Reliability Simulation for a Missile Tank Under Random Loading

This paper presents a Monte-Carlo simulation method to calculate intensity reliability for a missile tank under random loading. The cumulative damage mathematical model is established , and it adopts a direct simulation method to present random loading and o-riginal intensity for a missile tank. It can effectively predict intensity reliability for a missile tank in the environment of transport and flight.

PREDICTION OF FATIGUE LIVES OF RC BEAMS STRENGTHENED WITH CFL UNDER RANDOM LOADING

The investigation on fatigue lives of reinforced concrete （RC） structures strength- ened with fiber laminate under random loading is important for the repairing or the strengthening of bridges and the safety of the traffic. In this paper, two methods are developed for predicting the fatigue lives of RC structures strengthened with carbon fiber [aminate （CFL） under random loading based on a residual life and a residual strength model. To discuss the efficiency of the model, 12 RC beams strengthened with CFL are tested under random loading by the MTS810 testing system. The predicted residual strength approximately agrees with test results.

Statistical properties of fatigue damage of Gaussian random loadings

Firstly,the fatigue damages associated with the random loadings were always deemed as highcycle or very-high-cycle fatigue problems,and based on Chebyshev theorem,the number of rainflow cycles in a given time interval could be recognized as a constant by neglecting its randomness.Secondly,the randomness of fatigue damage induced by the distribution of rainflow cycles was analyzed.According to central limit theorem,the fatigue damage could be assumed to follow Gaussian distribution,and the statistical parameters:mean and variance,were derived from Dirlik's solution.Finally,the proposed method was used to a simulate Gaussian random loading and the measured random loading from an aircraft.Comparisons with observed results were carried out extensively.In the first example,the relative errors of the proposed method are 2.29%,3.52%and 1.16%for the mean,standard deviation and variation coefficient of fatigue damage,respectively.In the second example,these relative errors are 11.70%,173.32%and 18.20%,and the larger errors are attributable to non-stationary state of the measured loading to some extent.

ESTIMATION OF FATIGUE LIFE UNDER RANDOM LOADING WITH PLASTIC HYSTERESIS ENERGY THEOREM

Fatigue damage of materials includes static damage and cyclic damage.Static damage is a ratio of the plastic energy in first static loading to the statictoughness, while cyclic damage is the ratio of the cyclic plastic hysteresis energy to thefatigue toughness. In the calculation, cyclic hardening (or softening) of a material istaken into account, which results in the increase (or decrease) of the yield stress. Forsimplification, it is assumed that stress and strain in cyclic loading vary in accordancewith the hysteresis loop. Fatigue toughness of a material can be detennined bysymmetric cyclic stress controlled fatigue test. A method, rational and convenient forengineering, is proposed to estimate the fatigue life under random loading based onplastic hysteresis energy theorem. Preliminary verification by test is satisfactory.

LIFE PREDICTION APPROACH FOR RANDOM MULTIAXIAL FATIGUE

According to the concept of critical plane, a life prediction approach forrandom multiaxial fatigue is presented. First, the critical plane under the multiaxial randomloading is determined based on the concept of the weight-averaged maximum shear strain direction.Then the shear and normal strain histories on the determined critical plane are calculated and takenas the subject of multiaxial load simplifying and multiaxial cycle counting. Furthermore, amultiaxial fatigue life prediction model including the parameters resulted from multiaxial cyclecounting is presented and applied to calculating the fatigue damage generated from each cycle.Finally, the cumulative damage is added up using Miner's linear rule, and the fatigue predictionlife is given. The experiments under multiaxial loading blocks are used for the verification of theproposed method. The prediction has a good correction with the experimental results.

Effect of Band Width on Fatigue Life under Random Stress Response

A fatigue life estimation method for offshore structures under random stress response is studied in this paper. The method of broad band cumulative frequency number is used to determine the effect of band width of stress frequency spectra on fatigue. A formula of correction factor for fatigue under broad band stress spectra is suggested and compared with that given by P. H. Wirsching.

SIMPLIFYING AND CONDENSING A SET OF RANDOM SPECTRA FOR TRANSPORT

Crack growth tests and analyses of CCT specimens made of LY12CZ Al-uminium alloy and 30CrMnSiA high strength steel materials are carried out. The speci-mens are subjected to transport flight-by-flight random spectra of high loads encoun-tered 10 times per 1000 flights. The crack growth life is predicted with an equivalentmodel. Comparing the spectra based on 100 flights with those based on 1000 flights, theformer requires only 10 per cent data for cycles. Experiment results show that the differ-ences between two spectra are less than 10% for crack growth life. A more simply con-densed spectrum is derived, retaining groundtoair cycle during every flight and ar-ranging some constant amplitude cycles according to equivalent damage rule. The dataof this spectrum is 10 per cent less than that based on 100 flights, but the differences oftwo spectra whether the predicted or tested results for crack growth life are less than 15per cent. Accordingly, a complex random spectrum may arbitranly be changed to acondensed spectrum with equivalent damage rule, reducing calculation and test work.

A Probabilistic Model for Fatigue Crack Propagation Analysis

A simple probabilistic model for predicting crack growth behavior under random loading is presented. In the model, the parameters c and m in the Paris-Erdogan Equation are taken as random variables, and their stochastic characteristic values are obtained through fatigue crack propagation tests on an offshore structural steel under constant amplitude loading. Furthermore, by using the Monte Carlo simulation technique, the fatigue crack propagation life to reach a given crack length is predicted. The tests are conducted to verify the applicability of the theoretical prediction of the fatigue crack propagation.