Fatigue Strength Distribution Research Articles

Probabilistic evaluation of the Step-Stress fatigue testing method considering cumulative damage

A general testing and analysis framework for the Step-Stress fatigue testing method is identified, utilizing interval-censored data and maximum likelihood estimation in an effort to improve estimation of fatigue strength distribution parameters has been performed. The Step-Stress method’s limitations are characterized, using a simple material model that considers cumulative damage to evaluate load history effects. In this way, the performance including cumulative damage was evaluated and quantified using a probabilistic approach with Monte-Carlo simulations, benchmarked against the Staircase method throughout the work. It was found that the Step-Stress method, even when cumulative damage occurs to a wide extent, outperforms the Staircase method, especially for small sample sizes. Furthermore, positive results reaches further than the increase performance in estimating fatigue strength distribution parameters, where improvements in secondary information, i.e. S-N data gained from failure specimens, are shown to be distributed more closely to the fatigue life region of interest.

Quality of Low-Carbon Steel as a Distribution of Pollution and Fatigue Strength Heated in Oxygen Converter

Quality of Low-Carbon Steel as a Distribution of Pollution and Fatigue Strength Heated in Oxygen Converter

A Study on Very High Cycle Fatigue Properties of Axle Steel with Induction Hardening on the Surface

Rotating bending fatigue tests were performed to investigate the effect of induction hardening (HQI) on the very high cycle fatigue (VHCF) properties of the axle steel. In addition, finite element analyses (FEA) and scanning electron microscope (SEM) observations were conducted to elucidate the fundamental behavior. The results obtained are summarized as follows; (1) It was found that the fatigue strength of the axle steel was improved by almost 300 MPa in VHCF region by HQI, (2) A lot of specimens of the HQI had fractured in VHCF region, therefore, the consideration of VHCF properties should be taken into account in the design of railway axles, (3) Crack initiation sites can be classified into three forms; the surface of the HQI layer in the minimum section, the base metal beyond the HQI layer in the axial direction, and the internal base material in the minimum section. These can be reconfirmed through the comparison between the local fatigue strength distribution and the bending stress distribution obtained by FEA.

Study of Local Fatigue Methods (TCD, N-SIF, and ESED) on Notches and Defects Related to Numerical Efficiency

The fatigue strength of structural components is strongly affected by notches and imperfections. Both can be treated similarly, as local notch fatigue strength methods can also be applied to interior defects. Even though Murakami’s √area approach is commonly used in the threshold-based fatigue design of single imperfections, advanced concepts such as the Theory of Critical Distances (TCD), Notch Stress Intensity Factors (N-SIF), or Elastic Strain Energy Density (ESED) methods provide additional insight into the local fatigue strength distribution of irregularly shaped defects under varying uniaxial load vectors. The latter methods are based on the evaluation of the elastic stress field in the vicinity of the notch for each single load vector. Thus, this work provides numerically efficient methods to assess the local fatigue strength by means of TCD, N-SIF, and ESED, targeting the minimization of the required load case count, optimization of stress field evaluation data points, and utilization of multi-processing. Furthermore, the Peak Stress Method (PSM) is adapted for large opening angles, as in the case of globular defects. In detail, two numerical strategies are devised and comprehensively evaluated, either using a sub-case-based stress evaluation of the defect vicinity with an unchanged mesh pattern and varying load vector on the exterior model region with optimized load angle stepping or by the invocation of stress and strain tensor transformation equations to derive load angle-dependent result superposition while leaving the initial mesh unaltered. Both methods provide numerically efficient fatigue post-processing, as the mesh in the evaluated defect region is retained for varying load vectors. The key functions of the fatigue strength assessment, such as the evaluation of appropriate planar notch radius and determination of notch opening angle for the discretized imperfections, are presented. Although the presented numerical methods apply to planar simulation studies, the basic methodology can be easily expanded toward spatial fatigue assessment.

A comparative analysis of step loading and staircase testing for fatigue strength estimation of an engine component

AbstractStaircase testing is a standard method for evaluating the fatigue strength of components. However, staircase testing assumes a normal distribution, while components can display bimodal behavior due to flaws in material, or issues during the manufacturing process. Three unique step loading data sets on different production crankshafts provide evidence that step loading reliably identifies material or manufacturing issues, which lower a component's fatigue strength. Staircase testing has an 87% or greater chance of overestimating the component's fatigue strength, which in turn overestimates the component's expected reliability. For example, a component with a 99.9% reliability based on staircase testing would only have a 74% reliability based on step loading. If a component contains an undetectable manufacturing defect, staircase testing has a 99% chance of overestimating the component's fatigue strength. Step loading reliably improves the estimation of a component's fatigue strength distribution while providing insights into a component's defect tolerance.

