On plasticity and creep in solids

Abstract

1. When a distortional stress is applied to a solid it produces an instantaneous deformation, which would then remain constant so long as the stress was kept constant if the solid was perfectly elastic. All solids, however, show imperfection of elasticity under sufficiently large stresses, and many do so even when the stress is small. Such imperfection takes the form of a continuous increase of the deformation after the stress has been applied. In some cases the deformation appears to increase indefinitely with the time so long as the same stress is kept on; and in these cases a permanent deformation remains after the stress is removed. In other cases it tends to a finite limit, which is not surpassed unless the stress is further increased; and in many of these, when the stress is removed, the body first returns towards its original state by an amount equal to the original elastic distortion, but then proceeds to creep slowly in the same direction until the whole, or nearly the whole, of the deformation has been recovered. The former type of behaviour, involving permanent deformation, may be called plasticity, the latter elastic afterworking or creep. The distinction is important, but in some accounts of experimental work it does not appear that the stress was maintained long enough to ascertain whether the deformation was tending towards a definite limit, or that the body was sufficiently studied after removal of the stress to find out whether the original state was ultimately recovered; and in consequence phenomena have in some cases been attributed to plasticity that are really due to creep. The present paper gives first a new derivation of the equations of plastic flow and discusses its relation to some earlier work; second, a theory of creep and a discussion of its relation to experimental evidence; and third, some geophysical applications of the results.