This study investigates the small fatigue crack propagation behavior of commercially pure titanium (CP-Ti) using thin-walled cruciform specimens under in-plane biaxial loading, considering the effects of biaxial ratio and phase angle. Increasing phase angle results in more secondary cracks merging with main cracks perpendicular to the rolling direction (RD) and transverse direction (TD), a phenomenon attributed to the rise in shear stress that accelerates main crack growth. Higher loading biaxiality or a lower phase angle leads to decreased crack propagation rates and increased biaxial fatigue life. Electron backscatter diffraction (EBSD) analysis reveals that when the maximum normal stress aligns with the RD, prismatic slip primarily governs crack propagation, thereby accelerating crack propagation rates. Conversely, alignment with the TD reduces prismatic slip activity and crack propagation rates. Under equi-biaxial loading, prismatic slip activity decreases further, and crack propagation is dominated by multiple slip and twinning, consequently resulting in the slowest propagation rates. Additionally, a higher proportion of prismatic slip under high phase angle also accelerates crack propagation. Finally, incorporating Findley equivalent stress into the Chapetti model, which considers the crack length-dependent threshold effect, a highly accurate biaxial small fatigue crack propagation rate model is proposed.

中文翻译：

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CP-Ti 在双轴载荷作用下薄壁十字形试样中的小疲劳裂纹行为


本研究考虑了双轴比和相位角的影响，使用薄壁十字形试样研究了商用纯钛 （CP-Ti） 在平面内双轴载荷下的小疲劳裂纹扩展行为。增加相位角会导致更多的次生裂纹与垂直于滚动方向 （RD） 和横向 （TD） 的主裂纹合并，这种现象归因于剪切应力的增加，加速了主裂纹的扩展。较高的载荷双轴性或较低的相位角会导致裂纹扩展速率降低并延长双轴疲劳寿命。电子背散射衍射 （EBSD） 分析表明，当最大法向应力与 RD 一致时，棱柱滑移主要控制裂纹扩展，从而加快裂纹扩展速率。相反，与 TD 对齐会降低棱柱滑移活性和裂纹扩展速率。在等双轴载荷下，棱柱形滑移活性进一步降低，裂纹扩展以多次滑移和孪晶为主，因此导致扩展速率最慢。此外，在高相位角下，较高比例的棱柱滑移也会加速裂纹扩展。最后，将 Findley 等效应力纳入考虑裂纹长度依赖阈值效应的 Chapetti 模型中，提出了一种高精度的双轴小疲劳裂纹扩展速率模型。