Fatigue Life Prediction Framework Research Articles

Probabilistic framework for strain-based fatigue life prediction and uncertainty quantification using interpretable machine learning

Establishing a unified fatigue life prediction model and quantifying the uncertainty in the mechanical behavior of materials are critical to ensure the structural integrity and equipment performance. For the commonly-used strain-based fatigue methods, existing estimation methods exhibit inevitable deviations, while data-driven methods have shown poor extrapolation ability and interpretability. Therefore, this paper aims to develop a probabilistic framework for strain-based fatigue life prediction and uncertainty quantification (UQ) to provide an indication for fatigue design/assessment using interpretable machine learning (ML) techniques. Based on Shapley additive explanations (SHAP) and symbolic regression (SR), interpretable prediction models with concise expressions and outstanding prediction performance are established and optimized according to the priori physical knowledge. Moreover, accounting for the material variability, the probabilistic assessment with UQ excellently validates the prediction model, and quantifies the variability of ε-N curves. The proposed framework provides valuable reference and shows promising prospects in fatigue design for engineering components.

The effect of cold forming residual stresses in local fatigue approaches: A numerical perspective

Thin-walled structures generally rely on cold-formed mild steel profiles. Due to cold forming, a significant formation of residual stresses impacts their overall fatigue behaviour. In this work, a state-of-the-art framework for fatigue life prediction is proposed and applied to both roll-formed and press-braked full-scale profiles. In summary, the profile’s manufacturing process is numerically simulated to obtain a representative residual stress field. These results are then used as the initial state during a subsequent structural and fatigue analysis. A clear detrimental residual stress effect is verified. Importantly, however, is to note that prediction accuracy increases significantly when these effects are considered.

Digital twin Bayesian entropy framework for corrosion fatigue life prediction and calibration of bridge suspender

This paper proposes an intelligent digital twin framework for corrosion fatigue life prediction and calibration of suspender wires integrated with mechanism-driven, sensor-driven, and information fusion. A general probabilistic information fusion strategy is constructed to handle entropy-based external constraints and classical Bayesian updating. Statistical moment, range bound, and point data are considered to investigate the effect of various types and sequences of information. A small-time domain fatigue crack growth model is proposed to overcome the limitations of traditional cycle-based methods, which can capture the large and small cycles of random fatigue stress. The virtual sensor-based stress time-history response is obtained under different traffic flow densities through digital twin finite element model of a suspension bridge. The results show that with and without considering interval bound leads to different fatigue life prediction results, especially for statistical moment data fusion, and the maximum difference is approximately 54%. The average prediction life of suspender wires is gradually close to the actual service life as crack observations increase. The standard deviations of the corrosion fatigue life decrease by 88%, when simultaneously integrating moment, interval, and point data.

A fatigue life model accounting for the combined effect of surface roughness and microstructure: Application to SLM fabricated Hastelloy-X

This study introduces a microstructure-sensitive fatigue life prediction framework based on CP-FFT which includes the effect of surface roughness. The model is applied to flat Hastelloy-X specimens fabricated using Selective Laser Melting. The surface roughness measured is incorporated introducing a free surface with sinusoidal profile. The framework can accurately predict the fatigue life reduction of rough flat specimens using the fatigue parameters of polished bulk specimens and introducing the actual microstructure and roughness. A parametric study shows a monotonic reduction of life with the roughness amplitude but a minor effect of the surface waviness.

Pore-induced fatigue failure: A prior progressive fatigue life prediction framework of laser-directed energy deposition Ti-6Al-4V based on machine learning

Pores are major cause of fatigue failure in laser-directed energy deposition (L-DED) titanium alloy. For the safe application of L-DED titanium alloys, it is essential to establish a fatigue life prediction method based on pore-induced fatigue. This paper proposes a prior progressive fatigue life prediction framework based on ridge classification and kernel ridge regression algorithms. The fatigue life prediction was carried out on L-DED Ti-6Al-4V alloy in three steps: critical pore identification, fine granular area existence prediction and final fatigue life prediction. The fatigue life prediction method adopted in the current study outperform the others with a correlation coefficient as high as 0.951, followed by a comparison with the results derived from different machine learning algorithms. The results show that the proposed fatigue life prediction framework can predict the fatigue life of L-DED Ti-6Al-4V alloy based on computed tomography tests and microstructure features. Due to its strong generalization ability and effectiveness, the proposed prediction method is expected to be valuable for fatigue-resistant design of L-DED Ti-6Al-4V alloy.

