Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

An engineering method for reliability analyses of mechanical structures for long fatigue lives

Reliability analyses of mechanical structures designed for long fatigue lives require: some information on the probability distribution of material fatigue strength at long fatigue lives. In order to address this need, three-parameter P-S-N curves are adopted to represent the results of fatigue tests based on the conventional method. The parameters of the P-S-N curves are estimated by using the least squares fitting method and maximizing the correlation coefficient. The three-parameter P-S-N curves obtained are then used to estimate the fatigue strengths for different survival probabilities at an arbitrarily long fatigue life. These fatigue strengths are used to define the probability distribution of fatigue strength at the long fatigue life when a normal. distribution is used to approximate the probability distribution of fatigue strength. The method is illustrated by analyzing the results of fatigue tests of steel #45 (Chinese steel) notched specimens subject to axial loads with a stress concentration factor k_t = 2·0. Then, the method is applied to the fatigue reliability analysis of the runner of a hydraulic turbine. It is shown here that the reliability at long lifetimes can be easily estimated by the proposed engineering method and the conventional method may give a non-conservative design at long fatigue lives due to the assumption of bi-linear P-S-N curves.     

Influence of case-carburizing and micro-defect on competing failure behaviors of Ni–Cr–W steel under gigacycle fatigue

Axial loading test was performed to investigate the influence of case-carburizing and micro-defect on competing failure behaviors of Ni–Cr–W Steel under gigacycle fatigue. The interior failures induced from inclusion and microstructural inhomogeneity become the predominant failure mode in the life regime beyond 10⁵ cycles. The case-carburizing has no effect on the fatigue strength with interior failure. Compared with the lower limit values of experimental S–N data, the predicted results by using GP distribution is relatively suitable. From the viewpoint of reliability, the modeling method of interior S–N curve with the maximum defect size at a given probability is satisfactory.     

Influence of the Initiation Length in Predictions of Life in Fretting Fatigue

Abstract: Two different phases are usually distinguished in the crack growth process: initiation and propagation. Within the models used in determining fatigue life, there are many that combine both phases, determining total life as the sum of the number of cycles spent in initiation, N_i, and propagation, N_p. In order to apply these models, it is necessary to define the crack length at which it is considered that initiation finishes and propagation begins: initiation length, a_i. This length is usually defined a priori based on the size of the smallest detectable crack, on the definition of failure in the S‐N curve, or by choosing the value that better fits the experimental results. The object of this paper is to analyse the influence of this initiation length over the estimated fatigue life in fretting fatigue. The model used calculates the initiation phase from an S‐N curve where the propagation cycles from the defined initiation length have been subtracted. This model is applied to a group of fretting fatigue tests with spherical contact.     

A fuzzy approach for drawing S–N curves in the finite life region

In this work a fuzzy approach has been developed in order to estimate the probability of fatigue failure. In particular, with the proposed method the S–N curves of a material in the finite life region can be drawn. The experimental data are represented in terms of fuzzy sets and are fitted using a fuzzy linear regression. Data scattering and uncertainty in the empirical failure model are reflected in the definition of membership functions. Several examples are shown to illustrate the procedure. Failure probabilities and fatigue curves obtained by the fuzzy method are similar to those obtained by traditional statistical analysis, based on normal distributions of strength with standard deviation that remains constant with different load levels. In particular, the results obtained indicate that the possibilities offered by fuzzy systems are also applicable for estimating the Wöhler curve of a material under fatigue stresses. To evaluate its reliability, the proposed method is compared with the traditional one, with particular attention to the case in which a small amount of experimental data is available. The new fuzzy method is slightly less accurate than traditional statistical analysis to outline S–N curves in the finite life region. This is mainly due to the fact that the method is influenced by the nonuniformity of data dispersion at each level of stress.     

Proposal for a more accurate physically based S–N curve for welded steel joints

The present article proposes a more accurate S–N curve in the high cycle fatigue regime for fillet welded joints in steel subjected to constant amplitude loading. The S–N curves are constructed based on a physical model of the fatigue damage evolution. It is a two phase model where the crack initiation is treated by a local weld notch approach. The subsequent growth is based on the concept of the stress intensity factor at the crack front by applying the Paris law. According to the proposed model, the time to crack initiation becomes the dominant part of the fatigue life at low stress range levels. The resulting S–N curves are non-linear for a log–log scale and they do not predict any fatigue limit. The curves change slope gradually and the stress range continue to decrease with increasing number of cycles. The curves fit collected life data far better than the conventional bi-linear curves found in rules and regulations. The curves predict considerably longer fatigue lives at low stresses than the conventional curves do, despite the non-existence of a fatigue limit.     

