Probabilistic Stress-life Research Articles

Fatigue life prediction method for bolted joints based on equivalent structural stress under tensile–compressive loading

In this study, load amplitude–life (Fa–N) curves were obtained through tensile–compressive fatigue tests of bolted joints. It was observed that the correlation coefficient squared (R2) value of the Fa–N curve with the same geometric and pre-tightening parameters was high, but the R2 value of the Fa–N curve with all the parameters was low, indicating poor correlation and inability to meet the engineering requirements. Therefore, an equivalent structural stress model for the bolted joint was first developed based on a mechanical model with a strict mathematical definition to normalize these Fa–N curves, which considered the bolted joint loads as the input conditions and integrated the geometric and pre-tightening parameters. Subsequently, a classical beam–shell equivalent finite element model of the bolted joint was constructed. The nodal loads in the bolted connection zone were coupled with the forces and moments of the beam element nodes through finite element simulation, and the equivalent structural stress (σs) of the bolted joint was then obtained based on the equivalent structural stress model. Consequently, the equivalent structural stress–life (Ss–N) curve and probabilistic stress–life (P–Ss–N) curve normalized for different Fa–N curves were obtained by fitting the data of σs and N. Lastly, the accuracy of the fatigue life prediction method based on equivalent structural stress was verified by conducting the vibration fatigue test on the bolted joint structure of the subway antenna bracket.

Validation of crack initiation model by means of cyclic full-scale blade test

Wind turbine rotor blades are subject to highly dynamic loads and designed for life cycles of at least 20 years, which means that materials are subjected to high-cycle fatigue. Fatigue is a design-driving loading for current and future blades. Bond lines of blades are exposed to a multi-axial stress-state due to the anisotropic thin-walled blade structure and curved, tapered, twisted, and airfoil-shaped blade geometry. To eliminate undesirable failure modes and thus increase the reliability of wind turbine rotor blades, standards and guidelines recommend that the multi-axial stress-states be taken into consideration for the limit state analysis. In addition, thermal residual stresses that develop during manufacture can have a significant impact on the fatigue life of the bond line. By means of a cyclic full-scale blade test of a commercial 81.6m long offshore blade, we validate a crack initiation model, which takes into account multi-axial thermal and mechanical stress-states, as well as the probabilistic stress-life, to predict the edge of crack initiation in the adhesive as well as the span-wise position. Both observations agreed well with the simulations. All residual normal stress components and cross-sectional plane shear stress made up the major part of the mean equivalent stress, while the mechanical stress amplitude components - longitudinal, peel, and cross-sectional plane shear stress - made up the major part of the equivalent stress amplitude.

Probabilistic Approach for the Fatigue Strength Prediction of Polymers

One of the dominating factors in the fatigue of structures made from fiber-reinforced polymers, for example, wind turbine blades, is the polymer matrix. Traditionally, experimental stress–life data of polymers are approximated via a linear double-log Basquin model. Recently, the nonlinear stress–life formulation by Stüssi was found to provide a better fit of the experimental data with a substantially reduced standard deviation. Moreover, a nonlinear constant–life formulation, as proposed by Boerstra, can enhance the representation of the mean stress effect compared with state-of-the-art linear models given by the modified Goodman relation. To this end, Stüssi’s model was incorporated into the Boerstra relation to take account of the mean stress effects of an epoxy. This stress–life formulation was then enhanced with the Weibull probability function. The probabilistic–stress–life model provided a good approximation of the fatigue performance as a function of the stress ratio on the basis of an experimental data set. Finally, a stepwise engineering approach was suggested to derive the permissible stress–life with a view to practical design purposes. The procedure increased the reliability of the fatigue design evaluation compared with the state-of-the-art methodologies.

Multiaxial fatigue reliability assessment using a differential ant-stigmergy algorithm

This study presents a process of establishing a multiaxial Weibull model to assess S45C steel reliability and high-cycle fatigue. The proposed model includes multiaxial stress state, stress gradient and component size factors, and the probability of failure. The model was based on multiaxial fatigue theory, where the expressed damage parameter is a single value for one cycle of the multiaxial stress state, combined with the weakest link concept. Through the maximum likelihood method (MLE), a probabilistic stress-life (P-S-N) curve that reflects both failure and right-censored data was plotted; whereas optimal Weibull parameters were estimated via the differential ant-stigmergy algorithm (DASA). The completed multiaxial Weibull model was then applied to S45C steel tension-compression (TC) and zero-tension (ZT) fatigue test data, both of which agreed well. Afterward, the model was cross-checked with torsion fatigue test data results for validity.

