Multiaxial Fatigue Life Model And Reliability Study Of Notched Specimens Based On Weibull Distribution

As the most common parts in practical engineering structures,shaft parts often work under multiaxial loads.In the design and use of shaft parts,there are usually notched structures such as pin holes and keyways,which cause serious stress concentration.Meanwhile,complex stress-strain response and even local plastic deformation will occur near the notch,leading to non-uniform stress field(stress gradient effect),which has an important influence on fatigue analysis.Life prediction equations based on physical models often contain many material constants and require a large number of uniaxial and multiaxial fatigue data.Limited by various factors,it is often not possible to obtain sufficient experimental or historical data.Due to the randomness and uncertainty of fatigue data in reliability evaluation,it is not accurate enough to determine the parameters of fatigue life model through small sample data,especially in the face of fatigue reliability problems such as fitting P-S-N curve,such defects are particularly obvious.Therefore,the establishment of high-precision notched fatigue life prediction model based on finite data is particularly important for the development of multiaxial fatigue strength theory and the solution of practical engineering problems.According to the problems mentioned above,the effects of stress gradient and non-proportional additional strengthening effect on the fatigue damage evolution process of notched parts under multiaxial loads are analyzed based on the critical surface theory,and a multiaxial fatigue life prediction model is established based on Weibull distribution.Based on the modified Bootstrap method,the fatigue life data is extended,the relevant parameters of mixed Weibull distribution function are obtained by EM algorithm.Considering the fatigue damage evolution process of notched parts under the coupling action of various factors,the probability density function of mixed Weibull distribution is proposed.The main research contents are as follows:(1)Quantitative description of crack initiation orientation(critical plane)and stress field of notched parts under multiaxial load is given.Taking the maximum shear strain as the fatigue damage parameter,a method for calculating the critical surface of notched parts under multiaxial load is established.The stress and strain states on the critical plane are analyzed by finite element method(FEM),and von-Mises equivalent stresses on a specific integral path are extracted to establish a distribution function that could quantitatively describe the notch stress field.On this basis,the methods of solving stress gradient factor and field diameter of fatigue damage affected area are improved.The effective stress damage parameters are established based on the normalized treatment method combined with the path force function,and the evolution law of multiaxial fatigue damage of notched parts is revealed,which laid the foundation for the establishment of probabilistic life model.(2)Life and reliability analysis of notched parts based on Weibull distribution under multiaxial load is accomplished.Combined with the von-Mises criterion,the effects of non-proportional additional strengthening effect,stress gradient factor and stress concentration coefficient on the fatigue life of notched parts are considered comprehensively.The fatigue life probability model is established based on twoparameter Weibull distribution,and the reliability fatigue life analysis method based on macro structure is obtained.To obtain the mathematical relationship between load level and fatigue life under different failure probabilities,P-S-N curves under different failure probabilities are obtained by fitting small sample fatigue data,and the reliability of the method is analyzed by Bayes estimation.(3)Multi-factor probability model based on mixed Weibull distribution is proposed.The random number in(0-1)is introduced to modify the Bootstrap method,and the extended fatigue data is obtained.In order to further consider the influence of fatigue influencing factors in the probability model and reveal the interaction among the influencing factors,a multi-factor probability model is established by means of mixed Weibull distribution.Taking two-term mixed Weibull distribution as an example,the correlation parameters of mixed Weibull distribution are determined by the extreme value distribution and EM algorithm,and the life prediction model is established.The accuracy of the model is analyzed by the test data of 316 L stainless steel,and the correlation between the influencing factors and the fatigue life is analyzed by the multifactor probability model.