Multiaxial Fatigue Research Articles

Matching relationship of low-cycle fatigue life and fatigue design method of concentrically braced frames with H-section steel

Simulations on 192 concentrically braced frames with H-section steel (Q355B) are carried out to investigate their low-cycle fatigue performance. The fatigue life of a steel-braced frame is predicted using a multiaxial fatigue damage parametric model. To depict the fatigue failure sequence and the matching relationship of the fatigue life between the two components in the braced frame, the fatigue life ratio (β) is introduced. This ratio represents the gusset plate's fatigue life to the brace's fatigue life. Simulated results are analyzed, and β is found to be positively correlated with four influencing factors, the width-to-thickness ratio of the brace flange, connection coefficient, ratio of the column length to beam length, and slenderness ratio of the gusset plate. Also, β is found to be negatively correlated with the slenderness ratio of the brace. Based on the Bayesian updating method, a probabilistic model is formulated to predict β of a steel-braced frame. Accordingly, a fatigue design method is proposed, which contributes to avoiding the in-coordination of seismic capacity caused by the significant difference between the brace’s and gusset plate’s fatigue life within the steel braced frame. The proposed fatigue design method has the potential to serve as a reference for improving design specifications.

Key role of surface defects in the multiaxial fatigue life of additively manufactured unmachined 18Ni300 maraging steel

The study aims to estimate the role of surface defects in the fatigue life of age-hardened and unmachined additively manufactured 18Ni300 maraging steel and to verify the effectiveness of stress-based life prediction models. Axial-torsional cyclic loading paths involving in-phase and out-of-phase cases are applied. Scanning electron microscopy and micro-computed tomography are performed to detect the fatigue crack initiation sites and paths. The effectiveness of the classic models and a physics-constrained Gaussian process for regression in fatigue life prediction is estimated. Results show that the intrinsic orientation of the surface defects affects the fatigue mechanism by increasing the material sensitivity to axial stress. Additionally, the steel is insensitive to the phase shift between the axial and torsional loading components. The hydrostatic stress and the integrated shear stress amplitudes over the critical plane are pointed as the most effective load-related quantities for life prediction.

Advancements in stress‐based multiaxial fatigue prediction: A data‐driven approach and a new criterion

AbstractA highly accurate iteration of the Liu & Zenner multiaxial fatigue criterion is presented and validated against the FatLim dataset. The proposed criterion modifies the mean stress parameters of the original criterion while keeping the amplitude parameters unchanged. The investigation of the best‐performing stress amplitude parameters revealed that existing multiaxial fatigue criteria that rely on dimensional weight parameters exhibit a notable prediction bias. This bias leads to inaccurate fatigue assessments. The paper sheds light on the extent of this bias and its implications for common engineering practices. By introducing the refined criterion, the study addresses these limitations and provides a more reliable framework for multiaxial fatigue analysis. The comprehensive validation against the FatLim dataset demonstrates the superiority of the proposed criterion in accurately predicting fatigue behavior under diverse loading conditions. The findings underscore the significance of considering both amplitude and mean stress parameters in multiaxial fatigue criteria, offering valuable insights for enhancing the accuracy of fatigue assessments in engineering applications.

Multiaxial fatigue life prediction based on effective factor with shear/axial stress ratio for Ti60 titanium alloy in very high cycle regime

Fatigue failure mechanism of Ti60 titanium alloy under tension–torsion multiaxial loading in the very high cycle regime was studied first, and the results showed that the shear/axial stress ratio directly affects the failure mechanism. When the shear/axial stress ratio is relatively small, cracks tend to originate from the subsurface in single-point initiation mode, and the larger the shear/axial stress ratio, the more cracks tend to originate from the surface in multi-point initiation mode. Then, a pragmatic equivalent method for multiaxial to uniaxial load based on the law of shear/axial stress ratio on fatigue strength was proposed. Based on this method and uniaxial S-N curve, the fatigue lives of Ti60 specimens under shear/axial stress ratios of 1.37, 1.95, and 3.53 was predicted, and the experimental results showed that the prediction error is basically within a factor of 3.

Experimental and Simulation Investigation on Fatigue Performance of H13 Steel Tools in Friction Stir Welding of Aluminum Alloys.

