Fatigue Strength Coefficient Research Articles

Fatigue studies of CoCrFeMnNi high entropy alloy films using nanoindentation dynamic mechanical analyses

Films in the microelectromechanical systems are frequently subjected to the fatigue damage under cyclic loading, and the fatigue properties of the films greatly influence the reliability and life of MEMS. However, because of the small dimension of films, characterization of their fatigue properties is a daunting challenge. Nanoindentation dynamic mechanical analysis (DMA) provides a possible solution. However, the setting of loading cycles is crucial to the fatigue test. Using CoCrFeMnNi high entropy alloy films, we investigated the fatigue properties extracted using two different types of loading: fixed load ratio with different mean loads and fixed mean load with different load ratios. Our results showed that both types of fatigue loading were reliable for the evaluation of the fatigue properties of films and it was demonstrated by the fatigue strength coefficients and exponents extracted from the test results. For comparison, DMA was also performed on CoCrFeMnNi high entropy alloys. Compared to the bulk counterpart, the film had much higher fatigue lifetime because of the thickness confinement, the presence of high-density nanotwins and the much smaller grain size in the film.

Fatigue reliability estimation framework for turbine rotor using multi-agent collaborative modeling

To improve the computing accuracy and simulation efficiency of fatigue reliability estimation for turbine rotor, a multi-agent collaborative modelling (MACM) approach is proposed by absorbing the strengths of improved differential evolution (IDE) algorithm and neural network model into decomposed-collaborative strategy. The fatigue reliability estimation framework is presented in respect of MACM approach. Furthermore, the fatigue reliability estimation of a typical turbine rotor is considered as engineering case to evaluate the presented approach with respect to material variabilities, load fluctuations and model randomness. The estimation results reveal that the probabilistic fatigue life of a turbine rotor under reliability 99.87% is 6 050 cycles; fatigue strength coefficient σf′ and strain range Δɛt play a leading role on the fatigue life since their effect probabilities of 45% and 36%, respectively. The comparisons of methods (direct Monte Carlo simulation (MCS), quadratic polynomial (QP), neural network (NN), neural network agent (NNA)) show that the presented MACM approach holds high efficiency and accuracy for fatigue reliability estimation of turbine rotor.

Research on the Properties and Low Cycle Fatigue of Sc-Modified AA2519-T62 FSW Joint.

The aim of this research was to examine the mechanical and fatigue properties of friction stir welded Sc-modified 5 mm thick AA2519-T62 extrusion. The joint was obtained using the following parameters: 800 rpm tool rotation speed, 100 mm/min tool traverse speed, 17 kN axial, and MX Triflute as a tool. The investigation has involved microstructure observations, microhardness distribution analysis, tensile test with digital image correlation technique, observations of the fracture surface, measurements of residual stresses, low cycle fatigue testing, and fractography. It was stated that the obtained weld is defect-free and has joint efficiency of 83%. The failure in the tensile test occurred at the boundary of the thermo-mechanically affected zone and stir zone on the advancing side of the weld. The residual stress measurements have revealed that the highest values of longitudinal stress are localized at the distance of 10 mm from the joint line with their values of 124 MPa (the retreating side) and 159 MPa (the advancing side). The results of low cycle fatigue testing have allowed establishing of the values of the cyclic strength coefficient (k′ = 504.37 MPa) and cyclic strain hardening exponent (n′ = 0.0068) as well as the factors of the Manson–Coffin–Basquin equation: the fatigue strength coefficient σ′f = 462.4 MPa, the fatigue strength exponent b = −0.066, the fatigue ductility coefficient ε′f = 0.4212, and the fatigue ductility exponent c = −0.911.

