Dynamical Strength of an Ideal Solid with Definite Constitutive Equation

Abstract

The mechanical behavior of a solid is in general determined by the parameters of instantaneous elasticity, delayed elasticity with retardation time, flow with relaxation time and strength, the latter including resistance to plastic yield or fracture. A mechanical model which can represent these properties was proposed by Burgers [1]. Its constitutive equation was derived by Reiner [2]. In the present paper the thermodynamic theory of strength by Reiner and Weissenberg [3] is applied upon the strength behavior of a solid cylinder under the action of dynamic deformation by axial loads increasing in time at a given rate. According to this theory, failure will occur when the conserved part of the strainwork reaches a certain limit. It will be examined how the corresponding stress is affected by the rate of stress. It is known that, in general, with increased rate of stress the strength increases. This assertion will be examined under the conditions mentioned above.