疲劳裂纹形核寿命的细观概率模型

裂纹形核是结构疲劳损伤演化的初级阶段。基于Tanaka-Mura微裂纹形核机制,提出恒幅交变载荷下结构表面疲劳裂纹形核寿命的细观概率模型。设细观尺度的晶粒尺寸、晶粒取向欧拉角为随机变量,借助Schmidt因子建立细观主应力与分解切应力之间的关系。考虑到晶粒取向随机性和紧邻晶粒影响因素,导出分解切应力变程的概率分布。进一步运用矩法和次序统计量模型获得任一晶粒中疲劳裂纹形核寿命和结构热区晶粒群多裂纹分散形核寿命的概率分布。数值算例验证了所提模型与方法的可行性和合理性。新模型在裂纹形核寿命研究中引入了细观物理参数和几何参数的概率统计信息,可为多晶体金属结构件的疲劳可靠性评估和抗疲劳概率设计开辟精细化分析的新途径。

Meso-scale Probabilistic Model of Fatigue Crack Nucleation Life

Crack nucleation is an initial stage of damage evolution for high cycle fatigue of metallic material. Based on the Tanaka-Mura crack nucleation mechanism, a meso-scale probabilistic model is proposed for the analysis of surface crack nucleation life under constant amplitude loading. Let the grain size and Euler angle of crystal orientation be random variables, and the relationship between meso-scale principal stress and resolved shear stress is established by means of the Schmidt factor in the most possible sliding direction. The distribution function of resolved shear stress range is derived in consideration of grain orientation randomness and influence factors of nearest-neighbor grains. Furthermore, the probability density functions of crack nucleation lifes in any grain and grain group at the hotspot are derived by means of the moment method and order statistics models. A numerical example is given to show the feasibility and rationality of the proposed model and approach. The proposed model introduces probability statistic information of physical and geometrical variables on meso-scale, which can give a new path for probabilistic fatigue life assessment and anti-fatigue probabilistic design of polycrystalline metals structures.