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Neural network (NN) models have significantly impacted fatigue‐related engineering communities and are expected to increase rapidly due to the recent advancements in machine learning and artificial intelligence. A comprehensive review of fatigue modeling methods using NNs is lacking and will help to recognize past achievements and suggest future research directions. Thus, this paper presents a survey of 251 publications between 1990 and July 2021. The NN modeling in fatigue is classified into five applications: fatigue life prediction, fatigue crack, fatigue damage diagnosis, fatigue strength, and fatigue load. A wide range of NN architectures are employed in the literature and are summarized in this review. An overview of important considerations and current limitations for the application of NNs in fatigue is provided. Statistical analysis for the past and the current trend is provided with representative examples. Existing gaps and future research directions are also presented based on the reviewed articles. [ABSTRACT FROM AUTHOR]

A new fatigue life prediction method using the energy‐based approach under uniaxial and multiaxial random loadings is proposed. The uniqueness of the proposed model is based on a time‐derivative damage accumulation unlike classical cycle‐based damage accumulation models. Thus, damage under arbitrary random loading can be directly obtained using time‐domain integration without cycle counting. First, a brief review of existing models is given focusing on their applicability to uniaxial/multiaxial, constant/random, and high cycle fatigue/low cycle fatigue loading regimes. Next, formulation of time‐derivative damage model is discussed in detail under uniaxial random loadings. Then, an equivalent energy concept for general multiaxial loading conditions is used to convert the random multiaxial loading to an equivalent random uniaxial loading, where the time‐derivative damage model can be used. Finally, the proposed model is validated with extensive experimental data from open literature and in‐house testing under various constant and random spectrum loadings. [ABSTRACT FROM AUTHOR]

A probabilistic fatigue life prediction framework for concrete bridges is proposed in this study that considers the stress history from the construction stage to the operation stage. The proposed fatigue analysis framework combines the fatigue crack growth-based material life prediction model and a nonlinear structural analysis method. A reliability analysis is proposed using the developed probabilistic model to consider various uncertainties associated with the fatigue damage. A Bayesian network is established to predict the fatigue life of a concrete bridge according to the proposed framework. The proposed methodology is demonstrated using an experimental example for fatigue life prediction of a concrete box-girder. Comparison with experimental data of fatigue life shows a satisfactory accuracy using the proposed methodology, and the ratio of the posterior predicted mean (updating time n = 8) to the test value decreases to 33%–1% in the current investigation. [ABSTRACT FROM AUTHOR]

• Innovative framework to construct GP model for fatigue life prediction is developed. • Fatigue-based physics constraints were incorporated into the GP model. • GP trained on one-dimensional cyclic loading cases outperformed parametric models. • Fatigue-based physics constraints imposed on GP reduce the overfitting risk. Under multiaxial fatigue loading, the superposed static components are additional factors for life prediction models to be considered. The increased dimension in fatigue data imposes difficulties in pattern recognition using existing functional form models. A framework to build a Gaussian process (GP) model for lifetime prediction under multiaxial loading was developed to solve this problem. Physically consistent constraints were imposed by applying a novel technique on the GP model to control its behavior and to decrease an overfitting risk. The model consistency with the rotationally invariant principle of damage was provided by the application of the critical plane concept. The framework was demonstrated to have excellent prediction capability on S355 steel and 7075-T651 aluminum alloy. Five well-known fatigue models of functional forms were also implemented for comparison. Detailed parametric studies were presented for the training sample effect, GP kernel effect, and model predictability. [ABSTRACT FROM AUTHOR]

