Dislocation Motion in the Field of a Random Distribution of Point Obstacles: Solution Hardening

Abstract

Deformation rates of crystals, according to many experimental and theoretical studies, are controlled by thermal activation processes for surmounting various barriers. So far, the problems have been discussed using the following implicit solutions: (1) the processes are quasi-static and do not involve any dynamical aspects; (2) the frictional forces produced in materials are neither extremely large nor small. If the frictional forces due to the material are very small, the hypothesis (1) does not hold any more. This is the case of deformation of superconductors as described in the next chapter. Weertman [3.1] dissussed creep of ice on the basis of visco-elastic deformation theory developed by Eshelby [3.2]. According to ultrasonic attenuation experiments [3.3], B is 10⁷ times as large as that for metals. In this case, although the frictional force is still proportional to the velocity of dislocations, the time of motion in the area between barriers becomes longer than that needed to surmount each of them. In other words, the barriers are of no importance for the discussion of the rate of deformation. Accordingly, such a linear visco-elastic deformation may be put aside in the present discussion. As for studies of plastic deformation of crystalline materials, the past treatments of the case, where the frictional forces are very small, should be carefully reconsidered. In the present chapter, we discuss problems within the above framework, (1) and (2), and those outside of this will be discussed in the next chapter.