Fatigue Life Distribution Research Articles

Effect of pre-corrosion on fatigue life of high strength steel 38CrMoAl

The effect of pre-corrosion on fatigue behavior of high strength steel 38CrMoAl was investigated with a fatigue test method using the accelerated pre-corrosion specimen in the neutral salt spray environment. The methods of weight-loss and energy dispersive spectrum (EDS) were adopted. The corrosion weight-loss rate was fitted with the test time using power law, and the relationship between the corrosion weightloss rate and the time was formulated. Moreover, the fatigue behaviors of the steel for different pre-corrosion time were investigated by the axis-direction tensile fatigue test. The fatigue life distribution characteristics of the pre-corrosion specimens were studied using the statistical probability methods, and the mathematical expectations and the standard tolerances of the material fatigue lives after different pre-corrosion time were obtained. It was found that the crack initiation of the high strength steel was accelerated by the preferential corrosion at the local plastic deform areas. The fatigue life obeys the lognormal distribution perfectly. Furthermore, within the common time range of the engineering, the standard tolerances of the logarithm of the fatigue life were independent of the pre-corrosion time.

Probabilistic Study on Corrosion Damage Distribution and Fatigue Lives of LY12CZ Aluminum Alloy Structure

A probabilistic neural network was developed to classify corrosion damage depth ranges based on the aluminum alloy failure mode. The results obtained indicate that corrosion damage depth for aluminum alloy can be classified into three groups. Statistical study on classified corrosion damage was carried out. The results show that pitting corrosion depth for aluminum alloy is in conforms to Gumbel distribution. The normal distribution fits well with intergranular corrosion depth and the exfoliation corrosion depth is consistent with Weibull distribution law. It may be necessary to use several distribution functions rather than a single distribution to represent corrosion damage characteristics due to the large distribution of corrosion depth in aircraft materials. According to corrosion damage depth distribution, corrosion depth was simulated by Monte Carlo method and used as the starting crack size. Fatigue lives were estimated by using a life prediction program AFGROW and the results are in good agreement with the experimental data. A probabilistic analysis shows that the distribution of fatigue lives is strongly correlated to the distribution of corrosion damage depth and should be classified into several groups to study.

Experimental investigation of random loading sequence effect on fatigue crack growth

An experimental study is proposed to investigate the effect of random loading sequence effect on the fatigue crack growth behavior of Al 7075-T6. The testing matrix includes different overload cycle percentage, overload ratios, and deterministic and random loading sequences in the current investigation. Multiple specimen tests and statistical data analysis are performed to show the effect of random loading sequence on the median and scatter behavior of fatigue crack growth. The proposed experimental study suggests that extreme value distribution is a good approximation of fatigue life distribution. It is observed that the effect of uncertain loading is different under different loading spectrums. For high overload cycle percentage spectrums, the random loading sequence has no major impact on the probabilistic crack growth behavior compared to the deterministic loading sequence with identical load cycle distributions. For low overload cycle percentage spectrums, the random loading sequence has huge impact on the probabilistic crack growth behavior compared to the deterministic loading sequence with identical load cycle distributions, for both the median and the scatter of the fatigue crack length curves. Finally, all experimental observations are reported in table format in Appendix A for future numerical model development and validation for interested readers.

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.

Fatigue life prediction based on Bayesian approach to incorporate field data into probability model

In fatigue life design of mechanical components, uncertainties arising from materials and manufacturing processes should be taken into account for ensuring reliability. A common practice is to apply a safety factor in conjunction with a physics model for evaluating the lifecycle, which most likely relies on the designer's experience. Due to conservative design, predictions are often in disagreement with field observations, which makes it difficult to schedule maintenance. In this paper, the Bayesian technique, which incorporates the field failure data into prior knowledge, is used to obtain a more dependable prediction of fatigue life. The effects of prior knowledge, noise in data, and bias in measurements on the distribution of fatigue life are discussed in detail. By assuming a distribution type of fatigue life, its parameters are identified first, followed by estimating the distribution of fatigue life, which represents the degree of belief of the fatigue life conditional to the observed data. As more data are provided, the values will be updated to reduce the credible interval. The results can be used in various needs such as a risk analysis, reliability based design optimization, maintenance scheduling, or validation of reliability analysis codes. In order to obtain the posterior distribution, the Markov Chain Monte Carlo technique is employed, which is a modern statistical computational method which effectively draws the samples of the given distribution. Field data of turbine components are exploited to illustrate our approach, which counts as a regular inspection of the number of failed blades in a turbine disk.

