Part VII – July 1969 - Papers - A Modified Peierls Model for Thermally Activated Deformation in Bcc Metals

A modified Peierls model is Presented for the rationalization of the asymmetric plastic behavior of single crystals of bcc metals. The model assumes that the asymmetry of slip arises from a tendency toward asymnetric splitting of the a/2[111] screw dislocation. The approach differs from former theories however insofar as it assumes that the splitting is so minor ttut only the core energy is modified and that no real partial dislocations exist. As a consequence, the concepts of a line energy of a partial dislocation, interaction between partial dislocations, constriction energies, and stacking fault energies are not invoked. Instead the present analysis is based on a specialization of the Peierls mechanism which assumes an asymmetric dislocation core which is modified by the effective stress and permits cross slip. The theoretical predictions on the stress-temperature -strain rate and orientation relationship agree qualitatively with the limited experimental data that are currently available. Additional experimental work over wider ranges of conditions is suggested to provide more complete evaluation of the possible validity of this theory. RECENT experimental investigations on the low-temperature thermally activated deformation of bcc metals have confirmed the existence of several unique orientation effects. These will be described with the aid of the standard stereographic projection shown in Fig. 1. If slip were determined exclusively by crystal symmetry, the deformation characteristics would be symmetrical about X; = 0 and independent of whether the specimen were subjected to a tension or a compression stress, regardless of what combinations of slip planes might be operative. Experiments, however, reveal that neither of these symmetry based predictions are valid. A schematic representation of the commonly observed asymmetry of both the yield stress and the plane of slip is shown in Fig. 2. A reversal of the direction of stressing results in an inversion of the asvmmetric behavior. 1) Asymmetry bf Yielding. A detailed investigation on the asymmetric yielding in an Fe-2.7 pct Si alloy was repoEted by Tabka, Tikeuchi, and Furubayashi,1 Similar trends have been observed by Keh and Nakada on iron,' Stein on molybdenum,3 Bowen, Christian, and Taylor4 on columbium, Sherwood, Guiu, Kim, and pratt5 on Ta, Cb, and Mo. The degree of asymmetry not only depends on the atomic number and alloying but, in all cases that have been examined, it also increases with a decrease in the test temperature. 2) Asymmetry of the Slip Plane. Asymmetric $I-~: curves of the type shown in Fig. 2 have been found for several Fe-Si alloys6-8,1 and columbium.4 There is general agre_ement that near X: = 30 deg slip occurs by the [111](211) mode so that ?1 = 30 deg. As X; decreases it appears that [111](211) to [111](101) cross slip takes place leading to slip band traces on intermediate planes. And as xi approaches 0 deg, sharp