Fatigue behavior of epoxy alumina nanocomposite – role of particle morphology

In this work, epoxy alumina nanocomposites were synthesized with Al2O3 nanofiller by instant cross-linking process. Two different particle morphologies (viz. rod and spherical shape) were selected as filler to investigate their effect along with wt.% (0.5, 1.0, and 1.5 wt%) on the fatigue behavior of epoxy alumina nanocomposites. Stress to number of cycles to failure (S-N curve) as per ASTM D 7791 and fatigue crack growth (FCG) rate approach as per ASTM E 647 were used to evaluate fatigue life of epoxy alumina nanocomposites. Transmission and scanning electron microscopy were used to characterize dispersion and fracture surfaces of epoxy alumina nanocomposites. Particle morphology and wt.% influenced the fatigue life and FCG behavior of epoxy composite appreciably. Addition of spherical Al2O3 nanoparticles substantially improved the fatigue life of nanocomposites than unfilled epoxy at all levels of applied stresses. Fatigue life decreased with increase in wt.% of spherical Al2O3 nanoparticles and opposite trends is witnessed for nanorod filler. Higher resistance to FCG provided better fatigue life of spherical Al2O3 epoxy composites than nanorods and unfilled epoxy. Crack bowing and bifurcation, yielding, deep craters were the main fracture micro mechanism for high fatigue life of spherical Al2O3 nanoparticles reinforced epoxy composites. Various parameters like Young’s modulus, fatigue strength coefficient and exponent, Paris constants and strain energy were used to describe the fatigue and fatigue crack growth behavior.

Influence of inclusions on bending fatigue strength coefficient the medium carbon steel melted in an electric furnace

Abstract The parameters of high-grade steel are influenced by a combination of factors, including chemical composition and production technology. The impurity content is also a key determinant of the quality of high-grade steel. Inclusions may also play an important role, subject to their type and shape. Inclusions may increase the strength of steel by inhibiting the development of micro-cracks. The analyzed material was one grade of medium-carbon structural steel. The study was performed on 6 heats produced in an industrial plant in 140 ton electric furnaces. The experimental variants were compared in view of the five heat treatment options. The results were presented to account for the correlations between the fatigue strength coefficient during rotary bending, the diameter of and spacing between impurities. The relationship between the fatigue strength and hardness of high-grade steel vs. the quotient of the diameter of impurities and the spacing between impurities was determined. The proposed equations contribute to the existing knowledge base of practices impact of impurities with various diameters and spacing between non-metallic inclusion on fatigue strength.

Decomposed Collaborative Modeling Approach for Probabilistic Fatigue Life Evaluation of Turbine Rotor.

To improve simulation accuracy and efficiency of probabilistic fatigue life evaluation for turbine rotor, a decomposed collaborative modeling approach is presented. In this approach, the intelligent Kriging modeling (IKM) is firstly proposed by combining the Kriging model (KM) and an intelligent algorithm (named as dynamic multi-island genetic algorithm), to tackle the multi-modality issues for obtaining optimal Kriging parameters. Then, the decomposed collaborative IKM (DCIKM) comes up by fusing the IKM into decomposed collaborative (DC) strategy, to address the high-nonlinearity problems for accelerating simulation efficiency. Moreover, the DCIKM-based probabilistic fatigue life evaluation theory is introduced. The probabilistic fatigue life evaluation of turbine rotor is regarded as case study to verify the presented approach; the evaluation results reveal that the probabilistic fatigue life of turbine rotor is 3296 cycles. The plastic strain range ∆εp and fatigue strength coefficient σf′ are the main affecting factors to fatigue life, whose effect probability are 28% and 22%, respectively. By comparing with direct Monte Carlo method, KM method, IKM method and DC response surface method, the presented DCIKM is validated to hold high efficiency and accuracy in probabilistic fatigue life evaluation.

Characteristics and life expression of fatigue fracture of G105 and S135 drill pipe steels for API grade

Characteristics and life expression of fatigue fracture of drill pipe steels for API G105 and S135 grade were investigated experimentally. S135 steel with higher tensile strength has higher fatigue strength and fatigue limit than that of G105 steel with lower tensile strength. A modified model for the S-N data, revealing the correlation between the fatigue life and fatigue limit, equivalent stress amplitude reflecting the effect of stress ratio, is suggested for predicting the fatigue damage. The fatigue limit and the fatigue strength coefficient are correlated to the tensile properties. The mechanism of the fatigue fracture was examined by scanning electron microscopy.

Study on the Elastic-Plastic Correlation of Low-Cycle Fatigue for Variable Asymmetric Loadings.

