A mechanical analysis of the constitutive parameters in the semiviscosity flow equations under the superplastic tension conditions

Based on the review of the history of research on the constitutive parameters m and k of the semiviscosity flow equations under the superplastic tension conditions, the differential relation including m and k as variables is built. By means of the curve which imitates the relation between strain-rate sensitive index m and strain-rate , the analysis expression of m(), k() and the relations of k vs. m is theoretically obtained. It has been proved that m is the parameter of strain-rate sensitivity and the value of k is variable that can be determined with m . Therefore, a mechanical analysis theory on m and k is established. The theoretical curves fit well the practical curves for three types of alloys with superplastic property. The multinomial expression of curves m() and k() , which are accurately imitated for the above alloys, is given for the sake of quantitative calculation.

Based on the review of the history of research on the constitutive parametersm andk of the semiviscosity flow equations under the superplastic tension conditions, the differential relation includingm andk as variables is built. By means of the curve which imitates the relation between strain-rate sensitive indexm and strain-rate ε, the analysis expression ofm(ε),k(ε) and the relations ofk vs.m is theoretically obtained. It has been proved thatm is the parameter of strain-rate sensitivity and the value ofk is variable that can be determined withm. Therefore, a mechanical analysis theory onm andk is established. The theoretical curves fit well the practical curves for three types of alloys with superplastic property. The multinomial expression of curvesm(ε) andk(ε), which are accurately imitated for the above alloys, is given for the sake of quantitative calculation.