Fatigue Reliability Design Method for Large Aviation Planetary System Considering the Flexibility of the Ring Gear

As the foundation and core of various heavy aircraft transmission systems, the reliability level of large-scale aviation planetary mechanism restricts the economic affordability and service safety for the aircraft to a great extent. This paper takes the heavy helicopter planetary mechanism as the research object, and aims to improve the fatigue reliability level of the system. The fatigue load history of the gear teeth under the coupling of global elastic behavior of the system is calculated using a hierarchical finite element method, and the fatigue strength distribution of gear teeth is fitted based on the gear low circumference fatigue test with the minimum order statistics transformation method to provide cost-effective load and strength input variables for the system reliability prediction model. Based on this, a mapping path from the key structural elements of large-scale aviation planetary mechanism to the system reliability indexes is established, and then a new method of reliability-driven multi-objective optimization design for planetary mechanism structural dimensions is proposed. Finally, the influence law of ring gear rim thickness on the fatigue reliability of the planetary gear train is analyzed and the NSGA-Ⅱ genetic algorithm is used to determine the optimal stiffness matching result of the rim size of the designated type of large aviation planetary system. The stiffness potential of the core structural elements is maximized as a way to balance the contradiction between reliability and lightweight requirements of a large aviation planetary system.

Effect of the Torsion Box Dimensions on Local Stress Distribution and Fatigue Strength Assessment of a Container Ship

The aim of this paper is to estimate the influence of the dimensions of the torsion box (height and width), of a 2400 TEU feeder-class container ship, on local stress distribution and assessment of local fatigue strength by using a numerical approach based on the fatigue limit-state and ultimate limit-state in the midship region. In terms of the fatigue limit-state, the effect of the dimensions of the torsion box is obtained by geometrical modifications, in the connection between the side shell longitudinal stiffeners with the transverse web frame for nine structural details, referring to different arrangements of strengthening elements (brackets and flat bars). The process of comparing the different elements determines the most effective combination. This structural influence on the local stress distribution is assessed, along the longitudinal plates between ordinary stiffeners bounding the perimeter of the torsion box, by calculating the hull girder stresses, local buckling stresses and shear stress distribution induced by vertical and horizontal shear forces, Saint Venant and warping torques, and finally the shear stresses induced by a warping moment. Scantling criteria are obtained allowing for a better design of this very important region in container ships.

Digital Scanning of Welds and Influence of Sampling Resolution on the Predicted Fatigue Performance: Modelling, Experiment and Simulation

Digital weld quality assurance systems are increasingly used to capture local geometrical variations that can be detrimental for the fatigue strength of welded components. In this study, a method is proposed to determine the required scanning sampling resolution for proper fatigue assessment. Based on FE analysis of laser-scanned welded joints, fatigue failure probabilities are computed using a Weakest-link fatigue model with experimentally determined parameters. By down-sampling of the scanning data in the FE simulations, it is shown that the uncertainty and error in the fatigue failure probability prediction increases with decreased sampling resolution. The required sampling resolution is thereafter determined by setting an allowable error in the predicted failure probability. A sampling resolution of 200 to 250 μm has been shown to be adequate for the fatigue-loaded welded joints investigated in the current study. The resolution requirements can be directly incorporated in production for continuous quality assurance of welded structures. The proposed probabilistic model used to derive the resolution requirement accurately captures the experimental fatigue strength distribution, with a correlation coefficient of 0.9 between model and experimental failure probabilities. This work therefore brings novelty by deriving sampling resolution requirements based on the influence of stochastic topographical variations on the fatigue strength distribution.

Fatigue strength distribution and probabilistic evaluation on stainless steel welded components under mixed mode loading

Plane sheet specimens and their welded components were examined through fatigue tests, and the data were evaluated by the base line regression model. The three-parameter Weibull estimations showed the most accurate approximation of the measured values with the median rank treatment. The fatigue strengths, limits, lives and failure probabilities under different loading conditions became predictable. The fatigue strengths and limits under mixed mode loading were compared with the Gough–Pollard relation, and could be predicted from the load ratio of the torsion to bending. The notch factors of welded components were 1.24–2.55 at the load ratio of 0.31. The fatigue strengths and scatters mainly depended on the weld flank angle, and had excellent agreement with the weld shape parameter which included the influence of the weld toe radius. They varied with the material factor which included the influences of the non-uniform microstructure, weld imperfection, etc.

