近门槛区裂纹扩展曲面族的优化构建

描述裂纹扩展规律使用较广泛的是Paris公式,但对于接近裂纹扩展门槛值的数据点已不再适合用Paris公式。在本文中采用Donahue的三参数幂函数表达式描述da/dN-ΔK曲线。通过线性拟合相关系数的优化确定其中的3个系数,并得到拟合的裂纹扩展理论门槛值。采用弦截法进行优化求解,该方法具有收敛快、精度高的特点。根据裂纹扩展门槛值与应力比之间的关系,结合应力比对裂纹扩展速率影响的特点,提出了根据一组恒载下的裂纹扩展试验数据,构建变幅载荷下的P-R-da/dN-ΔK曲面族的方法,所构建的曲面族可为变幅和随机载荷作用下结构的疲劳断裂可靠性分析提供依据。

Optimal Construction of Surface Family of Crack Propagation Near Threshold Region

The Paris equation is widely used to describe crack propagation laws, but it is not appropriate to use it to describe data points near the crack propagation threshold value. Therefore the paper describes them using the Donahue three-parameter exponential function. The linear fitting correlation indices are optimized so as to determine the three among them and to gain the fitted theoretical crack propagation threshold value, which is, then, optimized using the secant method because of its fast convergence and high accuracy. According to the relationship between crack propagation threshold value and stress ratio, the influence of the latter on crack propagation rate being jointly considered, the paper puts forward a method for constructing the surface family under varied load according to a set of crack propagation test data under constant load. The surface family thus constructed serves as a foundation for the reliability analysis of structural fatigue cracks under varied and random loads.