冲击韧脆转变曲线数学模型的选择

分别利用Boltzmann函数和双曲正切函数两种数学模型对系列冲击试验中的试验数据进行拟合，得到了材料的冲击韧脆转变曲线，比较了这两种数学模型的优劣和适应性，并对数学模型中各参数的选择进行了讨论。结果表明：Boltzmann函数和双曲正切函数这两种数学模型是同一函数的不同表达式，在拟合冲击韧脆转变曲线过程中都具有同样良好的效果；当曲线上、下平台不明显时，合理地假设上、下平台值，是准确预测韧脆转变温度的前提。

Selection of the Mathematical Model on Ductile-brittle Transition Temperature Curve of Impact Test

Serial impact test datas were fitted with Boltzmann function and hyperbolic tangent function mathematical model separately and the ductile-brittle transition temperature curve were gained. Quality and applicability of these two models were compared and parameters selection of these two models were discussed. The results show that mathematical model of Boltzmann function and hyperbolic tangent function were two different expressions of the same function. They had equal effects on ductile-brittle transition curve fitting. When high level value and low level value were not obvious, it was the precondition of determining accurately ductile-brittle transition temperature to suppose logically high level value and low level value.