Fatemi Socie Criterion Research Articles

Multiaxial fatigue behavior and life estimation of Al‐Li alloy 2099 under strain‐controlled loading

AbstractAluminum‐lithium alloys are a class of advanced materials designed to reduce weight and improve performance in aerospace and other high‐tech applications. This paper presents a research investigation on the in‐phase and out‐of‐phase multiaxial fatigue behaviors of the third‐generation AW2099‐T83 aluminum‐lithium alloy that have not been addressed before. Additional hardening was observed under nonproportional loading condition at high strain amplitudes. Fatigue lives were estimated using von Mises equivalent strain and two critical plane models: the Fatemi‐Socie (FS) and the Smith‐Watson‐Topper (SWT). In addition, a supervised machine‐learning model (support vector machine—SVM) was employed to predict the fatigue life under the above‐mentioned loading conditions. The FS criterion was found to yield better fatigue life predictions than SWT. The estimations of FS model mostly fall within ±3× scatter bands with some data falling within the conservative and non‐conservative regions. The SVM model resulted in excellent predictions within ±2× scatter bands.

Experimental study of the fatigue failure behavior of aluminum alloy 2024-T351 under multiaxial loading

Multiaxial fatigue has been drawing much attention because it is more applicable to engineering practice. In this paper, an experimental study of aluminum alloy (AA) 2024-T351 was carried out under multiaxial loading with an aim to assess the damage evolution process and failure mechanism under in-phase and out-of-phase loadings. Firstly, fatigue life and stress response under multiaxial cyclic loads were obtained, and it found that although there is non-proportional hardening, the fatigue life subjected to proportional loading is significantly shorter than that of under a nonproportional loading, which was tried to be explained by the ductility of the material. Secondly, a detailed analysis of the damage evolution process based on the degradation of the elastic modulus and the fatigue failure process based on the digital image correlation (DIC) method was provided. Next, a micro-analysis of the specimens’ fracture appearance was conducted to obtain the fracture characteristics and found that AA2024-T351 presents a dominant shear fracture mode under proportional loading and a mixed mode of tensile and shear fracture under non-proportional loading. Last but not least, The Fatemi-Socie criterion was modified by considering the material’s ductility and the interaction between normal stress and shear stress acting on the critical plane. The multiaxial life prediction results of the modified FS model for AA2024-T351 in this paper were all within the scatter bands of 3 on life.

Effects of fretting wear on rolling contact fatigue

In this study, a three-dimensional (3D) continuum damage mechanics (CDM) finite element (FE) model was developed to investigate the effects of fretting wear on rolling contact fatigue (RCF) of bearing steels. In order to determine the fretting scar geometry, a 3D arbitrary Lagrangian-Eulerian (ALE) adaptive mesh (AM) FE model was developed to simulate fretting wear between two elastic bodies for different initially pristine fretting pressures (0.5, 0.75 and 1 GPa) and friction coefficients (0.15, 0.175 and 0.25) resulting in stick zone to contact width ratios, c/a = 0.35, 0.55 and 0.75. The resulting wear profiles were subjected to various initially pristine RCF pressures (1, 2.2 and 3.4 GPa). The pressure profiles for RCF were determined by moving the contact over the fretted wear profiles in 21 steps. These pressure profiles were then used in the CDM-FE model to predict the RCF life of fretted surfaces. The CDM-FE model uses Fatemi-Socie (FS) criteria for damage evolution and accounts for scatter in RCF life by implementing material topological variation through Voronoi tessellation. The results from CDM-FE RCF model indicate that fretting scar generated at 1 GPa with c/a = 0.35 has the most detrimental effect on RCF life at 1 GPa, reducing life by as much as 99.8% from pristine condition. However, it is to be noted that the remaining life expectancy at this RCF pressure (1 GPa) is significant and more than 17 billion cycles. As the RCF pressure increases (PRCF ≥ 2.2 GPa), the effect of fretting on RCF life decreases for all fretting pressures and c/a values, indicating that life is primarily governed by the RCF pressure. The results from CDM-FE model were also used to develop a life equation for evaluating the L10 life of fretted M-50 bearing steel for the range of tested conditions.

