Fatigue Life Distribution Research Articles

On the Relationship between Structural Quality Index and Fatigue Life Distributions in Aluminum Aerospace Castings

Tensile and fatigue testing results of D357 and B201 aluminum alloy aerospace castings reported in the literature have been reanalyzed. Yield strength–elongation bivariate data have been used as a measure of the structural quality of castings, and converted into quality index. These results as well as fatigue data have been analyzed by using Weibull statistics. A distinct relationship has been observed between expected fatigue life and quality index. Moreover, probability of survival in fatigue life was found to be directly linked to the proportions of the quality index distributions in two different regions, providing further evidence about the strong relationship between elongation, i.e., structural quality and fatigue performance.

Mean and design fatigue lives of SFRC containing cement-based materials

This paper examines the flexural fatigue performance of steel-fibre-reinforced concrete (SFRC) containing different cement-based materials in terms of mean and design fatigue lives. An experimental programme was designed to determine the fatigue lives of beam specimens of seven SFRC composites containing fly ash, silica fume, limestone powder and metakaolin as partial cement replacements in varying amounts. The fatigue life distributions of all mix combinations at different stress levels were statistically analysed using a two-parameter Weibull distribution. The Weibull modelling used to describe the distribution of cycles to failure is summarised. The Weibull distribution parameters as determined from fatigue/S–N equations were employed to determine the mean fatigue lives. The design fatigue lives were calculated corresponding to selected acceptable probabilities of failure (i.e. 0·01, 0·05, 0·10, 0·15 and 0·25). SFRC containing fly ash and silica fume in proportions of 20% and 10% by weight of binder respectively showed the best fatigue performance in terms of mean and design fatigue lives as compared with the other mix combinations.

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.

A regularized approach to linear regression of fatigue life measurements

Purpose – The linear regression technique is widely used to determine empirical parameters of fatigue life profile while the results may not continuously depend on experimental data. Thus Tikhonov-Morozov method is utilized here to regularize the linear regression results and consequently reduces the influence of measurement noise without notably distorting the fatigue life distribution. The paper aims to discuss these issues. Design/methodology/approach – Tikhonov-Morozov regularization method would be shown to effectively reduce the influences of measurement noise without distorting the fatigue life distribution. Moreover since iterative regularization methods are known to be an attractive alternative to Tikhonov regularization, four gradient iterative methods called as simple iteration, minimum error, steepest descent and conjugate gradient methods are examined with an appropriate initial guess of regularized coefficients. Findings – It has been shown that in case of sparse fatigue life measurements, linear regression results may not have continuous dependence on experimental data and measurement error could lead to misinterpretations of the solution. Therefore from engineering safety point of view, utilizing regularization method could successfully reduce the influence of measurement noise without significantly distorting the fatigue life distribution. Originality/value – An excellent initial guess for mixed iterative-direct algorithm is introduced and it has been shown that the combination of Newton iterative approach and Morozov discrepancy principle is one of the interesting strategies for determination of regularization parameter having an excellent rate of convergence. Moreover since iterative methods are known to be an attractive alternative to Tikhonov regularization, four gradient descend methods are examined here for regularization of the linear regression problem. It has been found that all of gradient decent methods with an appropriate initial guess of regularized coefficients have an excellent convergence to Tikhonov-Morozov regularization results.

Weibull statistical analysis of Krouse type bending fatigue of nuclear materials

A bending fatigue mini-specimen (Krouse-type) was used to study the fatigue properties of nuclear materials. The objective of this paper is to study fatigue for Grade 91 ferritic-martensitic steel using a mini-specimen (Krouse-type) suitable for reactor irradiation studies. These mini-specimens are similar in design (but smaller) to those described in the ASTM B593 standard. The mini specimen was machined by waterjet and tested as-received. The bending fatigue machine was modified to test the mini-specimen with a specially designed adapter. The cycle bending fatigue behavior of Grade 91 was studied under constant deflection. The S–N curve was created and mean fatigue life was analyzed using mean fatigue life. In this study, the Weibull function was predicted probably for high stress to low stress at 563, 310 and 265 MPa. The commercial software Minitab 17 was used to calculate the distribution of fatigue life under different stress levels. We have used 2 and 3- parameters Weibull analysis to introduce the probability of failure. The plots indicated that the 3- parameter Weibull distribution fits the data well.