Digital twin-driven framework for fatigue life prediction of welded structures considering residual stress

The welding of steel generates substantial welding residual stress (WRS), which exerts a significant impact on the fatigue life of steel bridges. In this study, a physical model for calculating the fatigue crack growth (FCG) life of welded specimens in the WRS field is established based on the weight function method. Experimental data validates the reliability and precision of the proposed physical model. The impact of WRS on the fatigue life of structural components is scrutinized and analyzed. On this basis, a digital twin (DT) framework driven by a physical-data model is proposed to consider the inherent parameter uncertainty in FCG behavior within the WRS domain. A dynamic Bayesian network (DBN) is used to characterize the evolution characteristics of fatigue crack states over time in the digital space. Particle filter algorithm is used as DBN inference method. The results show that the calculation of the physical model is in good agreement with the experimental values. Neglecting the influence of WRS distribution may lead to an overestimation of fatigue life in welded structures. The DT framework can update uncertain parameters online and realize the accurate prediction of the FCG life in the WRS field.

Microstructural size effect on the notch fatigue behavior of a Ni-based superalloy using crystal plasticity modelling approach

Fatigue performances of critical structures are strongly affected by the microstructural (e.g. grain, defect, inclusion, etc.) size effect, and it is thus important to quantify their detrimental effect. In this work, a numerical procedure is constructed to quantify the influence of microstructure on the mechanical and fatigue behaviors of Ni-based superalloy GH4169. Specifically, by combining sub-modelling approach with crystal plasticity constitutive model, a dual-scale modelling approach is developed for studying grain-level mechanical behavior of Ni-based superalloy GH4169 notched components. In addition, the dislocation-based Tanaka-Mura-Wu model is applied for fatigue crack initiation life prediction. The Paris law is then utilized for fatigue crack propagation analysis based on the simulated short crack. To study the microstructural size effect on fatigue crack initiation and propagation behaviors, sub-models containing various grain orientation, grain size, defect size/shape are built and analysed. Finally, a series of fatigue tests on notched specimens of Ni-based superalloy GH4169 were carried out for method validation. Results indicate that the established dual-scale modelling approach and fatigue life prediction framework yields good agreement with experimental results.

High-temperature high-cycle fatigue performance and machine learning-based fatigue life prediction of additively manufactured Hastelloy X

Uncertainties in fatigue life of laser powder bed fusion (L-PBF) additively manufactured parts arise from microstructural heterogeneities and randomly dispersed defects generated during the L-PBF. Stress-controlled fatigue performances of L-PBF-built Hastelloy X were examined in 400 °C and 600 °C high-temperature atmospheres. Given the inherent anisotropy of the L-PBF-built Hastelloy X, the fatigue tests were performed on the samples with distinct building orientations. Fatigue-induced damage evolution characteristics were meticulously analyzed after drawing the S-N curves with a 0.1 stress ratio, a 20 Hz loading frequency and varied stress amplitudes. We established a database of the fatigue test results with material properties of the L-PBF-built Hastelloy X to build a machine learning (ML) framework for fatigue life prediction, skipping the traditional fatigue-life mathematical models that are less applicable to L-PBF-built metals. For capturing the intricate influence of diverse factors on the fatigue life accurately, deep neural network (DNN) and support vector machine (SVM) were utilized and optimized within the ML-based framework. By comparing our ML-based approach with traditional methods for life prediction, it is indicated that ML techniques can transcend the physical limitations associated with the fatigue processes while simultaneously offering a unified depiction thereof.

Defect driven physics-informed neural network framework for fatigue life prediction of additively manufactured materials.

