Multiaxial Fatigue Loading Research Articles

Acoustic emission-based delamination investigation in drilled GFRP under mixed tensile and bending cyclic loading

The drilling process can cause various defects in glass fiber-reinforced polymer (GFRP), such as delamination, which ultimately leads to damage progression, especially under fatigue loading. Therefore, the current study aims to investigate the progression of failure in drilled composites subjected to cyclic bending and tensile loads using acoustic emission (AE), image processing, and mechanical behavior monitoring. The results show tyhat the fatigue diagram consists of three stages associated with resistance of fibers and matrix against delamination propagation, stable delamination progression, and ultimate spread of failure which are accurately identified by AE and mechanical methods. Additionally, the pattern and procedure of all fatigue diagrams under all loading conditions were similar and independent of loading parameters. Results from this study provide a strategy for real-time structural health monitoring (SHM) of delamination propagation in GFRPs under multi-axial fatigue loading.

Using physics-informed neural networks to predict the lifetime of laser powder bed fusion processed 316L stainless steel under multiaxial low-cycle fatigue loading

Axial-torsional Low-Cycle Fatigue (LCF) tests were conducted under strain control on Additively Manufactured (AM) 316L stainless steel using laser powder bed fusion. The tests covered various strain amplitudes under tension-compression, proportional, and pure shear loading paths. The AM 316L stainless steel exhibited cyclic softening and transgranular cracking under all the investigated loading conditions. The presence of deposition defects, predominantly the lack of fusion type, was identified as the main factor influencing the crack initiation and propagation, as well as the scatter in the fatigue lifetime. Therefore, to account for the damaging effects of these deposition related defects on fatigue lifetime, a novel physics-informed neural network was proposed. Subsequently, this neural network was combined with the critical plane approach, based on the tensile mode of failure, in order to predict the lifetime of AM 316L stainless steel. The predicted data exhibited a good correlation with the experimental results.

Life prediction based on fatigue-environment damage under multiaxial thermo-mechanical loading

In this paper, the competition mechanism between protectiveness and harmfulness of oxidation, as well as the effects of cycle period, mean stress and temperature on the damage behavior of TA15 titanium alloy are revealed under multiaxial thermo-mechanical fatigue loading. Based on the damage mechanism, a high-temperature environmental damage model is proposed under multiaxial thermo-mechanical fatigue loading first, then a life prediction method is developed by combining a multiaxial fatigue damage model. The experimental verification results under uniaxial and multiaxial thermo-mechanical fatigue loadings showed that almost all of the prediction errors are within a factor of 2.

Influence of proportional multiaxial fatigue loading on the residual mechanical properties of glass-reinforced plastic pipes

This work is dedicated to the experimental investigation of multiaxial cyclic loading influence on the residual mechanical properties of glass-reinforced plastic pipes (GRP pipes). Static, cyclic and combined (static after the preliminary cyclic loading) tests have been carried out on tubular specimens under tension with torsion. Residual stiffness curves have been made, their approximation has been carried out, using previously developed model, damage accumulation stages’ boundaries have been calculated. A specimen’s individual fatigue life prediction method, based on the initial parts of stiffness degradation curves, has been proposed. Influence of the preliminary multiaxial cyclic loading on residual Young’s modulus and tensile strength has been studied. Patterns of deformation and fracture processes have been studied, using digital image correlation method and acoustic emission method. A significant influence of fatigue damage on the residual properties of GRP pipes has been concluded.

Near real-time calculation of the critical plane in all surface nodes of large metallic structures under multiaxial fatigue loading by visualization of the solution space

Applications of critical-plane-based fatigue criteria on large FE meshes remain uncommon, primarily due to the absence of a search scheme capable of identifying the critical plane for multiaxial loading scenarios in a way that is both reliable and fast enough. To address this gap, we introduce a three-module optimization scheme based on the Maximum Variance Method (MVM), guided by insights learned from visualizing the solution space. These visualizations not only validate the MVM strategy but also reveal a symmetry axis, which in turn assists in selecting the most critical among reciprocal solutions. Through iterative refinement of optimization parameters on automatically generated loading signals, our algorithm achieves a significant speedup over existing methods, while improving accuracy. The potential that comes with a processing speed of 10k nodes per CPU minute is demonstrated on a design challenge involving an additively manufactured Ti–6Al–4V bearing house subjected to non-proportional loading. A full critical-plane-based fatigue analysis on the 100k surface nodes takes 75 s with C++ PPL across 16 threads, which is fast enough to enable integration into iterative procedures such as topology optimization, promising substantial advancements in both academic research and engineering practices.