Survival analysis of fatigue data: Application of generalized linear models and hierarchical Bayesian model

The survival analysis is introduced to describe the fatigue failure process in this paper for obtaining a set of flexible and accurate probabilistic stress-life (P-S-N) curves in fatigue reliability analysis. The generalized linear models (GLMs) are applied as well for expressing a trend and random errors of the P-S-N curves simultaneously. A GLM, including a linear Basquin relation and a shape-fixed Weibull hazard function, has been established for the P-S-N curves estimation, then a hierarchical Bayesian model is employed to estimate their parameters. The fatigue probability design curves are generated by the survivor function or the resulting predictive distributions. Finally, a comparative example is presented to verify the effectiveness of the method.

Fatigue Reliability Analysis of Steel Welded Member Using Probabilistic Stress-Life Method

This paper attempts to develop an analytical technique for fatigue reliability evaluation of a steel welded member. The probabilistic stress-life method is an important one for the fatigue reliability evaluation of a steel welded member. In this method, the stress range frequency distribution of the stress history of a steel welded member defined as a loading block is obtained from the stress frequency analysis and the parameters of the probability distribution for the stress range frequency distribution are used for numerical simulation. The probability of failure of the steel welded member under loading block is obtained from the Monte Carlo Simulation in conjunction with the Miner’s rule, the Modified Miner’s rule, and the Haibach’s rule for fatigue damage evaluation. Through this procedure, a fatigue reliability evaluation that can predict the number of loading block of failure and the residual fatigue life is possible. Also according to the 50, 90, and 99% reliability, failure times are indicated respectively.

The prediction of multiaxial fatigue probabilistic stress–life curve by using fuzzy theory

AbstractThe fuzziness of the traditional multiaxial fatigue prediction model is discussed and the fuzzy theory is applied into fatigue reliability analysis. The fuzzy linear regression analysis method is used to determine the fuzzy coefficients in the multiaxial stress–life equation under a small sample condition, and the corresponding multiaxial fatigue probabilistic stress–life curve is calculated with different confidence levels.

Modelling the effect of temperature on the probabilistic stress–life fatigue diagram of glass fibre–polymer composites loaded in tension along the fibre direction

Predicting the fatigue performance of composites has proven to be a challenge both conceptually, due to the inherent complexity of the phenomenon, and practically, because of the resource-intensive process of fatigue testing. Moreover, mechanical behaviour of polymer matrix composites exhibits a complicated temperature dependence, making the prediction of fatigue performance under different temperatures even more complex and resource intensive. The objective of this paper is to provide a method for the prediction of fatigue life of glass–polymer composites loaded in the fibre direction at various temperatures with minimal experimental efforts. This is achieved by using a static strength degradation approach to fatigue modelling, where only two parameters (including static strength) are temperature dependent, in conjunction with relationships for these two fatigue model parameters temperature dependence. The method relies on fatigue data at a single temperature and simple static tests at different temperatures to predict the effects of temperature on the material’s fatigue behaviour. The model is validated on experimental data for two unidirectional and one woven glass–epoxy composites and is found to accurately predict the effect of temperature on fatigue life of composites. A method to obtain probabilistic stress-life [Formula: see text] fatigue diagrams including temperature effects is also presented.

Weibull modeling of the probabilistic S–N curves for rolling contact fatigue

A Weibull modeling of the probabilistic stress–life (S–N) curves is proposed for rolling contact fatigue (RCF). Shape, scale and location parameters of Weibull distribution, the normal life confidence parameters and the exponent of S–N relation are all deduced from set of test data. Life confidence assessment is incorporated into the probabilistic curves for common applied case of limited samples. Applicability of the present modeling is checked by describing the test data of G20CrNi2Mo bearing steel. Results real that two-parameter (2-P) and three-parameter (3-P) Weibull distributions are acceptable models. But bigger difference is observed in high reliability district. The 3-P one has smaller standard deviation of lives and this deviation is constricted with increasing of stress levels, which is consistency with results of most classical fatigue experiments. While the 2-P modeling fails to well characterizing the test data. This indicates that an appropriate distribution determination is a primary task for RCF analysis. And the 3-P Weibull is a better modeling for the present test data.

