Dislocation movement through random arrays of obstacles

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Abstract
The detailed movement of a dislocation line through a random array of point obstacles in the glide plane has been examined, using a digital computer, on the basis of the line tension approximation. The breakaway criterion at each obstacle is a critical angle between the arms of the dislocation, corresponding to a critical force on the obstacle. The shear stress required to move the dislocation through the array has been determined for the complete range of breaking angles 0 to π and the result expressed in an empirical form. The dislocation is observed to move often by an 'unzipping' mechanism involving consecutive breakaway from obstacles on the dislocation. For weak obstacles the critical shear stress is appreciably less than for a regular array of the same density and corresponds exactly with the Friedel relation for the spacing of obstacles on a dislocation. For strong obstacles the dislocation motion is characterized by encircling movements and the severance of many closed loops, and the critical shear stress rises to a value of 0·81 μ/L, where L is the average spacing. The effect of thermal fluctuations is taken into account and the temperature dependence of the critical shear stress for point defect hardening is calculated. The relevance of these results to solution hardening is briefly discussed.
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