Uniqueness of uniaxial elastic-plastic interface motions

Abstract

The uniaxial motion of interfaces between regions deforming elastically and regions deforming plastically is considered. The governing constitutive, stress-rate/strain-rate equations in both elastic and plastic regions are taken to be non-linear. Discontinuity relations across such interfaces are established by the repeated differentiation of existing relations. The relations given by previous workers (especially R.J. Clifton, T.C.T. Ting, E.H. Lee and Th. von Kármán) are discussed. The precise situations in which they hold are considered, and it is shown that some of these relations, while apparently derived for different situations, can, in certain circumstances, be shown to be equivalent. It has been shown that six essentially different types of motion can occur, and, when the constitutive equations are linear, each type of motion is unique. This result is extended to the non-linear situation, by means of an established local expansion procedure. For the case of a meeting interaction of stress waves carrying initially linear profiles, the previous (linear) analysis given by L.W. Morland and A.D. Cox fails to distinguish between certain types of motion. This motion is reconsidered and it is shown how non-linearity in the constitutive laws serves to determine uniquely the type of motion that takes place.