Overview of laser-welded thin-walled joints fatigue performance and a statistical method for defect analysis

Welding always has a deteriorating effect on fatigue strength in structures under dynamic loading. Weld joints induce discontinuity in structure geometry and the microstructure. Welding induced discontinuity, and defects allow for potential fatigue cracks that lead to the failure of welded parts or structures. The laser welding process differs from conventional arc welding in process and joint type. The most significant advantage in laser welding comes from the deep penetrating mode of welding, which also brings challenges to the soundness of the weld. The benefits of laser welding are most evident in the manufacture of sheet metal products such as sandwich panels. In literature, laser welding is generally dealt with by using different parts of the overall process without taking the fatigue point of view into account. In this article, the process of laser welding is discussed, while keeping fatigue strength in perspective. The fatigue data of laser welded joints is studied in order to find defect distribution that explains fatigue strength distribution in tests. The suitability of traditional fatigue assessment for laser welding is also discussed.

A Method for Predicting the Effects of Specimen Geometry and Loading Condition on Fatigue Strength

Specimen geometry and loading condition usually have a great influence on the fatigue strength of metallic materials, which is an important issue in evaluating the reliability of component parts. In this paper, a rotating bending fatigue test is performed at first on an hourglass specimen and a notch specimen of a high strength titanium alloy. Experimental results indicate that, in terms of local stress, the notch specimen endures higher fatigue strength in comparison with the hourglass specimen due to its relatively smaller control volume. Then, a probabilistic control volume method is proposed for correlating the effects of specimen geometry and loading condition on the fatigue strength based on Weibull distribution and the concept of control volume. A simple formula is obtained for the fatigue strength in relation to control volumes, in which the parameter is the shape parameter of Weibull distribution of fatigue strength. The predicted results are in good agreement with the present experimental data for high strength titanium alloy and the data for the high strength steel and the full scale EA4T axle in the literature.

Experimental and numerical analysis of hybrid adhesively-bonded scarf joints

Adhesive joints have been largely used in many areas such as automotive and aeronautic industries, navy, electronic components and construction, among others. The increased application of this joining technique is due to an easy manufacturing, lower costs, easiness to joint different materials, more uniform distribution of stresses and higher fatigue strength. The scarf joint is one of the possible joint configurations and it excels in not requiring to change the initial shape of the component. Improved stress distributions over single and double-lap joints are obtained, although it has some complexity in the manufacturing process. In many practical applications, joining between different adherend materials is required due to design constraints, which poses additional difficulties because of the different stiffness of the materials. This work presents an experimental and numerical study on hybrid scarf joints, between composite and aluminium adherends, and considering different scarf angles (α) and adhesives (the brittle Araldite® AV138 and the moderately ductile Araldite® 2015). Comparison with joints having material balanced adherends is also performed numerically. The numerical analysis by Finite Elements (FE) enabled obtaining peel (σy) and shear (τxy) stresses using the software Abaqus®, which are then used to discuss the strength between different joint configurations. Cohesive Zone Models (CZM) were used to predict the joint strength and the results were compared with experiments for validation. A significant variation of the joints’ behaviour was found depending on α and the applied adhesive, which was directly linked to the stresses developed in the adhesive layer during loading. CZM were found to be an accurate design tool for the hybrid scarf joints.

Analysis of the dynamic response and fatigue reliability of a full-scale carbody of a high-speed train

For a vehicle operating under different line conditions, coupled with track irregularity and many other factors, the carbody is subjected to extremely complex random loads, and the load mainly exists in the form of an alternating load; therefore, the primary type of failure is fatigue failure. With the continuous improvement in train speed, lightweight designs of carbody structures and the application of high-strength aluminium alloy, the safety and reliability of a carbody require more attention. An investigation of the dynamic fatigue reliability of a full-scale carbody of a high-speed train under random load conditions is carried out. A dynamics model of the vehicle system has been established for acquiring the time history of forces acting on the carbody by each air spring (hereinafter referred to as ‘the load–time history’). A surrogate model (a simple model instead of a complex carbody model) of the carbody is established based on the Box–Behnken matrix design and the polynomial fitting method; then, the load–time history is transformed to the stress–time history of the points of concern, and the results are compared with the results of the transient analysis, which verify the accuracy and effectiveness of the surrogate model. Then, a stress block spectrum is obtained by rain flow counting, and the stress probability distribution is determined. Combined with the probability distribution of fatigue strength, a dynamic stress–strength interference model (the area of interference between strength and stress in the model changes over time) is established. The failure rate and dynamic reliability of the points of concern for two cases are analysed: without considering the strength degradation and considering the strength degradation. The results show that without considering the strength degradation during service, with increased service mileage, the fatigue strength reliability of the points of concern decreases continuously, and the corresponding failure rate of the points of concern decreases with time and reaches a steady value, which has the characteristics of the first two stages of the bathtub curve. By considering the strength degradation during service, the reliability of the points of concern decreases gradually, and the corresponding failure rate of the points of concern decreases and then increases, with all the features of the bathtub curve. In addition, compared with the base metal region, the fatigue resistance of the welded structure decreases due to welding. Under the same service conditions, the reliability of the welded region is relatively low, and fatigue failure is more likely to occur.

