Spectral Method For Multiaxial Fatigue Life Prediction Of Structures Under Random Vibration Loadings

Fatigue loadings usually tend to be multiaxial at the hotspot of engineering structures under random vibration loadings.Constant alterations of the principle stress directions result from the non-proportional variations of the stress components on structures of metal material,which makes it more difficult to evaluate fatigue lives of engineering structures under random vibration loadings.Compared to the time domain method for random vibration fatigue life analysis of structures,the spectral method(frequency domain method)is more efficient in numerical calculation and describes the random variables with stochastic parameters,which is becoming the preferred method for random vibration fatigue life analysis of structures.Multiaxial random vibration fatigue damage parameter is the control parameter of fatigue property evaluation of strutures under random vibration loadings,meanwhile the influence of stress gradient near notch root on fatigue property of structures needs to be considered in the fatigue life prediction of notched specimens,both of which are significant factors to multiaxial fatigue life prediction method of structures.Structures of metal material are most widely used in engineering at this stage,whose fatigue problems under random vibration loading draw the attention from a lot of researchers.Fiber reinforced composite laminates are playing a more and more important role in engineering practice for its advantages like high strength-to-weight ratio,high modulus-to-weight ratio,designable properties and so on.However,it makes the fatigue life analysis of composite structures under random vibration loadings much more difficult for reasons such as complex failure modes and failure mechanisms as well as combined action of multiaxial stresses.For the problems of multiaxial random vibration fatigue life analysis on metal structures and on composite laminates,the exploration on the fatigue life analysis method under random vibration loadings is carried out in this paper and the main research work is as follows:(1)The spectral method for multiaxial random vibration fatigue life analysis of metal material is proposed based on the principle of critical plane method in multiaxial fatigue.In this method,the fatigue hotspot of the structure under random vibration loadings is determined as the location where the expected value of shear stress amplitude takes its maximum value.The power spectral density(PSD)of the multiaxial equivalent stress is regarded as the fatigue damage parameter,which describes the physical mechanism of fatigue fracture and the correlation between the normal and shear stresses on the critical plane under random vibration loadings well.At last,fatigue life analysis is carried out based on Miner’s linear fatigue damage accumulation rule,combined with the S-N curve of material.(2)The critical distance spectral method for multiaxial random vibration fatigue life analysis for notched specimen of metal material is proposed based on the critical distance method.In this method,the supporting effect of the material within the critical distance in the notch root region is considered.The fatigue life analysis results by this method of the random vibration fatigue experiment on the thin-walled circular tube specimens with slots on the sides are found to be of high precision compared to the experiment results.This method is also adopted for the fatigue life analysis on the lifting lug structure of a missile under random vibration loadings,and the fatigue life analysis results are well correlated with the experiment results.(3)Constant amplitude fatigue test,modal test and random vibration fatigue experiment are successively carried out on the thin-walled circular tube specimens of 45 steel with slots on the sides for two different notches,which obtain the fatigue properties of material as well as the modal properties,dynamic response and vibration fatigue lives of the specimen structures.It is observed from the analysis results of the experiment that the notch type hardly influences the modal properties of the specimen structures but it has significant influence on the fatigue lives of specimens.On the other hand,randomness is observed for the location where fatigue failure takes place for the specimen so that it is more reasonable to describe it from the perspective of probability statistics.(4)A multiaxial fatigue damage parameter for composite laminates under random vibration loadings is proposed based on Tsai-Hill criterion,which constructs the spectral method for random vibration fatigue life analysis for composite laminates.This parameter is an equivalent stress PSD,which is the weighted average of the PSDs of the stress components in the fiber principle directions and considers the randomness and multiaxiality of the dynamic stress response of the composite laminates.This method is adopted for the case study on the noise fatigue experiment of the C/Si C panel specimen in the engineering project as well as on the random vibration fatigue experiment of CFRP perforated plate specimen from the literature,which indicates that it gives a satisfactory prediction result on fatigue life.