The mean stress effect in fatigue life varies by material and loading conditions. Therefore, a classical low cycle fatigue (LCF) model based on mean stress correction shows limits in asymmetric loading cases in both accuracy and applicability. In this paper, the effect of strain ratio (R) on LCF life is analyzed and a strain ratio-based model is presented for asymmetric loading cases. Two correction factors are introduced to express correlations between strain ratio and fatigue strength coefficient and between strain ratio and fatigue ductility coefficient. Verifications are conducted through four materials under different strain ratios: high-pressure tubing steel (HPTS), 2124-T851 aluminum alloy, epoxy resin and AZ61A magnesium alloy. Compared with current widely used LCF models, the proposed model shows a better life prediction accuracy and higher potential in implementation in symmetric and asymmetric loading cases for different materials. It is also found that the strain ratio-based correction is able to consider the damage of ratcheting strain that the mean stress-based models cannot.

Influence of transient liquid phase bonding followed by homogenization on the fatigue lifetimes of inconel 738 at elevated temperature

An ideal transient liquid phase (TLP) joint is achievable with the complete isothermal solidification and homogenization of the Diffusion Affected Zone (DAZ), in which case, a joint with a similar microstructure to the Base Metal (BM) is obtained. In this study, Inconel 738 (IN-738) was joined by TLP bonding using a BNi-2 filler alloy at 1120 °C for different hold times followed by a Standard Heat Treatment (SHT) for the homogenization of the joint. After a microstructural study of the joints, the BM and the homogenized TLP joint were fatigue tested at 850 °C under similar conditions. A comparison of the fatigue test results (SN curve) was indicative of the reduced fatigue lifetime of IN-738 as a result of TLP bonding which can be attributed to the shorter elongation of the joint, γ grain growth during the bonding, and the larger number of fatigue crack initiation sites at the homogenized joint compared with the BM. In addition, several grain boundary cracks were observed across the fracture of the homogenized joint that may have been due to the reduced cohesive strength of the material at the boundaries or the increased density of carbides at grain boundaries. Eventually, Basquin’s equation was presented to estimate the fatigue life of the joint and the fatigue strength coefficient and fatigue strength constant of the joint were calculated -0.049 and 325.65, respectively.

Low Cycle Fatigue Properties of Sc-Modified AA2519-T62 Extrusion.

This investigation presents the results of research on low cycle fatigue properties of Sc-modified AA2519-T62 extrusion. The basic mechanical properties of the investigated alloy have been established in the tensile test. The low cycle fatigue testing has been performed on five different levels of total strain amplitude: 0.4%; 0.5%; 0.6%; 0.7% and 0.8% with cycle asymmetry coefficient R = 0.1. For each level of total strain amplitude, the graphs of variations in stress amplitude and plastic strain amplitude in the number of cycles have been presented. The obtained results allowed to establish Ramberg-Osgood and Manson-Coffin-Basquin relationships. The established values of the cyclic strength coefficient and cyclic strain hardening exponent equal to k’ = 1518.1 MPa and n’ = 0.1702. Based on the Manscon-Coffin-Basquin equation, the values of the following parameters have been established: the fatigue strength coefficient σ’f = 1489.8 MPa, the fatigue strength exponent b = −0.157, the fatigue ductility coefficient ε’f = 0.4931 and the fatigue ductility exponent c = −1.01. The fatigue surfaces of samples tested on 0.4%, 0.6% and 0.8% of total strain amplitude have been subjected to scanning electron microscopy observations. The scanning electron microscopy observations of the fatigue surfaces revealed the presence of cracks in striations in the surrounding area with a high concentration of precipitates. It has been observed that larger Al2Cu precipitates exhibit a higher tendency to fracture than smaller precipitates having a higher concentration of scandium and zirconium.

Determining the fatigue parameters in total strain life equation of a material based on monotonic tensile mechanical properties

This paper summarized and evaluated a variety of low-cycle fatigue life estimation methods and gives the expression of fatigue strength coefficient, fatigue ductility coefficient, fatigue strength exponent, fatigue ductility exponent, successfully established the relationship among four parameters in total strain life equation and monotonic tensile parameters such as Young’s module, ultimate stress, yield stress, reduction in area, elongation. Therefore a new fatigue life prediction method has been proposed, with which various materials’ fatigue life have been predicted and acquired satisfied life prediction results. The influence of fatigue parameters in the total strain life equation on fatigue life prediction results has been evaluated and in the mid-high (104–106) life stage, fatigue life is very sensitive to the true fracture stress, if the stress is reduced by 5%, the fatigue life will be increased by about 50%. The Material’s Low-Cycle Fatigue Life Prediction System (the MLCFLPS) has been developed based on the Visual Basic which can evaluate parameters in total strain life equation more convenient and fast, which shows strong mechanical significance in life prediction of engineering structures.

