Multiaxial Fatigue Life Prediction Research Articles

Analysis of tooth root three-dimensional fatigue crack initiation, propagation, and fatigue life for spur gear transmission

The gears in aviation gear systems are susceptible to fatigue fracture due to high-speed, heavy-load, and load alternation operating conditions. Therefore, a numerical calculation model with multiple mesh positions loading form has been proposed in this paper to analyze the fatigue crack initiation and propagation behavior, and to estimate the fatigue life of these gears. The fatigue life of the gear is determined by separately calculating the fatigue crack initiation life and the fatigue crack propagation life. The tooth root fatigue stress and the fatigue initiation life are calculated by the multi-axial fatigue life prediction method with the Smith-Watson-Topper criterion and the critical plane method. Afterwards, the tooth root stress–strain field is calculated in Finite element (FE) software and the stress intensity factors of the crack tip are calculated in three-dimensional (3D) crack analysis software. Then, the tooth root fatigue crack propagation trajectory and the fatigue crack propagation life are obtained separately. Finally, the influence mechanism of the loading conditions, the geometry parameters of gears, and the initial crack positions on the tooth root fatigue crack initiation life, propagation life, and fatigue crack propagation trajectory are analyzed, and a tooth fatigue test bench is built for verifying the crack propagation trajectory.

Prediction of multiaxial fatigue life with a data-driven knowledge transfer model

A data-driven model is presented for accurate prediction of multiaxial fatigue life based upon the principle of transfer learning (TL). The Tradaboost framework is explored to adjust the weights of training data from different sources, actuating information transfer from domain knowledge to the data-driven modeling of multiaxial fatigue life. Subsequently, extensive experimental results tested under the proportional and non-proportional circle loadings are collected for model evaluation. The results demonstrate that the proposed model is more accurate than domain knowledge-based, conventional data-driven, and comparable TL-based models, with a low data requirement, showcasing good applicability for multiaxial fatigue life assessment.

In-plane biaxial fatigue life prediction model for high-cycle fatigue under synchronous sinusoidal loading

The unique advantage of in-plane biaxial loading is no rotation of the maximum principal stress during cyclic loading, which has a distinct effect on fatigue life. This study aims to propose a life prediction model for in-plane biaxial fatigue encompassing both in-phase and out-of-phase conditions. For synchronous sinusoidal loadings, an equivalent stress expression is derived using the integral method, accounting for the influences of shear and normal stresses across all planes. The equivalent stress is then compared to a reversed uniaxial constant amplitude loading to predict fatigue life. To validate and compare the model, in-phase and out-of-phase in-plane biaxial fatigue experiments were conducted using 24 nickel-based superalloy cruciform specimens at temperatures of 420℃, 550℃, and 600℃. The results show that the proposed model is superior to conventional stress-invariant based models, with most results staying within the ± 2 error bands. Using the proposed model, the effects of mean tensile stress, biaxiality and phase shift are discussed. Additionally, a novel non-proportional factor is introduced to enhance multiaxial fatigue life prediction by distinctly separating the effects of principal stress and its directional variations.

A new approach to multiaxial fatigue life prediction: A multi-dimensional multi-scale composite neural network with multi-depth

Many multiaxial fatigue life prediction methods tend to increase additional parameters and model depth as the complexity of the loading path increases. This leads to issues such as poor model robustness, limited flexibility, and single-dimensional approaches. In this study, a multi-dimensional multi-scale composite neural network with multi-depth is proposed to address these challenges and enhance prediction accuracy. Initially, physical and sensitive features serve as input data for the proposed model, to enhance the richness of input features. Subsequently, a multi-dimensional feature extraction module is deployed to extract feature information from the composite data. To process these features, an improved multi-domain query cascaded transformer network (IMQCT) is employed as the feature processing module of the proposed model. The proposed model is verified to have better prediction accuracy and extrapolation capability by using experimental data from nine materials and comparing its performance with six machine learning models.