Analysis of flexural fatigue failure of concrete made with 100% Coarse Recycled Concrete Aggregates

The paper presents results of an investigation carried out to analyze the flexural fatigue performance of concrete beams made with 100% Coarse Recycled Concrete Aggregates (RCA) and its comparison with that of concrete made with 100% Coarse Natural Aggregates (NA). The fatigue performance of concrete beams made with RCA as well as NA has been assessed in terms flexural fatigue life distributions and two-million cycle endurance limit. Experiments were conducted to obtain the flexural fatigue lives of concrete beam specimens made with 100% RCA as well as 100% NA under different stress levels and further compared with literature available on NA. Specimens of size 100mm×100mm×500mm were tested under four point flexural fatigue loads applied at a frequency of 10Hz. It has been shown that the fatigue life distributions of concrete mixes made with 100% RCA and 100% NA can be modeled by the two-parameter Weibull distribution. The values of the shape parameters of the Weibull distribution obtained for concrete made with RCA have been found to be smaller than that of concrete made with NA in present investigation and previous studies on NA, thus indicating higher variability in the distribution of flexural fatigue life of concrete made with RCA viz. a viz. concrete made with NA. The two-million cycles endurance limit for concrete made with 100% RCA has been found to be 50%, which is about 8% and 7% lower than that of concrete made with NA in present and previous studies respectively.

Anisomorphic constant fatigue life diagrams of constant probability of failure and prediction of P–S–N curves for unidirectional carbon/epoxy laminates

The effect of stress ratio on statistical distribution of fatigue life of a unidirectional carbon/epoxy composite has been examined. Furthermore, a method for efficiently predicting a family of S–N curves with probability of failure as the parameter for any stress ratio of constant amplitude loading has been developed. For this purpose, fatigue life data are first collected at each of different stress levels for tension–tension (TT), tension–compression (TC) and compression–compression (CC) fatigue loadings, respectively. The experimental results show that the scatter in fatigue life tends to become larger in order of TT, TC and CC loading. Lognormal distribution is used to quantify the statistics of the static tensile and compressive strength data and the fatigue life data for each of different stress levels and stress ratios. It is found that lognormal distribution is applicable approximately not only to the static strength data in tension and compression, but also to the fatigue life data for each of different stress levels and stress ratios. The parameters of the distribution of fatigue life are shown to be dependent on the stress ratio of fatigue loading. The experimental P–S–N curves are established for each of different stress ratios using the distributions fitted to the static strength and fatigue life data. Then, a method for constructing the anisomorphic constant fatigue life (CFL) diagrams of constant probability of failure is developed. The proposed probabilistic anisomorphic CFL diagram approach allows not only accurately predicting the P–S–N curves for different stress ratios, but also adequately describing the stress-ratio dependent scatter in fatigue life of the unidirectional composite.

The Fatigue Behavior Study of Intelligent Tower Crane by Finite Element Theory

Intelligent tower crane has large structure deadweight. The service life of the whole machine is dependent on the life of the structure. As a result, the metal structure should be designed by using correct and reasonable methods to obtain excellent fatigue properties. And it can guide the design, manufacturing, use and maintenance process for crane. And it has great significance to prevent the fatigue fracture accident. The theoretical mechanics and material mechanics theory is a semi-theoretical semi-empirical traditional design method, but it is not the suitable design method. Now, the finite element method, fracture mechanics, the boundary element method, the optimization design method, reliability design and fatigue design methods are widely used in the structure design of crane. In this paper, the intelligent tower crane structure is analyzed by finite element modeling. According to the actual situation, crane structure is studied by finite element statics analysis. Then mechanical property of this kind of structure is analyzed in detail. And the weak links of the structure are found out. The residual life can be estimated finally. As a result, designers can comprehensively understand the fatigue life distribution of different parts in the crane. Therefore, they can provide intuitive and comprehensive basis for comparing the advantages and disadvantages of different design schemes and fatigue performances for design improvement.

