钛合金因其优异的力学性能被广泛用于航空发动机压气机叶片等关键零部件。随着工程技术的发展，很多承受疲劳载荷的钛合金零部件其服役寿命需达到10⁷周次以上，即属于超高周疲劳范畴。虽然钛合金的疲劳行为研究已有很多报导，但是钛合金的疲劳机理仍未完全揭示，特别是超高周疲劳裂纹萌生和初始扩展机制还存在争议；同时，有关钛合金的高周和超高周疲劳性能模型仍不完善，诸如试样几何形状、缺陷等因素对破坏机制和性能的影响也需进一步的研究。本论文首先在实验研究基础上，探究了TC17钛合金超高周疲劳裂纹萌生与初始扩展机理，研究了试样几何形状和缺陷对钛合金高周和超高周疲劳行为的影响，然后研究耦合滑移和形变孪生的晶体塑性模型以及钛合金超高周疲劳行为模拟方法；最后，提出一种高周和超高周疲劳强度评估的连续测试与分析方法，并用于钛合金、钢等多种材料的疲劳强度评价。主要研究成果如下：

（1）提出钛合金超高周疲劳裂纹萌生与初始扩展机理模型。研究发现TC17钛合金超高周疲劳裂纹萌生与早期扩展区域存在{101(_)1}孪晶和{101(_)2}孪晶形变孪晶现象。对于{101(_)1}孪晶，多数母体晶粒的基面滑移系Schmid因子较小，而对于{101(_)2}孪晶，多数母体晶粒的基面滑移系Schmid因子较大。进一步计算分析表明，纳米晶粒的形成增大了局部区域微结构的不均匀性，使得纳米晶区域以及纳米晶和粗晶区域的边界成为裂纹萌生和早期扩展的有利位置。在实验研究与分析基础上，提出钛合金超高周疲劳裂纹萌生和早期扩展是疲劳载荷过程中位错塞积引起的局部高应力诱导位错/孪晶等相互作用导致晶粒细化进而形成微裂纹，以及某些局部区域的粗晶粒内或晶界等形成微裂纹共同作用所致。

（2）建立关联试样几何形状和缺陷的钛合金高周和超高周疲劳强度模型。研究发现柱形试样疲劳裂纹通常萌生于试样内部，而板形试样疲劳裂纹通常萌生于试样表面；表面人工缺陷会显著降低TC17钛合金的疲劳性能；在表面人工缺陷相同时，柱形试样的疲劳性能高于板形试样。在实验研究基础上，通过引入试样几何形状影响参数，发展了试样几何形状和缺陷对疲劳强度影响的模型。当不超过临界缺陷尺寸时，缺陷对疲劳强度没有显著影响；超过临界缺陷尺寸时，缺陷尺寸和疲劳强度在对数坐标系下呈线性关系。预测疲劳强度与实验数据符合很好。

（3）发展了耦合多种机制的晶体塑性有限元模拟方法。首先，基于位错密度演化规律及位错孪生相互作用，建立了耦合位错和孪生行为的晶体塑性有限元模型。然后，结合实验研究，提出滑移带诱导裂纹萌生、沿滑移面和非滑移面的解理开裂、晶粒细化等不同机制计算模型，通过虚拟网格叠加方法实现晶体塑性有限元框架下晶粒细化过程的模拟，并纳入同一个晶体塑性模拟框架。最后，采用Voronoi方法建立基于微观统计数据的代表性体积单元，并通过文献、实验观测和拉伸曲线拟合相结合的方法获取晶体塑性参数。模拟结果表明，该方法不但可以模拟超高周疲劳过程中纳米晶粒的形成，而且可以模拟不同失效机制下裂纹的萌生过程，模拟的微结构和裂纹萌生特征与实验结果吻合很好。

（4）提出一种新的高周和超高周疲劳强度连续测试与分析方法。基于概率统计理论，建立了一种新的高周和超高周疲劳强度测试与分析方法——连续测试法（continuous testing method，CTM）。实验结果和数值实验结果表明，相比于标准中的升降法（up-and-down method，UDM），CTM评价的疲劳强度更为合理、可靠。特别地，CTM还可以同时测试多个样品，大大缩短测试时间，比如16个有效样品的测试周期与UDM相比可以缩短2/3以上。该方法对于分散性较小的钛合金材料的疲劳强度测试有较好效果，为本文所提疲劳强度模型的应用以及一般的疲劳强度测试工作提供了支持。

