疲劳失效作为工程领域中的重要失效形式，对设备运行和人员安全构成严重威胁，并伴随着显著的经济社会损失。Paris公式已确立稳态疲劳裂纹扩展速率与应力强度因子幅度间的关联，并被广泛用于描述疲劳裂纹扩展现象。然而，作为经验公式的Paris公式，其物理机制尚存争议，尤其在不同的温度环境下，其背后的物理机制更为复杂。因此，本研究将与变形和损伤密切相关的位错作为切入点，在理想的各向同性单晶中，通过将位错运动作为裂纹扩展的模型，探索疲劳裂纹扩展行为规律与机理。本论文运用离散位错动力学（DDD）方法，主要研究内容及研究成果如下：

（1）发展高效且精确的加速算法以应对疲劳模拟过程中多计算步数与高位错密度对计算时长的挑战。在DDD中，位错相互作用是计算的耗时主体，若采用传统的一对一计算方法，几乎无法高效地完成对疲劳裂纹扩展的模拟任务。因此，我们考虑使用快速多极子算法（FMM）和快速傅里叶变换（FFT）来快速计算位错相互作用。尽管每种算法已经有相关的以位错为对象的应用研究，但是在同一框架下两种算法之间的效果差异并不明确。因此在对FMM进行网格优化，以及对FFT进行应力计算优化的基础上，我们对FMM和FFT在计算相互作用时的计算效率和误差进行了对比。结果表明，FMM在此两方面均显著优于FFT，实现了计算n个位错时，将计算复杂度从O (n²)降低至O (n)。

（2）提出不含经验参数且易于应用的统一应力强度因子幅度ΔK_eff以准确描述应力比对疲劳裂纹扩展的影响。在研究Paris指数m的固有物理意义之前，我们需先考虑外部因素对疲劳裂纹扩展的影响。现有的应力比影响模型大多是基于数据的经验模型或者在使用上并不方便。为此我们基于疲劳裂纹扩展门槛值随着应力比线性变化的特点，提出控制裂纹开闭的参数K₀，并推广至疲劳裂纹扩展阶段，提出ΔK_eff的表达式。该公式物理意义明确，表达简洁，便于应用，且得到了实验验证。相比于ΔK我们推荐使用ΔK_eff，并 在运用Pairs公式时，对ΔK_eff进行归一化处理，使得Pairs公式中的指前系数C₀拥有明确的物理意义，这样仅剩m的物理意义需要进一步研究。

（3）提出Paris指数m与位错滑移速率关系中的标度律指数相关。现有的Paris指数模型丰富了我们对单个m值的理解，但是如何理解连续变化的Paris指数的背后物理意义仍不清楚。我们将DDD中通常所采用的固定增殖时间扩展到和分解切应力相关的函数，这背后与滑移速率的标度律关系相关。采用不同的标度律关系，我们发现应力强度因子幅度通过影响位错源的增殖和位错在裂纹尖端前的运动来影响疲劳裂纹扩展，并进一步发现应力相关的位错增殖时间与Paris指数相关。

（4）揭示高温下的疲劳裂纹扩展行为规律和机理。我们先从单轴拉伸下的蠕变变形入手以阐明高温下位错滑移和攀移运动的作用机制。在较高应力状态下，尽管攀移在整体应变中的贡献较小，但其在高温下协助位错滑移，加速了裂纹扩展。此外，我们观察到高温下裂尖位错密度虽低，但裂尖屏蔽效应反而增强，这与位错分布密切相关。

上述工作不仅为理解疲劳裂纹扩展行为提供了新的模型，也为准确预测疲劳裂纹扩展提供了理论工具，有助于在工程应用中预防和减少疲劳失效问题，降低经济社会损失。

As a significant failure mode in the engineering field, fatigue failure poses a severe threat to equipment operation and personnel safety, accompanied by significant economic and social losses. The Paris equation has established the correlation between the steady-state fatigue crack growth rate and the stress intensity factor range, and it is widely used to describe fatigue crack growth. However, as an empirical formula, the physical mechanism of the Paris equation is still controversial, especially under different temperature conditions, where the underlying physics becomes more complex. Therefore, this study takes dislocation, which is closely related to deformation and damage, as an entry point. In an ideal isotropic single crystal, we explore the laws and mechanisms of fatigue crack growth behavior by modeling dislocation movement as crack propagation. Using the discrete dislocation dynamics (DDD) method, the main research contents and findings of this dissertation are as follows:

(1) Developing an efficient and accurate acceleration algorithm to address the challenges posed by the large number of computational steps and high dislocation density in fatigue simulations. In DDD, dislocation interactions are the main computational burden. Traditional one-to-one calculation methods are almost infeasible for efficiently simulating fatigue crack growth. Therefore, we consider using the fast multipole method (FMM) and fast Fourier transform (FFT) to rapidly calculate dislocation interactions. Although each method has been studied for dislocation-based applications, the differences in their effectiveness within the same framework are unclear. Based on grid optimization for FMM and stress calculation optimization for FFT, we compared the computational efficiency and errors of FMM and FFT in calculating interactions. The results show that FMM significantly outperforms FFT in both aspects, reducing the computational complexity from O(n²) to O(n) when calculating n dislocations.

(2) Proposing a unified stress intensity factor amplitude ΔK_eff, without empirical parameters and easy to apply, to accurately describe the effect of stress ratio on fatigue crack growth. Before exploring the inherent physical meaning of the Paris exponent m, we need to consider the external factors affecting fatigue crack growth. Most existing models for the effect of stress ratio are based on empirical data or are inconvenient to use. Therefore, based on the linear variation of the fatigue crack growth threshold with stress ratio, we propose a parameter K₀ that controls crack opening and closing, and extend it to the fatigue crack growth stage, deriving the expression for ΔK_eff. This formula has clear physical meaning, concise expression, and is easy to apply, validated by experiments. Compared to ΔK, we recommend using ΔK_eff and normalizing it when applying the Paris equation, giving the pre-exponential factor C₀ in the Paris equation a clear physical meaning. Only the physical meaning of m remains to be further studied.

(3) Proposing that the Paris exponent m is related to the scaling exponent in the relationship between dislocation slip rate and stress. Existing Paris exponent models have enriched our understanding of a single m value, but how to interpret the physical meaning behind continuously varying Paris exponents remains unclear. We extend the fixed nucleation time typically used in DDD to a function related to the resolved shear stress, which is linked to the scaling relationship of slip rate. Using different scaling relationships, we find that the stress intensity factor range affects fatigue crack growth by influencing the nucleation of dislocation sources and the movement of dislocations ahead of the crack tip. Furthermore, we discover that stress-dependent dislocation nucleation time is related to the Paris exponent.

(4) Revealing the laws and mechanisms of fatigue crack growth behavior at high temperatures. We started by investigating creep deformation under uniaxial tension to clarify the mechanisms of dislocation slip and climb at high temperatures. Under high stress conditions, although climb contributes less to overall strain, it assists dislocation slip at high temperatures, accelerating crack growth. Additionally, we observe that although the dislocation density at the crack tip is low at high temperatures, the crack tip shielding effect is enhanced, closely related to dislocation distribution.

The above work not only provides a new model for understanding fatigue crack growth behavior, but also offers theoretical tools for accurately predicting fatigue crack growth. It contributes to preventing and reducing fatigue failure problems in engineering applications, thereby reducing economic and social losses.