Random Fatigue Limit Model Research Articles

Probabilistic models for the fatigue resistance of welded steel joints subjected to constant amplitude loading

S-N curves found in various rules and regulations are the basic tool for the practicing engineer when carrying out life predictions for welded details in dynamically loaded structures. The present work is investigating the expected fatigue life and associated scatter for welded steel joints subjected to Constant Amplitude (CA) loading. The objective is to obtain more reliable life predictions based on advancements in the probabilistic model fitted to collected life data. A Random Fatigue Limit Model (RFLM) is proposed to obtain fatigue resistance curves at given probability levels of survival. As a distinction to more conventional statistical methods, the model is treating both the fatigue life and the fatigue limit as random variables. The focus is on high cycle fatigue and long-life data and runouts are included in a rational and logical manner by using a maximum likelihood method. Life data for a transverse fillet welded attachment originally designated as a category 71 detail in Eurocode 3 Part 1-9 are collected and analysed. The plate thickness of the specimens ranges from 20 mm to 32 mm and the steel quality is mild and medium strength Carbon-Manganese steel. The results are compared with the results obtained by conventional S-N curves. The compatibility between the fitted probabilistic models and the underlying fatigue damage mechanisms is emphasized.

Mid- and High-Cycle Fatigue of Welded Joints in Steel Marine Structures: Effective Notch Stress and Total Stress Concept Evaluations

The characteristic far field response spectrum of welded joints – the governing fatigue sensitive locations in steel marine structures – is predominantly linear elastic, meaning mid- and high-cycle fatigue (MCF and HCF) is most important for design. Using the effective notch stress- and the total stress concept, involving respectively Se and ST as intact- and cracked geometry fatigue strength criterion, one MCF-HCF resistance curve has been obtained for all welded joints. A generalised random fatigue limit model explicitly incorporating the MCF life time and HCF strength limit scatter provides statistically the most accurate fatigue strength and fatigue life time estimates. Similar MCF performance is obtained for Se and ST. Although crack growth dominates the MCF damage process, the results for an initiation related criterion like Se and natural crack growth related criterion like ST are similar. Adopting Se rather than ST as fatigue strength criterion naturally related to the crack initiation dominated HCF region showing the largest data scatter may explain the better effective notch stress concept HCF performance. Since the HCF resistance scatter is relatively large, the MCF-HCF generalised random fatigue limit model design curves show approximately 1-slope behaviour. meaning that for design purposes a linear Basquin model approximation rather than a piecewise continuous bi-linear MCF-HCF formulation according to guidelines, standards and classification notes should be adopted.

Piecewise stochastic rainflow counting for probabilistic linear and nonlinear damage accumulation considering loading and material uncertainties

A new framework is proposed for probabilistic fatigue life prediction considering randomness from both loadings and material properties. Piecewise stochastic rainflow counting (PSRC) is proposed to transform random loading spectrums to block loadings in a piecewise way with block randomization. The PSRC can be integrated with both linear and nonlinear damage accumulation rules. Mean stress corrected random fatigue limit model is proposed for uncertainty quantification of material fatigue properties under constant amplitude loadings. Probabilistic fatigue life prediction with both loading and material uncertainties is conducted using Monte Carlo simulation and is validated with experimental data from literature and in-house testing. Impact of different mean stress correction models on the fatigue life prediction under random loadings is investigated in detail. The influence of block piece length and block sequence randomization is discussed with respect to the mean and scatter behavior of the probabilistic life prediction results.

Fitting fatigue test data with a novel S-N curve using frequentist and Bayesian inference

In design against fatigue, a lower bound stress range vs. endurance curve (S-N curve) is employed to characterize fatigue resistance of plain material and structural details. With respect to the inherent variability of the fatigue life, the S-N curve is related to a certain probability of exceedance, a percentile of the fatigue life. This paper is concerned with modelling and estimating uncertainties in fatigue resistance of welded joints under constant amplitude loading. A new S-N curve format is proposed and fitted to fatigue test data by using the Maximum Likelihood Method. The results have been compared with the Random Fatigue Limit Model and the Bilinear Random Fatigue Limit Model. The proposed S-N curve appears to be more accurate in describing the S-N relation in high-cycle fatigue: it presents a smooth transition from finite to infinite-life regions and, differently from previous non-linear S-N relations with fatigue limit, this transition is controlled by an independent model parameter. Thereby it provides more flexibility for statistical fitting. In addition, a Bayesian framework is defined to fit the proposed relation including informative and non-informative prior distributions.