The increasing demand for energy and the global threat of climate change have driven the search for alternative energy sources, with hydrogen emerging as a prominent substitute for fossil fuels. The fatigue behavior of pipeline steels under gaseous hydrogen is a critical problem that is impeding the industry's adoption of hydrogen into the current natural gas infrastructure. A brief review of existing hydrogen-assisted fatigue crack growth (HA-FCG) studies, which reveal several key gaps, is given first. Existing HA-FCG models predominantly address constant amplitude loading, while the realistic driving force is random loading in gas pipelines. Also, the current uncertainty quantification studies for HA-FCG focus on material randomness and overlook the large uncertainties associated with random pressure fluctuations. To address these issues, this study proposes a HA-FCG model that utilizes a time-based subcycle approach, allowing for direct application to random spectrum loads without the need for cycle counting. A model parameter as a function of hydrogen operating conditions is introduced to capture the different regimes in HA-FCG, and the model predictions are compared with ASME B31.12 code. Following this, statistical analysis of random pressure fluctuation data collected from natural gas pipelines at multiple locations is performed. The realistic industry pressure data shows distinct statistical features, and it is observed that the high-fidelity data (high sampling frequency) is beneficial for accurate fatigue life predictions. Uncertainty quantification and load reconstruction are performed by the Karhunen–Loève expansion with a post-clipping procedure, leading to a probabilistic HA-FCG analysis. The paper concludes with key findings and suggests directions for future research. • A hydrogen-assisted fatigue crack growth model accounting for uncertainties in pipe material grade and operational conditions. • Fatigue life prediction for pipeline steels for future hydrogen transport subjected to realistic random pressure fluctuations. • Probabilistic FCG analysis for hydrogen gas pipelines and comparison with ASME B31.12 code. • Uncertainty quantification for random pressure loads and load reconstruction using Karhunen–Loève expansion. [ABSTRACT FROM AUTHOR]

• Probabilistic Physics-guided Neural Network (PPgNN) is proposed for fatigue data. • PPgNN is flexible and does not impose restrictions on function types. • PPgNN includes known physics/knowledge constraints in the machine learning model. • PPgNN produces both accurate and physically consistent results. • Extensive experiments for fatigue P - S - N curves are conducted for model validation. A Probabilistic Physics-guided Neural Network (PPgNN) is proposed in this paper for probabilistic fatigue S - N curve estimation. The proposed model overcomes the limitations in existing parametric regression models and classical machine learning models for fatigue data analysis. Compared with explicit regression-type models (such as power law fitting), the PPgNN is flexible and does not impose restrictions on function types at different stress levels, mean stresses, or other factors. One unique benefit is that the proposed method includes the known physics/knowledge constraints in the machine learning model; the method can produce both accurate and physically consistent results compared with the classical machine learning model, such as neural network models. In addition, the PPgNN uses both failure and runout data in the training process, which encodes the runout data using a new proposed loss function, and is beneficial when compared with some existing models using only numerical point value data. A mathematical formulation is derived to include different types of physics constraints, which can deal with mean value, variance, and derivative/curvature constraints. Several data sets from open literature for fatigue S - N curve testing are used for model demonstration and model validation. Next, the proposed network architecture is extended to include multi-factor (e.g., mean stress, corrosion, frequency effect, etc.) fatigue data analysis. It is shown that the proposed PPgNN can serve as a flexible and robust model for general fitting and uncertainty quantification of fatigue data. This paper provides a feasible way to incorporate known physics/knowledge in neural network-based machine learning. This is achieved by properly designing the network topology and constraining the neural network's biases and weights. The benefits for the proposed physics-guided learning for fatigue data analysis are illustrated by comparing results from neural network models with and without physics guidance. The neural network model, without physics guidance, produces results contradictory to the common knowledge, such as a monotonic decrease of S - N curve slope and a monotonic increase of fatigue life variance as the stress level decreases. This problem can be avoided using the physics-guided learning model with encoded prior physics knowledge. [ABSTRACT FROM AUTHOR]

