Dislocations Peach-Koehler force

Of particular interest in kinetics is the non-conservative dislocation motion (climb). The net force on a dislocation line in the climb direction (per unit length) consists of two parts Kei is the force due to elastic interactions (Peach-Koehler force), Kcbcm is the force due to the deviation from SE equilibrium in the dislocation-free bulk relative to the established equilibrium at the dislocation line. Sites of repeatable growth (kinks, jogs) allow fast equilibration at the dislocation. For example, if cv is the supersaturated concentration and c is the equilibrium concentration of vacancies, (in the sense of an osmotic pressure) is... 

Here (T33 and ajj are the stresses at the origin, where the first dislocation is situated, due to the presence of the other dislocation at (x3,Zo). This is known as the Peach-Koehler force on a dislocation arising from the stress field of the other. This can be generalized to mean that under application of a stress a dislocation experiences a force Ft whose exact relationship is given by the above expressions. 

If we assume that this is accomplished by a constant force, called the Peach-Koehler force Fpk, acting uniformly along the dislocation line, then the work done by this force will be given by... 

The mechanism for the spreading of the dislocations is illustrated by the schematic of Fig. 11(b). Spreading is driven by the Peach-Koehler force on... 

If this segment has an edge component of the right sign, it may provide strain relief When the critical thickness is exceeded, the force resulting from strain relief exceeds the force necessary for dislocation extension (the Peach Koehler force [9]) and a misfit relief segment is created. 

The physical interpretation of this result is that it is the force per unit length of dislocation acting on a segment by virtue of the presence of the stress field a. This expression is the famed Peach-Koehler formula and will be seen to yield a host of interesting insights into the interactions between dislocations. 

By exercising the instructions dictated by the Peach-Koehler formula using the state of stress given above, the force on dislocation 2 is given by... 

Pande and Suenaga [ ] have recently claimed that grain boundary flux pinning is caused by the elastic interaction between the dislocations constituting the grain boundaries and the fluxoids. The interactions between dislocations and fluxoids have long been the subject of studies. The two modes of interaction are (1) the first-order, or volume difference, effect, and (2) the second-order, or shear modulus difference, effect. The former usually dominates The Peach-Koehler equation [ ] can be used to calculate the interaction force between the stress field of the fluxoid lattice (a calculation of which has recently become available [ " ]) and the strain field of the dislocations. In the experiments of this study, the calculation of fpL... 

Here we used the fact that the force is perpendicular on the dislocation line. If the orientation between the stress tensor a, the dislocation line /i and the Burgers vector b is arbitrary, the Peach-Koehler equation... 

Peach M., Koehler J.S., The forces exerted on dislocations and the stress fields produced by them. Phys. Rev. 1950 80 436-9. 

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