Dislocation line tension

When a dislocation segment of length L is pinned at the ends under the influence of an applied shear stress t, a balance between the line tension and the applied stress produces a radius of curvature R given by [37]... 

Solution. The line-tension forces acting on a curved differential segment of dislocation having a radius of curvature R due to its line tension will be as shown in Fig. 11.14. The net force exerted on the segment toward the concave side is then... 

Figure 11.14 Line tension forces on a curved dislocation segment.

When a metal crystal free of applied stress and containing screw dislocation segments is quenched so that supersaturated vacancies are produced, the screw segments are converted into helices by climb. Show that the converted helices can be at equilibrium with a certain concentration of supersaturated vacancies and find an expression for this critical concentration in terms of appropriate parameters of the system. Use the simple line-tension approximation leading to Eq. 11.12. We note that the helix will grow by climb if the vacancy concentration in the crystal exceeds this critical concentration and will contract if it falls below it. 

Show that regardless of the orientation of a straight dislocation line and its Burgers vector, there will exist a stress system that will convert the dislocation line into a helix whose axis is along the position of the original dislocation when the point-defect concentration is at the equilibrium value characteristic of the stress-free crystal. Use the simple line-tension approximation leading to Eq. 11.12. 

The effect of dislocation line oscillations on the probability of its separation from the defect was accounted for by Natsik [211, 212], who has considered the following model A dislocation line moves in the slipping plane under the action of the one-axis stress. The dislocation is characterized by the linear mass density p and tension coefficient C. Pinning in A and B sites is considered to be rigid, and the dislocation detachment from the defect located in the zero point is considered (Figure 21). At a li, I2 < d [d is... 

An alternative to the full machinery of elasticity that is especially useful in attempting to make sense of the complex properties of three-dimensional dislocation configurations is the so-called line tension approximation. The line tension idea borrows an analogy from what is known about the perturbations of strings and surfaces when they are disturbed from some reference configuration. For example, we know that if a string is stretched, the energetics of this situation can be described via... 

Further, we choose a configuration in which bi = b2 = bi + b2, corresponding to the three edges of one of the faces of the Thompson tetrahedron. The significance of this geometric choice is that it guarantees that the line tensions of all three dislocation segments of interest will be equal. 

Energy of Curved Dislocation in Line Tension Approximation We wrote down the energy of a curved dislocation as... 

Line Tension Model for Dislocation Junctions Reproduce the arguments culminating in eqn (8.119). 

Recall from the discussion on line tension and dislocation bow-out given in... 

In considering the energetics of extended defects, we have repeatedly resorted to locality assumptions as well. In particular, in the context of dislocations we have invoked the line tension approximation to assign an energy of configuration to a dislocation of the form... 

Whereas the line tension was invoked as a way to capture the self-energy of dislocations from an elastic perspective, there are also ways of capturing core effects on the basis of locality assumptions. Recall that in our treatment of dislocation cores we introduced the Peierls-Nabarro model (see section 8.6.2) in which the misfit energy associated with slip displacements across the slip plane is associated with an energy penalty of the form... 

Line Tension Dislocation Dynamics. Though our discussion above has given a generic feel for the dislocation dynamics strategy and has emphasized the full treatment of interactions between different segments, a watered down version of... 

---