A Novel Conditional Probability Density Distribution Surface for the Analysis of the Drop Life of Solder Joints Under Board Level Drop Impact

The scattering of fatigue life data is a common problem and usually described using the normal distribution or Weibull distribution. For solder joints under drop impact, due to the complicated stress distribution, the relationship between the stress and the drop life is so far unknown. Furthermore, it is important to establish a function describing the change in standard deviation for solder joints under different drop impact levels. Therefore, in this study, a novel conditional probability density distribution surface (CPDDS) was established for the analysis of the drop life of solder joints. The relationship between the drop impact acceleration and the drop life is proposed, which comprehensively considers the stress distribution. A novel exponential model was adopted for describing the change of the standard deviation with the impact acceleration (0 → +∞). To validate the model, the drop life of Sn-3.0Ag-0.5Cu solder joints was analyzed. The probability density curve of the logarithm of the fatigue life distribution can be easily obtained for a certain acceleration level fixed on the acceleration level axis of the CPDDS. The P–A–N curve was also obtained using the functions μ(A) and σ(A), which can reflect the regularity of the life data for an overall reliability P.

Investigation on tension–tension fatigue performances and reliability fatigue life of T700/MTM46 composite laminates

Tension–tension fatigue performances of T700/MTM46 composite laminates were investigated in this paper and the fatigue limit was determined. Failure modes of the fatigue specimens are mainly characterized by severe delamination throughout the whole gauge length while the static tension specimens exhibit brittle fractures within a small region. The stiffness degradation shows a quasi-linear slow decline during approximately 0–80% fatigue life and has a sharp decline since 80% fatigue life. Damage evolution was studied by fatigue specimens’ edge view, which showed the damage in 90° plies initiate firstly and propagate most seriously during fatigue. The distribution of fatigue life was determined. Single side allowance factor was proposed to calculate the reliability fatigue life with both reliability and confidence level. The results show that reliability fatigue life reduces more when the reliability increases than when confidence level does to the same degree. A new fatigue model (p–γ–S–N curve) was also established to predict the reliability fatigue life.

Fragility analysis of wind-excited traffic signal structures

Traffic signal structures are prone to fatigue failure due to wind-induced excitation that is often difficult to characterize due to the variable response arising from a combinations of along- and across-wind effects and the uncertainties associated with the fatigue and fracture phenomena. A probabilistic framework is proposed to predict structure component fatigue life. To solve the problem of wind-induced fatigue, the model is introduced to inter-relate wind hazard to structural response and hence fatigue damage. Stress range demand variabilities are considered separately from the randomness associated with the fatigue capacity. To characterize the natural wind response of a representative structure, full-scale structural monitoring is conducted, and the data were incorporated into an example application of the framework. To successfully demonstrate the efficacy of the proposed framework, resulting wind-induced fatigue life distributions are compared against compiled inspection records for a large traffic signal structure population in Wyoming.

Stochastic fatigue life and reliability prediction based on residual strength

A randomized approach is developed to solve a deterministic equation. The method uses random deterministic approach to achieve the fatigue life based on residual strength and S-N curve. We propose a one-to-one transformation method to deduce the distribution of fatigue life from the residual strength. The proposed method is simple and effective, and can be used for fatigue life prediction. An example is given to illustrate how the method works.

