描述钢淬透性的一个新数学模型

提出了一个新的描述钢淬透性的数学模型及淬透性表征参数．根据端淬实验数据和实验曲线导数变化规律，用线性试探法建立了端淬曲线微分方程，然后解得硬度分布函数．硬度分布函数将端淬曲线描述为直线段和曲线段构成的分段函数：直线段描述试样端部获得全部马氏体区域的硬度，在此区域硬度保持恒定最高值；在曲线段硬度递减，最后趋近恒定最低值．钢的淬透性值用数学参数来表示，它数值上等于从原点到硬度分布曲线拐点的距离．用非线性模拟程序代入实验值获得了淬透性值．模拟结果表明，所获得的模型与实验值吻合很好．

A NEW MATHEMATICAL MODEL FOR HARDENABILITY OF STEELS

A new mathematical model and a parameter describing the hardenability of steels were suggested. A differential equation of the Jominy curves has been constructed according to the Jominy experimental data and the change of derivative of the Jominy curve. The linear trial method was used to choose the optimal type of function. The model for calculating the hardness distribution has been described as the subsection functions consisting of straight line and curve. The straight depicts the hardness of the entire martensite region, which has a constant maximum value. In addition, the hardness is continuously reduced in the region of the curve until the hardness approaches a minimum value. The hardenability of steel has been expressed as a parameter equal to the distance from origin to inflexion of Jominy curve in numerical value, which can be obtained by a method of the non-linear curve fitting to the Jominy test data. Very good agreements have been obtained between the simulated curves and the experimental measurements.