Show that the strain energy (per unit length) associated with the screw dislocation model of Example 15.2

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Show that the strain energy (per unit length) associated with the screw dislocation model of Example 15.2 is given by:

Wscrew MB  -log- 4 Ro Re

where Ro is the outer radius of the crystal and Rc is the core radius of the dislocation. This quantity is sometimes referred to as the self-energy. The radial dimensions are somewhat arbitrary, although Rc is sometimes taken as five times the magnitude of the Burgers vector.

Data from example 15.2

Next consider the screw dislocation case, as shown in Fig. 15.4. For this problem the material is again cut

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