疲劳裂纹扩展曲线的正交多项式与三参数指数函数拟合法

Orthogonal Polynomial and Three Parameter Exponent Function Model to Treat Fatigue Crack Growth Curve

回顾了疲劳裂纹扩展a -N曲线的拟合方法。对三参数幂函数拟合方法进行了改进 ,这种方法避免了原方法搜索范围受局限的特点 ;提出了两种新的a-N曲线拟合方法 :正交多项式法和指数函数法 ,并给出了参数估计算法。正交多项式法拟合a -N曲线 ,其相关系数随最高次数的增加而提高 ,指数函数法比改进三参数幂函数拟合精度高 ;指数函数法与正交多项式法相比 。

According to the principle of maximum linear relation coefficient, an improved power function model with three parameters to describe a-N curves is firstly developed. Compare with the previous method, its merit lies in that it breaks up the parameter value range limit on the previous method. Then, on the basis of theory of Taylor series, an orthogonal polynomial model of a-N curves is proposed to have more polynomial degree, and higher relation coefficient. A new exponent function being able to describe the initial, the stable and the unstable stages of a-N curves is presented by the principle of maximum linear relation coefficient. This model may give higher fitting precision than the power function method with three parameters. Compared with the polynomial model, the three parameter exponent function model has clear physical meaning. Finally, a successful application and contrast analysis example of these three models is given.