An investigation into various failure criteria on rolling contact fatigue through an improved probabilistic model

This work presents an improved probabilistic continuum damage mechanics (CDM) finite element (FE) model to simulate the degradation of material as a function of cycle in order to estimate rolling contact fatigue (RCF) life of critical tribological components. Traditionally, CDM-FE models consider the shear reversal to be the damage causing stress in RCF; however, in this investigation, the CDM-FE model also considers the octahedral shear stress, the maximum shear stress, the Fatemi-Socie criteria, and the Dang Van multi-axial fatigue parameter as failure criteria. The critical damage material parameters (σr and m) were obtained from open literature torsion fatigue results. Further, to enable a probabilistic CDM-FE model, the critical damage material parameters (σr and m) were described via a distribution as opposed to fixed values. This allows for the variation of a material’s resistance to fatigue that is present in both torsion and rolling contact fatigue to be captured. Forty unique material microstructure models were created using Voronoi tessellations to capture the random pathways for crack growth. RCF simulations were conducted at five contact pressures between 1.0 GPa and 3.4 GPa. Regression analysis between contact pressure and cycles to failure for each of the failure criteria yielded five unique predictive fatigue life equations, one for each failure criteria investigated. These fatigue life equations were then compared to Lundberg-Palmgren theory considering appropriate material and lubrication factors. The results demonstrated that the Fatemi-Socie and shear stress reversal failure criteria compared favorably to Lundberg-Palmgren theory. Notably, the Fatemi-Socie criteria exhibited closer agreement with Lundberg and Palmgren theory at higher contact pressures, in contrast to the shear reversal criteria.

Multiaxial fatigue of Inconel 718 produced by Selective Laser Melting at room and high temperature

This work investigates the fatigue and cyclic plasticity of Inconel 718 produced by Selective Laser Melting (SLM) at room and elevated temperature. Strain-controlled axial, torsional and proportional tests with Rɛ=0 were carried out at 20 °C and 450 °C using thin-walled specimens, resulting in fatigue lives ranging from 103 to 105 cycles. SLM Inconel 718 exhibits a columnar microstructure along the build direction, and the dominant defect related to the manufacturing process was gas pores. Fatigue crack initiation occurred a carbides and/or metallic inclusions for all tests and, therefore, intrinsic defects related to the manufacturing process did not induce premature initiation of fatigue cracks. The orientation of macroscopic fatigue cracks was consistent with the plane of maximum shear stress for all loading conditions. The fatigue crack propagation mechanism of SLM Inconel 718, on the other hand, depends on the loading path and temperature. Both the equivalent strain amplitude and the Fatemi–Socie criterion could correlate fatigue life of all loading conditions at 20 °C and 450 °C within factor-of-two boundaries. As a general trend, the fatigue endurance of SLM Inconel 718 is inferior to its forged counterpart, especially at 450 °C. The cyclic plasticity behaviour of SLM and forged Inconel 718 is similar at both 20 °C and 450 °C and can be simulated by the Chaboche model.

Torsional-loaded notched specimen fatigue strength prediction based on mode I and mode III critical distances and fracture surface investigations with a 3D optical profilometer

Torsional and axial fatigue tests were performed on steel 42CrMo4+QT and aluminium alloy 7075-T6, and a 3D optical profilometer was used for the investigations of the fracture surfaces. The mode I and mode III critical distances of the two materials were regarded as reference scales for evaluating the initial orientation of the cracks and then identifying the tests valid for the calibration of the normal and those for the shear-fatigue models. The torsional strength of blunt notched specimens was then predicted with the Smith-Watson-Topper and the Fatemi-Socie criteria, combined with the critical distances and the Chaboche model for the steel.

Residual Stress Distribution Design for Gear Surfaces Based on Genetic Algorithm Optimization

The rolling contact fatigue of gear surfaces in a heavy loader gearbox is investigated under various working conditions using the critical plane-based multiaxial Fatemi–Socie criterion. The mechanism for residual stress to increase the fatigue initiation life is that the compressive residual stress has a negative normal component on the critical plane. Based on this mechanism, the genetic algorithm is used to search the optimum residual stress distribution that can maximize the fatigue initiation life for a wide range of working conditions. The optimum residual stress distribution is more effective in increasing the fatigue initiation life when the friction coefficient is larger than its critical value, above which the fatigue initiation moves from the subsurface to the surface. Finally, the effect on the fatigue initiation life when the residual stress distribution deviates from the optimum distribution is analyzed. A sound physical explanation for this effect is provided. This yields a useful guideline to design the residual stress distribution.