Prediction of the crack density evolution in multidirectional laminates under fatigue loadings

An innovative procedure is proposed for the prediction of the crack density evolution in multidirectional laminates subjected to cyclic loadings. The crack initiation and propagation phases are treated separately and described by means of a master S-N curve and a Paris-like curve, respectively. A damage-based multiscale strategy is adopted for the prediction of multiple crack initiation, accounting for the statistical distribution of fatigue strength and crack propagation resistance within a ply. The procedure has been implemented in a Matlab® code for the simulation of the fatigue damage evolution in multi-directional symmetric laminates. Comparisons with experimental results taken from previous works show a very good agreement.

A 3-D model for quantification of fatigue weak-link density and strength distribution in an A713 cast aluminum alloy

A quantitative model which took into account the 3-D effects of pores on the local stress/strain fields was developed to quantify the fatigue weak-link density and strength distribution in an A713 Al alloy. In the model, a digital pore structure was first constructed using single-sized pores (15μm in diameter) that had a total volume fraction same as that of the pores measured experimentally in the alloy. In the surface randomly selected by cross-sectioning through the simulated pore structure, the stress and strain fields around each pore in the surface were quantified using a 3-D finite element model under an applied cyclic stress, and the fatigue crack incubation life at the pore was estimated with a micro-scale Manson-Coffin equation. The quantified rate of fatigue crack initiation at these pores was found to be a Weibull function of the applied stress, which was consistent with the experimental result measured in the alloy. The density and strength distribution of fatigue weak-links could then be derived and used to evaluate the fatigue crack initiation properties of the alloy. By matching to the experimentally measured fatigue weak-links, the minimum critical pore size for fatigue crack initiation was determined to be 11μm in diameter at the cyclic maximum stress of 100% yield strength of the alloy.

Quantification of Fatigue Weaklinks in High Strength Al Alloys

Fatigue weak-link density and strength distribution are materials fatigue properties which are useful in evaluation of alloy quality in terms of the fatigue crack nucleation behavior. This paper reports: 1) an experimental methodology developed to measure fatigue weak-link density and strength distribution by measuring surface crack population as a function of the maximum applied stress, and 2) a quantitative model to quantify fatigue weak-links, based on the 3-D effects of pores in cast alloys. The experimental method could be employed to characterize the fatigue crack initiation behaviors and their anisotropy in wrought and cast Al alloys such as AA8090 Al-Li, AA2026, AA7075 and A713 alloys. It was found that the crack populations were a Weibull function of the applied maximum stress. By fitting this measured curve, fatigue weak-link density could be quantified in these alloys. The derivative of the measured Weibull function resulted in the strength distribution of the fatigue weak-links. The fatigue weak-links could also be quantified from the reconstructed microstructure of a cast Al alloy by analyzing the stress/strain fields around a micro-pore (an elasto-plastic media) under cyclic loading as a function of pore position in depth on surface using a 3-D finite element method. The incubation life for the fatigue crack initiated from a surface pore could be estimated using a microscopic scale Manson-Coffin equation. The results obtained using the 3-D pore-sensitive model were consistent with the experimental results, i.e., the crack population was a Weibull function of the applied stress. The percentage of crack initiation life was found to increase with decrease in cyclic load, i.e., at the stress just above the fatigue limit, it was over 95% the total fatigue life, compared to just 62.5% at the maximum stress of 110% yield strength.

