On plasticity, elastic relaxation phenomena, and a stress-strain relation which characterizes Schofield-Scott Blair media

Abstract

A generalization is given of the author's theory for plasticity phenomena. The theory includes the possibility of both stress and strain relaxation in the preplastic range. Methods of non-equilibrium thermodynamics are used. The plasticity phenomenon is explained by introducing a physical assumption concerning the phenomenological coefficients. A yield function is proposed which includes the Bauschinger effect and strain hardening. If the free energy f has the form f=f ⁽¹⁾+f ⁽²⁾, where f ⁽¹⁾ is a function of the temperature and the elastic strains and f ⁽²⁾ is a function of the temperature and the inelastic strains, and if cross effects between the plastic flow and elastic relaxation phenomena may be neglected, the proposed yield function is such that the derivative with respect to time of the deviator of the plastic strain tensor is given by $\eta \left( {{{\partial \Phi } \mathord{\left/ {\vphantom {{\partial \Phi } {\partial _{\tau \alpha \beta } }}} \right. \kern-\nulldelimiterspace} {\partial _{\tau \alpha \beta } }}} \right)$, where Φ is the yield function, ταβ is the mechanical stress tensor, and η is a coefficient which vanishes in the preplastic range. If the equations of state may be linearized the proposed yield function reduces to a function which is analogous to a yield function proposed by Freudenthal. If the plastic flow phenomenon is not associated with changes in the microscopic structure of the medium the proposed yield function reduces to the Von Mises function. It follows from the theory that in a first approximation elastic relaxation phenomena in the preplastic range may be described by the equation for Poynting-Thomson media (standard linear solids). An equation which characterizes Schofield-Scott Blair media is also derived from the developed theory.