• A multiaxial fatigue criterion is proposed for arbitrary complicated loadings. • The effect of hydrostatic energy is included in the proposed criterion. • A loading transformation is proposed based on distortional and dilatational energy. • The proposed model is validated under tension-tension and tension-torsion loadings. • The influence of hydrostatic component in damage is discussed. A new energy-based fatigue life prediction model is proposed for arbitrary multiaxial constant loadings in this paper. First, a brief review for existing multiaxial fatigue models is given, especially focusing on energy-based models. It is observed that most multiaxial model formulation and validation are suitable for axial-torsional loadings, but may not be appropriate for biaxial tension-tension loading. One possible reason is the ignorance of hydrostatic stress-state difference under these two types of loadings. In view of this, a new model is proposed by including fatigue damage contributions of equivalent tensile energy, torsional energy, and hydrostatic energy. Next, a loading transformation is proposed to transfer a complicated three-dimensional loading to an effective loading for life prediction. Detailed discussion of different types of multiaxial loading and its relationship with the ratio of distortional energy and dilatational energy is given. The hysteresis energy can be calculated integrating the proposed model with the Garud cyclic plastic model, which is directly linked to the damage accumulation and fatigue life prediction. The proposed model is validated with extensive experimental data under both tension-torsion loadings and biaxial tension-tension loadings from open literature. Comparison with several widely used multiaxial model is also given to show the model performance with respect to different biaxial tension-tension loadings. Finally, concluding remarks and future work based on the investigated materials are discussed. [ABSTRACT FROM AUTHOR]

[Display omitted] • Subcycle fatigue crack growth formulation is extended to consider the near-threshold behavior. • EIFS concept is integrated with subcycle time-domain FCG for life assessment under random loadings. • Both uniaxial and multiaxial fatigue life assessments can be performed using the same framework via time-domain integration. • Validation with both constant and random spectrum loading experimental data shows majority assessment accuracy within the life factor of 3. A novel fatigue-life prediction methodology combining a subcycle fatigue crack growth (FCG) analysis and equivalent initial flaw size (EIFS) concept is proposed in this paper. This research focuses on extending a previously developed time-based subcycle fatigue crack growth model to a near-threshold regime and under multiaxial loadings. First, the threshold FCG behavior using subcycle FCG is discussed, and a new temporal kernel function to include intensity factor corresponding to the near-threshold region is proposed. Following this formulation, the multiaxial load case scenario is considered for mixed-mode FCG using a critical plane approach. Next, the general multiaxial loading is converted to an equivalent uniaxial loading for life prediction. Next, model predictions under arbitrary loadings (e.g., uniaxial and multiaxial, constant and variable amplitude loading, and random spectrums) are compared with experimental data from open literature and internal testing. Multiple conclusions and potential future work have been suggested using the proposed model. [ABSTRACT FROM AUTHOR]

This study introduces an innovative methodology for predicting fatigue properties of additively manufactured Titanium alloy (Ti–6Al–4V) fabricated using laser powder bed fusion (LPBF). This study entails two key components: a classification model to identify sites likely to initiate cracks and a Probabilistic Physics-Guided Neural Network (PPgNN 2.0) to forecast fatigue life. The classification model capitalizes on parameters related to surface roughness and internal defects. This methodology minimizes false positives and negatives by leveraging computed tomography (CT) images for accurate surface topology and internal defects morphology. Data augmentation techniques were employed to address the challenge of imbalanced data distribution. PPgNN 2.0 represents an advancement over classical regression models due to its incorporation of physics-based constraints and probabilistic approaches, leading to highly accurate and physically consistent predictions. Training of the model involves multiple stress–fatigue life (S–N) curve datasets from literature and pertinent morphological data, while evaluation uses data extracted from in-house testing and imaging. The key strength of PPgNN 2.0 lies in its ability to offer flexible and robust fatigue life predictions, encompassing point estimates and uncertainties in the form of mean and standard deviation. A new loss function is proposed, which effectively captures the underlying distribution, contributing to minimizing prediction errors. • A methodology for extracting microstructural information from CT scan-built STLs. • Formulation of crack initiation site prediction as a classification problem. • Physics and data fusion using physics-guided neural network design. • Probabilistic fatigue life prediction using uncertainty-aware neural network. [ABSTRACT FROM AUTHOR]