Multiaxial failure behavior and fatigue life prediction of unidirectional composite laminates

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

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

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

A strain energy density field method to predict the life of metallic notched components under multiaxial fatigue loading

A method based on strain energy density field (SEDF) has been proposed to predict the angle of fatigue critical points and multi-axial life of the notched parts under multi-axial cyclic loading. The point bearing the maximum strain energy density was taken as the fatigue crack initiation point (fatigue critical point). The influence of stress-strain gradient around the notches were considered via combining SEDF and the critical distance theory (TCD) to calculate the multi-axial notch life. The predictive results indicate that the maximum deviation of the fatigue critical point (FCP) was 7.0°. The most of the predictive life was within the 3-time error band.

Implementation of the Peak Stress Method for the automated FEA-assisted design of welded joints subjected to variable amplitude multiaxial fatigue loads

Implementation of the Peak Stress Method for the automated FEA-assisted design of welded joints subjected to variable amplitude multiaxial fatigue loads

Development of a novel tool used to support design and failure analysis of multiaxial fatigue loading: A case of steering knuckle

The steering knuckle requires a lot of attention when designing because once it is damaged it must be replaced with a new one. In automotive industry, since the structure of steering knuckles is very complex and different from each other; it is difficult to design it separately for each vehicle. In order to address this problem, an innovative idea to solve this problem was developed and named as analysis support tool for steering knuckle of the entire vehicle. In addition to that, the development of computer tool that can assist designers in the analysis phase can save the design time. For this purpose, analysis support tool for steering knuckles of entire vehicles has been developed. The part is first modeled by Free CAD 0.2 software considering the precision of the geometry. Based on scientific approach analysis support tool for steering knuckle of all vehicles is developed which can provide analysis of all forces acting on the component, maximum displacement, fatigue damage, maximum deflection, slope, factor of safety, life expectancy, stress and strain amplitude by stress and strain method and compare the results from Morrow, Smith Watson and Walker equations. In addition to that doing experiment of multiaxial is very expensive and time taking for the designer; therefore, developing simple, accurate and robustness tool used to determine life expectancy and cumulative fatigue damage of multiaxial which can be applied to entire materials is very crucial. The developed tool would be universal, effective, simple, and efficient method used to estimate the life expectancy and Cumulative fatigue damage of multiaxial. Finally, data’s from open literatures are used to validate the accuracy and capabilities of the proposed tool for multiaxial fatigue loading. The end result is a computer tool that can be dedicated and run on any computer without using any internet connection

Physics-constrained Gaussian process for life prediction under in-phase multiaxial cyclic loading with superposed static components

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.

Theoretical and experimental investigations of crack propagation behavior and delamination in GLARE specimens affected by non-proportional fatigue loadings

In actual operation conditions, the structural parts of automotive, aerospace and other significant industrial applications undergo the multi axial fatigue loading with non-proportionality states. Fiber metal laminates (known as FML) are the best options to manufacture these structural parts. The current study examines the effects of a specific condition of multi-axial fatigue loadings (repeated tension with static shear stresses) on the behaviors of crack growth and delamination in GLARE specimens (abbreviated of glass laminates aluminum reinforced epoxy). Analytical model with idea of maximum tangential stress criterion modification has been adopted to represent the non-proportionality state of fatigue loading. Paris equation, equivalent stress intensity factor range, fiber-bridging effects and delamination shape were included in this model. The current idea was compared with a previous idea that depends on the principal stresses in representation of non-proportional multi-axial fatigue loadings. Specimens have coding GLARE_2A 2/1 were fabricated by VARTM technique (vacuum assisted resin transfer molding technique). Special treatments have been done on the aluminum surfaces before specimen fabrication to increasing delamination resistance. Novel fatigue apparatus was manufactured to guarantee apply the under study conditions for multi axial fatigue loading and to introduce experimental investigation of crack and delamination growths in GLARE specimens. The obtained results of the current idea were in a considerable agreement with that of the previous idea of the principal stresses. The maximum deviations between analytically extracted results were less than 1% for crack growth, 5.4% for bridging stress, 4.8% for crack opening and 6.3% for delamination growth. Experimentally, the measured results have been compared with analytical results for the purpose of validation. Acceptable matching between results with maximum difference of 7.65% was the important outcome of this study.