As the central component in friction stir welding, the design and manufacture of welding tools for aluminum alloys have garnered substantial attention. However, the understanding of tool reliability during the welding process, especially in terms of fatigue performance, remains unclear. This paper focuses on the welding of AA2219-T4 as a case study to elucidate the predominant failure mode of the tool during the friction stir welding (FSW) of aluminum alloys. Experimental methods, including FSW welding and fracture morphology analysis of the failed tool, coupled with numerical simulation, confirm that high-cycle mechanical fatigue fracture is the primary mode of the tool failure. Failures predominantly occur at the tool pin's root and the shoulder end face with scroll concave grooves. The experimental and simulation results exhibit a noteworthy agreement, validating the reliability of the simulation model. The FSW Arbitrary Lagrangian-Eulerian (ALE) model developed in this study analyzes stress distribution and variation under the thermo-mechanical coupling effect of the tool. It reveals that stress concentration resulting from structural changes in the tool is the primary driver of fatigue crack initiation. This is attributed to exposure to alternating cyclic stresses such as bending, tension, and torsion at the tool pin's root, manifesting as multiaxial composite mechanical fatigue. Among these stresses, bending alternating cyclic stress exerts the most significant influence. The paper employs the Tool Life module in DEFORM software to predict the fatigue life of the tool. Results indicate that reducing welding speed or increasing rotation speed can enhance the tool's fatigue life to some extent. The methodology proposed in this paper serves as a valuable reference for optimizing FSW structures or processes to enhance the fatigue performance of welding tools.

Mechanical Behavior and Life Prediction of a Low Nickel/High Nitrogen Austenitic Steel under Pure Torsion, Uniaxial Tension-Compression, and Multiaxial Fatigue

Abstract Fatigue life prediction, crack growth, and propagation mechanisms are important details to consider for a structure to be used in service without fear of early failure. This is especially important for a new material for which very limited information is available. In this study, austenitic stainless steel P558 with low nickel content and high nitrogen content was subjected to fatigue testing at room temperature in multiaxial (static compression and cyclic torsion), pure torsion, and uniaxial tension-compression modes. The material generally depicts cyclic softening in the three loading conditions; although the multiaxial experiments experienced some initial hardening, those with a high shear stress and axial stress combination furthermore experienced a secondary hardening before softening. The Fatemi-Socie model predicts the pure torsion and multiaxial fatigue well but fails to predict fatigue lives for uniaxial tension-compression. On the other hand, the Smith-Watson-Topper model predicts fatigue lives for the uniaxial fatigue and pure torsion sufficiently but is poor in predicting fatigue lives for the multiaxial fatigue loading conditions. The cracking behavior was observed to be dependent on the loading condition and the strain amplitude with Mode II cracks or shear-oriented cracks observed for the high strain amplitudes (resulting in shorter lives) whereas Mode I cracks, or tensile-oriented cracks, were observed from low strain amplitudes (resulting in higher lives). A mixed mode was also observed for specimens in the midrange strain amplitudes, which exhibited a branching from shear to tensile cracks. The static compressive stress is believed to have a negative influence on the cracking behavior and the fatigue life by the rubbing of the crack surfaces, which in turn reduces the load-holding capability of the material. The same friction at the crack tip could also be the reason for the heating up of the specimens.

The strain ratio-dependent multiaxial low cycle fatigue behaviour and life prediction of 316L stainless steel based on critical plane at elevated temperature

The study mainly investigates the effect of strain ratio on the multiaxial low cycle fatigue behaviour of 316L at 550 °C. The evolution of both axial and torsional stress amplitude is observed to go through three stages: cyclic hardening, softening and fracture. What's different is that the torsional loading experiences fewer cyclic hardening cycles compared to the axial loading. Regarding the interaction between axial and torsional stresses, it is observed that as the torsional strain increases, the axial deformation response presents a lower peak stress and a higher softening rate, while the torsional peak stress and softening rate hardly changes with the increase of axial strain amplitude. The fracture pattern is obtained through three-dimensional (3D) depth-of-field observation. It is discovered that as the strain ratio increases, the fracture pattern transits from tensile failure mode to shear failure mode. Furthermore, the orientation angle of the fracture surface increases and lies between the critical plane angle of maximum shear strain and maximum normal strain, indicating a mixed failure mode. Additionally, a comparison of nine representative critical plane models reveals that the energy-based models can better predict the multiaxial fatigue life influenced by the strain ratio. Finally, based on the analysis of deformation and failure mechanisms, a normal damage parameter weakening factor (NDWF) is introduced into the KBM-R model, and an improved normal stress component (INSC) is introduced into the Wu-R model. The two modified models well capture the impact of strain ratio and accurately predict the multiaxial fatigue life of both 316L and P92 steel.

