Multiaxial Fatigue Life Prediction Model Research Articles

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.

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.

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.

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.

A novel multiaxial fatigue life prediction model based on the critical plane theory and machine-learning method

In order to characterize the fatigue failure and damage mechanism under complex multiaxial loads, several multiaxial semi-empirical fatigue models, such as Fatemi-Socie (FS), Smith-Watson-Topper (SWT) and Wang-Brown (WB) models, were proposed to explain the relationship between fatigue life and stress/strain based on experimental analysis or observation. Although the semi-empirical model is widely used in practice because of its simplicity, but it is difficult to uniformly model the mean stress effect of a wide range of materials and loading conditions. To address this issue, a multiaxial fatigue life prediction model based on critical plane theory and machine learning is proposed in this work. Through the multi-layer stacking mechanism, the model comprehensively utilizes domain knowledge and original data information, and integrates the advantages of different models in capturing data and utilizing features. The experimental results showed that the proposed model achieves stable and highly accurate fatigue life prediction of the GH4169, wrought Ti-6Al-4V and TC4 materials with complex working conditions.

Finite element analysis of stress field and fatigue life prediction of notched specimens under multiaxial load

PurposeThe stress state near the notch affects fatigue damage directly, but quantifying the stress field is difficult. The purpose of this study is to provide a mathematical description method of the stress field near the notch to achieve a reliable assessment of the fatigue life of notched specimens.Design/methodology/approachFirstly, the stress distribution of notched specimens of different materials and shapes under different stress levels is investigated, and a method for calculating the stress gradient impact factor is presented. Then, the newly defined stress gradient impact factor is used to describe the stress field near the notch, and an expression for the stress at any point along a specified path is developed. Furthermore, by combining the mathematical expressions for the stress field near the notch, a multiaxial fatigue life prediction model for notched shaft specimens is established based on the damage mechanics theory and closed solution method.FindingsThe stress gradient factor for notched specimens with higher stress concentration factors (V60-notch, V90-notch) varies to a certain extent when the external load and material change, but for notched specimens with relatively lower stress concentration factors (C-notch, U-notch, stepped shaft), the stress gradient factor hardly varies with the change in load and material, indicating that the shape of the notch has a greater influence on the stress gradient. It is also found that the effect of size on the stress gradient factor is not obvious for notched specimens with different shapes, there is an obvious positive correlation between the normal stress gradient factor and the normal stress concentration factor compared with the relationship between the shear stress gradient factor and the stress concentration factor. Moreover, the predicted results of the proposed model are in better agreement with the experimental results of five kinds of materials compared with the FS model, the SWT model, and the Manson–Coffin equation.Originality/valueIn this paper, a new stress gradient factor is defined based on the stress distribution of a smooth specimen. Then, a mathematical description of the stress field near the notch is provided, which contains the nominal stress, notch size, and stress concentration factor which is calculated by the finite element method (FEM). In addition, a multiaxial fatigue life prediction model for shaft specimens with different notch shapes is established with the newly established expressions based on the theory of damage mechanics and the closed solution method.

Multiaxial fatigue life prediction model for notched specimen based on modified energy gradient and critical plane method

The distribution of energy field on the crack initiation plane directly affects the crack initiation behavior. Therefore, studying the energy gradient is of crucial help for accurate evaluation of the fatigue performance for the notched specimen. Firstly, the energy distribution on the critical plane is characterized by the sixth-order polynomial. Meanwhile, the relative energy gradient is adopted to calculate the critical distance. Secondly, considering the influence of energy gradient, size effect and non-proportional additional strengthening, a general procedure is explored. Finally, the experimental data of Al7050, En8 and C40 is utilized for model validation and the comparison results show that prediction results of the proposed model in this paper is superior to other models.

An Improved Multiaxial Low-Cycle Fatigue Life Prediction Model Based on Equivalent Strain Approach

The fatigue life of the materials is significantly reduced under non-proportional loading. In this study, the factors affecting additional hardening are explored, and a hardening function is proposed. Firstly, the stress and strain states of the specimen under multiaxial loading are analyzed, and the deficiencies of the equivalent strain models are discussed. Secondly, the factors affecting the additional hardening are analyzed from both stress and strain perspectives, and the effect of phase differences on fatigue life is investigated. The stress on the critical plane is considered to reflect its effect on crack initiation and growth. An improved multiaxial low-cycle fatigue life prediction model is developed based on the equivalent strain approach. Finally, experimental data from five metals are used to verify the established model and are compared with existing classical models. The results show that the proposed model has good accuracy.

