Hybrid models of dislocations
In a Volterra dislocation the relative displacement by the Burgers vector appears abruptly in the dislocation core so that the core has no width. This leads to divergent stresses and strains, which are unrealistic. Hybrid models correct this failure by considering a balance of forces that results in a finite core width, and finite stresses and strains throughout. Interatomic forces tend to constrict the core and elastic forces tend to widen it. The Frenkel-Kontorova model comprises two interacting linear chains of atoms as a representation of an edge dislocation, with linear springs between adjacent atoms of each chain. The Peierls-Nabarro model assumes the core is confined to two parallel atomic planes sandwiched between elastic continua. This model enables the stress to move the dislocation to be calculated, and it leads to the concept of dislocation kinks. These models highlight the role of atomic interactions in affecting ductility.