Probability Distribution Of Fatigue Life Research Articles

Novel Mathematical-Statistical Models for the Distribution of Fatigue Life and Residual Strength for Fiber Reinforced Polymer Composites

For the distribution prediction of fatigue life and residual strength of fiber reinforced polymer composites, the existing models have the disadvantages of imprecision, instability and single applicability. A novel S–N curve model and a residual strength degradation model were first developed, which are independent and uncorrelated. After verifying their reliability, the statistical distribution models of fatigue life and residual strength were further derived and verified by using experimental data from literature. Compared with the other models, the proposed models can perfectly predict the probability distribution of fatigue life and residual strength under different materials, stacking sequences and stress levels, showing excellent prediction accuracy, stability and applicability.

Fatigue life prediction of tire sidewall using modified Arrhenius equation

Prolonged exposure of tires to sunlight leads to hardened and cracked sidewall rubber, which significantly decreases the fatigue life of the tire. Aging changes the rubber properties, which affects the safety of the sidewall, reduces the ride comfort, and even causes accidents. Hence, fatigue test procedures and regulations for tire materials are necessary to ensure the safety and reliability of vehicle tires. However, when developing a new tire sidewall, manufacturers typically only test the changes in physical properties of compounds. This study proposes a method of evaluating the fatigue life of aged tire sidewalls. In this process, by applying the Arrhenius equation, each aging condition is converted into its equivalent room temperature aging condition to predict the fatigue life changes with respect to aging. Moreover, a new fatigue parameter is presented to analyze the fatigue behavior of aged rubber and elucidate the cause of fatigue life changes. The probability distribution of fatigue life is expressed using Weibull distribution, and the durability performance is evaluated by comparing the fatigue life of unaged and aged tires.

Experimental study on flexural fatigue performance of rubberised concrete for pavement

ABSTRACT In order to study the probability distribution of flexural fatigue life of self-compacting rubberised concrete (SCRC), the flexural fatigue tests were carried out on 100 × 100 × 400 mm size beam specimens at different stress levels. The test results show that the probability distributions of fatigue life of SCRC can be approximately modelled by two-parameter Weibull distribution, and their fitting correlation coefficients are over 0.9. The shape parameter and scale parameter (two parameters of Weibull distribution) were estimated by different methods, namely the graphical method, the method of moments and the method of maximum likelihood estimates respectively, and it has been showed that the variability of fatigue life distribution of SCRC is higher when compared to plain concrete. The Pf – S – N curve (failure probability Pf , stress level S and fatigue life N) has been generated from the fatigue test data to predict the failure probability and corresponding stress level of the two-million cycle fatigue strength of SCRC. It has been proved that the fatigue performance of SCRC is better than that of the plain concrete by the S – N curve. And the fatigue failure process of SCRC was analyzed by acoustic emission (AE), showing obvious three-stage characteristic with the time.

Identifying the Probability Distribution of Fatigue Life Using the Maximum Entropy Principle

It is well-known that the fatigue lives of materials and structures have a considerable amount of scatter and they are commonly suggested to be considered in engineering design. In order to reduce the introduction of subjective uncertainties and obtain rational probability distributions, a computational method based on the maximum entropy principle is proposed for identifying the probability distribution of fatigue life in this paper. The first four statistical moments of fatigue life are involved to formulate constraints in the maximum entropy principle optimization problem. An accurate algorithm is also presented to find the Lagrange multipliers in the maximum entropy distribution, which can avoid the numerical singularity when solving a system of equations. Two fit indexes are used to measure the goodness-of-fit of the proposed method. The rationality and effectiveness of the proposed method are demonstrated by two groups of fatigue data sets available in the literature. Comparisons among the proposed method, the lognormal distribution and the three-parameter Weibull distribution are also carried out for the investigated groups of fatigue data sets.