Cooling rate effects on fatigue life prediction using hardness measurements for in-service steel patch-welds with and without TIG dressing treatment

In-service patch welding is commonly used to repair corroded or damaged steel infrastructures. However, the in-service conditions may unfavorably affect the long-term mechanical and structural integrity. The present research studies the fatigue behavior of fillet welded patch repairs with and without TIG-dressing (TD). Six types of panels were constructed under various in-service cooling conditions. Specimens cut from the main panels were subjected to high-cycle fatigue, hardness, and metallography tests. The fatigue life of the specimens was also predicted using a novel numerical approach. The model incorporated micro-hardness test data from the weldment section. Macrographic and microhardness data were used for the zoning of the weldment section. The harness data were then employed to define the post-weld mechanical properties of the materials in different weldment zones. The fatigue life was estimated using the microhardness data, stress and strain data obtained from the finite element analysis of the specimen, a UVARM subroutine, and several multiaxial fatigue life prediction models. The numerical fatigue life estimations showed reasonable agreement with the experimental data. Both experimental and numerical modeling results proved significant improvements in the fatigue life of the TD specimens. Regardless of the welding conditions/treatments, the best fatigue life estimates were provided by the BMM, SWT, Glinka, and KBM criteria, respectively.

MFLP-PINN: A physics-informed neural network for multiaxial fatigue life prediction

In this study, a physics-informed neural network (MFLP-PINN), combining multiaxial fatigue critical plane model and the neural network, is proposed for life prediction. First, a multiaxial fatigue life prediction model based on the critical plane approach is proposed, which takes the equivalent strain amplitude on the critical plane as the main damage parameter, and considers the normal strain energy on the critical plane. Then, a total of four prediction models including the new critical plane model are integrated into the loss function of a neural network to build the MFLP-PINN. The accuracy of the proposed critical plane criterion and the MFLP-PINN are respectively verified using multiaxial fatigue test data of three materials. Finally, the results show that the prediction model integrated into the loss function has a significant impact on the neural network prediction. For a specific material, integrating a life prediction model with good prediction ability to this material as the loss function into a neural network model is helpful to improve prediction accuracy. Conversely, integrating a life prediction model with poor prediction ability to this material as the loss function into a neural network model will reduce the prediction accuracy.

Multiaxial fatigue prediction and uncertainty quantification based on back propagation neural network and Gaussian process regression

Engineering structures are often suffering multiaxial stress which leads to multiaxial fatigue failures. Accurate and reliable multiaxial life prediction is a challenging issue in fatigue analysis due to the intricate deterioration mechanisms of the fatigue failure and the large uncertainty in the material parameters at the microscopic scale. Moreover, conventional multiaxial fatigue life prediction models are empirical or semi-empirical. To tackle this problem, a data-driven method is presented, which combines the back propagation neural network (BPNN) and the Gaussian process regression (GPR). The BPNN-GPR method can predict the multiaxial fatigue life and quantify the uncertainty simultaneously. This method is validated using six materials including the uniaxial, multiaxial proportional and multiaxial nonproportional loading cases. All the predicted lives fall within a life factor of ± 3, which indicates that the BPNN-GPR method has the satisfactory capability for multiaxial fatigue life prediction. In addition, results also show the prediction capability of the BPNN-GPR method for unknown multiaxial nonproportional loading paths.

Multiaxial fatigue life prediction model with relative stress gradient and size effect

AbstractTo investigate the effects of notched root stress gradient and geometric size parameters on the fatigue performance of engineering components, a new multiaxial fatigue life prediction model is established. First, based on the energy‐critical plane method, the location of the dangerous plane is determined with the help of finite element (FE) analysis. Second, the sixth‐order multinomial stress function is used to study the stress/strain distribution state on the critical plane, and the relative stress gradient (RSG) function is used to find the stationary point to determine the RSG value and the magnitude of the fatigue damage zone boundary value. Specifically, for specimens with different notch types, the indexes to determine the high‐stress influence zone and the size influence factor are proposed. Finally, a multiaxial fatigue life prediction model considering RSG and size effect is established, and the compared results show that the new model has a high fatigue life prediction capability.