B21 確率乗法定理に基づいた一般化ワイブル分布とP-S-N曲線および寸法効果 : 従来理論の問題点とその解決(OS2 最新機械要素技術(1))

Recently, in Lundberg-Palmgren theory pertaining to the rating life and load rating of rolling bearings, it was found that a P-S-N (Probabilistic Stress-life) curve for the structural fatigue has not been established and an imperfect product law of probabilities without a minimum life in the Weibull life theory has been applied considering as the Weibull slope depends on the strength of materials. Therefore, the Lundberg-Palmgren theory has included various questions. In accordance with the published rolling bearing theories since the Lundberg-Palmgren era till present these questions are summarized. Further, the P-S-N curve and size effect as well as their application principles are discussed.

Weibull Distribution Function Application to Static Strength and Fatigue Life of Materials

A rigorous study on the Weibull distribution function proposed by Weibull in 1939 and the dynamic capacity and the life formula for rolling bearings postulated by Lundberg-Palmgren in 1947 is performed especially with reference to the stressed volume, which relates to the number of individual probability in the product law of probabilities used in reliability function and probabilistic stress-life (P-S-N) relationship for structural materials as well as probabilistic force-life (P-F-L) relationship for rolling bearings. By means of the three-parameter Weibull distribution function with a minimum strength/life as the third parameter independent of statistical strength, a new statistical theory for treating the static strength/fatigue life of materials, a linkage between structural fatigue and rolling contact and P-F-L curve of ball bearings, is discussed and examined. As a result, the stressed volume proposed by Weibull for structural materials in the equal stress field yields a stressed volume, stressed area, stressed length, and/or stressed point corresponding to a critical stress of failure depending on the acting stresses, because they are expressed by the number of product law of probabilities. It has been established that a 50% stress rating for static strength and a 90% stress rating for fatigue life of materials as well as a 90% stress rating for the race of ball bearings could be specified. The linkage example can be shown by using the alternating torsion P-S-N test for JIS SUJ2/AISI 52100 steel and the race of ball bearings. Furthermore, it is also found that the stress-life/load-life exponent that depends on the strength of the materials is independent of the Weibull slope as well as the stressed volume, which were introduced in Lundberg-Palmgren's theory.

A03 材料疲れの寿命データに基づいた転がリ軸受の新寿命理論(OS2 最新機械要素技術(1))

New life theory for rolling bearings is propounded by a linkage between the rating life data converted into the same size with bearing races in relation to the characteristic data of material carried out by alternating torsion probabilistic stress-life (P-S-N) test for hourglass shape specimens (Weibull slope ms_2=3/2, D_eo=φ8 mm) and the theoretically equivalent rating life data for bearing races (m= 10/9 for point contact bearings and m =21120 for line contact bearings). The 90% load rating formulas for races and a whole bearing are developed with a linkage factorβ, and then a newly introduced 100% load rating formulas are postulated with a linkage factor βby using the minimum life data for the life distribution data of ball bearings #6206. Consequently,β = 2A,β' = 2.16 and a reduction factor of rating loadλ=β'/β = 0.9 can be evaluated.

Fatigue Reliability Assessment of Steel Member Using Probabilistic Stress-Life Method

The fatigue reliability of a steel member in a bridge is estimated by using the probabilistic stress-life method. The stress history of a member is defined as the loading block when a truck passes over a bridge, and the stress range frequency distribution of the stress history is obtained by a stress range frequency analysis. A probabilistic method is applied to the stress range frequency distribution, and the parameters of the probability distribution for the stress range frequency distribution are used in a numerical simulation. To obtain the probability of failure of a member under a loading block, Monte Carlo simulation is performed in conjunction with Miner's rule, the modified Miner's rule, and Haibach's rule for fatigue damage evaluation. Through these analyses procedures, we obtain an evaluation method for fatigue reliability that can predict the block number of the failure load and residual fatigue life.

