Abstract The mechanical behavior of crack tip under mode I and mixed-mode I-II fatigue loading for commercial pure titanium at negative load ratios are carried out by finite element method in this paper. The effects of maximum fatigue load, load ratio, loading angle and normalized crack length on the mechanical behavior of crack tip are discussed. The change of mechanical behavior of crack tip is analyzed through the evolution of strain energy. The results show that the increase of maximum fatigue load and crack length increase the plastic strain accumulation at crack tip in mode I fatigue crack growth (FCG), which causes the crack tip release more fracture energy to drive crack growth and affect the distribution of stress-strain field. The decrease of load ratio also increases the plastic strain accumulation and the plastic energy dissipation at crack tip. In mixed-mode I-II FCG, the larger loading angle increase the resistance of crack deflection and cause more plastic strain accumulation at crack tip. After the crack deflects, the crack growth increases the crack tip plastic zone and the morphology of plastic zone changes continuously, which cause the crack growth path move away from the mode I crack growth direction. Different loading angles produce different crack growth paths, which deviates from mode I crack growth direction with the increase of loading angle.

中文翻译：

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负载荷比下 I 型和混合型 I-II 疲劳载荷下裂纹尖端力学行为的数值研究

摘要 本文采用有限元方法研究了商业纯钛在负载荷比下I型和混合型I-II疲劳载荷下裂纹尖端的力学行为。讨论了最大疲劳载荷、载荷比、载荷角和归一化裂纹长度对裂纹尖端力学行为的影响。通过应变能的演化来分析裂纹尖端力学行为的变化。结果表明,在I型疲劳裂纹扩展(FCG)模式下,最大疲劳载荷和裂纹长度的增加增加了裂纹尖端塑性应变的积累,导致裂纹尖端释放更多的断裂能驱动裂纹扩展并影响应力分布。 -应变场。载荷比的降低也增加了裂纹尖端的塑性应变积累和塑性能量耗散。在混合模式 I-II FCG 中，较大的加载角增加了裂纹偏转的阻力，并在裂纹尖端引起更多的塑性应变积累。裂纹偏转后，裂纹扩展使裂纹尖端塑性区增大，塑性区形态不断变化，导致裂纹扩展路径偏离I型裂纹扩展方向。不同的加载角度产生不同的裂纹扩展路径，随着加载角度的增加，裂纹扩展方向偏离I型裂纹扩展方向。裂纹扩展使裂纹尖端塑性区增大，塑性区形态不断变化，导致裂纹扩展路径偏离I型裂纹扩展方向。不同的加载角度产生不同的裂纹扩展路径，随着加载角度的增加，裂纹扩展方向偏离I型裂纹扩展方向。裂纹扩展使裂纹尖端塑性区增大，塑性区形态不断变化，导致裂纹扩展路径偏离I型裂纹扩展方向。不同的加载角度产生不同的裂纹扩展路径，随着加载角度的增加，裂纹扩展方向偏离I型裂纹扩展方向。