Section A. -Mathematical and physical sciences. - The deformation of crystals of β-brass

Abstract

It is shown that β-brass, which has a crystal structure similar to that of α-iron, behaves in a similar, though not identical, manner when distorted. The peculiar feature of the distortion of iron crystals, namely, the fact that slip does not occur on a definite crystallographic plane, is repeated in β-brass within a certain range of orientations of the crystal axes in the specimen. On the other hand, in another range of orientation slip occurs on a definite crystal plane of type {110}. The conditions which determine which of these types of distortion will occur in any given case are investigated, and it is shown that the determining cause is the variation in resistance to shear which occurs as the plane of slip rotates about the direction of slip. This variation is calculated from the experimental results within the range to which they apply, and it is shown that resistance to shear is least when the plane of slip coincides with a crystal plane of type {110}. On either side of this position shear stress increases linearly, there being a discontinuity in the rate of change of shear strength with orientation of plane of slip. This peculiar property is also possessed by the model consisting of hexagonal rods proposed by the author and Miss Elam, and by Mr. Hume Rothery’s model, which, from this point of view, is identical with the model of hexagonal rods. The assumptions made in a recent paper by Mr. Hume Rothery are discussed, and it is shown that in a body-centred cubic structure like a-iron they lead, when analysed, to the conclusion that slipping should always take place parallel to a crystal plane of type {110}, and not, as he stated, to the conclusion that slip should occur on the non-crystallographic planes which were actually found. It is shown also that in β-brass resistance to slipping in one direction on a given plane of slip is not the same as resistance offered to slipping in the opposite direction. Such a difference is to be expected from crystallographic symmetry, but was not observed in α-iron.