Probabilistic analysis of shear fatigue life of steel plate girders using a fracture mechanics approach

Probabilistic analysis of shear fatigue life of steel plate girders of two railway bridges with welded connections, designed according to Indian Railway Standards, is presented in this paper. The fatigue life is determined using a fracture mechanics based procedure. Deterministic and probabilistic sensitivity analyses are carried out and, based on the results of these sensitivity analyses, the random variables having significant influence on fatigue life are identified. The probability distribution of fatigue life is determined using the Monte Carlo simulation technique and a relation for estimating the characteristic fatigue life is proposed.

Study on the Fatigue Reliability Model Based on Probability Distribution of Fatigue Life under Spectrum Loading

Under variable amplitude load history the exact distribution of fatigue strength corresponding to a specified number of life cycles cannot be obtained exactly by test, fatigue strength distribution can be obtained from fatigue life distribution. According to statistical property analysis of Miner cumulative damage rule, probability distribution of fatigue life under variable amplitude load history is predicted based-on constant amplitude median Sa-Sm-N surface. In the end, a fatigue reliability model is established to calculate fatigue reliability according to stress distribution as well as fatigue life distribution function. The model is applicable to calculate fatigue reliability under stochastic load environments.

On the prediction of P– S– N curves of 45 steel notched elements and probability distribution of fatigue life under variable amplitude loading from tensile properties

In the present study, attempts are made to use the fatigue formula developed before for predicting the expressions of fatigue life curves with given survivability ( S v), the so-called P– S– N curves of 45 steel notched elements from tensile properties. Then, the probability distribution of fatigue life under variable amplitude loading (VAL) can be predicted by using the predicted P– S– N curves and the linear cumulative damage rule and compared with test results. It is shown that the predicted P– S– N curves of 45 steel notched elements are in good agreement with test results but a little conservative. Both the predicted fatigue lives and the test results of 45 steel notched elements under VAL follow the log–normal distribution. The predicted fatigue life of 45 steel notched elements with 50% survivability agrees well with the test results. However, the standard deviation of the predicted fatigue life of 45 steel notched elements under VAL is a little higher than that of test results. The reason behind it should be further investigated. Based on the results mentioned above, it confirms again that the fatigue formula used in this study is a good one, which provides the possibility and the basis to predict the P– S– N curves and the probability distribution of fatigue life of 45 steel notched elements under VAL from tensile properties. Besides, the fatigue formula mentioned above could cover the whole range of fatigue life from 1/4 cycle to infinite, showing a horizontal asymptote in really geometrical and physical significance, which is expressed by the fatigue threshold. Finally, the measures are proposed to reduce the dispersion of fatigue test results and improve the prediction accuracy of the fatigue life under both constant and variable amplitude loading.

Probability distribution of fatigue life controlled by defects

An equation is derived for determining the cumulative probability distribution of fatigue life controlled by the defects in the material, and a method is proposed to determine the most deleterious to the fatigue life group of defects. The equation avoids some serious drawbacks of the classical approach to determine the fatigue life distribution, which are revealed on the basis of counter-examples. The theoretical relationships derived have been verified by Monte Carlo simulations.

Prediction of fatigue life and its probability distribution of notched friction welded joints under variable-amplitude loading

In the present study, fatigue tests under constant-amplitude loading (CAL) and variable-amplitude loading (VAL) are carried out on the notched friction welded (FW) joints of 45 (0.45%C) carbon steel, which is similar to the AISI 1045 steel. Statistical and regression analysis on the fatigue test results under CAL shows that the fatigue life of 45 steel notched FW joints with small size can be expressed as the function of the equivalent stress amplitude, and the values of the fatigue resistant coefficient and threshold are thus obtained. From the probability distribution of fatigue resistant coefficient and threshold, the expressions of the fatigue life with given survivability, i.e., the so-called P–S–N curves of 45 steel notched FW joints are obtained, which can cover the whole life region, in particular, the long life range and are used to determine the probability distribution of fatigue strength of 45 steel notched FW joints. Furthermore, the so-obtained expressions for P–S–N curves and Miner's rule are directly applied to predict the fatigue life and its probability distribution of 45 steel notched FW joints considering that 45 steel is of non-continuous strain-hardening characteristic and thus nil overloading effect. The prediction procedures for fatigue life with given survivability of 45 steel notched FW joints under VAL by using Miner's rule and the expressions of P–S–N curves are outlined. The fatigue life and the critical cumulative fatigue damage of 45 steel notched FW joints under VAL predicted by using the above procedures follow the log-normal distribution, and checked by test results under one type of programmed block loading and the statistical analysis. The procedures mentioned above may be applicable in predicting the probability distribution of fatigue life of the notched elements of metals with non-continuous strain-hardening characteristic, including the notched friction welded joints under VAL.