OS1304 欠陥の最大値分布とき裂伝播特性に基づく2種類のMg合金の疲労寿命分布特性の評価(OS13-1 応力特異場の解析と材料強度-1,OS-13 応力特異場の解析と材料強度)

In this study, fatigue tests were carried out using a diecast Mg alloy AZ91 and an extruded Mg alloy AZ61 to study the distribution of fatigue lives under constant stress amplitudes. During the fatigue process of the diecast Mg alloy, cracks initiated from the casting defect existing inside of the specimen. In the case of extruded Mg alloy, cracks were initiated from the inclusions existing on the specimen surface. The extreme-value distribution of the defect sizes, and of the spatial positions of the defects were investigated experimentally in detail. The distributions of the fatigue lives of two kinds of Mg alloys under the constant stress amplitudes were evaluated using the Monte-Carlo simulation. An increase of scatter in the distribution of the fatigue life with lowering of the stress amplitude could also be predicted using the simulation.

Fatigue Properties of Borosilicate Glass Coated with Ceramics and Effect of Proof testing on Life Distribution

In this work, a borosilicate glass was coated with ceramic thin films by sputtering method. Roughness, hardness and static bending strength were measured as static characteristics of coated glass. Fatigue tests of coated glass were conducted under three-point bending. Although a large scatter was observed in fatigue life distributions, it was clarified that the fatigue strength was improved by coating ceramic thin films on glass. Specimens having lower lives in fatigue life distribution were adequately removed by proof testing. Therefore, it was suggested that proof testing for fatigue was effective as a screening procedure.

Statistic characteristics of fatigue properties in magnesium alloy

The knowledge of statistic characteristics in mechanical properties is important for designers in order to assess the reliability of structures. Scatter characteristics of fatigue limit, fatigue life and tensile strength for magnesium alloy were investigated in this study. At least 20 specimens were tested to obtain the scatter data of fatigue limit, fatigue life and tensile strength, respectively. The probability distributions of fatigue limit, fatigue life and tensile strength were evaluated by using Normal distribution and Weibull distribution function. The values of the Weibull modulus, m were 159, 10, 175 for fatigue limit, fatigue life and tensile strength, respectively. Therefore, it can be concluded that scatter of fatigue limit is small and almost coincides with that of tensile strength, while scatter of fatigue life is significantly large compared to those of fatigue limit and tensile strength. The large scatter of fatigue life will be due to crack nucleation and small crack growth processes, which strongly depend on local microstructure near the crack nucleation region.

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 fatigue lives of diecast and extruded Mg alloys

In this study, fatigue tests were carried out on both diecast and extruded Mg alloys to study their distributions of fatigue lives under constant stress amplitudes. During the fatigue process of the diecast Mg alloy, cracks initiated from the casting defects inside of the specimen, and then propagated prior to final failure of the specimen. While in the extruded Mg alloy, cracks initiated from the inclusions located on the specimen surface. With assuming the above defects as the initial cracks, the initial maximum stress intensity factors K imax were evaluated. There are common relations between the initial maximum stress intensity factors K imax and fatigue lives N f, regardless of the stress amplitudes for the both Mg alloys at the constant R ratio of −1. The lower K imax, the longer N f becomes. Integrating the fatigue crack propagation law from the initial maximum stress intensity factor K imax to the fatigue fracture toughness K fc, the relations K imax vs. N f can be successfully evaluated. Distributions of fatigue lives at the constant stress amplitudes can be represented by the Weibull distributions. Dispersion in the fatigue lives becomes larger at the lower stress amplitude as compared with those at the higher stress amplitudes. This trend is observed commonly for both diecast and extruded Mg alloys.

Fatigue life distribution and size effect in ductile cast iron for wind turbine components

The present paper deals with the experimental determination and statistical analysis of high cycle fatigue properties of EN-GJS-400-18-LT ductile cast iron. Constant amplitude axial fatigue tests were performed at room temperature at R = 0 and R = −1. In order to evaluate the size effect, fatigue tests were carried out on two sets of specimens with different dimensions. The specimen diameters were 21 mm and 50 mm. Statistical analysis of fatigue data was done by means of the Weibull distribution, and P– S– N diagrams were established. The established P– S– N diagrams showed that the Weibull distribution is well fit to the scatter of the experimentally obtained fatigue life data. Weibull’s weakest-link method was used to evaluate the size effect. It made a satisfactory prediction of the fatigue strength for specimens with different dimensions.

