Non Probabilistic Reliability Study On Fatigue Crack Growth Of Titanium Alloy For Submersible

The titanium alloy pressure shell of the deep sea manned submersible will bear periodic reciprocating stress due to the sea water pressure during its service,and the fatigue damage caused by it may produce cracks,which may affect the structural safety.The titanium alloy material is affected by uncertain factors in the process of crack growth,so it is necessary to study the reliability of the fatigue crack growth of the titanium alloy material.The traditional reliability method based on probabilistic fracture mechanics is widely used in the fatigue reliability research,but it requires a high number of samples and statistical information and a large amount of calculation.Therefore,it is of great significance to apply the non probabilistic method to the reliability research of crack growth for simple and efficient fatigue reliability analysis.In this paper,based on fracture mechanics and crack growth model,the non probabilistic reliability analysis of fatigue crack growth of titanium alloy is carried out by using interval convex set model and ellipsoid convex set model.The main work is as follows:Firstly,a new type of titanium alloy was selected as the research object to carry out the fatigue crack growth rate test.According to the test data,the crack growth model and the design life of titanium alloy are determined.The limit state equation is established by the fracture failure criterion,and the statistical characteristics of the uncertain parameters are analyzed.The uncertain parameters which obey normal distribution are transformed into interval form by 3σ criterion,which lays a foundation for non probabilistic reliability analysis.Secondly,based on the convex set theory and interval mathematical method,the interval model is constructed for the uncertain parameters that affect the crack growth of titanium alloy without considering the correlation between the variables.The reliability index based on dimensionless form and the reliability based on interval possibility are calculated by changing the interval interference degree.It is found that the latter is more intuitive to describe the reliability state of titanium alloy.Combined with Monte Carlo method,the feasibility of non probabilistic reliability method of interval model is verified,and the result is more conservative than that of probabilistic method,and the maximum deviation is less than 5.5%.Then,based on the mathematical characteristics and operation methods of ellipsoid,considering the correlation between variables,the ellipsoid model is constructed by interval model,normal distribution model and Khachiyan algorithm.Different limit state equations are obtained by changing the coefficient κ the first order approximation method and Monte Carlo method are used to calculate the reliability of the ellipsoid model.The feasibility of non probabilistic reliability method of ellipsoid model is verified and the difference between ellipsoid model and probabilistic method is compared.In the reliability analysis of crack growth of titanium alloy,when κ is less than or equal to 2,Khachiyan algorithm is preferred to build ellipsoid model;when κ is greater than 2,interval model is preferred to build ellipsoid model.Finally,the design life of titanium alloy material in the interval model is reduced to real number,and the same calculation conditions as ellipsoid model are realized.The influence of interval degradation is analyzed.It is found that the real number after interval degradation has a great influence on the deviation of reliability calculation results,and the calculation deviation increases from 0 to 100%.The results of reliability calculation under different limit state equations are compared between the interval model and three ellipsoidal models.The conservative degree of reliability calculation under the two models is different.Generally speaking,the interval model is more conservative.The characteristics of each uncertainty domain are analyzed,and the influence of the correlation between the uncertain parameters on the uncertainty domain is compared and demonstrated.When the correlation coefficient is 0,the uncertainty domain is an axial ellipsoid,and the correlation between the parameters may be different in the ellipsoid model constructed by different methods.