Dislocations force between parallel

Figure 8. Interaction force between parallel dislocation lines with Burgers vector 4 [110] for NijAl. The radial component F tangential component Fg, and radial component for an isotropic material F, (iso) are normalized by (2-Krb ), where r is the distance between dislocations and b is the magnitude of the Burgers vector. The orientation of the dislocation lines varies from the direction of the Burgers vector, [110] (Reproduced by permission of Pergamon Press from Yoo, 1987a)...

Equations (3.66-3.72) are based on the expressions in Sect. 3.3.9, specifically Sects. 3.3.9.1 and 3.3.9.2 for screw and edge dislocations, respectively. In Fig. 3.48a and b, the Burgers vectors are parallel to the z and x axes of the screw and edge dislocations, respectively. As mentioned in Sect. 3.3.11.1, there is a repulsive force between same-signed dislocations, an attractive force between unlike dislocations. When y = 0, Eq. (3.69) reduces to... 

Due to the stress field around dislocations, there is an interaction between dislocations. Dislocations of like sign attract and dislocations of opposite sign repel. The force between two parallel screw dislocations and the force between two parallel edge dislocations are given, respectively, by ... 

One may conclude from Eqn. (3.6) that an (arbitrary) stress a exerts both a glide force and a climb force on edge dislocations, but no climb force on screw dislocations (s 6 F=0). Equation (3.6) can also be used to calculate the interaction between two dislocations, that is, the force which the stress field of one dislocation exerts on the unit length of another dislocation at a given coordinate. For parallel dislocations, this force can be written as [J. P. Hirth, J. Lothe (1982)]... 

N is the density of the dislocations participating in the climb process (or the density of the sources), A is the area swept out by a loop in a pile-up and 2r is the separation between those pile-ups. The stress necessary to force two groups of dislocation loops to pass each other on parallel slip planes must be greater than (in terms of shear stress it is ). When this relation is satisfied, an estimate for r may be made ... 

The general behavior of a long straight dislocation parallel to an interface between two isotropic elastic materials is well established. A configurational force acts on the dislocation due to its proximity to the interface. The direction of the force is normal to the interface, a direct consequence of the invariance of the conhguration under translation in any direction within the interface. The magnitude of the force varies with the inverse of the distance from the interface and, hnally, whether the force is attractive or repulsive depends on the relative magnitudes of the elastic constants of the two materials. For a screw dislocation, the force exerted by the interface... 

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