A Statistical Theory of Solid Solution Hardening

The critical shear stress τc to move a dislocation through a random array of obstacles in the glide plane is calculated using a statistical theory. The result is an expression for τc in terms of the obstacle concentration, the line tension of the dislocation, and of the interaction force between the dislocation and a single obstacle. Fleischer's solution of the same problem is not reproduced by the statistical theory. Quantitatively the two results are not very different, but our new result is supported by some recent experimental evidence. Furthermore the theory provides a definite prescription how to combine the concentrations and interaction forces of obstacles of different kinds in the expression for τc.