Statistical Rate Theory Of Metals - I.* Mechanism Of Flow And Application To Tensile Properties

MANY theories have been advanced to explain the phenomena of elastic and plastic deformation. The object of this report is to present a mechanism for deformation, not radically differing from existing theories, but embodying certain principles and concepts of these theories. This proposed theory cannot be the complete answer to the age-old problem of deformation but it is believed that it will be a step further in the proper direction. The plastic properties of solids have recently been reviewed by Seitz and Read.1 Zener2 has reviewed and correlated the existing work on the anelasticity of metals. With these and othersa3,4,5 present theories of deformation are well-known. Of the many theories now extant, those receiving most attention have been proffered by Griffith,6 Becker,7 Smekal,8 Polanyi,9 Orowan10 and Taylor.11Although differing quite widely in details, these theories are based more or less on a common principle of flaws or dislocations that exist in the crystal lattice. The effect of stress concentrations surrounding a flaw or crack has been treated most recently by Fisher and Hollomon.12 The various authors differ as to the exact nature of the flaws or dislocations, the causes of their appearance, or the manner in which they initiate slip. All of the theories agree that the number of dislocations increases with progressing deformation. It is universally agreed that the shearing process is not a simple gliding of ideally perfect atomic lattice planes. It is also agreed that the "macroscopic process of gliding, or slip, is brought about by the spreading of a large number of locally initiated "glide steps" through the whole crystal. The occurrence of these "glide steps" is closely related to the presence of some kind of deviations from the "ideal" lattice structure, even in the undeformed crystal. These deviations are overcome "one at a time," in a manner of speaking, due to some stress-concentrating effect." PROPOSED THEORY Many solids show a continuously increasing deformation if subjected to a constant load of suitable magnitude in an extended range of temperature for a sufficient time. This deformation, or flow, may be said to be due, in general, to the tendency of the atoms or molecules in an elastically stressed body to readjust themselves in such a way that if the deformation were kept constant, a release of stress would take place. If rupture does not occur, this process of relaxation causes the rate of flow to obtain a final constant value, as shown in the curve (Fig I) obtained by Taylor and Quinney.14 In. this state the release of stress by relaxation exactly counterbalances the increase due to the elastic strain on the test pieces. .