Semiviscosity flow equation with variable parameters under superplastic tension conditions

Abstract

The accurate multinomial expression of the relation of$\lg \sigma - \lg \dot \varepsilon$ of the three typical superplastic alloys is given. Then by means of the analytic expression of the constitutive parameters$m(\dot \varepsilon )$ and$k(\dot \varepsilon )$, the semiviscosity flow equation in whichm andk are both variable can be obtained. And the equation includes the three parametersm _m ,m _k and η, which are related to the curve of$m - \lg \dot \varepsilon$. Finally, it is pointed out that the bigger the values ofm, η andm _m /m _k , the better the superplasticity of alloys. Furthermore, the Backofen's equation is only one of the special cases of semiviscosity flow equations with variable parameters.