为了研究微结构对高循环疲劳分散性的影响, 发展了考虑多晶材料微结构特征的极值概率分析方法. 首先, 通过Voronoi算法构造了近似多晶合金微结构的随机多晶胞元模型. 其次, 应用基于内变量的晶体塑性本构理论, 模拟了不同应变幅下处于结构表面和内部多晶微结构胞元的循环应力应变响应. 通过计算有限数量的随机多晶微结构, 采用疲劳指示参数表征剪应变主导的裂纹萌生驱动力, 从而得到不同应变及边界约束情形下的疲劳指示参数分布. 最后, 应用极值概率理论分析了多晶胞元中疲劳指示参数的极值分布规律. 以TC4合金为例, 计算结果表明: 高循环疲劳分散性随应变幅降低而上升, 且在弹性极限附近变化显著; 此外, 相比于构件内部晶粒, 处于表面的晶粒具有更高的裂纹萌生驱动力.

Empirical approaches to characterize the variability of high cycle fatigue have been widely used. However, little is understood about the intrinsic relationship of randomness of microstructure attributes on the overall variability in high cycle fatigue. The ability of quantifying the dispersivity of high cycle fatigue with physics based computational methods has great potential in design of minimum life and can aid in the improvement of fatigue resistance. To investigate the effects between microstructure attributes and high cycle fatigue dispersivity, the microstructure-sensitive extreme value probabilistic framework is introduced. First, the Voronoi algorithm is used to construct random polycrystalline microstructure representative volume elements. Different kinds of periodic boundary conditions are proposed to simulate the interior and surface constraints in polycrystalline microstructure representative volume elements. Then mechanical responses of both interior and surface microstructure representative volume elements under different strain amplitudes are simulated by internal state variable based crystal plasticity. The fatigue indicator parameter is introduced to characterize the driving force for fatigue crack formation dominated by maximum shear plastic strain amplitude. By computing a limited number of random polycrystalline microstructure representative volume elements, the distributions of fatigue indicator parameter under different strain amplitudes are obtained and analyzed with extreme value probability theory. The study with a kind of titanium alloy with material grade TC4 supports that the high cycle fatigue dispersivity increases with the decrease of the strain amplitude, especially under elastic limit. The extreme value of fatigue indicator parameter from random polycrystalline microstructure representative volume elements correlates well with the Gumbel extreme value distribution. Besides, the lower the average stress under different strain amplitudes, the fewer grains in polycrystalline microstructure representative volume element yield. Moreover, the grains on surface tend to have higher probability to initiate fatigue cracks and lower dispersivity in fatigue crack formation.