Effect of temperature on high-cycle fatigue and very high cycle fatigue behaviours of a low-strength Cr–Ni–Mo–V steel welded joint

Axially push–pull fatigue tests of a low-strength Cr–Ni–Mo–V steel welded joint were conducted up to very high cycle fatigue regime at room temperature and 370 °C. The S–N curve at room temperature shows a duplex shape, while the S–N curve at 370 °C is continuously decreasing with lower fatigue strength. The welds at 370 °C undergoes dynamic strain ageing and has an enhanced load–defects interaction, leading to equal distribution of failures among different parts of the welds. The Z parameter model, with micro-defect location incorporated, having sound physical representation, is life-controlling of the welds at high temperature.     

Low‐cycle fatigue/high‐cycle fatigue interactions in notched Ti‐6Al‐4V*

Combined low‐cycle fatigue/high‐cycle fatigue (LCF/HCF) loadings were investigated for smooth and circumferentially V‐notched cylindrical Ti–6Al–4V fatigue specimens. Smooth specimens were first cycled under LCF loading conditions for a fraction of the previously established fatigue life. The HCF 10⁷ cycle fatigue limit stress after LCF cycling was established using a step loading technique. Specimens with two notch sizes, both having elastic stress concentration factors of K_t = 2.7, were cycled under LCF loading conditions at a nominal stress ratio of R = 0.1. The subsequent 10⁶ cycle HCF fatigue limit stress at both R = 0.1 and 0.8 was determined. The combined loading LCF/HCF fatigue limit stresses for all specimens were compared to the baseline HCF fatigue limit stresses. After LCF cycling and prior to HCF cycling, the notched specimens were heat tinted, and final fracture surfaces examined for cracks formed during the initial LCF loading. Fatigue test results indicate that the LCF loading, applied for 75% of total LCF life for the smooth specimens and 25% for the notched specimens, resulted in only small reductions in the subsequent HCF fatigue limit stress. Under certain loading conditions, plasticity‐induced stress redistribution at the notch root during LCF cycling appears responsible for an observed increase in HCF fatigue limit stress, in terms of net section stress.     

Fatigue properties of rock salt subjected to interval cyclic pressure

Due to the influence of gas pressure operational modes, surrounding rock of salt carven underground gas storage always suffers combined stress composed of cyclic pressure and intervals of no stress (or small stress). We conducted comparisons between conventional fatigue tests and (six groups of) interval fatigue tests, which combine spaced stress cycles and normal stress cycles. Experimental measurements demonstrate that the combined cyclic stress has a strong impact on the fatigue activity of rock salt. In interval fatigue tests, the residual strain of a spaced stress cycle is notably larger than that of a normal stress cycle. As the conventional tests can be actually considered as a kind of fatigue tests with transitory intervals, the accumulative rate of residual deformation increases with the duration of the interval in all test groups. The testing results show the fatigue lives of samples from interval fatigue tests dramatically reduce in a certain range; when intervals extend beyond the value 120 s, fatigue lives perform with a slight rise. Based on the S–N curve and the S–T curve, an experiential model fitting the relationship between fatigue life and interval was established.     

A statistical model for scatter representation in stress life curves

Fatigue life reliability often is accounted for through minimal material data. To provide this information within structural calculation, experimental data from specimen testing needs to be processed with statistical methods. The results are either mean or worst case material data. However, in a robust design environment, scatter itself must be numerically available. In this paper, fatigue test results of a nickel‐based super alloy at two temperatures are taken from literature. These data are processed according to ASTM standard E739 to identify median and standard deviation, based on a stress life curve (S—N curve) in double logarithmic coordinates first proposed by Basquin. In addition, a new method for non‐constant standard deviation is applied to the dataset. The S—N curve parameters are treated with a statistical distribution to account for scatter in the material data. The basic parameter set is perturbed by Monte Carlo simulation to generate pseudo‐scatter in the life result, which can be plotted as a Wöhler field. This pseudo‐scatter is analysed and compared to the ASTM constant standard deviation regression. Statistical methods are used to show that a realistic prediction of fatigue life is feasible using the Perturbation approach. Both models represent the literature fatigue data very well, whereas the Perturbation approach provides more flexibility. It is especially recommended for black box Monte Carlo studies of structural lifing. The Perturbation approach is additionally capable of including runouts and using other life curves than such of S—N type.     

