Fatigue Life Distribution Of Notched Component And Its Sensitivity Analysis

There are numerous notched components in engineering structures. Their fatigue life or strengthdetermine that of structures. So complete and accurate data of fatigue life distribution of notchedspecimens is the basis for the fatigue reliability analysis of structures. Due to the variety of types anddimensions of notched specimens, the cost involved in getting their fatigue life distribution throughexperiments is very high. On the contrary, the cost for the fatigue life distribution of smoothspecimens is quite small. So the research in predicting the fatigue life distribution of notchedspecimens from fatigue life test data of smooth specimens has significant value in both theory andpractical engineering.There are many factors that cause the randomness of fatigue life of notched specimens. Two ofthem are considered in this work. They are the dispersion of local stress and strain, and thenon-homogeneity of microstructure. The randomness of fatigue life induced by the latter can beobtained from the fatigue life test data of smooth specimens. So the research emphasis is placed onthe dispersion of local stress and strain.In the beginning, based on the weakest-link theory and the stress field intensity approach, a newlocal stress and strain parameter, fatigue effective stress, is proposed. It can express the fatigueseverity of notch in the sense of probability. Employing this parameter to refer to the fatigue life testdata of smooth specimens would lead to the fatigue life of notched specimens. This model reflects theinfluence of both stress gradient and component size on the notched specimen fatigue life.Then, the calculation for the dispersion of local stress and strain using the stochastic finite elementmethod(SFEM) is studied, including four parts. Firstly, based on the relation between the elasticmodulus and the hardness，the correlation characteristics of the elastic modulus random fields for twometals are determined, by experimental measurements of Rockwell hardness values at a series ofpoints on the specimen and a statistical analysis of the test result utilizing the correlation function.Secondly, the Galerkin-type procedure for Karhunen-Loève expansion of a random field isinvestigated. The shape function of the random field element is chosen to be the basis to implementthis procedure. Details regarding how to realize the procedure when the random field mesh iscomposed of quadrilaterals are given. The corresponding algorithmic routine is compiled. A exampleshows that the accuracy of this routine is high, meeting the requirement of engineering computation.Thirdly, the perturbation stochastic finite element method based on the variational principle is studied.According to the idea of this method, a stochastic finite element calculation program for two dimensional plane stress problem is developed. The precision of this program is moderately satisfying.Fourthly, A method for the probability distribution of the stress at a single point at notch root isproposed. In this method, the factors which affect the probability distribution of the stress areseparated into two parts, the load and the material. The contribution of the material is approximatelyequivalent to be a normal random variable. Then the stress can be expressed as a linear combinationof the random variable of the load and the random variable of the material. Thus the probabilitydistribution of the stress can be easily obtained. This treatment is accurate and effective.Finally, the calculation model based on SFEM for fatigue life distribution of notched specimens isestablished. In this model, the dispersion of the fatigue effective stress worked out by SFEM isorganically combined with the randomness of fatigue life induced by the non-homogeneity ofmicrostructure to eventually obtain the fatigue life distribution of notched specimens. Making use ofthis calculation model, a sensitivity analysis for fatigue life distribution of notched specimens withregard to three types of design variables with uncertainty (material, load and geometry) is carried out.The result shows that the load has the largest influence on the fatigue life distribution of notchedspecimens, then the geometry, lastly the material. However, the values of sensitivity of these threefactors are at the same magnitude.