Based on state equation that stress is the function of strain, strain-rate and temperature, the paper establishes the differential constitutive equation used for analyzing load-stability and the variational constitutive equation used for analyzing geometry-stability during superplastic tensile deformation, which contain strain hardening index, strain-rate sensitivity index, temperature sensitivity index introducted for the first time and temperature undulation index introducted for the first time in the paper. And then, based on the universal condition of plastic elementary theory, the paper analyzes load-stability and geometry-stability under continuously rising temperature and under the non-uniform temperature along the axes of specimen respectively. The results prove the impact of continuously rising speed and non-uniform value of temperature on deformation stability is that the faster temperature rises and the more non-uniform temperature is, the smaller the corresponding uniform strain of load-stability and geometry-stability are; strain hardening index is the necessary condition of stability during superplastic tensile deformation, and geometry-instability will not happen when load-instability occurs, but happen when uniform deformation has lasted after load-instability; in the superplastic temperature field, constant temperature is not necessary condition of superplasticity, but during the deformation, the slower temperature rises and the more uniform temperature is, the more stable deformation is.
SONG Yuquan GUAN Zhiping WANG Minghui SONG Jiawang
Strain rate sensitivity index m is one of the vital mechanical parameters for deter- mining material superplasticity. In this paper, the existing formulae for measuring m value are reviewed, and it is found that the m values can be classified into three classes: mi under constant length, mv under constant velocity, and mP under con- stant load. The constraint equation of the generalized m value is established ac- cording to the tensile constitutive equation and the basis theory for plastic me- chanics. Based on three typical deformation paths, the m value is redefined. Fur- thermore, from the formula of generalized m value, the formulae for measuring mi, mv and mP are theoretically deduced. The precise methods with numerical simula- tion are presented. The results prove that the m value is a non-constant and its dependence on ε changes with the deformation path. Under different deformation paths, the m values calculated from the same formula are different. Using different formulae, the m values under the same deformation path are also different. There- fore, deformation path and corresponding formula should be given during the measurement of the m value. Moreover, it is explained theoretically and experi- mentally that why the mv value under constant velocity is sometimes negative but the mP value under constant load is sometimes lager than 1. The aim of the analysis and measurement of the m value is to facilitate the study on the relationship be- tween macroscopical mechanical laws and microscopic physical mechanisms during superplastic deformation.