A probabilistic life prediction framework for vibration fatigue of turbine blade based on refined polynomial chaos expansion

AbstractVibration fatigue is a typical form of multiaxial fatigue. In this study, initial vibration fatigue tests were conducted on rocket turbine blades, and significant dispersion in fatigue life was found. Consistent with this finding, a novel probabilistic life prediction framework was proposed. This framework integrates sensitivity analysis and sequential sampling technology and introduces polynomial chaos expansion as a computationally efficient alternative to finite element analysis. And a continuous mechanics‐based damage evolution model was employed to examine the vibration fatigue life of turbine blades. The findings validate the effectiveness of the framework, as no significant difference was found between the experimental results and simulated predictions at the 95% confidence level. Furthermore, comparison with the Monte Carlo simulation indicated that this framework achieves comparable prediction accuracy, while significantly reducing the required samples by 2 orders of magnitude, which effectively addresses the fatigue problem of small sample data. This framework enables rapid and accurate multiaxial fatigue probabilistic life prediction, which holds important implications for the reliability design of reusable spacecraft.

Effect of interference magnitude on fretting wear and fatigue strength of scaled press-fitted railway axles

Railway axles represent a typical example of interference fit structures that are vulnerable to fretting fatigue induced by rotational bending loads. This study investigated the influence of interference magnitude on the fretting wear and fatigue of scaled press-fitted railway axles. In this study, the fretting fatigue strength was tested at three interference magnitudes within the standard range, and the fretting wear and fretting cracks were analyzed. The results indicate a trend where the fretting fatigue strength initially rises and then declines with increasing interference magnitude. 3D finite element models, with and without considering the fretting wear, were developed to investigate the variation in contact parameters in the press-fitted region, and the Smith-Watson-Topper multiaxial fatigue model was employed to evaluate the fretting fatigue behavior. The results demonstrate that the competition between contact pressure and axial slip produces relatively slight fretting wear when the interference magnitude takes the middle value, thereby causing a minor stress concentration and ultimately leading to higher fretting fatigue strength.

A novel model considering combined effects of as-built roughness and notch for multiaxial fatigue life prediction of L-PBF Ti6Al4V

Additive Manufacturing (AM) has emerged as a promising manufacturing technology. However, there is still a lack of effective methods for evaluating the influence of as-built roughness, especially for notched components under complex fatigue loading. In this paper, a method based on damage mechanics for multiaxial fatigue life prediction is proposed for addressing the individual and combined effect of as-built surfaces and macro notches. Chaboche material model is coupled with a damage variable to describe the elastic–plastic deformation around the notch. The effect of as-built roughness is integrated into the damage evolution law developed by Chaudonneret, taking into account the degree of roughness, the orientation-dependent effect, and the variation of roughness effect with stress levels. The proposed model is numerically implemented by UMAT and validated through experimental data from literature under four types of fatigue loading including axial, torsion, in-phase axial-torsion and 90° out-of-phase axial-torsion. The predicted results agree well with the experimental values and the combined effect of the as-built roughness and notch is well analyzed.

A framework proposal for new multiaxial fatigue damage and extreme response spectra in random vibrations frequency analysis

Fatigue Damage Spectra (FDS) and Extreme Response Spectra (ERS) are well-established tools for characterizing and evaluating the impact of vibration loads on mechanical structures. While this is particularly valuable in producing test-tailored specifications, their current application is limited to uniaxial analysis despite evidence indicating their inadequacy in representing real-world loads, which are often multiaxial.The proposed method offers a system-oriented approach to characterize and compare multiaxial environments in terms of their severity, independently or not of any physical structure. In addition, it introduces a generalization of the FDS and ERS, referred to as Fatigue Damage multi-Spectrum (FDmS) and Extreme Response multi-Spectrum (ERmS) respectively. These extensions allows for the consideration of multiaxial phenomena, such as correlation and modal proximity. Finally, this paper demonstrates through several case studies the method’s capability to capture phenomena not addressed by established uniaxial approaches.

