Numerical Investigation Of Stress Intensity Factors For Hole-Edge Cracks Involving Contact Problem In Engineering

Components containing holes, such as bolted joints, are widely used in engineering structures. Cracks often exist at hole-edge because of stress concentration, contact interaction between components. Stress intensity factors are the important parameters in evaluating the crack growth, residual strength, and fatigue life of the cracked structures. Therefore, in order to ensure safety and make full use of the materials, accurate determination of stress intensity factors for cracked structures have great practical significance. The hole-edge crack problems involving contact interaction can be divided into two cases: (1) crack face contact problems, such as hole-edge crack problem under dynamic loading; and (2) problems of cracked components loaded through contact with another component, such as bolted joints with cracks. The problem of the hole-edge crack involving contact interaction is quite complicated. Usually, it is very difficult to obtain the analytical solution for the cracked problems. In this dissertation, the stress intensity factors of four hole-edge crack problems are investigated by using finite element method. The first problem is the numerical investigation of the stress intensity factors for the quarter-elliptical corner cracks at the bolt-hole of mechanical joints subjected to remote tension. The second one is the effect of contact between the crack surfaces on the dynamic stress intensity factors for a single edge horizontal crack at the center hole of a finite plate under compressive impact loading parallel to the crack. The third is the numerical investigation of the dynamic stress intensity factor for a single edge slant crack emanating from a circular hole in a finite plate subjected to compressive impact loading. The fourth is the numerical investigation of the stress intensity factors for a semi-elliptical surface crack at the T-root groove of a turbine disc under centrifugal loading.Finite element analysis models of the problems mentioned above are created by ANSYS. The square-root stress singularity around the crack front is simulated by quarter point singular elements. From classical theory of linear elastic fracture mechanics, the formulas for stress intensity factors for two-dimensional crack and elliptical crack are derived by using the displacement extrapolation method. These formulas provide a convenient method for the determination of stress intensity factors for those problems mentioned above.In the analysis of the first problem, contact interaction between the bolt-hole and the bolt (or pin) is considered, and the effects of the amount of clearance between the hole and the pin on the contact pressures and stress intensity factors are investigated. It is found that the contact pressure and contact region are variable in clearance. In the case of clearance being present, it is not appropriate that the contact interaction between the hole and the pin is replaced by applying uniform or cosine pressure distribution on bolt-hole boundary. Numerical results of the stress intensity factors show that the mode I stress intensity factors along the bolt-hole corner crack front increase with an increase in clearance between the hole and the bolt. These results indicate that the amount of clearance has a significant influence on the stress intensity factors for mode I, and its proper consideration is required to evaluate the crack growth, residual strength, and fatigue life of the cracked mechanical joints. At the same time, it is also discovered that the mode I stress intensity factor for bolt-hole corner crack reaches its maximum value at the deepest point. In the investigation of the second one, contact interaction between the crack surfaces is considered, and the effects of crack face contact on the dynamic stress intensity factors are investigated. The dynamic stress intensity factors with and without contact elements along crack surfaces are evaluated. Numerical results show that the negative mode I and a interpenetration or overlap between the crack surfaces may be prevented by taking account of the contact interaction of the crack edges, and crack face contact has a significant influence on mode I dynamic stress intensity factors. A more accurate analysis for a cracked problem under dynamic loading should include the contact interaction of the crack faces, otherwise the calculated dynamic stress intensity factors for mode I are significantly different from the true values. The third problem discusses the effect of the friction between the crack surfaces on the dynamic stress intensity factors. Results indicate that, with increasing friction, the tangential relative displacements at the crack edges and dynamic stress intensity factors for mode II decrease, and the frictional contact between the crack surfaces has a great influence on mode II dynamic stress intensity factors. If the friction between the crack surfaces is ignored, the mode II dynamic stress intensity factors may be overestimated. Additionally, it can be discovered that the friction at the crack edges has little influence on dynamic stress intensity factors for mode I, normal relative displacements, and contact pressures of the crack surfaces. In the fourth problem, finite element model with cyclic symmetry boundary conditions is used, and the contact interaction between the blade root and its groove is considered. Numerical results indicate that the mode I, II, and III stress intensity factors for semi-elliptical surface crack at the T-root groove of a turbine disc reach the maximum values of their individual modes at surface point, and the surface cracks can not be considered as pure mode I even if only centrifugal loadings are applied. Additionally, the mode I stress intensity factor along the corner crack front at T-root are investigated. Main result is the stress intensity factor for mode I reaches the maximum value at the deepest point of the corner crack. These results have a great practical valve for strength evaluation and fatigue life prediction of the cracked blade and disc.In conclusion, there are many problems involving crack and contact in engineering structures. The study of the paper may be regarded as a reference for solutions of the problems encountered in engineering practices.