纤维桥连疲劳裂纹扩展的首次穿越扩散过程模型

纤维桥连效应对纤维加强基体复合材料疲劳过程中的裂纹增长具有重要影响。由于纤维桥连疲劳裂纹相关的数据呈现出一定的统计特性,因此本文建立了纤维桥连疲劳裂纹扩展的首次穿越扩散过程随机模型。首先基于Paris定律,考虑到材料的非均匀性和外载的随机性,将纤维桥连疲劳裂纹增长过程假定为扩散的Markov过程,且应用随机平均法,建立了转移概率密度满足的FPK方程;其次建立了首次穿越纤维桥连疲劳裂纹扩展时间的条件矩应满足的微分方程,并且解得第k阶条件矩。从数值结果得出,建立的随机模型对于模拟纤维桥连是比较有效的。

FIRST CROSSING DIFFUSIVE PROCESS MODEL OF FIBER-BRIDGING FATIGUE CRACK GROWTH

Fiber-bridging effect has significant influnce on the crack growth of fiber reinforced matrix composites.A first crossing diffusive process stochastic model of fiber-bridging fatigue crack growth was established on account of statistical characteristics of related data of the fiber-bridging fatigue crack.First,based on Paris law,the material inhomogeneity and loads randomicity were considered,the fiber-bridging fatigue crack growth process was assumed to be a diffusive Markov process and the stochastic averaging method was employed to establish the FPK equation with the transition probability function satisfied.Second,the differential equation,of which the kth order conditional moment of the first crossing fatigue crack growth time is satisfied, was established and the kth order conditional moment was solved.From the numerical results,the established stochastic model is comparatively effective for simulating the fiber-bridging effect.