Non local multiaxial fatigue modeling of defects : A unified approach to interpret size and shape effects

This paper deals with the effect of defect size and shape under high cycle fatigue for metallic alloys. A large simulation campaign based on a multiaxial fatigue criterion and a non-local approach is presented. A relative defect size based on a ratio between the defect size and a characteristic length introduced by the non-local approach is defined. A normalized Kitagawa–Takahashi diagram is then obtained. A competition between the highly stressed volume size and the local maxima due to the defect is observed and seem dependent on the relative defect size. The effect of the loading mode (uniaxial and pure shear) and of the plasticity are discussed. Finally, a comparison of the simulation results with experimental data on a 316L L-PBF demonstrates the robustness of the proposed approach and explains the negligible effect of the defect morphology compared to its size.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Multiaxial low cycle fatigue behavior and life prediction of wire arc additive manufactured 308L stainless steel

Wire arc additive manufacturing (WAAM) is a technique that has gained popularity in various industrial sectors due to its high productivity and flexibility. However, the comprehension of cyclic deformation and fatigue behaviors in WAAM austenitic stainless steel (SS), particularly under complex multiaxial loading conditions, is much less advanced compared to conventional manufacturing methods. This study aims to fill some of these gaps by performing fatigue tests of WAAM 308L SS under axial, torsional and axial–torsional multiaxial loadings. Similar tests were carried out on the hot-rolled 308L SS as a basis for comparison. WAAM 308L SS exhibits notable distinctions in cyclic deformation, fatigue life, cracking mode and fatigue failure mechanisms compared to its hot-rolled counterparts as a result of its distinct manufacturing technologies and resulting microstructures. To assess all fatigue life data, three critical plane criteria, namely FS, SWT and CXH criteria, were employed. The CXH model, which considers the effects of both tensile and shear damage on fatigue properties, has the ability to predict the fatigue life of both hot-rolled and WAAM 308L SS.

Multiaxial fatigue behavior and crack orientation prediction for steel and cast iron

This study investigates multiaxial fatigue behavior of ductile construction steel S355 and cast iron EN-GJS-500-14. Fatigue lives and crack initiation orientations are measured. Three critical plane models are evaluated for predicting fatigue life and crack initiation angles. While all models achieve decent accuracy in predicting fatigue life, crack initiation angle predictions are less satisfactory. Weak correlation is observed between the quality of fatigue life and crack orientation prediction, particularly for the Smith–Watson–Topper (SWT) and Fatemi-Socie (FS) models. The SWT model performs better in predicting fatigue life and crack angles for cast iron, while the FS model shows higher accuracy for S355. The short-crack model (SC) provides the best overall fatigue life prediction but crack orientation estimation is not superior.

Multiaxial failure behavior and fatigue life prediction of unidirectional composite laminates

Complex coupling mechanisms exist between longitudinal and shear stress on the multiaxial fatigue behavior of composites. A thorough reanalysis of matrix shear failure mechanism under multiaxial fatigue loading is presented. Longitudinal single splitting fracture were analyzed and validated as an independent failure mode under multiaxial loading by analogy to the failure mechanism of natural composites. A new multiaxial fatigue life prediction model was established by double projection on the critical and subcritical fracture planes. Experiments on unidirectional tubular specimens were carried out under combined tension-torsion loadings to separate and identify the multiaxial fatigue failure behavior of composites. The proposed model has been verified using unidirectional laminates subjected to cyclic tension-torsion and off-axis loading, and the results showed that the predicted life is in good agreement with the experimental ones. Applications of three-dimensional digital image correlation (3D-DIC) and microscopy regarding verification in multiaxial damage mechanism are also addressed.