Prediction of probability distribution of fatigue life of 15MnVN steel notched elements under variable-amplitude loading

Attempts are made to develop procedures for predicting the probability distribution of the fatigue life of notched elements of a high-strength low-alloy steel, 15MnVN steel, under variable-amplitude loading (VAL). First, expressions for the fatigue life of 15MnVN steel with given survivabilities are obtained by fitting the test data of the fatigue life with corresponding survivabilities. Then procedures are outlined for predicting the probability distribution of the fatigue life of notched elements of 15MnVN steel, which has a non-continuous strain hardening characteristic, under VAL, based on the assumption that Miner's rule and the expression with given survivability could be directly used to predict the fatigue life with corresponding survivability under VAL. The predicted probability distribution of the fatigue life of 15MnVN steel notched elements under VAL follows a log-normal distribution and is checked by testing notched specimens under two types of block loading. The procedures mentioned above are of general applicability in predicting the probability distribution of the fatigue life of notched elements of metals with non-continuous strain-hardening characteristic. A criterion is also tentatively proposed for omitting small loads in the load spectrum in life prediction under VAL.

Fatigue Life under Random Loading (1 st Report)

Main purpose of this investigation is to estimate fatigue life or allowable stress under random loading without using well known cumulative damage laws. Basis of the analysis is to obtain fatigue strength diagrams, namely S-N curves, under random loading, and to determine fatigue life or allowable stress directly from the above S-N curves.Therefore, it is necessary to develop reasonable fatigue test method under random loading and to get S-N curves for random loading experimentally or analytically.For this reason, it is required to study statistical characteristics of fatigue life under random loading and to compare with results of constant loading tests under various conditions, for example, kind of materials ; type of loading ; shape of specimen or model structure ; range of fatigue life, etc.To achieve the above purpose, the following experiments were carried out and obtained statistical values of fatigue life and cumulative damage sum by Miner's Rule. The experiments are axial reversed fatigue tests with about 30 pieces of mild steel plain specimen in life range of about 3×104 cycles, and loading conditions are (a) constant loading amplitude, and (b) load and strain controlled random loadings with exponential distribution.From results of these tests, the following conclusions were obtained.(1) It was found that probability distribution of fatigue life under the above loading conditions conformed with normal or logarithmic normal distribution approximately, by plotting tests on the probability paper and X2 tests.(2) Using F tests, it was clarified that scatter band of fatigue life under random loading was considerably narrower than that of constant loading and the band of the life under strain controlled random loading was little smaller than that of load controlled random loading.(3) Probability distribution of cumulative damage sum is nearly equal to normal distribution.(4) Cumulative damage sum is less than 1 and arithmetic mean value of the sum is O.222 for load controlled loading tests and 0.551 for strain controlled ones.

Bayesian Approach for the Estimation of the Probability Distribution of Fatigue Life

An application of Bayes theorem to the estimation of the probability distribution function of fatigue crack initiation life was discussed. Digital simulations and (simplified) experiments with multi-circular-hole specimen showed that this method could reduce the time needed for the experiments.Though a Weibull distribution with no minimum life was assumed in this study, the general procedure is applicable to the any other possible distribution. The fact that it is not necessary to decide the time to the fatigue crack initiation but to identify the cracked locations after a certain number of load cycles made the experiment much easier.