Evaluation of different strain-based damage criteria for predicting the fatigue life of friction stir spot-welded joints under multi-axial loading conditions

In this article, fatigue life of dissimilar friction stir spot welds in Cross-Tension and Lap-Shear specimens is predicted using a number of fatigue damage criteria. The results revealed a relatively good correlation between predicted fatigue crack initiation lives and experimental data. Also, it has been shown that in the whole range of applied load levels, the least discrepancy between predicted fatigue lives and experimental data is related to the Smith–Watson–Topper criterion. Finally, an excellent agreement was found in predicting the location of the crack tips using the Fatemi–Socie criterion in both types of specimens.

Multiaxial fatigue experiments and life prediction for silicone sealant bonding butt-joints

Uniaxial and multiaxial fatigue experiments were conducted on the adhesively bonded hollow cylindrical butt-joint specimen under load-controlled mode, and several prediction criteria were used for multiaxial fatigue life prediction. The experimental results showed that the fatigue life of uniaxial tensile cycle was shorter than that of uniaxial torsional cycle, and the fatigue life of the non-proportional circular loading path was shorter than that of the proportional loading path. In addition, the multiaxial fatigue life prediction results showed that Smith-Watson-Topper criterion based on the maximum principal strain as the critical plane had a conservative life prediction for the non-proportional circular loading path. Fatemi-Socie criterion mainly considered the influence of shear strain which yielded the non-conservative prediction for some data points of proportional loading path. Chen-Xu-Huang criterion combined energy density and critical plane achieved better fatigue life predictions than those from the previous two criteria. Furthermore, considering general failure modes of the adhesively bonded butt-joints, the modified Chen-Xu-Huang model was proposed, and the predicted results are good agreement with the experiments.

A fatigue crack initiation and growth life estimation method in single-bolted connections

Fatigue life estimation accuracy of mechanical parts and assemblies has always been the source of concern in different industries. The main contribution of this article lies in a study on the accuracy of different multiaxial fatigue criteria, proposing and investigating the accuracy of four optimized fatigue crack initiation life estimation methods—volume, weighted volume, surface and point, thereby improving the multiaxial fatigue life estimation accuracy. In order to achieve the goal, the fatigue lives of bolt clamped specimens, previously tested under defined experimental conditions, were estimated during fatigue crack initiation and fatigue crack growth and then summed together. In the fatigue crack initiation part, a code was written and used in the MATLAB software environment based on critical plane approach and the different multiaxial fatigue criteria. Besides the AFGROW software was utilized to estimate the crack growth share of fatigue life. Experimental and numerical results showed to be in agreement. Furthermore, detailed study and comparison of the results with the available experimental data showed that a combination of Smith–Watson–Topper approach and volume method results in lower error values, while a combination of Fatemi–Socie criterion and surface or point method presents estimated lives with lower error values. In addition, the numerical proposed procedure resulted in a good prediction of the location of fatigue crack initiation.

Multiaxial fatigue behavior of 2618 aluminum alloy

The purpose of the present research project is to study multiaxial fatigue behavior of 2618 alloy. The influence of mean stress on the fatigue behavior under tension and torsion is particularly investigated. Fatigue tests under combined tensile-torsion, in or out of phase, as well as combined tensile-torsion-internal pressure tests have also been conducted. Multiaxial fatigue results are analyzed according to Fatemi-Socie criterion to predict the fatigue life.

Cyclic Deformation and Low-Cycle Fatigue for 316LN Stainless Steel under Non-proportional Loading

The effects of loading path and strain amplitude ratio on the cyclic behavior and fatigue life were investigated on a 316LN nuclear grade stainless steel employing a series of symmetrically strain-controlled fatigue tests at room temperature. The loading paths of Uniaxial, Torsional, Proportional, Rhombic, Rectangular, and Circular were employed with the constant equivalent strain amplitude of 0.5%. The strain amplitude ratio of 2.35, 1.73 and 1.27, defined by the ratio of shear strain amplitude to the axial strain amplitude, was realized by changing the shear strain amplitude under Proportional, Rhombic, Rectangular and Elliptical loading paths. As expected, the significant non-proportional additional hardening was observed. It’s interesting to note that the axial cyclic stress response varied with the strain amplitude ratio, and the law was different under different loading paths. The fatigue life of all the tests were evaluated by three critical plane criteria proposed by Smith-Watson-Topper (SWT), Fatemi-Socie (FS) and Chen-Xu-Huang (CXH). Results show that the SWT criterion significantly overestimated the fatigue life of non-proportional loading because the effect of shear damage was not considered. The CXH criterion for tensile-type failure yielded good prediction results except for two torsional data points. The FS criterion provided better predictions than other models.