• A time-derivative fatigue crack growth formulation and no need for cycle counting in the presence of arbitrary loadings. • Unified methodology for high-cycle fatigue, low-cycle fatigue, and their interactions. • Demonstrated and validated with uniaxial and multiaxial random loadings. • Fatigue life prediction using crack growth analysis with explicit near-threshold modeling. A novel fatigue life prediction method under random multiaxial loadings is proposed in this paper. One unique benefit of the proposed method is that it is based on the time-derivative fatigue crack growth formulation and does not need cycle counting under arbitrary loadings. First, a brief review of subcycle fatigue crack growth (FCG) analysis and the equivalent initial flaw size (EIFS) concept for life prediction is introduced. Next, the existing subcycle fatigue crack growth model is extended to near-threshold conditions. An intrinsic fatigue threshold of the material is introduced, and a hypothesis is proposed that the crack only grows when the local stress intensity factor is beyond the intrinsic threshold. Following this, the analogy of stress intensity factor and strain intensity factor is used to extend the fatigue life prediction model to strain-based fatigue analysis. Correction for large plastic deformation is included to handle low-cycle fatigue life prediction. The novelties of this model are that it considers the FCG at the threshold and near-threshold region and it is able to predict both HCF and LCF conditions using FCG-based life prediction. Following this, extensive in-house and literature data for AL-7075-T6 under uniaxial and multiaxial, constant, and random loadings are used for model validation. Discussions for the effect of model parameters are provided based on parametric analysis. Conclusions and future work are mentioned. Code and data are released in public cloud service for interested readers. [ABSTRACT FROM AUTHOR]

• Subcycle fatigue crack growth (FCG) formulation is extended to consider the surface roughness of additively manufactured parts. • Arola-Ramulu model for effective stress concentration along with an asymptotic stress intensity factor interpolation method are integrated with subcycle time-domain FCG for life assessment. • Validation with uniaxial and multiaxial, constant amplitude loading data from both in-house experiments as well as literature data shows majority assessment accuracy within a life factor of 2. Additively Manufactured (AM) components are prone to fatigue damage due to defects accompanied by the manufacturing process, such as surface roughness, internal porosity, and anisotropy due to differences in build directions. This is especially true for as-built components with significant surface roughness, where the surface polishing and treatments are not possible due to resource or space limitations. This paper proposes a crack growth-based methodology for the fatigue life assessment of AM components subjected to uniaxial and multiaxial, constant and variable loading conditions. The work is based on a previously developed subcycle fatigue crack growth model. The developed FCG model is extended with the stress concentration factor due to surface roughness and an asymptotic stress intensity factor (SIF) interpolation method for notched specimens. The proposed model approximates the surface roughness as an equivalent notch having the same stress concentration as that posed by the irregularities on the surface. Fatigue life assessment is performed based on the concept of equivalent initial flaw size (EIFS) and FCG analysis. The proposed methodology is validated against in-house as well as experimental data from the available literature. [ABSTRACT FROM AUTHOR]

A new crack growth-based corrosion fatigue life prediction method for aging reinforced concrete beam is proposed in this paper. The proposed method couples the corrosion growth kinetics and fatigue crack growth kinetics together. The relationship between corrosion damage morphology and corrosion loss is investigated by the experimental results. A phenomenological model is proposed to obtain the stress concentration factor model under different corrosion loss conditions. Following this, the developed model is integrated with an asymptotic method to calculate the stress intensity factor for the crack at corrosion pit roots. The fatigue life is predicted by the integration of the fatigue crack growth rate curve from the equivalent initial flaw size to the critical length. Probabilistic analysis methodology is proposed to consider various sources of uncertainties for the fatigue life prediction. Fatigue life prediction results are validated with experimental observations for various corroded steel bars and beams available in the literatures. [ABSTRACT FROM AUTHOR]