Models for Variable-Stress Accelerated Life Testing Experiments Based on Wener Processes and the Inverse Gaussian Distribution

Variable-stress accelerated life testing trials are experiments in which each of the units in a random sample of units of a product is run under increasingly severe conditions to get information quickly on its life distribution. We consider a fatigue failure model in which accumulated decay is governed by a continuous Gaussian process W(y) whose distribution changes at certain stress change points to < t _l < < … <t _k , Continuously increasing stress is also considered. Failure occurs the first time W(y) crosses a critical boundary ω. The distribution of time to failure for the models can be represented in terms of time-transformed inverse Gaussian distribution functions, and the parameters in models for experiments with censored data can be estimated using maximum likelihood methods. A common approach to the modeling of failure times for experimental units subject to increased stress at certain stress change points is to assume that the failure times follow a distribution that consists of segments of Weibull distributions with the same shape parameter. Our Wiener-process approach gives an alternative flexible class of time-transformed inverse Gaussian models in which time to failure is modeled in terms of accumulated decay reaching a critical level and in which parametric functions are used to express how higher stresses accelerate the rate of decay and the time to failure. Key parameters such as mean life under normal stress, quantiles of the normal stress distribution, and decay rate under normal and accelerated stress appear naturally in the model. A variety of possible parameterizations of the decay rate leads to flexible modeling. Model fit can be checked by percentage-percentage plots.     

Investigation of fatigue damage to welded joints under variable amplitude loading spectra

The paper presents the results of the investigation on the effect of loading spectra with different mean stresses on the validity of Miner’s rule, and the effect of stresses below the constant amplitude fatigue limit (CAFL) on the fatigue performance of two types of weld joint. In support of understanding the mechanism for any deficiency to Miner’s rule, fracture mechanics analysis was carried out by measuring and predicting the crack growth in specimens tested under both constant amplitude and variable amplitude loading. The experimental results showed that, although Miner’s rule would predict the same fatigue life for each type of specimens tested under the same spectrum, in fact the actual value of Σ(n/N) at failure strongly depended on the sequence applied. The influence of the loading sequence on Σ(n/N) was in agreement with that on crack growth rates. The deficiency in Miner’s rule was attributed primarily to the stress interaction effects resulting from the type of loading sequence used. The experimental results also showed that, under certain circumstances, stress ranges well below the fatigue limit were found to be as damaging as implied by the S–N curve extrapolated beyond the CAFL without changing the slope. The value of the minimum fully damaging stress range was found to depend on the basic fatigue strength of the weld joint.     

Rapid evaluation of fatigue limit in AZ31B magnesium alloy using acoustic emission

Acoustic emission (AE) was used in a fatigue experiment to characterise AE signals and to rapidly determine the fatigue limit of AZ31B magnesium (Mg) alloy. The AE signals during fatigue were characterised according to waveforms and frequency. Meanwhile, the energy dissipation in the process of fatigue, which was represented by the accumulative AE energy, can be used to determine the fatigue limit. Based on the AE parameters, the fatigue limit was 97?MPa, with an 8% error value when compared with the results obtained by the conventional S–N curve method. This model only requires the accumulated energy of the signals during strain hardening. Therefore, the fatigue limit can be determined rapidly.     

Experimental estimation of the probability distribution of fatigue crack growth lives

This paper deals with a method to estimate numerically the reliability of fatigue sensitive structures with respect to fatigue crack growth. A method is proposed to experimentally determine the probability distribution functions of material parameters of the Paris law, da/dN = C(ΔK/K₀)^m, using stress intensity factor controlled tests. The auto-correlation function of the resistance to fatigue crack growth, 1/C, is also estimated from the experimental data. The results of a high tensile strength steel show that the distribution of the parameter, m, is approximately normal and that of 1/C is a 3-parameter Weibull. The merit of the proposed method is that only a small number of tests are required to determine these functions. The probability distribution of the fatigue crack length after a given number of load cycles or the number of load cycles for a crack to reach a given length can be estimated by simulations of non-Gaussian random processes having these functions.     

Probabilistic fatigue S–N curves including the super-long life regime of a railway axle steel

A concurrent probability method is proposed for estimating probabilistic fatigue S–N curves including the super-long life regime. This work is based on experimental investigation of LZ50 railway axle steel. Test results reveal that fatigue cracks are initiated from the weakest surface phase and the damage preferentially follows a competition mechanism between the surface quality and subsurface inclusions. The curves are estimated by the test data in the mid-long life regime and the fatigue limits, which were connected together in concurrent probability levels. The accuracy of the curves was verified by the test data in the super-long life regime.     