Multi-Surrogate Collaboration Approach for Creep-Fatigue Reliability Assessment of Turbine Rotor

The creep-fatigue resistance of turbine rotor seriously affects the reliability performance and service lifetime of aircraft engine. Creep-fatigue reliability assessment is an effective measure to quantify the uncertain creep-fatigue damage and evaluate the creep-fatigue reliable life for turbine rotor. To improve the modeling accuracy and simulation efficiency of creep-fatigue reliability assessment, a multi-surrogate collaboration approach (MSCA) is proposed by absorbing the strengths of the proposed dynamic neural network surrogate (DNNS) into distributed collaborative strategy. The creep-fatigue reliability assessment of a typical turbine rotor is regarded as one case to estimate the presented MSCA with respect to the fluctuations of multi-physical variables and the variabilities of multi-model parameters. The assessment results reveal that the creep-fatigue reliable life of turbine rotor under reliability degree of 0.998 7 is 629 cycles, and the fatigue strength coefficient and holding creep time play a leading role on creep-fatigue reliable life since their effect probabilities of 27 % and 19 %, respectively. Comparison of various methods (direct Monte Carlo simulation, response surface, neural network surrogate, DNNS) shows that the presented MSCA holds high efficiency and accuracy in creep-fatigue reliability assessment of turbine rotor.

Numerical assessment of fatigue strength of transcatheter mitral bioprosthetic stent based on the titanium nickelide model

This study is devoted to assessing the fatigue strength of a self-expanding Nitinol frame for a prosthetic heart valve when reconstructing the conditions of primary implantation in the mitral position. The object of research is a stent-like supporting frame, which is a cellular structure that performs the function of the main fastening and maintaining the shape of the leaflets and cover. The study included two stages of the formation of the stress-strain state of the frame: the creation of a mathematical model that provides an assessment of the state of the structure of the support frame in the final state and an assessment of the fatigue strength. It is shown that during the packaging of the frame in the delivery system (compression), a high degree of localization of inelastic deformations leading to surface destruction of a number of cells and joints at the final stage of the compression process, is noted. In a number of cell vertices and frame junctions, the fatigue strength coefficient exceeded its limit value, which indicates their destruction under the influence of long cyclic alternating loads. The main effect on the fatigue strength of the structure is the stress-strain state obtained at the stages of compression and implantation. To meet the conditions of static and fatigue strength, a modification of the support frame structure is required.

On the strain-life fatigue parameters of additive manufactured plastic materials through fused filament fabrication process

In this paper, the effects of part build directions or raster orientations have been studied on the strain-life fatigue parameters of a wide range of 3D printed plastic materials. These materials have been manufactured through Fused Filament Fabrication (FFF), also known under its trademarked name Fused Deposition Modeling (FDM). To do so, precise analyses of fatigue data with the Ramberg-Osgood form of stress-strain curves were utilized through a strain-based approach to fatigue. The effects of different load ratios and types of loading on fatigue parameters have also been studied. Materials considered in this study were Ultem 9085, Polycarbonate (PC), and Polylactic Acid (PLA). Additive manufactured plastic parts that are FDM-processed exhibited large anisotropy of strain-life fatigue parameters. Hence, the upper and lower bounds for fatigue life prediction were introduced based on the strongest and weakest part build directions or raster orientations of 3D printed materials. For all materials studied in the present paper, fill densities, which seem to have significant impact on fatigue strength of 3D printed parts, have been selected based on the maximum fatigue strength of each part. Results showed that, in some build orientations, the transition fatigue life does not exist. In other orientations, in which the plastic strain components are high enough, transition fatigue lives vary roughly between 20–400 cycles. This means that if the part design in very low cycle fatigue regime is of interest, plastic strains and more complicated plasticity analysis are needed. Results show that the load ratio has no major impact on the fatigue parameters of 3D printed PC parts. In addition, changing in the loading type from tensile fatigue to rotating bending fatigue can significantly impact the fatigue strength coefficient of 3D printed PLA specimens however, it does not noticeably alter the fatigue strength exponents.