Influence of carbonation on fatigue of concrete with high volume of ground granulated blast-furnace slag

The effect of carbonation on fatigue performance of ground granulated blast-furnace slag concrete was investigated. Based on the static compression tests of carbonated GGBS-concrete, the correlation between carbonation depth and compressive strength was analyzed and an equation between carbonation depth and compressive strength was put forward. Meanwhile, fatigue S-N curves of various carbonation depths were fitted, and the influence of carbonation on fatigue life and strength was studied. Carbonation has a dual effect on the fatigue behavior of GGBS-concrete. A fatigue equation based on the depth of carbonation was established. Also, the probabilistic distribution of fatigue life of carbonated concrete at a given stress level was modeled by the two-parameter Weibull distribution.

Fatigue life prediction: A comparative study for a three layer EN45A parabolic leaf spring

Article history: Received 6 January, 2015 Accepted 10 May 2015 Available online 12 May 2015 There are literally several studies accomplished to predict the fatigue life of leaf springs but estimation of fatigue life of a parabolic leaf spring by using CAE tools has not yet been executed in the past. Parabolic spring is an important component in a vehicle suspension system. It needs to have excellent fatigue life and in today’s scenario manufacturers rely on constant loading fatigue analysis. The objective of this work is to perform the fatigue analysis of parabolic leaf spring by three different methods where CAE analysis is performed to observe the distribution of stress fatigue life and damage using Goodman approach. In this work, fatigue life of the parabolic leaf spring is determined as per SAE spring design manual and experimentally by testing on full scale fatigue testing machine. ANSYS is used for CAE solution for the prediction of leaf springs fatigue life considering stress theory. The fatigue life estimated by all three modes is then compared for the purpose of validation. The methodology used in this paper brings a practical approach to the professionals in the industries who are engaged for design of mechanical components. © 2015 Growing Science Ltd. All rights reserved.

Probabilistic Modeling of Fatigue Damage Accumulation under Spectrum Loading

A probabilistic methodology for modeling fatigue damage accumulation and fatigue life under variable amplitude loading is proposed in this paper. With probabilistic modifications, the calculative consistency between fatigue damage and life is achieved in the model and the load sequence effects are properly accounted for variable amplitude loading. This damage model overcomes the inherent deficiencies in the linear damage accumulation rule but still preserves its simplicity for engineering application. With Monte Carlo sampling method, numerical verification of this model is conducted under two-level spectrum loading. The predicted probabilistic distributions of fatigue life are validated by the fatigue tests on Al-alloy straight lugs.

Duplex S-N fatigue curves: statistical distribution of the transition fatigue life

In recent years, very-high-cycle fatigue (VHCF) behavior of metallic materials has become a major point of interest for researchers and industries. The needs of specific industrial fields (aerospace, mechanical and energy industry) for structural components with increasingly large fatigue lives, up to 1010 cycles (gigacycle fatigue), requested for a more detailed investigation on the experimental properties of materials in the VHCF regime. Gigacycle fatigue tests are commonly performed using resonance fatigue testing machines with a loading frequency of 20 kHz (ultrasonic tests). Experimental results showed that failure is due to cracks which nucleate at the specimen surface if the stress amplitude is above the conventional fatigue limit (surface nucleation) and that failure is generally due to cracks which nucleate from inclusions or internal defects (internal nucleation) when specimens are subjected to stress amplitudes below the conventional fatigue limit. Following the experimental evidence, the Authors recently proposed a new statistical model for the complete description of SN curves both in the high-cycle-fatigue (HCF) and in the VHCF fatigue regions (Duplex S-N curves). The model differentiates between the two failure modes (surface and internal nucleation), according to the estimated distribution of the random transition stress (corresponding to the conventional fatigue limit). No assumption is made about the statistical distribution of the number of cycles at which the transition between surface and internal nucleation occurs (i.e., the transition fatigue life). In the present paper, the statistical distribution of the transition fatigue life is obtained, according to the statistical model proposed. The resulting distribution depends on the distance between the HCF and the VHCF regions and on the distribution of the random transition stress. The estimated distribution can be effectively used to predict, with a specified confidence level, the number of cycles for which an internal nucleation may probabilistically occur in a VHCF test and it is also informative for properly choosing the end of HCF tests in terms of number of cycles. A numerical example, based on experimental datasets taken from the literature, is provided.