Titanium alloys have been widely used in some essential parts such as aeroengine blades due to their prime mechanical performances. With the development of engineering, many parts made from titanium alloys should endure more than 10⁷ cyclic loadings in service, i.e., enduring very high cycle fatigue. Although there have been many researches concerning fatigue behaviors of titanium alloys, the fatigue mechanisms for titanium alloys are still not fully disclosed, especially for the crack initiation and early propagation mechanism of very high cycle fatigue; at the same time, the models of high cycle and very high cycle fatigue performance of titanium alloys are still imperfect, and the effects of factors such as specimen geometry and defects on the failure mechanism and fatigue performances need further research. This dissertation first investigated the mechanism of very high cycle fatigue crack initiation and propagation of TC17 titanium alloy, and the high cycle and very high cycle fatigue strength models of titanium alloys related to specimen geometry and defects on the basis of experimental research. Then the crystal plastic model coupling slip and deformation twinning as well as the simulation method for very high cycle fatigue of titanium alloys are studied. Finally, a continuous testing and analysing method for high cycle and very high cycle fatigue strength evaluation is proposed and employed to evaluate the fatigue strength of titanium alloys, steel, and so on. The main research results are as follows:

(1) Fatigue crack initiation and early propagation model for titanium alloys of high cycle and very high cycle fatigue is proposed. It is found that {101(_)1} and {101(_)2} twin variants form in crack initiation and early propagation regions enduring very high cycle fatigue loading of TC17 titanium alloy. For {101(_)1} twin variants most parent grains have smaller Schmid factors for basal slip systems, while for {101(_)2} twin variants most parent grains have larger Schmid factors for basal slip systems. Further calculation and analysis show that the formation of nanograins increases the heterogeneity of local microstructure, rendering the nanograin regions and the boundary between them and coarse grains favorable locations for crack initiation and early propagation. Experimental research and analysis suggest that the initiation and early propagation of very high cycle fatigue cracks in titanium alloys can be attributed to the combined effects of the grain refinement formed in the localized high stress regions due to dislocation pile-up induced slip/twinning and their interactions, and the microcracks formed in coarse grains or grain boundary in local regions.

(2) High cycle and very high cycle fatigue strength model of titanium alloys associated with sample geometry and defects are established. It is found that the colume specimens usually fail from the interior, while the plate ones usually fail from the surface. The fatigue properties of TC17 titanium alloy can be significantly reduced by artificial surface defects. The fatigue performance of colume specimens are higher than that of plate specimens with the same artificial surface defects. On the basis of experimental research, a model for the influence of specimen geometry and defects on fatigue strength was developed by introducing a shape parameter for specimen geometry. When the critical defect size is not exceeded, the defect has no significant effect on fatigue strength When the critical defect size is exceeded, the defect size and fatigue strength exhibit a linear relationship in the logarithmic coordinate system. The results show that the prediction is in good agreement with experiments.

(3) A multi-mechanism coupled crystal plastic finite element method is developed. First, a crystal plastic finite element model coupling dislocation and twinning is established based on the dislocation evolution law and the interactions between dislocation and twinning. Then a computing model of different mechanisms including slip bands induced crack initiation, grain refinement induced crack initiation, and cleavage along slip planes and non-slip planes is proposed based on the experimental studies. The grain refinement process is achieved by a virtual mesh overlapping method. All aforementioned are incorporated into the same simulation framework. Finally, the Voronoi method was used to establish the representative volume element conforming to the microscopic statistical data, and the parameters of the crystal plasticity model were obtained through the combination of literature, experimental observation and tensile curve fitting. The simulation results show that this method can not only simulate the formation of nanocrystalline grains, but also simulate the crack initiation process with different failure mechanisms. The simulated microstructure and crack initiation characteristics are in good agreement with the experimental results.

(4) A continuous testing and analysing method for high cycle and very high cycle fatigue strength evaluation is proposed. A new fatigue strength evaluation method, CTM (continuous testing method), was established based on probability statistical theory. Experiments and simulation demonstrate that CTM is more reasonable and reliable than the up-and-down method (UDM) in standards. Especially, CTM can significantly improve the test efficiency compared to UDM by testing simultaneously, e.g., the testing period for 16 effective samples of CTM is 2/3 shorter than that of UDM. This method has a good effect on fatigue strength testing of titanium alloy materials with low dispersion, providing support for the application of the fatigue strength model proposed in this paper and general fatigue strength testing work.