Notch Effect Analysis: The axial stress across the cross-section of a bolt rod is uniform, without any stress gradient, which implies that cracks can potentially initiate over the entire cross-section. However, the surface grains are less constrained by neighboring grains compared to those in the interior, making them more prone to plastic deformation. According to modern fatigue theory, microcrack initiation and propagation are driven by cyclic plastic strain. The extent of this deformation depends on the maximum shear stress component, meaning that fatigue cracks typically form on the plane of maximum shear stress at the free surface. When the applied stress slightly exceeds the fatigue limit, even a small crack forming on the surface can lead to further propagation, as the local stress becomes higher than elsewhere. Consequently, only one primary crack source usually develops.
In contrast to a smooth bolt, the thread root acts as a potential site for fatigue crack initiation due to stress concentration. Under an axial load (e.g., in the x-direction), the stress at the notch root is amplified, resulting in a higher tensile stress (Rx > R). Meanwhile, the stress in the y-direction (Ry) is minimal, while Rz lies in between under plane strain conditions. Based on slip line field theory, Ry equals zero on the free surface, so the maximum shear stress is Smax = ½(Rx - Ry) = Rx/2. Plastic deformation is thus 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. Over time, with repeated loading, when cyclic plastic deformation reaches a critical level, fatigue cracks begin to form. Since the depth and radius of curvature of the thread notch are consistent, stress concentration is uniform, leading to multiple crack initiation sites along the notch root. The higher the stress concentration or applied load, the more fatigue sources develop. If the thread surface is improperly treated, defects or microcracks may form at the root, acting as initial crack sites that propagate under alternating loads, ultimately causing fatigue failure.
Finite Element Analysis: According to reference [9], high-strength bolts used in bolt-and-ball joint grids are typically standard threaded. The specifications range from M12 to M64. This study focuses on eight typical bolt sizes: M14, M20, M24, M30, M33, M52, and M60. Finite element software was used to analyze 40Cr high-strength bolts of these specifications.
Computational Model:
1) Geometric Model: Based on previous research on threads, the helix angle's influence is often neglected. Some studies suggest that if the thread angle is less than 4°, it has minimal impact on the load distribution. Under axial loading, the bolt can be simplified as an axisymmetric problem. All the bolt specifications studied here have angles below 3°, meeting the axisymmetric condition.
Unit Type and Meshing: Since the model is a 3D solid, the 20-node SOLID95 tetrahedral element was selected. Meshing significantly affects calculation accuracy. Using surface elements and rotating them into body units leads to irregular meshing near the notch, reducing accuracy. Therefore, the three-dimensional solid model was directly meshed, with automatic refinement applied at the notch region.
The stress concentration caused by the gap effect is a major contributor to fatigue failure in high-strength bolts. To improve notch sensitivity and fatigue performance, the following conclusions were drawn:
1) Thread root stress concentration is the most severe, serving as the main crack initiation site. Therefore, surface quality has a significant impact on fatigue strength. Whenever possible, improving surface finish through cold working and reducing surface roughness can enhance fatigue life.
2) Simply using higher-strength materials does not necessarily improve notch sensitivity or fatigue performance. It is recommended to reduce the grade of high-strength bolts under the same safety factor, achieving a better balance between strength, ductility, and toughness, thereby improving fatigue performance.
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