Research On Fatigue And Fracture Reliability Based On Stochastic Finite Element Method

Fatigue is the main failure form of components and structures under variable amplitude loading. It is reported that about 80 percent failures of components and structures in modern industry fields such as axle, connecting rod, gear, steam turbine blade, bolt, spring, pressure vessel, pipe, vehicle, plane, offshore platform, submarine and jointed steel bridge are caused by fatigue. For the reason of machining, erode and abrasion, engineering structures and components are inevitably containing cracks or some defects like crack. These cracks or defects expand under variable amplitude loading and cause the fracture of structures and components at last. There is a dispersal of the fracture behavior of structures and components because of the uncertainties on material properties , the component geometry, load history, environment condition, crack propagation direction and length. It's important to ensure the fracture probability keep the minimum under the influence of these random factors. The reliability analysis is made for plane structures which contain the I mode crack and the I-II mixed-mode crack by application of Stochastic Finite Element Method(SFEM) and the improved first-order second-moment method. There are five chapters in this thesis and the details are as follows: Chapter One The engineering background of the reliability of fatigue and fracture is summarized and the development of the fatigue and fracture reliability in our country and outside is emphasized and the theoretical meaning and the applicated engineering meaning of this thesis is discussed. Chapter Two Algorithms of SFEM are summarized and the ideas as well as the merits and shortcomings of TSFEM ,PSFEM and NSFEM are discussed and the improved first-order second-moment method is introduced. Chapter Three The application of Monte Carlo Method in the reliability of fatigue and fracture is presented. The generation of pseudo-random number and sample of variables are emphasized. Chapter Four The reliability analysis is made for plane structures which contain the I mode crack and the I-II mixed-mode crack by application of SFEM and the improved first-order second-moment method at the view of probability theory and mathematical statistics in which main uncertainties are regard as random variables. Monte Carlo Simulations are made for fatigue cracks and the results are compared with results which are get by SFEM, the sensitivity analysis is presented finally. Chapter Five Draw a conclusion to this thesis and prospect is proposed for future work. Conclusions are as follows: 1. Based on the theory of fracture mechanic and by means of triangular quarter-point elements, the Stress Intensity Factors(SIF) are calculated with good precision and high efficiency. 2. The reliability model for the fatigue cracks expanding life is presented by means of SFEM and the reliability analysis in which the most sensitive uncertainties regard as random variables. The method is fit for any fatigue cracks and any structures and components and can be considered the random of material properties , the component geometry, load history, environment condition, crack propagation direction and length and to discuss the reliability of any design life or any crack length. This is valuable for engineering design. 3. It is found that crack angles are becoming smaller and the end crack angle is becoming zero which make the I-II mixed mode crack changing to the most...