Rapid determination for fatigue parameters of AZ31B magnesium alloy based on evolution of temperature under high cyclic fatigue

Abstract

Based on the infrared thermography method, experiments are carried out to investigate the evolution of temperature field of the extruded AZ31B magnesium alloy specimens under high cyclic fatigue load. The experimental results show that the superficial temperature of specimen under cyclic fatigue load changes with the number of cycles. According to the characteristics of surface temperature change, we propose a formula to calculate the residual fatigue life using energy approach. The proposed formula to assess the fatigue parameters (fatigue limit, residual fatigue life, fatigue life and S–N curve) achieves good results for AZ31B magnesium alloy. Furthermore, the fatigue limits (Δσ_eSN?=?90·3 MPa) derived from the traditional method through 10⁷ cycles were compared with the values predicted by the infrared thermographic method (Δσ_eTM?=?87·3 MPa) and the energy approach (Δσ_eΦ?=?86·2 MPa), and the comparison results of percentage differences are 3·3 and 4·5% respectively.     

Probabilistic anisomorphic constant fatigue life diagram approach for prediction of P–S–N curves for woven carbon/epoxy laminates at any stress ratio

A general engineering methodology to construct a family of anisomorphic constant fatigue life (CFL) diagrams with probability of failure as the parameter that allows efficiently predicting P–S–N curves at any stress ratios is developed and validated for a plain weave fabric carbon/epoxy laminate. Constant amplitude fatigue tests are first performed to obtain statistical samples of fatigue life at different stress levels and stress ratios, respectively. Static tensile and compressive strength data are also collected. The Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests suggest that both two-parameter lognormal and Weibull distributions are acceptable as the distributions for the static strength and fatigue life data, respectively, at the significance level of 5%. Then, we attempt to develop a methodology for efficient construction of the anisomorphic CFL diagrams for different constant values of probability of failure. It requires the P–S–N curves for any percentile points of the distribution for the critical stress ratio. To come up with this requirement, a probabilistic scaling law is formulated. It takes account of the probability-of-failure dependence of the critical stress ratio and the stress-ratio dependence of the P–S–N curve for the critical stress ratio. Finally, the anisomorphic CFL diagrams for different constant values of probability of failure are predicted using the proposed methodology, and they are shown to be in good agreement with the experimental results. It is also demonstrated that the P–S–N curves can efficiently and accurately be predicted for the woven CFRP laminate at any stress ratios using the proposed probabilistic anisomorphic CFL diagram approach.     

Application of the weakest link analysis to the area of fatigue design of steel welded joints

A new approach in the area of fatigue life assessment of steel welded joints is being proposed with the following features: (i) methodology of fatigue life calculation is independent from geometry of welded element; (ii) fatigue life assessment is based on fatigue characteristic of introduced efficient material – suitable for different steel welded joints; (iii) the fatigue life assessment is carried on the desired level of failure probability.In the proposed method a material volume surrounding the weld is divided into volume elements and regarded as a serial system having its definition in the reliability theory (the weakest link concept). Failure probability distribution of the welded structure is characterized by the proposed S–N curve for efficient material and the shape parameter introduced to describe the volume effect.     

Experimental study on very high cycle fatigue of martensitic steel of 2Cr13 under corrosive environment

Rotating bending fatigue test at very high cycle regimes was carried out on martensitic steel of 2Cr13 in air and 3.5% NaCl environment. The result showed that the S–N curve presents a stepwise tendency over the range of 10⁶–10⁸ cycles in both air and 3.5% NaCl environment. In air fatigue, cracks initiated from the sample surface and inclusions at subsurface and no typical fish eye feature in very high cycle fatigue were observed for all samples tested up to 6 × 10⁸ cycles. In 3.5% NaCl solution, a fatigue limit over the range of 10⁶–10⁸ cycles exhibited with the corrosion fatigue strength reduced by 47% compared to the air fatigue. Multiple cracks initiated from surface and the number of crack origins increased with increasing stress level and surface proportion of fatigue propagation increased as number of cycles increased.     

Fatigue crack growth model for constant amplitude loading

A fatigue crack growth model under constant amplitude loading has been developed considering energy balance during growth of the crack. The plastic energy dissipated during growth of a crack within cyclic plastic zone and area below cyclic stress–strain curve was used in the energy balance. The near crack tip elastic–plastic stress and strain were calculated on the basis of Hutchinson, Rice and Rosengren (HRR) formulations. Fatigue crack growth rate in linear and near threshold region of da/dN versus ΔK curve can be determined on the basis of the proposed model in terms of low cycle fatigue (LCF) properties determined on smooth specimen. The predictions of the model have been compared with the experimental and theoretical results available in the literature using mechanical and fatigue properties. The model compares well in the threshold and intermediate region of the da/dN versus ΔK curve for wide range of material tested.