Stress-Based Model for Calculating the Opening Angle of Notch Cracks in a Magnesium Alloy under Multiaxial Fatigue

This paper presents a model to calculate the opening angle of crack initiation in notched fractures subjected to multiaxial loading. To validate the proposed model, a study was performed on polished AZ31B-F magnesium alloy specimens under multiaxial high-cycle fatigue loading. The specimens exhibited a notch in the smaller cross-sectional area, which was created with a special drilling jig to promote the formation of fatigue cracks in this localized area of the specimen. The load paths used in the experiments and numerical analyses were proportional and non-proportional, resulting in different stress states in the crack front opening, which were determined by finite element analysis to validate the proposed model. To obtain more accurate numerical results for these estimates, these finite element analyses were performed using the nonlinear Chaboche plasticity model of ABAQUS® 2021 software. A sensitivity analysis was also performed to determine which load component—axial or torsional—has a greater influence on the fatigue strength and contributes significantly to the crack opening process. The results show that the type of load path and the stress level of each load component—axial and torsional—has a strong influence on the opening angle of the notch crack and the fatigue lifetime of the specimen. This result is confirmed not only by the experimentally determined fatigue strength, but also by a fractographic analysis performed on the surface of the specimens for both load paths. Moreover, the results show an acceptable correlation between the experimental results and the estimates obtained with the proposed model and the stresses obtained with the finite element analysis.

Multiscale-based multiaxial fatigue model of short fiber reinforced polymer composites under high-cycle proportional loading

Due to the inhomogeneity and anisotropy of short fiber-reinforced polymers (SFRP), even uniaxial loading can induce multiaxial stress states inside them, which significantly increases the difficulty of grasping their fatigue behavior. To efficiently predict the fatigue life of SFRP under proportional multiaxial stress, a multiaxial high-cycle fatigue model is proposed, relying upon the multiscale modeling strategy capable of integrating the influence of fiber microstructure. Taking the fiber-matrix interface stress at the critical region as the internal driving factor of fatigue fracture is the core assumption verified by microscopic observations. Off-axial fatigue tests with different orientations and stress ratios are performed to validate the fatigue model. Results show that the prediction accuracy has reached an acceptable level, and the quadratic polynomial surface can well represent the relationship between fatigue life and multiaxial stresses. This work provides an efficient tool for multiaxial fatigue life prediction and expounds the failure behavior of SFRP from multiscale perspectives.

Uncertainty quantification in multiaxial fatigue life prediction using Bayesian neural networks

In practical engineering scenarios, unforeseen failures may result in significant costs and risks. Assessing the uncertainty related to multiaxial fatigue life prediction is crucial for engineering applications. However, establishing a reliable multiaxial fatigue life prediction model remains challenging due to uncertainties in physical models, material properties, and measurement data. This paper proposes an effective Bayesian Neural Network (BNN) model for quantifying the uncertainty in multiaxial fatigue life prediction. Fatigue parameters in the multiaxial fatigue life prediction model are used as inputs for the BNN. The BNN method utilizes No-U-turn Sampler (NUTS) and Automatic Differentiation Variational Inference (ADVI) to address the inference problem in the model and perform life predictions for unknown non-proportional loading paths and different materials. Validation using experimental data from six different materials confirms the effectiveness of the BNN model. Experiments show that the performance of BNN models is beneficial in most cases compared to classical ML models, assessed through different error standards, statistical tests, Taylor diagrams, uncertainty analysis, and scatter index analysis. The proposed method provides a clear understanding of the uncertainty in multiaxial fatigue life prediction, offering a promising approach for simulating fatigue life under multiaxial loading in engineering applications.

The importance of aeroelasticity in estimating multiaxial fatigue behaviour of large floating offshore wind turbine blades

The trend toward longer blades in offshore wind turbines poses a significant structural design challenge, given their flexibility and larger load variations. While the study of aeroelastic models of very long blades has gained attention in recent discussions, there is a gap in comprehensive studies examining the impact of different aeroelastic models on fatigue analysis. This study focuses on a comparative evaluation of different aeroelastic models under identical conditions, with a specific focus on multiaxial fatigue. The primary objective is to compare and assess the discrepancies in predicting the lifetime, spatial damage distribution, and critical wind speed conditions. The findings of this study highlight a substantial impact of the aeroelastic model selection on the expected lifetime, revealing durations of 23.2, 3.7, and 1.2 years for the geometrically exact beam theory, Euler-Bernoulli beam, and rigid body assumption. In contrast, the spatial distribution of fatigue damage and critical wind speed conditions remain relatively stable across the models.