Distribution of Fatigue Lives for the Diecast Magnesium Alloy

. In this study, fatigue tests were carried out using a diecast Mg alloy AZ91 to study the distribution of fatigue lives under constant stress amplitudes. During the fatigue process of the diecast Mg alloy, cracks initiated from the casting defect within inside of the specimen, and then propagated prior to final failure of the specimen. Distributions of fatigue lives at the constant stress amplitudes can be represented by the Weibull distributions. The scatter in the distribution of fatigue lives becomes larger at the lower stress amplitude of 80 MPa as compared with those at the higher stress amplitudes. There is a common relationship regardless of the stress amplitudes between the initial maximum stress intensity factors Kimax and fatigue lives Nf. The lower Kimax, the longer Nf becomes. Integrating the fatigue crack propagation law from the initial maximum stress intensity factor Kimax to the fatigue fracture toughness Kfc, the relation Kimax vs. Nf can be successfully evaluated.

A Mixed-Effect Multi-Failure-Mechanism Fatigue Reliability Model

Based on the concept of multilevel statistics, mixed-effect fatigue reliability models are presented, by which fatigue reliability can be directly calculated according to stress distribution and fatigue life distribution function condition to stress. Mathematically, the fatigue reliability is estimated as the expectation of a conditional survival probability function to the stochastic stress history. Especially, such models are capable of estimating the fatigue reliability of a component with competing failure mechanisms such as conventional fatigue and giga-cycle fatigue, where two groups of P-S-N curves are involved.

Coupled Thermal-Stress Analysis for FC-BGA Packaging Reliability Design

In order to improve electronics packaging design, it is important to evaluate the cooling performance and reliability of the electronics packaging structure of a product. To that end, it is necessary to predict the temperature, deformation, and stress distributions of the package under field conditions. In the case of a packaging structure comprising a flip-chip ball grid array package, a heat spreader, thermal grease, a cooling structure, solder joints, and a motherboard, an increase in the contact thermal resistance may occur, depending on the interface contact condition between the cooling structure and the heat-spreader due to the thermal deformation of the package. Contact thermal resistance problems involve the interactive relationship of the thermal and stress distributions. A coupled thermal-stress analysis, with consideration of the time-space variation of contact thermal resistance, was conducted to duplicate the behavior of temperature, deformation, and stress distributions of a flip-chip ball grid array package under field conditions. It was found that: 1) the average contact thermal resistance across the interface between the heat-spreader and the plate fin, which was predicted by the coupled thermal-stress analysis, increased compared to the average contact thermal resistance in the case of uniform contact pressure, and 2) the contact thermal resistance will vary depending on the deformation mode, such as convex upward and downward, due to heat dissipation under field conditions. In addition, a reliability prediction method for thermal fatigue failure of solder bumps based on coupled thermal-stress analysis and statistical and probabilistic methods was proposed in order to select a suitable packaging solution at an early stage of design. It was found that the sensitivity of uncertain variables and the thermal fatigue life distribution of solder joints could change significantly depending on a combination of factors concerning the failure sites of solder bumps and the boundary conditions of the motherboard.

On the distributions of fatigue lives and defect-sizes in the die-cast magnesium alloy AZ91

In this study, fatigue tests were carried out using a diecast Mg alloy AZ91 to study the distribution of fatigue lives under constant stress amplitudes. During the fatigue process of the diecast Mg alloy, cracks initiated from the casting defect existing inside of the specimen, and then propagated prior to final failure of the specimen. The probabilistic distributions of the defects densities, of the defect sizes, and of the spatial positions of the defects were investigated experimentally in detail. The distributions of the fatigue lives of the diecast Mg alloys under the constant stress amplitudes were evaluated using the Monte-Carlo simulation, in which the random numbers corresponding to the above probabilistic distributions for the casting defects are used. There was a good fit between the evaluated distribution of the fatigue lives by the computer simulation and the experimental one. An increase of scatter in the distribution of the fatigue life with lowering of the stress amplitude could also be predicted using the simulation.

