自 Backofen 等人提出应变速率敏感性指数 m 值,并在实验的基础上建立起似粘性的超塑性本构方程以来,已历时近二十年了。由于不论是似粘性本构方程σ=kε~m 还是粘塑性本构方程σ=kε~n■~m,都把 m 视为常数。所以其适合的应变速率变化范围很窄,用予描述超塑性变形规律与实际偏差很大,也难以说明变形过程中的一些关键问题。因此,本文拟用余弦函数和负幂函数模拟 m—log■曲线,通过求解 m 值定义的微分方程和力学状态的微分方程,建立一套变 m 值的本构方程。对所得方程进行理论分析及实验比较。判明二者比似粘性方程和粘塑性方程的近似程度都高,而且用余弦函数模拟比用负幂函数模拟的近似程度更高。但是用负幂函数模拟所得的本构方程可直接写成用σ表达■的解析式,这对处理某些实际问题是必要的。此外,对变m值本构方程的实验建立等有关问题也予以讨论。 Since Backofen et al. Proposed the strain rate sensitivity index m and established the viscous superplastic constitutive equation based on the experiment, it has lasted for nearly two decades. Since either the viscous constitutive equation σ = kε ~ m or the visco-plastic constitutive equation σ = kε ~ n ~ ~ m, m is regarded as a constant. Therefore, the suitable range of strain rate is very narrow. It is difficult to describe some key problems in the deformation process by describing the superplastic deformation law and the actual deviation greatly. Therefore, in this paper, the cosine function and negative power function are used to simulate the m-log ■ curve. By solving the differential equation defined by m and the differential equation of mechanical state, a constitutive equation with variable m is established. The theoretical analysis of the equation and experimental comparison. It is found that both are more approximate than the viscous and viscoplastic equations, and the cosine function is more approximate than the negative power function. However, the constitutive equation modeled by a negative power function can be directly written as an analytic expression of σ, which is necessary to deal with some practical problems. In addition, the establishment of experiments on the constitutive equation of variable m is also discussed.