Technical Papers and Notes - Institute of Metals Division - Substitutional Solid-Solution Strengthening in Copper Alloys

THE concept of alloying to increase the strength of metals originated during the bronze age. However, at the present time there is no single theory capable of explaining all of the observed strengthening effects of alloying elements on the mechanical properties. In general, it may be said that solid solutions are stronger than the pure metal and that the strengthening effect increases with increasing alloy content. Various theories for solution hardening have been proposed, the first of which was presented by Rosenhain who suggested that the alloying elements roughened the slip planes, thereby requiring a higher stress to initiate slip. Recent work by French and Hibbard2 confirmed Norbury's3 conclusion that those alloying elements which cause a greater change in lattice parameter have larger effects on hardness. However, a given change in lattice parameter produced by different alloying elements does not cause the same change in hardness. A further refinement was suggested by Dorn, Pietrokowski, and Tietz4 who considered differences in valence between the solute and solvent with the change in lattice parameter to explain the plastic properties of aluminum alloys. Allen, Schofield, and Tate5 further investigated the valency contribution to solution strengthening by testing some copper-base solid-solution alloys having constant electron densities. Tensile tests performed on these alloys gave identical stress-strain curves even though the atomic size effect, which varied by a factor of two, was neglected. The advent of dislocation theory6-8 provided a new and powerful tool capable of explaining many phenomena of plastic deformation and indicated new approaches to solution hardening. The basic con- cept of recent theories is that solution hardening is not due to stresses associated with randomly dispersed solute atoms, but rather to a nonuniform distribution of the solute. This conclusion was reached by consideration of the effective tension present on each dislocation line and the ability of a dislocation to pass an obstacle. cottrell suggested the possibility that the internal stresses due to randomly distributed solute atoms would offer essentially no resistance to the passage of dislocations. He reasoned that an edge dislocation may be considered as a rigid line discontinuity. As the dislocation moved through a crystal, the random stress fields would be equally distributed along its length. Since half of the stress fields would be acting to move the dislocation forward and the other half trying to move it back, the net effect on the dislocation would be zero. Thus the randomly distributed solute atoms would not contribute appreciably to solution strengthening. Mott and Nabarro10 considered the dislocation as a flexible, rather than a rigid, discontinuity. They obtained a simple model for a dislocation moving in a lattice having precipated particles, where the dislocation would actually bend around the obstacle until it would loop back onto itself to rejoin and then continue onward. Their work indicated that the minimum radius of curvature of the dislocation line, under the action of an external stress and in the region of an internal stress, would be such that the dislocation would be unable to pass through a matrix containing small closely spaced precipates by the looping process. The dislocations would tend to remain rather straight, approaching the condition of Cottrell's rigid dislocation. Hence, the strengthening must not be due to random solute atoms; however, it might be due to the concentration of atoms, either as clusters of like atoms or as short-range ordered regions, or to the concentration of solute atoms around dislocations. To date, four mechanisms of solution strength-