Notch Effect Analysis: The axial stress on the cross-section of a bolt rod is uniform, with no stress gradient, meaning that crack initiation can occur across the entire section. However, the surface grains are less constrained by neighboring grains compared to inner grains, making them more prone to plastic deformation. According to modern fatigue theory, microcrack initiation and propagation result from cyclic plastic strain, and the extent of this deformation depends on the maximum shear stress component. As a result, fatigue cracks typically form on the plane of maximum shear stress at the free surface. When the applied stress slightly exceeds the fatigue limit, any crack initiated on the free surface will grow because the local stress there is higher than elsewhere. Consequently, only one primary crack source usually forms.
In contrast, threaded bolts have notches at the thread roots, which act as potential sites for fatigue crack initiation. Under an axial load (e.g., in the x-direction), the stress concentration at the notch causes the maximum tensile stress in the axial direction to increase to Rx > R. Meanwhile, the stress component Ry is minimal in front of the notch, while Rz is intermediate under plane strain conditions. Based on slip line field theory, Ry equals zero on the free surface, so the maximum shear stress becomes Smax = 1/2(Rx - Ry) = Rx/2. Plastic deformation is then confined to the xy plane. As we move away from the notch root, Rx decreases rapidly while Ry increases, causing Smax to drop quickly. This limits plastic deformation to a small area near the notch root. After repeated loading, when the accumulated plastic strain reaches a critical level, a fatigue crack initiates. Since the notch depth and curvature radius are consistent along the thread, the stress concentration is uniform, leading to multiple fatigue sources along the thread root. Higher stress concentrations or greater applied loads result in more fatigue sources. Therefore, improper surface treatment during threading can introduce defects or microcracks at the thread root, which become the starting point for fatigue cracks and eventually lead to failure under cyclic loading.
Finite Element Analysis: According to reference [9], high-strength bolts used in bolt-and-ball joint grids are mostly standard threads, ranging from M12 to M64. This study focuses on eight typical bolt sizes: M14, M20, M24, M30, M33, M52, and M60. These 40Cr high-strength bolts were analyzed using finite element software.
Computational Model:
1) Geometric Model: Based on previous research, the thread angle is often neglected since its effect on load distribution is minimal when the helix angle is less than 4b. Under axial loading, the bolt can be treated as an axisymmetric problem. All the bolt specifications studied here have angles below 3b, meeting the axisymmetric condition.
Unit Type and Meshing: Since the model is a 3D solid, the 20-node SOLID95 tetrahedral element was chosen. Mesh quality significantly affects simulation accuracy. Using surface elements and rotating them into 3D units may result in irregular meshing near the notch, reducing accuracy. To ensure precision, the 3D solid model was directly meshed, with automatic refinement applied at the notch region.
The stress concentration caused by the notch effect is a major contributor to the fatigue failure of high-strength bolts. Based on the analysis, the following conclusions can be drawn regarding improving notch sensitivity and enhancing fatigue performance:
1) Thread root notches exhibit the most severe stress concentration, acting as the primary site for fatigue crack initiation. Therefore, surface quality plays a crucial role in fatigue strength. Under process constraints, it's advisable to improve surface finish through cold working to reduce roughness.
2) Simply using higher-strength materials does not necessarily enhance notch sensitivity or fatigue performance. Instead, it is recommended to lower the bolt grade slightly while maintaining the same safety factor, ensuring a balance between strength, ductility, and toughness, which ultimately improves fatigue resistance.
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