Micromechanical simulation for texture induced uncertainty in fatigue damage incubation using crystal plasticity model

Crystallographic texture of wrought aluminum alloys has significant influence on the fatigue damage incubation and small-crack growth in the high cycle fatigue (HCF) regime. HCF lives have demonstrated fairly large scatters due to the random textural feature and its stochastic interaction with fatigue damage evolution. The fatigue life of an individual specimen is deterministic, which manifests the specific microstructure in the specimens and its interference with fatigue. In this paper, micromechanical simulations were conducted to quantify the grain orientation and grain boundary mismatch effects to fatigue damage incubation in a wrought 7075-T651 Al alloy. Fatigue damage incubated at fractured intermetallic particles near or at the surface [Xue et al. 2007]. Many intermetallic particles fractured after a few initial loading cycles; however, only one or a few fractured particles induced a crack into the matrix. One of these microcracks eventually grew and became a dominate crack and caused the final failure. The size of the particles, the orientation of the grain in which the particle resides, the particle spatial location to the grain boundary, the mismatch of the grain boundary, and the interaction of all these factors comprise the primary reason for the fatigue damage incubation. But no systematic investigation exists to provide general guideline for fatigue design and structural prognosis applications.In this research, a crystal plasticity constitutive model is implemented to simulate the microplasticity at the fractured intermetallic particles in single crystal and bicrystals, in which the crystallographic orientation mimics the typical rolling texture. The spatial location of the particle with respect to the grain and grain boundary is designed to represent those observed on the fractographs fatigued in the high cycle fatigue regime. The non-uniform loading distribution due to the heterogeneity of textured alloy is investigated by simulating on a representative unit cell with grain size and orientation taken from the realistic stereomicrograph of the sample. This approach is an initial high-order mechanistic multistage fatigue modeling approach, which can be implemented to estimate the uncertainty of the fatigue life prediction and fatigue life distribution using Monte Carlo simulation. Eventually, the reliability of fatigue life predictions will be accessed and the model evaluated as a mathematically rigorous tool for the structural integrity prognosis of aerospace structures that use wrought aluminum alloys.

A New Methodology for Predicting Fatigue Properties of Bearing Steels: From X-Ray Micro-Tomography and Ultrasonic Measurements to the Bearing Lives Distribution

Abstract This work aims at developing a new methodology for predicting the distribution of fatigue lives of bearings versus steel microstructure, namely, concentration, morphology, and properties of residual inclusions in steel. On the experimental side, X-ray micro-tomography and high frequency ultrasonic testing are used to provide the required inclusion characteristics. A physically based model is used to compute the number of cycles to crack nucleation and crack propagation up to the surface. For the statistics predictions, the inclusions and/or stringers are distributed randomly in the bearing steel according to the concentration of stringers provided by ultrasonic data. The distributions of the fatigue lives predicted by the model are compared successfully to the experimental distributions determined by fatigue tests performed on flat washer machines. Finally, it is shown that the model is able to predict the influence of the orientation of stringers on the fatigue lives.

Safe-life analysis accounting for the loading spectra variability

The scatter of the variable load spectra is considered separately from the scatter of the aircraft structure to assess the safe-life of a fleet. Suppose the fatigue life under the specified load spectrum follows the log-normal distribution with a constant coefficient of variation, and the load spectra damage follows the log-normal distribution with a constant standard deviation, the theoretical distribution function of fatigue life of the fleet that accounts for the variability of the structure and the load spectrum is derived with the conditional probability model. Monte-Carlo simulation shows that the distribution of the fleet fatigue life can be described approximately by a log-normal distribution function, and the log expectation is the log mean life under variable load spectra and the variation equals the sum of the structural variation and the load spectra variation. The scatter factor method is then adopted to assess the safe-life. The scatter factor of the individual aircraft with definite load spectrum, as well as the scatter factor of the in-service fleet that takes the actual load scatter into consideration are listed.

E24 深溝玉軸受の寿命分布と信頼性に関する研究(OS2 最新機械要素技術(1))

The purpose of this work is to establish a database of fatigue life distribution and a reliability of rolling bearing. Fatigue life test of deep groove ball bearing #6206 lubricated by Lithium grease lubrication is carried out under pure radial loads F_r=9.14, 10.64, 12.13kN. The fatigue life distribution, the basic dynamic load rating and the load life exponent are estimated and discussed from the test results.

PS54 The Relationship between pore size and fatigue life distributions of AM60B magnesium alloy

The fractographic defect size distribution of die-cast AM60B magnesium alloy tested under four point bending fatigue test was investigated. The defect size distributions of AM60B were compared with that of die-cast A365 aluminum alloy. Porosity which was found to be the most hannful defect to fatigue life was quantified by SEM images of the fatigue test specimens. Defect size and fatigue life data were then statistically analyzed using Weibull distribution function. The scatter in pore size distribution indicated by Weibull modulus, m was in agreement with those obtained for fatigue life distribution. This confirms the inference that the scatter in fatigue life is attributed by the deviations in the size of pores.