Institute of Metals Division - A Discussion of the Importance of Line Tension on Cottrell's Theory of the Sharp Yield Point

The activation energy required to break a pinned dislocation line away from its condensed atmosphere of impurity atoms is calculated as a .function of applied stress, without neglecting line tension. Reasows are presented for not assuming the effect of line tension to be negligible when considering the problem of freeing a small segment of dislocation from an impurity atmosphere. The dislocation is considered to he pinned at each atomic size along its length and the pinning points are assumzed immobile. The development is a refinement of the origznal cottrell-bilby1 theory. The solution is compared to recent approximations developed by cottrell3 and Haasen5 in which line tension con- IN 1949 Cottrell and bilby1 considered the problem of determining the force required to pull a dislocation away from its condensed atmosphere of impurity atoms. They also examined the effect of thermal fluctuations on this force. The dislocation line was pictured as bowing out in a triangular loop under the action of an applied stress, and the activation energy necessary to free the dislocation from its atmosphere was calculated as a function of stress, line energy, and dislocation-solute atom interaction. siderations were neglected. A qualitative explanation of the yielding process in terms of the activation of Frank-Read sources is presented, but the lack of a realistic solution to the dynamic dislocation problem involved prevents an extension of the model at present. A self-consistent correlation between the present calculations and experimental data for delay time associated with yielding and the temperature dependence of the upper yield stress was made. Favorable agreement was noted. It is concluded that extension of the original Cottrell-~ilby' theory which includes line tension effects can just as well describe the yielding process as other approximations3,5 which neglect line tension. Cottrell and Bilby found the form of the activation energy vs stress curves to be almost independent of the line energy and the interaction energy (i.e., these parameters only affected the activation energy U by a scale factor). A check of the theory was accomplished by comparison with the experimental data of McAdam and Mebs2 for the lower yield stress as a function of temperature. cottrell,3 in 1957, attempted to obtain a simple closed-form solution for the activation energy as a function of stress by linearizing the quartic equation relating displacement of the dislocation line and applied stress. It was argued that since the contribution to the line energy/atomic plane of a dislocation is made by the long-range stress field of the dislocation through a term of the type (Gb3/2p)ln A/ro, where