The resistivity of polycrystalline wires in relation to plastic deformation, and the mechanism of plastic flow

Abstract

The subject of metallic conduction of electricity has long been a source of difficulties, which are far from having been overcome by the many admirable and ingenious theories recently put forward. The peculiarities of the different individual metals, as exemplified, for instance, in the variation of the Wiede-mann-Franz ratio from metal to metal seem to fall right outside any scheme so far elaborated. At present it is only possible to treat a metal as if it were a homogeneous crystal, the insufficiency of which assumption may be the source of many of those discrepancies between theory and experiment now attributed to fundamental properties of the electron in metal. Any experimental evidence concerning variations in electrical conductivity which can be produced in one pure metal by mechanical treatment should therefore be of some interest for the general problem. In particular the effect of permanent deformation upon electrical conductivity in metals is full of obscurity, and seems to offer a field for experiment. It was decided to investigate the variations of conductivity with certain simple types of deformation which attend the flow of soft metals. The flow of polycrystalline wires under constant stress has been investigated by one of us, and the changes of mechanical properties with time examined. The process of flow can be analysed into three phases:—an initial stretch which occurs within a very short time of the application of the stress; a continuous flow, the rate of which decreases with time, called, from the constant used to express it, the β-flow; and a flow at constant rate per unit length which occurs simultaneously with the β-flow and continues until the wire breaks. The formula expressing the flow is l = l 0 (1 + β t ⅓ ) e kt where l is the length at time t , and l 0 , β and k are constants. Since the formula was first put forward analogous formulæ, involving t ⅓ , have been found by other workers for different substances. Thus Filon and Jessop found for celluloid l = l 0 + at ⅓ + bt , and Peirce has expressed the decrease of the couple required to maintain constant torsion in a cotton fibre by a formula c = c 0 + ae - β t ⅓ , so that a term in t ⅓ apparently represents with some generality the observed behaviour of solids during flow. In former publications the general features of the behaviour were expressed in terms of crystal structure, but at the time no evidence from other sources could be adduced to support the hypothesis. The object of the present investigation is to measure the specific resistivity of the metal during the plastic extension, and to use the data so obtained to elucidate the changes of structure which take place in a polycrystalline wire when it is extended. One of the chief results has been to show that the β-flow has a real physical significance, and is due to the rotation of the axes of the crystallites which constitute the polycrystalline wire. Experiments have also been carried out on the resistivity of single crystal wires, the results of which will be published in the near future.