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Center for Nonlinear Studies |
Five decades ago, Mura has shown that the stress field of anisotropically elastic materials generated by a periodic dislocation network can be expressed analytically in reciprocal space. One can thus quickly obtain the Peach-Koehler forces on individual dislocations that drive the evolution of the dislocation substructure. This model is applicable primarily to close-packed metals in which the glide of dislocations is governed by the Schmid law. However, it cannot be used for bcc metals due to the non-planar cores of their 1/2<111> screw dislocations and the associated breakdown of the Schmid law. Our molecular statics studies on isolated 1/2<111> screw dislocations in bcc Mo and W (and more recently in Nb, Ta, V and Fe) have provided detailed database of the dependence of the Peierls stress to move the dislocation at 0 K on the orientation and character of the applied load. These were incorporated into a model of thermally activated dislocation glide that provides an analytical expression of the activation enthalpy to initiate the plastic flow. The purpose of this presentation is to demonstrate how these detailed calculations can be incorporated into a mesoscopic Eulerian framework in which we consider three slip systems on which the 1/2[111] screw dislocation can move. Besides anisotropically elastic interactions between dislocations that are automatically included in the model, we incorporate a thermally activated cross-slip through which the dislocations can jump between the three {110} planes of the [111] zone. The numerical solution of the evolution equation, which contains the information obtained previously using atomistic and thermodynamic models, leads to the formation of a mesoscopic texture. This is represented by a non-trivial distribution of slip traces whose orientations depend on the character of the applied load.
Host: Turab Lookman