Low-cycle multiaxial random fatigue life prediction model based on equivalent stress transformation

PurposeUnder multiaxial random loading, the material stress–strain response is not periodic, which makes it difficult to determine the direction of the critical plane on the material. Meanwhile, existing methods of constant loading cannot be directly applied to multiaxial random loading; this problem can be solved when an equivalent stress transformation method is used.Design/methodology/approachFirst, the Liu-Mahadevan critical plane is introduced into multiaxial random fatigue, which is enabled to determine the material's critical plane position under random loading. Then, an equivalent stress transformation method is proposed which can convert random load to constant load. Meanwhile, the ratio of mean stress to yield strength is defined as the new mean stress influence factor, and a new non-proportional additional strengthening factor is proposed by considering the effect of phase differences.FindingsThe proposed model is validated using multiaxial random fatigue test data of TC4 titanium alloy specimens and the results of the proposed model are compared with that based on Miner's rule and BSW model, showing that the proposed method is more accurate.Originality/valueIn this work, a new multiaxial random fatigue life prediction model is proposed based on equivalent stress transformation method, which considers the mean stress effect and the additional strengthening effect. Results show that the predicted fatigue lives given by the proposed model are in well accordance with the tested data.

Critical plane-based fatigue life model under multiaxial random loading

PurposeEngineering components/structures are usually subjected to complex and variable loads, which result in random multiaxial stress/strain states. However, fatigue analysis methods under constant loads cannot be directly applied to fatigue life prediction analysis under random loads. Therefore, the purpose of this study is how to effectively evaluate fatigue life under multiaxial random loading.Design/methodology/approachFirst, the average phase difference is characterized as the ratio of the number of shear strain cycles to the number of normal strain cycles, and the new non-proportional additional hardening factor is proposed. Then, the determined random typical load spectrum is processed into a simple variable amplitude load spectrum, and the damage in each plane is calculated according to the multiaxial fatigue life prediction model and Miner theory. Meanwhile, the cumulative damage can be calculated separately by projection method. Finally, the maximum projected cumulative damage plane is defined as the critical plane of multiaxial random fatigue.FindingsThe fatigue life prediction capability of the method is verified based on test data of TC4 titanium alloy under random multiaxial loading. Most of the predicting results are within double scatter bands.Originality/valueThe objective of this study is to provide a reference for the determination of critical plane and non-proportional additional hardening factor under multiaxial random loading, and to promote the development of multiaxial fatigue from experimental studies to practical engineering applications.

Multiaxial fatigue life prediction model based on an improved strain energy density criterion

Based on the critical plane approach and the shear damage model, a new damage parameter based on the strain energy density criterion is proposed. This parameter takes into account the interaction between shear stress and hydrostatic stress during microcrack initiation and the contribution of hydrostatic strain energy density to fatigue damage. On this basis, a new multiaxial fatigue life prediction model is established by combining the Basquin-Manson-Coffin equation. The analysis results of five metal materials show that the predicted life correlated well with the experimental observations. The merits of the proposed model are further highlighted by the comparison between the results of the proposed method and those of two fatigue damage prediction models.

Multiaxial fatigue life prediction model considering stress gradient and size effect

Stress gradient effect (SGE) and notch size effect (NSE) have important influences on the fatigue performance of engineering components. In this paper, a new multiaxial fatigue life prediction model is developed by considering the effects of both. Firstly, with the help of the coordinate transformation principle (CTP), the location of the dangerous critical plane is found according to the energy-critical plane (ECP) method, and the equivalent stress gradient factor (SGF) within the fatigue damage zone is calculated by analyzing the equivalent stress distribution on the critical plane. Secondly, considering the size of the notch, the effect of stress concentration at the notch is analyzed. Meanwhile, a size influence factor is introduced to characterize the NSE and construct a new fatigue strength reduction factor. Further, combining with the Manson-Coffin equation (MC equation), a new fatigue life prediction model for multiaxial notched components is proposed by considering SGE and NSE on fatigue damage. Finally, the experimental data of fatigue specimens with different notch sizes processed by En8 and GH4169 materials are used for model validation and comparison with other three classical models, and the results show that the prediction life of the new model for proportional and non-proportional loads is within two-fold dispersion band and the prediction ability is better than the other three classical models.