Effect of the residual stress on contact fatigue of a wind turbine carburized gear with multiaxial fatigue criteria

Carburized gears are extensively applied in heavy duty machines such as wind turbines. The variations of hardness and residual stress introduced by carburizing and quenching processes remarkably affect the rolling contact fatigue (RCF) during repeated gear meshing. The present work attempts to study the effect of the residual stress on rolling contact fatigue and predict the rolling contact fatigue life of a wind turbine carburized gear based on multiaxial fatigue criteria. A finite element elastic-plastic contact model is developed which takes the gradients of hardness and initial residual stress into account. Initial residual stress distribution is obtained through experimental measurements. The stabilized stress strain field is carried out by considering the shakedown state under the heavy load conditions. The Fatemi–Socie and the Brown–Miller criteria are used to estimate the contact fatigue damage of the carburized gear. Numerical results reveal that the effect of the initial residual stress on the contact fatigue failure can be reflected by the Fatemi–Socie criterion whereas it is not reflected by the Brown–Miller criterion since the two strain parameters appeared in the criterion are not influenced by residual stress. In terms of the Fatemi-Socie criterion, under modest load conditions where elastic response occur, a considerable compressive residual stress would alter the plane orientations of crack initiation, while under extremely heavy load conditions where plasticity occur, the influence of the initial residual stress on contact fatigue damage is limited within the near-surface non-plastic zone. The effect of the initial residual stress on contact fatigue life represents a bilinear curve. As the magnitude of the tensile residual stress increases, the RCF life decreases linearly. As the magnitude of the compressive residual stress exceeds a certain value, the RCF life does not increase anymore.

Computational framework for multiaxial fatigue life prediction of compressor discs considering notch effects

Aero engine components like compressor discs normally operate under harsh conditions like complex multiaxial stress states. Notch effect is often critical for structural integrity assessment in virtue of complex structure and discontinuities. According to the notch effect under cyclic loadings, a computational framework for multiaxial fatigue analysis of compressor discs is established by coupling finite element (FE) simulation of stress gradient with Fatemi-Socie (FS) criterion. Specifically, a notch support extension method accounting for stress gradient effect is elaborated through elasto-plastic FE analysis, which can be determined for fatigue life prediction of arbitrary shaped components. Experimental fatigue data for smooth and notched specimens of TC4 and GH4169 alloys demonstrated the appropriateness of the proposed computational approach. The applicability and performance of the prediction model to a compressor blade-disc attachment subjected to field spectra is presented. Results show that testing effect can be significantly reduced by using this framework with acceptable prediction accuracy.

Critical plane–based multiaxial fatigue life prediction of turbine disk alloys by refining normal stress sensitivity

For engineering components subjected to complex multiaxial loadings, critical plane approaches like Fatemi–Socie criterion have been commonly utilized for life prediction of these components. Within the Fatemi–Socie criterion, the normal stress sensitivity parameter k is usually fitted from additional experimental data, which introduces inconvenience for practice especially under limited testing data conditions. In this regard, a simple critical plane–based damage parameter is put forward with no additional material constants, which attempts to provide a robust method for multiaxial fatigue analysis of turbine disk alloys. Using experimental datasets of TC4 and GH4169 alloys under different loadings, the proposed model provides better correlations with fatigue life of the two alloys than the models of Smith–Watson–Topper and Wang–Brown.

Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks

In the present study, a computational-experimental framework is developed for fatigue reliability assessment of turbine bladed disks. Within the framework, the overspeed testing is innovatively combined with stochastic finite element (FE) analysis for quantifying uncertainties in the experimental data, material properties and loads. Meanwhile, two schemes are elaborated based on probabilistic S-N curves and stochastic FE simulation coupling with sampling technique. The stochastic FE simulation incorporates the Chaboche constitutive model with Fatemi–Socie criterion for fatigue behavior modeling and life prediction. Moreover, experimental deformation and numerical FE analysis are conducted with regard to the full-scale bladed disk test with increased step-stress overloading. Reliability sensitivity analysis is performed to provide an importance ranking of random variables for fatigue design of the bladed disk. Results indicate that stochastic FE analysis-based scheme provides more conservative predictions than the probabilistic S-N curves-based one.