A frequency domain enhanced multi-view neural network approach to multiaxial fatigue life prediction for various metal materials

Fatigue damages and failure widely exist in engineering structures, particularly in industries such as aerospace, automotive, and construction, where components are often subjected to complex multiaxial loading conditions. Accurate prediction of fatigue life is critical for ensuring the safety and longevity of these structures. In this study, a novel multi-view deep learning model incorporating frequency domain analysis for fatigue life prediction is proposed. The proposed model integrates a Convolutional Neural Network (CNN), a Long Short-Term Memory Network (LSTM), and FNet that combines frequency domain analysis, in a parallel structure to extract features from the loading paths of materials. These extracted features are then connected to a fully connected neural network to predict fatigue life. The model was validated using fatigue data collected from 6 different materials, encompassing 17 loading paths and 336 samples. Additionally, ablation experiments were conducted, and the extrapolation capabilities were evaluated using specifically designed test sets. The results demonstrate that the proposed model exhibits excellent predictive performance and extrapolation capabilities. We anticipate that the multi-view approach, along with its accuracy and applicability, can offer potential applications in engineering fields that require reliable, data-driven models to assess material durability under complex loading scenarios.

A deep learning dataset for metal multiaxial fatigue life prediction

Multiaxial fatigue failure of metals, a common issue in industrial production, often leads to significant losses. Recently, many researchers have applied deep learning methods to predict the multiaxial fatigue life of metals, achieving promising results. Due to the high costs of fatigue testing, training data for deep learning is scarce and labor-intensive to collect. This study meets this need by creating a large-scale, high-quality dataset for multiaxial fatigue life prediction, consisting of 1167 samples from 40 materials collected from literature. The dataset includes key mechanical properties (elastic modulus, yield strength, tensile strength, Poisson’s ratio) and 48 loading paths, along with additional relevant information (composition ratios, processing conditions). Common deep learning models validated the dataset’s effectiveness. This dataset aims to support researchers applying deep learning to fatigue life prediction, addressing the long-standing issue of data scarcity, thereby advancing the intersection of artificial intelligence and metal fatigue research.

An optimized multiaxial fatigue life prediction model based on the subcritical plane method

Since a more rigorous requirement is raised for the performance of aero-engine increases, the multiaxial fatigue problem of its components turns out to be increasingly severe. In this study, a multiaxial fatigue life prediction model is developed by using the subcritical plane method, where the effect of non-proportional additional hardening under non-proportional loading is considered by both the deflection angle of the subcritical plane and the combined parameters of strain on the subcritical plane. Moreover, the cyclic strain hardening index in the traditional model is substituted with an additional strengthening material coefficient that is characterized by the static strength of the material, which reduces the difficulty in calibrating the parameters of the multiaxial life model. The effectiveness of the proposed model is validated by comparing the predicted fatigue life with some fatigue test data, and the errors between the predicted and the testing data fall into a factor of two error bands. In general, the proposed multiaxial life prediction model simplifies the calibration of model parameters, and the prediction accuracy is still ensured, which promotes the model to facilitate engineering application.

A data augmentation method for multiaxial fatigue life prediction based on physics-informed tabular generative adversarial network

Abstract Currently, in the multiaxial fatigue life prediction problem, machine learning (ML) algorithms are still limited by small samples. For ML tasks requiring large amounts of data, this paper proposes a Conditional Tabular Generative Adversarial Network (CTGAN) model using a physical equation as a generation constraint. The proposed method can make synthetic samples satisfy specific physical knowledge. The method is evaluated using two datasets of different materials. ML-based algorithms verify the feasibility of using synthetic datasets for life prediction. Verification analysis shows that the proposed method successfully synthesizes high-quality multiaxial fatigue datasets and effectively improves the prediction accuracy of ML algorithms.