Reliability-based fatigue life investigation for a medium-scale composite hydrokinetic turbine blade

As the most important, expensive component of a hydrokinetic turbine system, the composite turbine blade must achieve a long operating life (10–20 years). The investigation of fatigue life for the composite turbine blade is essential when designing a cost-effective hydrokinetic composite turbine system. A reliability-based fatigue life analysis methodology was developed for a medium-scale, horizontal axis, hydrokinetic turbine blade. Finite element method, coupled with the blade element momentum theory, was used to find the stress response on the turbine blade. The fatigue behavior of the blade was studied in stress-critical zones. A metamodel was constructed for the stress response according to simulations at specified design points. Accounting for uncertainties in material properties and the material S–N curve, the reliability analysis method was employed to estimate the fatigue life distribution of the hydrokinetic turbine blade. The effect of river velocity models on the fatigue life of turbine blades was also studied. The fatigue life of the composite blade was sensitive to composite material properties. Transverse strain E22 is particularly dominant which is related to the matrix cracking as the fatigue failure mode. The statistical distribution of S–N data implies a significant dependence of fatigue life on composite S–N data.

Research on the Effect of Seasonal Environmental Loads on Bohai Bay Offshore Platform

In recent decades jacket platforms are widely used for facilitating the offshore oil industries in order to reach their demands of producing oils. In this regard given analyses shows the influence of seasonally based environmental loads acting on the offshore platform structure situated at Bohai Bay northeast of China. This paper studies and summarizes the structure reliability theory with jacket platform as the research object; it is the first time to aim and finds the most dangerous season effecting Bohai Bay offshore platforms by considering seasonal environmental loads. Finite element analysis ANSYS software is used for model analyses and optimisation of the structure spatial correlation seasonal loads. Environmental design data is extracted according to its geographical conditions in the form of wave, wind and current forces. Since most of the control management nodes work below the surface of the water so the distribution of stress and fatigue life of the pipe node under multi-axial loading is in different forms. The analysis mainly focuses on the stress and fatigue life appropriate characteristics to the actual situation of multi-axial loading case of the K-joint welding location and mainly environmental effect on the platform.

Fatigue performance of plain and steel fibre reinforced self compacting concrete using S–N relationship

The paper presents the results of the study conducted to explore the fatigue performance of plain self compacting concrete (SCC) and steel fibre reinforced self compacting concrete (SFRSCC). Approximately 250 flexural fatigue tests and 195 complementary static flexural tests were executed on beam specimens of size 100mm×100mm×500mm under four point flexural loading. The distribution of fatigue life of SCC and SFRSCC was examined at different stress levels, which is a prerequisite for estimating the mean and design fatigue lives. The flexural fatigue performance of SCC and SFRSCC containing three different fibre volume fractions was evaluated in terms of mean and design fatigue lives, and two-million cycles of fatigue strengths/endurance limits. The flexural fatigue performance of SCC as well as SFRSCC was found to be better than the conventionally vibrated concrete (CVC) and fibre reinforced concrete (CVFRC).

A global procedure for the time-dependent reliability assessment of crane structural members

This paper aims at developing a probabilistic fatigue assessment procedure for crane structural members, using a structural reliability method, namely the stress–strength interference method. A crane member strength law is found by fitting fatigue life distribution parameters using finite element results and experimental data. The stress model is developed by using on-site data to determine probabilistic parametric distributions defining crane member loading. The efficiency of the proposed stress–strength interference method for tower crane member reliability assessment in fatigue is demonstrated on a jib chord member connection.