Additive manufacturing (AM) has attracted many attentions because of its design freedom and rapid manufacturing; however, it is still limited in actual application due to the existing defects. In particular, various defect features have been proved to affect the fatigue performance of components and lead to fatigue scatter. In order to properly assess the influences of these defect features, a defect driven physics-informed neural network (PiNN) is developed. By embedding the critical defects information into loss functions, the defect driven PiNN is enhanced to capture physical information during training progress. The results of fatigue life prediction for different AM materials show that the proposed PiNN effectively improves the generalization ability under small samples condition. Compared with the fracture mechanics-based PiNN, the proposed PiNN provides physically consistent and higher accuracy without depending on the choice of fracture mechanics-based model. Moreover, this work provides a scalable framework being able to integrate more prior knowledge into the proposed PiNN. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Digital twin-driven fatigue life prediction framework of mechanical structures using a power density theory: Application to off-road vehicle front axle housing

Accurate fatigue life prediction is beneficial for fatigue maintenance of complex mechanical structures of off-road vehicles. For fatigue life prediction of mechanical structures subjected to non-stationary random loads during operation, this paper proposes a digital twin-driven fatigue life prediction method for mechanical structures. The core consists of improved fatigue theory, stress online measurement, and fatigue damage verification. In this study, a digital twin (DT) prediction framework containing multiple correction factors is established, in which the actual stress values in the physical world and the stress predictions of the estimated twin model can be obtained in real time. The remaining strength degradation of the structure and material can be compared to correct the prediction accuracy of fatigue analysis. In addition, based on the power density theory, combined with the short-time Fourier transform, a fatigue life analysis method that can comprehensively calculate the effect of load amplitude and frequency on fatigue is proposed. A test case has been demonstrated using a front axle housing of the off-road vehicle. The difference between the results predicted by the method in this paper and the actual fatigue results in failure time is only 2.65 h, with a relative error of only 3.95 %. In terms of failure location, the relative error is only 3.15 %.

A probabilistic fatigue life prediction method under random combined high and low cycle fatigue load history

In this paper, a probabilistic high and low cycle fatigue (H-LCF) life prediction framework is proposed to consider random load history into fatigue life prediction of structures. First, the random load history is generated and quantified by finite element analysis (FEA) and Monte Carlo simulation (MCS). Subsequently, based on the quantification approach and an improved H-LCF damage curve, the framework of probabilistic H-LCF life prediction is then established. A turbine shaft is analyzed by the proposed method, which confirms the superior accuracy of the proposed method than the existing ones. Overall, the proposed method provides an effective way for structures’ fatigue life and reliability assessment.

A new data-driven probabilistic fatigue life prediction framework informed by experiments and multiscale simulation

Traditional probabilistic fatigue life test requires long time, a large number of samples and high cost due to dispersion, randomness and complexity. A new data-driven probabilistic fatigue life prediction framework informed by experiments and multiscale simulation, was proposed and applied to a Ni-based superalloy FGH96. It exhibits the advantages of less tests and fully consideration of the effects of microstructure dispersion on fatigue crack initiation, small fatigue crack (SFC) and long fatigue crack (LFC) propagation. The fatigue crack initiation life was accurately predicted by a stored energy model of persistent slip band (PSB) based on microscale crystal plasticity (CP) theory. The usage of artificial neural network (ANN) leads to the capability of rapidly obtaining CP parameters through the macroscopic Ramberg-Osgood (RO) relationship. Bayesian neural networks (BNN) was trained to predict probabilistic fatigue crack initiation life, SFC and LFC growth rates based on results obtained from CP modellings and carefully designed experiments. With BNN as a probabilistic distribution generator, a Monte Carlo (MCs) model is developed to capture the complete fatigue failure processes, including the crack initiation, SFC and LFC propagation. The total fatigue life and the proportions of life at different stages of superalloy FGH96 were predicted by MCs, which agree well with the experimental data. This work provides a new pathway for structural safety assessment and damage tolerance design.

Microstructure sensitive fatigue life prediction model for SLM fabricated Hastelloy-X

A microstructure-sensitive fatigue life prediction framework based on CP-FFT is proposed to study SLM fabricated Hastelloy-X. The microstructure enters in the model through the shape, size and orientation distributions of grains in the RVEs, which are generated from experimental EBSD data. The framework has been applied to specimens built in two different directions with different polycrystalline microstructures and is able to accurately predict their fatigue life, using just two experiments for calibration. The model reproduces the better fatigue performance found experimentally at high stresses for samples built in transverse direction, identifying the origin of this anisotropy in grain aspect ratios.