Neural network integrated with symbolic regression for multiaxial fatigue life prediction

In the realm of structural engineering, accurately predicting multiaxial fatigue life presents a formidable challenge, stemming from the complex interplay of stress and strain across multiple directions. This research introduces the Symbolic Regression-Neural Network (SR-NN) framework, a novel integration of symbolic regression-derived expressions with neural networks aimed at enhancing predictive accuracy in this field. Initiated by selecting salient features through SHAP-informed Recursive Feature Elimination, our approach effectively minimized dimensionality while pinpointing key feature groups. Symbolic regression, newly applied to guide neural network training in the prediction of alloy material fatigue life, facilitated the generation of meaningful expressions that describe the fatigue processes. These expressions were incorporated into the network’s loss function alongside MSE loss, refining the model’s learning dynamics. Our proposed SR-NN framework demonstrated substantial improvements over traditional models in rigorous testing, notably reducing MSE by 55.4% compared to RF and 45% against SVM models, underscoring the potential of merging symbolic regression with machine learning to tackle the inherent variability and complexity of fatigue behavior across diverse materials and loading conditions. This study highlights the transformative impact of symbolic regression in improving the interpretability and accuracy of predictive models within structural engineering.

Research on multiaxial fatigue life prediction of lifting equipment based on symbol corrected equivalent stress spectrum

Research on multiaxial fatigue life prediction of lifting equipment based on symbol corrected equivalent stress spectrum

An engineering applicable method for multiaxial fatigue under proportional and non-proportional loads based on the octahedral plane projection

Present multiaxial fatigue models have achieved satisfactory performance in predicting multiaxial fatigue life of different loading paths; however, many of them require critical plane calculations and additional material constants. In this study, a novel multiaxial fatigue life prediction model based on octahedral shear strain energy is proposed. In the proposed model, the maximum octahedral shear strain energy serves as the damage parameter without requiring any additional material parameters. All material constants in this model can be derived from material strength constants and uniaxial fatigue constants, greatly simplifying the life prediction process. Moreover, based on the actual physical phenomenon of non-proportional additional hardening, the multiaxial non-proportional correction factor is incorporated into the plastic stage of the life equation, aligning more closely with fundamental principles in physics. Then, by utilizing the experimental data from the literature for four materials, a comparison is made between the prediction results of the novel model and those of four commonly employed models. The findings demonstrate that the new model exhibits superior simplicity and accuracy. Subsequently, through life prediction outcomes for DZ411 material across various paths, the stability and precision of the octahedral energy model are substantiated, rendering it suitable for practical engineering applications.

A New Type of S–N Equation and Its Application to Multi-Axial Fatigue Life Prediction

Abstract The S–N equation is one of the most important equations in fatigue model investigation. A majority of fatigue models, including multi-axial fatigue model and mean effect models, are established on the basis of the S–N equation. Obviously, an accuracy of the S–N equation is very important. Taking into account that the S–N equation is, in fact, an empirical one in which the material constants are determined by numerical fitting fatigue experimental data, in this study, the S–N equation can be improved, by further processing these fatigue experimental data, to present a new type of S–N equation that is more accurate than the S–N equation. The new type of S–N equation is called a similar S–N equation in this study. By using a large number of experimental data of metallic materials reported in the literature, an accuracy of the similar S–N equation has been proven.

Multiaxial fatigue life prediction based on modular neural network pretrained with uniaxial fatigue data

PurposeData-driven models are increasingly being used to predict the fatigue life of many engineering components exposed to multiaxial loading. However, owing to their high data requirements, they are cost-prohibitive and underperforming for application scenarios with limited data. Therefore, it is essential to develop an advanced model with good applicability to small-sample problems for multiaxial fatigue life assessment.Design/methodology/approachDrawing inspiration from the modeling strategy of empirical multiaxial fatigue models, a modular neural network-based model is proposed with assembly of three sub-networks in series: the first two sub-networks undergo pretraining using uniaxial fatigue data and are then connected to a third sub-network trained on a few multiaxial fatigue data. Moreover, general material properties and necessary loading parameters are used as inputs in place of explicit damage parameters, ensuring the universality of the proposed model.FindingsBased on extensive experimental evaluations, it is demonstrated that the proposed model outperforms empirical models and conventional data-driven models in terms of prediction accuracy and data demand. It also holds good transferability across various multiaxial loading cases.Originality/valueThe proposed model explores a new avenue to incorporate uniaxial fatigue data into the data-driven modeling of multiaxial fatigue life, which can reduce the data requirement under the promise of maintaining good prediction accuracy.

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.

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 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.

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 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.

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.