A multi-axial and high-cycle fatigue life prediction model based on critical plane criterion

Accurate prediction of fatigue failure behavior and fatigue life of structures or materials under multi-axial loading are important for engineering application. In this work, a multi-axial and high-cycle fatigue failure model based on the critical plane criterion is proposed with considering the influences of material property and loading path on the initiation and growth of fatigue cracks. A material parameter, defined as the ratio of tensile yield strength σy and torsional yield strength τy, is introduced to describe the mechanical properties of the material. For σy/τy<3, it is considered that the crack growth under the multi-axial fatigue load is mainly controlled by the maximum normal stress. While for σy/τy>3, it is considered that the crack growth under the multi-axial fatigue load is mainly controlled by the maximum shear stress. Experimental results of three kinds of material were applied for model validation. For all materials, most predictions are within the ±2 times scatter band of fatigue life and only few data are around ±3 times scatter band. Good agreements of the predicted fatigue life by the model with experimental results illustrated the model applicability. The model provides meaningful tool for predicting multi-axial fatigue life of materials under different loading parameters.

Multiaxial fatigue life prediction method considering notch effect and non-proportional hardening

Engineering components with geometric discontinuous structures generally appear notch effect, which might eventually induce fatigue failure. In this study, a novel multiaxial fatigue prediction model is established for notched components by incorporating the notch effect and non-proportional hardening. Firstly, according to the notch effect, a computational procure of damage parameters is presented by combining the notion of stress intensity with finite element simulations based on the critical plane method. Secondly, considering the non-proportional hardening effect of path modes and material properties, a new modified non-proportional hardening factor is proposed. Particularly, the relationship between the relative stress gradient and the fatigue life is investigated under different stress concentration factors. Finally, with the help of the Manson-Coffin equation, a multiaxial fatigue life prediction model is developed subjected to multiaxial proportional/non-proportional loadings. Experimental data of medium steel En8 and GH4169 alloys are utilized to evaluate and validate the proposed model as well as four other classical models (FS model, MSWT model, Yu model and CXH model). The result indicates that the proposed model yields a higher accuracy on multiaxial fatigue life than other four models, and the majority of prediction results are within the ±2 life factor.

A novel method of multiaxial fatigue life prediction based on deep learning

It is well-known that conventional multiaxial fatigue life prediction models are generally limited to specific materials and loading conditions. To remove this limitation, a novel attempt is proposed in this work based on the deep learning (i.e., an improvement of artificial neural network in machine learning approaches, which is powerful to learn representations of data with multiple levels of abstraction). To comprehensively evaluate the prediction capability of proposed deep learning-based method, six series of existing fatigue data of different materials are, respectively, analyzed, in which the main loading conditions concerned in the low-cycle and high-cycle fatigue researches are included, such as loading modes (stress-controlled/strain-controlled modes), loading levels (stress/strain amplitude and mean stress/strain), and loading paths (uniaxial/multiaxial and proportional/non-proportional paths), as well as for low-cycle and high-cycle fatigue regimes. Comparison of the predicted and experimental results shows that: all the loading conditions mentioned above can be handled satisfactorily by the proposed deep learning-based method; excellent prediction accuracy is achieved, and the predicted lives in each study case fall almost within the scatter band of 1.5 times. In addition, four groups of specifically designed data are used to evaluate the extrapolation capability of the proposed method, and the results show that the extrapolation capability gets weaker if the distinctions between the loading paths involved in the training dataset and test one increase.

A new microstructure‐based multiaxial fatigue life prediction model for A319 casting alloys

AbstractThis paper describes a microstructure‐based multiaxial nonproportional fatigue life prediction model applied to A319 alloy. The materials made with different casting cooling rates and Sr modification are characterized and quantified in terms of secondary dendrite arm spacing, size, and aspect ratio of eutectic Si particles. Multiaxial nonproportional fatigue tests have been performed on six groups of A319 alloys to systematically analyze the effect of microstructure and loading path on the fatigue properties of Al–Si cast alloy. The first part of the paper is focused on microstructure quantitative characterization to determine the influence of different casting conditions, followed by stress response behavior and fatigue fracture analysis. Finally, a new multiaxial fatigue life prediction model for Al–Si alloy is proposed, for which 56% of the data points fall in the bound lines of factor of 2 and 83% of the data points fall in the bound lines of factor of 3.