A statistical-mechanical theory of forest hardening was developed in which yielding arose as a phase transition. The simple case of a single dislocation loop moving on a slip plane through randomly distributed forest dislocations (treated as point obstacles) was considered. The occurrence of slip at the sites occupied by the obstacles was assumed to require the expenditure of an amount of work which was commensurate with the strength of the obstacle. The case of obstacles of infinite strength was treated in detail. It was shown that the behavior of the dislocation loop, as it swept through the slip plane under the action of a resolved shear stress, was identical to that of a lattice gas or of the 2-dimensional Ising model. In particular, there existed a critical temperature below which the system exhibited a yield point. That is, the slip strain increased sharply when the applied resolved shear stress attained a critical value. Above the critical temperature, the yield point disappeared and the slip strain depended continuously upon the applied stress. The critical exponents which described the behavior of the system near to the critical temperature coincided with those of the 2-dimensional spin-½ Ising model.

Plastic Yielding as a Phase Transition. M.Ortiz: Journal of Applied Mechanics, 1999, 66[1], 289-96