Although the emergence of fracture mechanics has only been half a century, with the unremitting efforts of scholars all over the world, it has developed rapidly and has been widely used in engineering applications. In terms of fracture criterion, there are stress intensity factor Fracture Criterion and energy release rate criterion to analyze elastic fracture behavior. COD and J-integral theory can be used to study elastic-plastic fracture behavior. These fracture criteria are different, but they all have certain value in engineering application.
In the aspect of fatigue crack life prediction of spur gears, based on the fatigue cumulative damage theory, the nominal stress method, local stress-strain method and field strength method are developed to predict the crack initiation life; In predicting crack growth life, there are cumulative damage model under constant amplitude cyclic stress and crack growth model under variable amplitude loading. In these theories, stress intensity factor has always been the focus of research. This chapter focuses on the stress intensity factor theory and crack propagation criterion used to study the fatigue crack of spur gear root.
There are various defects in actual parts, including cracks, pores, impurities, knife marks left in the processing process and so on. In terms of cracks, there are hot cracks, reheat cracks, cold cracks, welding cracks and corrosion cracks. Cracks are classified from the geometric and mechanical characteristics of cracks in fracture mechanics.
According to the analysis of mechanical characteristics, there are three types, as shown in the figure:
Type I crack (open type): it can be seen from the above figure that the open type crack is formed by the relative displacement and angle of the crack surface under the action of tensile stress perpendicular to the crack surface. The characteristic is that the point at the crack front is not related to the displacement component in the stress direction after the crack opens.
Type II crack (sliding open type): the stress characteristic of sliding open type crack is that the shear stress is parallel to the crack surface and perpendicular to the crack front, resulting in relative sliding of the crack surface along the direction of shear stress to form a crack, and the sliding displacement perpendicular to the crack front is discontinuous.
Type III crack (tearing type): the tearing type crack is generated under the action of shear stress parallel to the crack surface and parallel to the crack front, which causes the crack surface to form a crack by relative sliding outside the crack surface (i.e. in the shear stress direction). The displacement components of the upper and lower crack surfaces in the shear stress direction are discontinuous.
According to the geometric relationship between crack and solid, it can be divided into the following three types:
(1) Through crack: through crack refers to the thickness of the crack leading edge penetrating through the entity in a certain direction. However, in the actual treatment process, extending the crack leading edge beyond the entity thickness is generally regarded as a through crack, and the crack leading edge is treated as an ideal straight line. The actual crack leading edge is mostly curved or toothed, and the straight line treatment is conservative.
(2) Surface crack: the surface crack is located on the solid surface or the crack depth is very small relative to the solid thickness. In most cases, it is regarded as a semi elliptical flake crack in crack analysis and simulation. Semi elliptical cracks are mostly caused by pitting or surface defects caused by surface contact.
(3) Deep buried crack: deep buried crack means that the crack is located inside the entity, and no crack information can be obtained from the appearance of the entity. Deep buried cracks are caused by bubbles and impurities produced in the casting process, which will develop into cracks under the action of external load.