• A new framework for probabilistic fatigue life prediction under random loadings. • PSRC is proposed to transform random loading in a piecewise and randomized manner. • Mean stress corrected random fatigue limit model is proposed. • Both loading and material uncertainties are considered. • Influence of step size and block sequence randomization in PSRC is discussed. A new framework is proposed for probabilistic fatigue life prediction considering randomness from both loadings and material properties. Piecewise stochastic rainflow counting (PSRC) is proposed to transform random loading spectrums to block loadings in a piecewise way with block randomization. The PSRC can be integrated with both linear and nonlinear damage accumulation rules. Mean stress corrected random fatigue limit model is proposed for uncertainty quantification of material fatigue properties under constant amplitude loadings. Probabilistic fatigue life prediction with both loading and material uncertainties is conducted using Monte Carlo simulation and is validated with experimental data from literature and in-house testing. Impact of different mean stress correction models on the fatigue life prediction under random loadings is investigated in detail. The influence of block piece length and block sequence randomization is discussed with respect to the mean and scatter behavior of the probabilistic life prediction results. [ABSTRACT FROM AUTHOR]

• Uncertainty quantification for fatigue S - N curves with sparse data is studied. • A novel Hierarchical Bayesian data augmentation (HBDA) method is proposed. • HBDA shows significant performance gain, especially with small sample size. • HBDA is applied to fatigue quantification of the Pearl Harbor Memorial Bridge. A novel statistical uncertainty quantification (UQ) method for fatigue S- N curves with sparse data is proposed in this paper. Sparse data observation is very common in fatigue testing due to various reasons, such as time and budget constraints, availability of testing materials and resources. A brief review of existing UQ methods for fatigue properties with sparse data is given. Following this, a new method, called Hierarchical Bayesian data augmentation (HBDA) is proposed to integrate the hierarchical Bayesian modeling (HBM) and Bayesian data augmentation (BDA) to deal with sparse data problem specifically for fatigue S - N curves. The key idea is to use: (1) HBM for analyzing the variability of S-N curves both within one stress level and across stress levels; (2) BDA to build up a large-size sample of fatigue life data based on the observed sparse samples. Four strategies to estimate the probabilistic S-N curves with sparse data are proposed: (1) hierarchical Bayesian modeling (HBM) only, (2) Bayesian data augmentation (BDA) only, (3) posterior information from HBM used as prior information for BDA (HBM + BDA), and (4) augmented data from BDA used by HBM (BDA + HBM). The strategy (3) and (4) are named HBDA hereafter. Next, the four strategies are validated and compared using aluminum alloy data and laminate panel data from open literature. Convergence study and confidence estimation is performed, and it is shown that the HBDA methods (i.e., HBM + BDA or BDA + HBM) have better performance compared with the classical method and HBM/BDA alone. The performance gain is especially significant when the number of available data samples is small. Finally, the proposed methodology is applied to a practical engineering problem for fatigue property quantification of the demolished Pearl Harbor Memorial Bridge, where only limited samples are available for testing. Conclusions and future work are drawn based on the proposed study. [ABSTRACT FROM AUTHOR]

• A stress-based fatigue model under arbitrary random multiaxial loading is proposed in this paper. • The proposed model is based on the Liu-Mahadeven critical plane concept. • An equivalent stress transformation reduces a random loading to a simple constant loading. • The model is validated successfully for Al-7076-T6 under different loading conditions. A multiaxial fatigue life prediction model under general multiaxial random loadings is proposed in this paper. First, a brief review for existing multiaxial fatigue models is given with a special focus is on the Liu- Mahadevan critical plane concept, which can be applied to both brittle and ductile materials. Next, the new model development based on the Liu-Mahadevan critical plane concept for random loading is presented. The key concept is to use two-steps to identify the critical plane: identify the maximum damage plane due to normal stress and calculate the critical plane orientation with respect to the maximum damage plane due to normal stress. Multiaxial rain-flow cycle counting method with mean stress correction is used to estimate the damage on the critical plane. Equivalent stress transformation is proposed to convert the multiaxial random load spectrum to an equivalent constant amplitude spectrum. The equivalent stress is then used for fatigue life predictions. The proposed model is validated with both literature and in-house testing data generated using an Al 7075-T6 alloy under various random uniaxial and multiaxial spectrums. Comparison between experimental and predicted fatigue life lives shows good agreements; thus, demonstrating efficacy of the proposed model. Finally, concluding remarks and future work based on the results obtained are discussed. [ABSTRACT FROM AUTHOR]