20414 軸受鋼SCM420Hにおける両振りねじり寿命試験のP-S-N研究(OS8 進化を続ける転がり機械要素(2),オーガナイズドセッション)

SCM420H has been used for rolling bearings, linear bearings and ball screws, etc. It is thought that for this material when the fatigue test is carried out, in the domain of high cycle fatigue of the S-N curve so-called the Wohler curve, a fatigue limit appears. This type of fatigue limit has been used in the ISO-2007 with a life modification factor a_<ISO> for rolling bearings. However, at present even in the life test of bearing or S-N fatigue test of material, the experimental data does not show any apparent sign of the fatigue limit. In this paper, alternating torsion fatigue test for probabilistic stress-life (P-S-N) evaluation is carried out under standard stress values, from τ = 0.93 GPa to τ = 0.53 GPa for five lots made up of a total of 108 samples, and P-S-N curves were determined based on the three-parameter Weibull and the log-normal distribution function.

Probabilistic Stress-Life (P-S-N) Study on Bearing Steel Using Alternating Torsion Life Test

Probabilistic stress-life (P-S-N) studies using alternating torsion life test were conducted with the bearing steel JIS SUJ2/AISI 52100 having a hardness range of Rockwell C scale of 58-62 HRC to determine the existence of a fatigue limit for this through-hardened steel. One hundred and fifty (150) alternating torsion tests were performed at six torsion maximum shear stress amplitudes of 0.5, 0.63, 0.76, 0.80, 0.95, and 1.0 GPa. The number of specimens that were run at each stress amplitude varied from 19 to 33. There is no observable fatigue limit for JIS SUJ2/AISI 52100 bearing steel. On log-log plotted data, life is linear and is inversely proportional to shearing stress to a 10.34 exponent. The failure mode of the experiment is due to the conjugate tensile and compressive alternating stresses in accordance with alternating shearing stresses. The three-parameter Weibull life distribution function with a constant value of the Weibull slope m = 3/2 was found to have the best conformity followed by the log-normal distribution and the two-parameter Weibull distribution function. The shear stress-life exponent (A = 10.34) for JIS SUJ2/AISI 52100 bearing steel was independent of the Weibull slope.

Fatigue assessment of a riveted shear splice based on a probabilistic model

A procedure for estimation of probabilistic fatigue S–N curves for notched structural components is described. Plain material strain–life data is used to identify a statistical Weibull strain–life model and, using an adequate elastoplastic analysis, material strain–life probabilistic curves are converted into probabilistic stress–life curves of the structural component. The performance of the proposed model is illustrated by a practical example of a riveted shear splice, from a Portuguese railway bridge, for which experimental resistance data is available. A simplified elastoplastic analysis based on the Neuber and the Glinka rules are used, supported by the results of an elastic finite element analysis of the riveted connection. The paper demonstrates the success of the proposed probabilistic model since it correlates satisfactorily with the available experimental data for the riveted connection. The achieved results confirm the proposed probabilistic model as well suited for notched structural components with a whole fatigue life dominated by crack initiation.

A Study on Fatigue Behavior of SM490A Steel under Low Temperature

This paper deals with the fatigue behavior and its statistical properties of SM490A steel at various temperatures, which is utilized in the railway vehicle. For these goals, the tensile ad fatigue tests were performed by using a servo-hydraulic fatigue testing machine at three temperatures: +20°C, -10°C and -40°C. The static strength and fatigue limits of SM490A steel were increased with decreasing of test temperature. The probabilistic properties of fatigue behavior are investigated by means of probabilistic stress-life (P-S-N) curve and they are well in conformance with the experimental results regardless of temperature. Also, based on P-S-N curves, the variation of fatigue life is investigated and as the temperature decreases, the variation of fatigue life increases moderately.

Life Distribution and Reliability for Rotating Bending S-N Test on Highly Hardened Bearing Steel

A study on the fatigue behavior of bearing steel by using rotating bending fatigue test rigs is carried out for bearing steel (JIS SUJ2) heat-treated to HRC58-62. P-S-N (Probabilistic Stress Life) curves and fatigue life distributions, such as Weibull and log-normal, are used for discussion. As a result, the best fit for a life distribution of six lots with each sample size of around thirty specimens, at the stress levels from 0.94 to 1.27 GPa, is obtained by 3-parameter Weibull distribution, followed by the log-normal distribution as second, and 2-parameter Weibull distribution as the third. From the observation of broken section in test piece the initiation point of fatigue failures are almost started from subsurface non-metallic inclusions, TiN, CaO-Al2O3 and CaO-MgO-Al2O3. The fatigue limit for the bearing steel could not be observed from the experimental result. It is also made clear that the statistical distribution and P-S-N curve model must be described from the same formula, and a rating stress such as bearing rating load is successfully introduced to the 3-parameter Weibull and log-normal distribution.