Finite element and experimental analysis of pinion bracket-assembly of three gorges project ship lift

The pinion bracket-assembly (PBA) is a major part of three gorges project (TGP) ship lift drive system. The static strength, fatigue strength and stress distribution of hinge pin of PBA were analyzed by ANSYS, and the structure of PBA was optimized. The results show that after the optimization, the maximum comprehensive stress is 259.59 MPa, the maximum fatigue cumulative damage of weld joints is 0.94 and the maximum vertical deformation of hinge pin is 0.14 mm. The elastic deformation, hydropneumatic spring cylinder (HSC) load response and the vibration characteristics of PBA were studied by the bearing test when PBA bore the load caused by different water level errors. The results indicate that when the water level of ship chamber ranges from 3.4 m to 3.6 m, the vertical elastic deformation of the pinion shaft is between −8.58 and 10.50 mm. When upward outage-load(1580 kN) is imposed by the test-rack, the vertical elastic deformation of the pinion shaft is 13.42 and 14.07 mm and HSC load response is 795.80–800.80 kN. In the process of imposing load on the pinion by the test-rack, the maximum vibration amplitude and acceleration of PBA internal components are 0.37° and 2.67 rad/s2, respectively; the maximum impact on the pin caused by vibration is 19.89 kN; the pinion shaft vertical displacement and HSC load response do not fluctuate. There is a great difference between the frequency of meshing force of the pinion and the rack (1.06 Hz) and first-order natural frequency of PBA(8.41 Hz), thus PBA will not resonate. From all above, PBA meets the static strength and fatigue strength requirements. The vibration of PBA internal components has no effect on the vertical displacement of the pinion shaft, HSC load response and smooth operation of PBA. There is a liner relationship in the ratio of 2:1 between the thrust imposed by the test-rack and HSC load, thus HSC can limit the load imposed on the pinion.

The anisotropy of fatigue crack nucleation in an AA7075 T651 Al alloy plate

Abstract Four-point bend fatigue tests were conducted on the L–T (Rolling–Transverse), L–S (Rolling–Short transverse) and T–S planes of an AA7075 T651 alloy plate, respectively, at room temperature, 20 Hz, R=0.1, in air. The populations of crack initiation sites (i.e., fatigue weak-links), measured on these surfaces, were found to be a Weibull-type function of the applied maximum cyclic stress, from which fatigue weak-link density and strength distribution could be determined. The alloy showed a profound anisotropy of fatigue weak-links with the weak-link density being 11 mm−2, 15 mm−2 and 4 mm−2 on the L–T, L–S and T–S planes, respectively. The fact that cracks were predominantly initiated at Fe-containing particles on the L–T and L–S planes, but only at Si-bearing particles on the T–S plane, profoundly demonstrated that the pre-fractured Fe-containing particles were responsible for crack initiation on the L–T and L–S planes, since the pre-fracture of these particles due to extensive deformation in the L direction during the prior rolling operation could only promote crack initiation when the sample was cyclic stressed in the L direction on both the L–T and L–S planes. The fatigue strengths of the L–T, L–S and T–S planes were measured to be 243.6, 273.0 and 280.6 MPa, respectively. The difference in grain structure and particle between these planes was responsible for the anisotropy of fatigue strength on these planes.

The Effect of the Microstructure and Defects on Crack Initiation in 316L Stainless Steel under Multiaxial High Cycle Fatigue

The aim of this study is to analyse the influence of both the microstructure and defects on the high cycle fatigue behaviour of the 316L austenitic stainless steel, using finite element simulations of polycrystalline aggregates. High cycle fatigue tests have been conducted on this steel under uniaxial (push-pull) and multiaxial (combined in-phase tension and torsion) loading conditions, with both smooth specimens and specimens containing artificial semi-spherical surface defects. 2D numerical models, using a cubic elastic constitutive model, are created to determine the degree of heterogeneity of the local stress parameters as a function of the defect size. This has been done for one microstructure using several orientation sets generated from the initial texture of the material. The grains are explicitly modelled and the anisotropic behaviour of each FCC crystal is described by the generalized Hookes law with a cubic elasticity tensor. From the simulations carried out with different defect sizes and orientation sets that are representative of the real texture of the tested material, statistical information regarding mesoscopic mechanical fields provides useful insight into the microstructural dependence of the driving forces for fatigue crack nucleation at the mesoscopic scale (or the scale of individual grains). The results in terms of the stress fields and fatigue crack initiation conditions are determined at both the mesoscopic and macroscopic scales. The results from these FE models are used along with an original probabilistic mesomechanics approach to quantify the defect size effect. The resulting predictions, which are sensitive to the microstructure, include the probability distribution of the high cycle fatigue strength.

Strength Evaluation of Unidirectional Composites Using Monte-Carlo Simulation

A statistics method was carried out to characterize the fatigue strength distribution of GF/PP composites. Based on the stress of yarn bundles, the Weibull distribution parameters were determined. Also, we had presented an expression of interfacial shear stress between yarn tows and matrix. A Monte-Carlo simulation with 2D shear-lag equation had been used to analyze the tensile strength and simulate the failure process of unidirectional stretch of composites. Good agreements were obtained between the predicted results and experimental data.