Study and modelling of anodized 2618 aluminum behavior subjected to multiaxial fatigue

Anodized Aluminum alloys are widely used in aeronautic construction due to their specific mechanical properties. However, anodization process often leads to a decrease of the fatigue resistance of the alloys. In order to identify and characterize the different mechanisms involved in the detrimental effect of anodization of 2618-T851 alloy on its fatigue life and to determine the impact of loading nature, several tests have been performed on specimens with different surface states at various stress ratios. It was found that roughness of machining has no effect unlike the stress ratio or mean stress in tensile tests. The tests on the pickled, anodized, impregnated and sealed specimens showed it was the anodic oxidation step which was the more detrimental for fatigue resistance under tensile loading comparing to the other steps. It has been also observed that no such detrimental effect occurred under torsion loading. Concerning the prediction of fatigue life, two critical plane-based analysis approaches have been used (Morel and Fatemi-Socie criteria) to make fatigue life prediction for uniaxial and multiaxial fatigue test. Comparisons showed that both criteria gives overestimated fatigue life for uniaxial tensile loading under compression mean stress and underestimated fatigue life for tensile-torsion in phase loading.

Probabilistic framework for multiaxial LCF assessment under material variability

The influence of material variability upon the multiaxial LCF assessment of engineering components is missing for a comprehensive description. In this paper, a probabilistic framework is established for multiaxial LCF assessment of notched components by using the Chaboche plasticity model and Fatemi-Socie criterion. Simulations from experimental results of two steels reveal that the scatter in fatigue lives can be well described by quantifying the variability of four material parameters {σf′,εf′,b,c}. A procedure for choosing the safety factor for fatigue design has been derived by using first order approximation.

A numerical investigation on critical plane orientation and initiation lifetimes in fretting fatigue under out of phase loading conditions

This study focuses on application of critical plane approach to in-phase and out-of-phase loading conditions in fretting fatigue problems. The efficacy of various multiaxial damage criteria is analysed to determine critical plane orientation and initiation life, and is investigated for the first time in case of out-of-phase loading condition. Furthermore, our study focuses on the estimation of initiation angle and initiation lives using multiaxial damage criteria. For analysis purpose, the damage criteria are categorized as stress-based (Findley parameter and McDiarmid criterion), strain-based (Brown-Miller criterion and Fatemi-Socie criterion) and virtual strain energy-based (Smith-Watson-Topper criterion and Liu 1 and 2 criteria). It is observed that shear stress and shear strain-based criteria are able to predict both critical plane orientation and fretting fatigue lifetimes, whereas energy-based criteria, which employ normal stress and strain, are only suitable to predict initiation life. The deviation in estimation of initiation life for stress-based criteria is observed to be higher than others if the internal stresses are higher than yield stress. It is shown that initiation can occur on either of the preferred shearing plane depending upon material and loading conditions. The phase difference of 90° and 180° increases and decreases the initiation life respectively as compared to in-phase loading. In addition, 90° phase difference introduces more shearing planes for damage nucleation.

Fatigue of extruded AZ31B magnesium alloy under stress- and strain-controlled conditions including step loading

Fatigue of extruded AZ31B magnesium alloy under stress- and strain-controlled loading conditions was investigated. The experimental program included uniaxial and axial−torsion tests conducted under constant amplitude loading and step loading. Observed fatigue lives and cracking orientations were used to evaluate two critical plane multiaxial fatigue criteria, namely, the Jiang criterion and the Fatemi–Socie criterion. The Jiang criterion is found to give satisfactory fatigue life predictions and a reasonable description of the cracking behavior. The Fatemi–Socie criterion provides a similar performance for most of the loading cases. For some of the uniaxial stress-controlled experiments, the fatigue life and early cracking predictions by the Fatemi–Socie criterion do not agree well with the experimental results. A discussion on the implications of stress-controlled loading conditions to fatigue modeling is presented.