Probabilistic notch fatigue assessment under size effect using weakest link theory

Notch and size effects exerts significant influence on the fatigue performances of engineering components. In the present study, a probabilistic framework for fatigue life prediction of the notched components is proposed based on the calibrated weakest link theory considering size effect. Specifically, a probabilistic method considering the notch effect is elaborated utilizing FE analysis, which inherently considers the size effect and can be used for fatigue life prediction of components with arbitrary shapes. Model validation and comparison are carried out using experimental data of GH4169, TC4 and TC11 alloys with various specimen geometries as well as a full-scale compressor disc. Results indicate that the proposed model presents better prediction accuracy than the other three traditional methods.

A physically consistent framework for fatigue life prediction using probabilistic physics-informed neural network

Machine learning has drawn growing attention from the areas of fatigue, fracture, and structural integrity. However, most current studies are fully data-driven and may contradict the underpinning physical knowledge. To address this issue, we propose a physically consistent framework for fatigue life prediction that uses a probabilistic physics-informed neural network (PINN) to incorporate the physics underpinning the fatigue mechanism. Particularly, we consider the scatter of the fatigue life using a probabilistic neural network with the output to parametrize the fatigue life distribution. Then use neural networks' inherent backpropagation capabilities to automatically compute the derivatives that represent the physical knowledge. Finally, construct a composite loss function to encode the derivatives with certain physical constraints and uses a negative log-likelihood function to consider both failure data and run-out data. This enforces the network training process to learn a continuous function that describes the stress-life relationship satisfying both experimental data and physical knowledge. We demonstrate the proposed framework with sensitivity analysis and a comparison to the fully data-driven neural networks and the conventional statistical methods using the fatigue test data of three different materials. The results show that the proposed framework has a robust performance to effectively reflect the underlying physical knowledge and prevent overfitting issues. The findings provide a better understanding of neural networks’ application to fatigue life prediction and suggest that one should be cautious when using a fully data-driven approach in scientific applications.

Thermal fatigue life predication of thermal barrier coatings by 3D hill-like model and GA

In previous studies, the coating interface was simplified to a 2D axisymmetric model in order to solve the thermal stress of thermal barrier coatings (TBCs). But the 2D TBCs model ignored the circumferential roughness, which influenced the accuracy of thermal fatigue life predication. To solve the problem, a 3D hill-like TBCs model is established by cylindrical coordinate equation, and solved by finite element method (FEM). A life prediction method of the 3D TBCs is proposed by combining Manson-Coffin equation, linear cumulative damage theory and Genetic Algorithm (GA). The life prediction results of 3D hill-like TBCs model are compared with the 2D TBCs model. The result shows that the thermal stress distribution of the 3D hill-like TBCs model is similar to that of the 2D TBCs model. However, the circumferential positive stress is greater than the axial positive stress, which is hardly obtained by classical 2D TBCs model. The analysis of thermal stress in TC layer with 4 μm TGO thickness at different time shows that the thermal stress reaches 255.8 MPa (maximum value) at 1050 °C (maximum temperature in one cycle). Moreover, the maximum value of thermal stress is located at circumferential direction near the peak of the 3D hill-like TBCs model, and this phenomenon indicates that the risk point will appear in this area. The maximum fatigue life prediction error of 3D hill-like TBCs model is reduced by 153% compared with the 2D TBCs model, and all predicted fatigue results are located in ±1.66 scattering zone. The efforts of this study provide a framework for the thermal fatigue life prediction of TBCs.