Stochastic fatigue limits and fatigue life variability in oriented–PVC pipe

Fatigue data has been collected on oriented polyvinyl chloride (PVC-O) pipe samples up to fatigue lifetimes of 107 cycles. A random fatigue limit model based on the work of Pascual and Meeker has been used to establish the fatigue limit in this material. This model assumes that the fatigue limit is a stochastic quantity and that the fatigue life is conditional on the fatigue limit. Moreover, it allows the use of censored data in establishing the fatigue limit magnitude. Although the most appropriate distributions for the fatigue life and the fatigue limit were difficult to determine unambiguously, the presence of a fatigue limit in PVC-O was established. This statistical analysis of the fatigue data allowed failure probability quantiles to be calculated for PVC-O pipe materials.

Stochastic fatigue limits and fatigue life variability for unplasticised PVC pipes

This paper uses the random fatigue limit (RFL) model of Pascual and Meeker to address fatigue limits for PVC pressure pipes. This model differs from previous ways of describing fatigue data for PVC by recognising that the fatigue limit is a stochastic quantity rather than a single valued stress amplitude below which fatigue failures will not occur. By analysing published fatigue data, it is demonstrated that the RFL model is capable of quantifying fatigue limit variability and its influence on fatigue life variability. Moreover, the RFL model was used to illustrate the risks associated with defining fatigue limits based on small quantities of high-cycle fatigue data. In particular, it is shown that fatigue failure can occur below the mean fatigue limit and that the RFL model is capable of quantifying the probability of failure at a given level of stress amplitude.

A comparison of maximum likelihood models for fatigue strength characterization in materials exhibiting a fatigue limit

In this study, various probabilistic models were considered to support fatigue strength design guidance in the ultra high-cycle regime (beyond 10 8 cycles), with particular application to Ti-6Al-4V, a titanium alloy common to aerospace applications. The random fatigue limit model of Pascual and Meeker and two proposed simplified models (bilinear and hyperbolic) used maximum likelihood estimation techniques to fit probabilistic stress-life curves to experimental data. The bilinear and hyperbolic models provided a good fit to large-sample experimental data for dual-phase Ti-6Al-4V and were then applied to a small-sample data set for a beta annealed variant of this alloy, providing an initial probabilistic estimate of beta annealed Ti-6Al-4V fatigue strength in the gigacycle regime. The bilinear and hyperbolic models are recommended for use in estimating probabilistic fatigue strength parameters in support of very high-cycle design criteria for metals with clearly defined fatigue limits and fairly constant scatter in fatigue strength.

Effects of microstructure and temperature on fatigue behavior of E319-T7 cast aluminum alloy in very long life cycles

The effects of microstructure and temperature on the fatigue behavior of a commercial Al–Si–Cu alloy used in automotive engine components were investigated for lifetimes as long as 10 9 cycles using ultrasonic fatigue instrumentation operating at 20 kHz. The primary finding of this study is that the influence of microstructure on the cyclic properties is greater than the influence of the testing temperature. Fractographic studies indicated that most fatigue cracks initiate from microshrinkage pores located at or very near to the specimen surface, while a much smaller number of cracks initiate from twin boundaries. Increasing test temperature resulted in a modest decrease in endurance limit by about 12% from 20 to 150 °C, while a significant decrease in endurance limit by about 23% was observed from 150 to 250 °C at high number of cycles. Using fatigue data developed in this study, a statistical model, the random fatigue-limit model (RFL), was evaluated for its utility in estimating fatigue behavior in the gigacycle regime.

Optimal Test Planning for the Fatigue-Limit Model When the Fatigue-Limit Distribution is Known

This article discusses tools for planning life tests under the random fatigue-limit model, when the form of the fatigue-limit distribution is completely specified. Expressions for the Fisher information matrix elements are provided. Test-plan objectives, such as minimum variance of quantile or parameter estimator, can be written in terms of these expressions. Under Type I censoring, all experimental conditions can be described by a standardized slope parameter & a standardized log(censoring time). This article provides equivalence theorems, which can be used to check the optimality of test plans which often have two levels. The best three-level standard test plans are not optimal, but, in general, involve fewer extrapolations to low stresses than the optimal plans. Test plans for a titanium-alloy fatigue test are presented to illustrate the methods.