Effect of strain rate on fatigue property of A356 aluminium casting alloys containing pre-existing micro-voids

This study aims to investigate the dependence of fatigue life on strain rate variations by loading frequency, and simultaneously, to evaluate the mutual relation between the strain rate and microporosity on the fatigue property in terms of the defect susceptibility of fatigue life to microporosity variation. The test specimen was prepared from the rim section of an automotive wheel fabricated by low-pressure die-casting on an A356 alloy. The high-cycle fatigue test was carried out in a strain rate range corresponding to the frequency range of 0.3–30 Hz at a stress ratio of R = −1. The strain rate increased to a two-order interval from 10−2 to 100 s−1 as the loading frequency increased from 0.3 Hz to 30 Hz. The nominal fatigue strength coefficient and exponent decreased from 754 MPa and 0.18 to 293 MPa and 0.09, respectively, with increasing strain rate. The fatigue life in low-stress amplitude slightly increased with the strain rate, while it remarkably decreased with the strain rate as the stress amplitude increased. This is because the elastic/plastic strain component ratio (Δεe/Δεp) decreased upon increasing the plastic strain component, accompanied by increasing strain rate. The plastic strain component was remarkably increased with the strain rate and stress amplitude, and decreased by the strain-hardening effect on the lapse of fatigue cycle, even though the elastic strain component remained at a constant level, depending mainly upon the stress amplitude. Additionally, the contribution of microporosity to the variation of fatigue life was underestimated as the strain rate increased, and became more sensitive with the variation of the elastic/plastic strain component in the fatigue cycle as the stress amplitude increased. The main propagation path of fatigue cracks is changed from a mixed mode of the cracking failure by the damage evolution of eutectic Si particle and the matrix penetration by shear deformation of matrix region, to a cracking failure mode where the damage evolution of eutectic Si particles dominated as the strain rate increased.

Effect of Zr on the high cycle fatigue and mechanical properties of Al–Si–Cu–Mg alloys at elevated temperatures

The Zr-modified Al–Si–Cu–Mg alloy with 0.14 wt%Zr addition was studied against the counterparts of commercially used EN-AC-42000 (Al7Si0.5Cu) baseline alloy for the effect of Zr on the high cycle fatigue (HCF) and mechanical properties at elevated temperatures of 150, 200, 250 °C. It was found that the fatigue life was significantly improved by 8–10 times at the high stress amplitude of 140 MPa in the Zr-modified alloy at all different temperatures. The fatigue strength coefficient, σf', of the baseline alloy was 574.9, 589.8, and 514.8 MPa at 150, 200, and 250 °C, respectively, which was greatly increased to 1412.3, 620.1, and 821.6 MPa for the Zr-modified alloy. The tensile strength was considerably improved by 34%–50%, dependant on the testing temperatures. The improved fatigue and tensile properties in the Zr-modified alloy could be mainly ascribed to: (1) the refined microstructure, with α-Al grain size decreasing from 335 to 253 μm and the secondary dendrite arm spacing (SDAS) dropping from 39 to 28 μm; (2) the reduced porosity; and (3) the additional precipitates strengthening effect by the nano-sized Al–Si–Zr–Ti dispersoids.

Influence of hydrothermal ageing on the fatigue behaviour of a unidirectional flax-epoxy laminate

Although the research and development in plant fibre composites is growing rapidly, these materials still require specific considerations before being adopted by industry in structural applications. One of the main issue is related to their durability. The objective of this study is to investigate the influence of hydrothermal ageing on the fatigue behaviour of an unidirectional flax-epoxy laminated composite by implementing the fatigue tests in a water bath. Results show that while the quasi-static strength and rigidity are significantly affected by the ageing, the fatigue strength is however improved. The fatigue strength coefficient is more than two times lower after ageing, indicating a lower decrease of the maximum stress with the increasing number of cycles. After ageing, the maximum stress level for an expected lifetime of 5.3 106 cycles is approximately 90 MPa, which is comparable to the one of unaged specimens. It is also pointed out that the remaining quasi-static tensile properties and behaviour of the aged specimen are not significantly affected after 1.3 106 cycles at a stress level of 90 MPa.

Reliability-Based Low Fatigue Life Analysis of Turbine Blisk with Generalized Regression Extreme Neural Network Method.