A probabilistic fatigue life prediction for adhesively bonded joints via ANNs-based hybrid model

The paper is aimed at developing an efficient and robust probabilistic fatigue life prediction framework for adhesively bonded joints. This framework calibrates the fatigue life model by quantifying uncertainty in the fatigue damage evolution relation using a set of experimental fatigue life data. Probabilistic assessment of fatigue life is simulated through damage evolution along the bondline and Bayesian inference via the Markov chain Monte Carlo (MCMC) sampling method for inverse uncertainty quantification (UQ). To expedite the fatigue life simulation, a hybrid model composed of physics-based fatigue damage evolution relation and a data-driven artificial neural networks (ANNs) model is employed. The degradation of the adhesive is evaluated by the fatigue damage evolution relation which is then mapped to the strain redistribution along the bondline using the ANNs model. Once the mapping is learned by the ANNs, through data from FEA simulations, the probabilistic fatigue life prediction framework involves three successive modules: (I) fatigue damage growth (FDG) simulator, (II) uncertainty quantification (UQ), and (III) confidence bounds for fatigue life prediction. The FDG simulator can be used for simulating fatigue degradation rapidly for a given geometric configuration under any arbitrary fatigue loading spectra. The quantified uncertainties from the framework correspond to the intrinsic statistical material properties that can be used for probabilistic fatigue life prediction in any joint configuration with the same adhesive material. The probabilistic framework is verified using a single lap joint (SLJ) by quantifying uncertainties which are then used for probabilistic fatigue life prediction in laminated doublers in the bending (LDB) joint, that uses the same adhesive material as SLJ, and successfully compared with experimental data. The framework is also tested and validated by estimating probabilistic fatigue life in other joint configurations under constant and variable amplitude fatigue loading spectra.

A Coupled Peridynamic and Finite Element Approach in ANSYS Framework for Fatigue Life Prediction Based on the Kinetic Theory of Fracture

A Coupled Peridynamic and Finite Element Approach in ANSYS Framework for Fatigue Life Prediction Based on the Kinetic Theory of Fracture

A framework for fatigue life prediction of materials under the multi-level cyclic loading

Fatigue life prediction of materials under the cyclic loading is still a particularly challenging task remains to be resolved. This study aims to develop a generic framework for fatigue life prediction under the multi-level cyclic (MLC) loading with consideration of the loading sequence effects. Firstly, a conditional probability density function (PDF) model is presented to quantify the fatigue life distributions of materials under any constant amplitude cyclic (CAC) loading. Subsequently, a fatigue damage accumulation model is proposed from the perspective of cumulative failure probability, which is capable of accounting for the nonlinear characteristics of damage accumulation and the loading sequence effects. Finally, a generic framework for fatigue life prediction of materials under the MLC loading is developed based on the proposed models. The fatigue life data of fiber reinforced composites under the two-level and three-level cyclic loading are utilized to verify the proposed framework. The results show that the predicted fatigue lives agree well with the fatigue test data of fiber reinforced composites. Moreover, the proposed framework can be easily extended to calculate fatigue life of materials under any MLC loading.

Digital Twin-driven framework for fatigue life prediction of steel bridges using a probabilistic multiscale model: Application to segmental orthotropic steel deck specimen

Accurate fatigue life prediction facilitates the fatigue maintenance of steel bridges. Since Digital Twin can simulate the lifecycle for physical objects at various scales, this study aims to provide a Digital Twin-driven framework for non-deterministic fatigue life prediction of steel bridges. A probabilistic multiscale model was developed to depict the fatigue evolution throughout the bridge lifecycle. The small crack initiation period was well described by the modified Fine and Bhat model considering microstructure uncertainties. After obtaining the critical model parameter via crystal plastic finite element simulation, the modified model was further calibrated using the assumed historical fatigue data in Digital Twin database. Based on the initiated half-penny-shaped small crack, the small crack initiation period was connected to the macrocrack extension period. Given the uncertainties of macrocrack propagation, the Paris’ law with random growth parameters was adopted. The Bayesian inference of the growth parameters realized the real-time calibration of the macrocrack growth model using Markov chain Monte Carlo simulation. The feasibility of the proposed framework was demonstrated through fatigue tests on a segmental steel deck specimen with mixed-mode deformed U-rib to diaphragm welded joints. The results show that the predicted fatigue initiation life and residual fatigue life are in good agreement with the experimentally observed life results. In summary, the proposed framework enhances our understanding of the fatigue evolution mechanism throughout the bridge lifecycle and provides an entirely new approach to accurately predict the fatigue life of steel bridges under various sources of uncertainties.