The random fatigue-limit model in multi-factor experiments

The Random Fatigue-Limit (RFL) model in Pascual and Meeker (1999a) was motivated by the need to describe fatigue life of certain materials. The RFL model describes the relationship between lifetime (measured in cycles) and a single factor, often the applied stress on the material. It has been found to be particularly useful for modeling high-cycle fatigue (HCF), that is, lifetimes that exceed 10 million cycles. Outputs from this model can be used as input for system models for lifetimes of jet engines for design purposes. Understanding how well parts hold up as a function of stress and other environmental variables would be valuable to engineers designing new and better engines. In this article, we show how the RFL model can be extended from single factor (single stress) to multi-factor situations. We fit the proposed model extensions to available data and describe methods to assess the adequacy of the fits.

Estimating Expected Information Gains for Experimental Designs With Application to the Random Fatigue-Limit Model

Expected gain in Shannon information is commonly suggested as a Bayesian design evaluation criterion. Because estimating expected information gains is computationally expensive, examples in which they have been successfully used in identifying Bayes optimal designs are both few and typically quite simplistic. This article discusses in general some properties of estimators of expected information gains based on Markov chain Monte Carlo (MCMC) and Laplacian approximations. We then investigate some issues that arise when applying these methods to the problem of experimental design in the (technically nontrivial) random fatigue-limit model of Pascual and Meeker. An example comparing follow-up designs for a laminate panel study is provided.

Theory for Optimal Test Plans for the Random Fatigue-Limit Model

This article presents methodology for planning life tests based on the random fatigue-limit model (RFLM). The RFLM describes the relationship between fatigue life and the applied load in the presence of fatigue limits. A standardization of the RFLM is presented, and corresponding expressions for the elements of the Fisher information matrix are given. Different test plan criteria that express various objectives that the practitioner may have in conducting experiments under the RFLM are discussed. These criteria include estimation of life quantiles, estimation of stress/strain levels that yield a specific life quantile, estimation of fatigue-limit quantiles, and D and Ds optimality. Equivalence theorems used to verify optimality of test plans are also presented. The methods are sufficiently general so they can be applied to criteria based on any function of the model parameters. They are demonstrated using a nickel-base superalloy experiment.

A Standardized Form of the Random Fatigue-Limit Model

This article discusses a standardization of the random fatigue-limit model (RFLM) presented by Pascual and Meeker (Pascual, F. G., Meeker, W. Q. (1999). Estimating fatigue curves with the random fatigue-limit model (with discussion). Technometrics 41:277–290). The basic RFLM has five model parameters and describes the relationship between fatigue life and applied stress, for example, in high-cycle fatigue behavior of materials used in jet engines. Possible extensions of the RFLM are also presented to generalize the model. The discussions here show that the model can be reparameterized so that the probability distribution function (pdf) and the cumulative distribution function (cdf) are indexed by a standardized stress, standardized slope, and a scale parameter. This “standardization” simplifies the computation of the pdf and cdf necessary for maximum likelihood estimation. This also allows for more efficient tabular and graphical presentation of quantiles. A practical example is presented to illustrate how tables and graphs of standardized quantiles can be used to obtain actual quantiles.

Estimating Fatigue Curves with the Random Fatigue-Limit Model

In a fatigue-limit model, units tested below the fatigue limit (also known as the threshold stress) theoretically will never fail. This article uses a random fatigue-limit model to describe (a) the dependence of fatigue life on the stress level, (b) the variation in fatigue life, and (c) the unit-tounit variation in the fatigue limit.We fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions. Small quantiles of the life distribution are often of interest to designers. Lower confidence bounds based on likelihood ratio methods are obtained for such quantiles. To assess the fits of the model, we construct diagnostic plots and perform goodness-of-fit tests and residual analyses.

Estimating Fatigue Curves With the Random Fatigue-Limit Model

In a fatigue-limit model, units tested below the fatigue limit (also known as the threshold stress) theoretically will never fail. This article uses a random fatigue-limit model to describe (a) the dependence of fatigue life on the stress level, (b) the variation in fatigue life, and (c) the unit-tounit variation in the fatigue limit.We fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions. Small quantiles of the life distribution are often of interest to designers. Lower confidence bounds based on likelihood ratio methods are obtained for such quantiles. To assess the fits of the model, we construct diagnostic plots and perform goodness-of-fit tests and residual analyses.