Turbine blisk low cycle fatigue (LCF) is affected by various factors such as heat load, structural load, operation parameters and material parameters; it seriously influences the reliability and performance of the blisk and aeroengine. To study the influence of thermal-structural coupling on the reliability of blisk LCF life, the generalized regression extreme neural network (GRENN) method was proposed by integrating the basic thoughts of generalized regression neural network (GRNN) and the extreme response surface method (ERSM). The mathematical model of the developed GRENN method was first established in respect of the LCF life model and the ERSM model. The method and procedure for reliability and sensitivity analysis based on the GRENN model were discussed. Next, the reliability and sensitivity analyses of blisk LCF life were performed utilizing the GRENN method under a thermal-structural interaction by regarding the randomness of gas temperature, rotation speed, material parameters, LCF performance parameters and the minimum fatigue life point of the objective of study. The analytical results reveal that the reliability degree was 0.99848 and the fatigue life is 9419 cycles for blisk LCF life when the allowable value is 6000 cycles so that the blisk has some life margin relative to 4500 cycles in the deterministic analysis. In comparison with ERSM, the computing time and precision of the proposed GRENN under 10,000 simulations is 1.311 s and 99.95%. This is improved by 15.18% in computational efficiency and 1.39% in accuracy, respectively. Moreover, high efficiency and high precision of the developed GRENN become more obvious with the increasing number of simulations. In light of the sensitivity analysis, the fatigue ductility index and temperature are the key factors of determining blisk LCF life because their effect probabilities reach 41% and 26%, respectively. Material density, rotor speed, the fatigue ductility coefficient, the fatigue strength coefficient and the fatigue ductility index are also significant parameters for LCF life. Poisson’s ratio and elastic modulus of materials have little effect. The efforts of this paper validate the feasibility and validity of GRENN in the reliability analysis of blisk LCF life and give the influence degrees of various random parameters on blisk LCF life, which are promising to provide useful insights for the probabilistic optimization of turbine blisk LCF life.

On the cavitation resistance of deep rolled surfaces of austenitic stainless steels

In the present work, two austenitic stainless steels (AISI 304 and AISI 316) were evaluated in cavitation tests with deep rolling treatments (DRT) on their surfaces. The results show that both steels exhibited better behaviour after the deformation process than in untreated conditions; however, the wear rate did not stabilize for the deformed surfaces due to the gradient of properties, attributed mainly to hardness profile of the material after DRT. A correlation between the cavitation erosion resistance and the fatigue strength is presented, with the cavitation wear rate and incubation time showing a good correlation with the fatigue strength coefficient in the case of high-cycle fatigue. In the case of low-cycle fatigue, a good correlation was established for the cavitation wear rate considering the Manson-Coffin theory of strain fatigue, assuming that the cavitation wear rate is inversely proportional to the fatigue life and using a fracture strain equal to the fatigue-ductility coefficient. In this case, a proportional constant around of 103 was found to establish the correlation for both steels. On the other hand, a linear correlation between the cumulative mass loss and surface roughness was separately established for steels under DRT conditions and untreated conditions. In addition, it was demonstrated that DRT is a great possible method for reducing the cost by wear.

Models of Printed Circuit Boards Conductive Pattern Defects

Abstract A number of PCB defects, though having passed successfully the defect identification procedure, can potentially grow into critical defects under the influence of various external and (or) internal influences. The complex nature of the development of defects leading to PCB failures demands developing and updating the data measuring systems not only for detection but also for the prediction of future development of PCB defects considering the external influences. To solve this problem, it is necessary to analyse the models of defect development, which will allow predicting the defect growth and working out the mathematical models for their studies. The study uses the methods of system analysis, theory of mathematical and imitation modelling, analysis of technological systems. The article presents four models for determining the theoretical stress concentration factor for several types of common defects, considering the strength loss of PCB elements. For each model the evaluation of parameters determining its quality is also given. The formulas are given that link the geometry of defects and the stress concentration factor, corresponding to four types of defects. These formulas are necessary for determining the number of cycles and time to failure, fatigue strength coefficient. The chosen models for determining the values of the stress concentration factor can be used as a database for identifying PCB defects. The proposed models are used for software implementation of the optical image inspection systems.