Consider a circular dislocation loop of diameter, d, in a crystal under a shear stress, . The

Consider a circular dislocation loop of diameter, d, in a crystal under a shear stress, τ. The region inside the circle has slipped relative to the material outside the circle. The presence of this dislocation increases the energy of the crystal by the dislocation energy/length times the length of the dislocation. The slip that occurs because of the formation of the dislocation under the stress, τ, lowers the energy of the system by τAb. (τA is the shear force and b is the distance the force works through.) If the diameter of the loop is small, the energy will be reduced if the loop shrinks. If the loop is large enough, the loop will spontaneously expand. Find the diameter of critical size loop in terms of b, G, and τ. For simplicity take EL = Gb2 .

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Answer The energy of the system due to the presence of the dislocation loop can be expressed as EL Gb2 where G is the shear modulus b is the magnitude of the Burgers vector and EL is the dislocation e... View the full answer