Peach-Koehler equation

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... 

As the energies must agree for arbitrary I2, the Peach-Koehler equation results ... 

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