a-N曲线的四参数方程拟合

用目前普遍采用的三参数方程对 5组裂纹扩展a N试验数据进行拟合时发现 ,该方程对裂纹扩展全过程试验数据的拟合精度不高 ,特别是当N接近断裂寿命时误差变得很大。为此 ,提出了四参数方程 ,将确定方程中未知参数的问题化为求多元函数极小点的数学规划问题 ,用四参数方程来拟合裂纹扩展全过程a N试验数据时可得到比三参数方程更好的拟合精度。

Fitting a-N Curve with Four Parameter Equation

When employing the currently widely used three-parameter equation to fit 5 groups of a-N test data of crack propagation, it is found that the fitting precision of the equation for the whole course test data of crack propagation is not high. Especially when N approaches the fracture life, the fitting error is getting very large. Therefore, the authors put forward a four-parameter equation, in which the unknown parameters can be obtained by evaluating the extreme value points of poly-function. It is indicated that when fitting the whole course a-N test data of crack propagation, the fitting precision of the four-parameter equation is higher than that of three-parameter equation.