Unified Theory of Grain Boundaries. An Update

Abstract

An extensive theory of grain boundaries is developed in which the structure of the boundary is described in terms of surface dislocations. This approach is shown to be consistent with the most generalized formulation of a Burgers circuit.

Grain Boundaries Revisited

“…Analogous to the expressions given by (6) to (8), for the horizontal array of Fig. 3a, where -L --m and +L -+ my the stress fields become On the other hand, the component of stress cxz, given by (42), is seen to riot fall off with distance y, but t o attain a constant value.…”

Relationship between rotation, deformation, and cell structure

“…As is clear from the previous discussion, cell walls, to a good approximation, may be viewed in terms of grain boundaries. On the other hand, i t has been clearly demonstrated that the classical theory of grain boundaries, which consists solely of a uniform array of lattice dislocations, is conceptually incorrect [3,4]. As illustrated in Fig.…”

“…Although attempts have been made t o relate some of these variables [2], the general problem remains essentially unsolved. The main stumbling block seems to have been a failure to recognize the incorrectness of the classical model of grain boundaries [3,4] t o which the cell wall is closely related [ 5 ] . It will be the purpose of the present study to formulate a very simple model which accounts for most of the observations associated with dislocation cell walls.…”

The Role of Surface Dislocations in the Continuum Theory of Lattice Defects

“…where @ is the plastic distortion given by where u: is the plastic displacement. The plastic strain in (6) can also be written in terms of the displacements as follows :…”

“…It has been shown repeatedly [l to 51 that the concept of surface dislocations allows any problem dealing with the mechanical behavior of matter to be solved with a high degree of mathematical rigor and with deep physical insight. For the specific case of grain boundaries, this approach was found to be indispensable in clarifying the nature of such boundaries [6,7]. It would therefore appear quite logical a t this point to inquire into the reasons as to why the concept of surface dislocations does not appear in the beautifully abstract continuum theories of lattice defects such as developed by Kroner [8,91.…”