfect crystal. Sh
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