Approximate Method for the Motion of Dislocations among Random Obstacles in the Presence of Viscous Drag

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Abstract
The motion of dislocations among random obstacles in the presence of a viscous drag is studied using techniques based on von Kármán's integral method for fluid flow problems. An approximate method is developed for the case of a dislocation bowing between two discrete obstacles, and examples are presented to illustrate its application to various arrays of obstacles with a continuous force field (both attractive and repulsive) of random strengths. The approximate method gives sufficiently accurate values for such parameters of interest as average velocity, total strain, strain rate, penetration distance, and breakthrough time at a given obstacle.