Using hybrid physics-informed neural networks to predict lifetime under multiaxial fatigue loading

In this article, a machine learning approach is utilized to predict lifetime under multiaxial fatigue loading. A novel hybrid physics-informed neural network is proposed, where a combination of a LSTM/GRU cell and a fully connected layer is used to extract the damage parameter of a loading cycle. A newly proposed logarithmic activation function is then used to introduce the power law relationship between the damage parameter and the predicted fatigue life. In addition, the selected parameters of the suggested network are physically guided. Two data pre-processing methods are used to ascertain the rotational invariance of the axial–torsional loading conditions. The prediction capability of the suggested approach is demonstrated by the experimental datasets that consist of axial–torsional test results obtained for 42CrMo4 steel and for 2024-T3 aluminium alloy. A good correlation between the predicted and experimental data was achieved. Finally, the extrapolation capability of the proposed approach is demonstrated through modelling the stress-life curves for the data-points outside the experimental data range.

Path-dependent multiaxial fatigue behavior of A319 aluminum alloy under non-proportional loading conditions

Abstract In the multiaxial low fatigue test study, four multiaxial non-proportional fatigue loading paths were used including rectangular, square, rhombic and circular. The effect of loading condition changes on the fatigue behavior and cyclic damage characteristics of A319 aluminum alloy was investigated by means of stress response curves, stress–strain hysteresis lines, fatigue fracture morphology, and dislocation substructure morphology in combination with material microstructure. The non-proportional hardening behavior exhibits strong loading path dependence, and the fatigue plastic deformation in the torsional direction is greater in the circular and rhombic paths, and the fatigue damage is more severe, resulting in a shorter fatigue life of A319 aluminum alloy. The axial directions under non-proportional multiaxial loading all have tensile and compressive asymmetric behavior. The differences in loading paths result in different fatigue crack expansion modes. The non-proportional additional hardening behavior under different loading paths is closely related to the dislocation substructure. In the rhombic and circular paths, the alloys have higher dislocation density and strong interaction between dislocations and precipitation phases, which is macroscopically expressed as stronger non-proportional hardening ability in the rhombic and circular loading paths.

A moment quadrature method for uncertainty quantification of three-dimensional crack propagation via extremely few model runs

The finite element-based three-dimensional crack propagation analysis has increasingly been used in many design assessment applications, particularly those high reliability-demanding structures subject to complex multi-axial fatigue loading. Such analysis is computationally intensive and poses a great challenge to current uncertainty quantification methods, which normally require a substantial number of finite element model runs. This study proposes a new method for uncertainty quantification of finite element-based three-dimensional crack propagation analysis under material uncertainty via extremely few, normally 2d, model runs, and d is the number of uncertain variables. When the classical two-parameter Paris’ equation is employed as the fatigue crack growth rate model, a total number of 4 model runs are sufficient. The method employs the Hankel matrix of moments associated with the uncertainty variables to determine the optimal nodes and weights in the variable space for Gauss quadrature under prescribed distributions. A two-step time integration scheme is employed to further reduce the number of propagation steps within an individual finite element model run. The accuracy of the proposed method is validated using a practical case with realistic fatigue testing data and analytical solutions. The holistic method is applied to two three-dimensional crack propagation problems to demonstrate the effectiveness. It is shown that using 4 model runs the mean and variance of the crack front can be accurately captured under material uncertainty.

Life prediction method based on damage mechanism for titanium alloy TC4 under multiaxial thermo-mechanical fatigue loading

In this paper, a life prediction method based on damage mechanism for titanium alloy TC4 under multiaxial thermo-mechanical fatigue loading is proposed. Temperature and time dependent influence factors are proposed and introduced into the strain amplitude-life curve method to consider the temperature and time dependence of damage, respectively. The increase in fatigue and oxidation damages caused by tensile mean stress and non-proportional additional hardening is expressed by the mean stress in Macaulay brackets and by using a multiaxial damage parameter, respectively. A fast cracking influence factor is proposed to consider the influence of fast cracking of materials caused by the combined action of high temperature, tensile stress and shear stress on damage behavior. The material constants are identified by test data under uniaxial and proportional loadings, and are further used for prediction under non-proportional loading. The failure life results of uniaxial isothermal fatigue tests with and without dwell time, uniaxial and multiaxial thermo-mechanical fatigue tests are used to verify the proposed method. The value of the scatter band of life prediction result is less than ± 2, as well as the maximum and mean relative errors between predicted and experimental strain amplitudes are 18.49% and 6.54%, respectively.

Implementation of the Peak Stress Method for the automated FEA-assisted design of aluminium welded joints subjected to constant amplitude multiaxial fatigue loads

The Peak Stress Method (PSM) is a FE-oriented local approach to the fatigue strength assessment of welded structures subjected to fatigue loading. Starting from the peak stresses calculated at the V-notch tip nodes defining weld toes or the weld roots, the PSM defines an equivalent peak stress which allows to estimate the fatigue failure location and fatigue lifetime of welded structures, in compliance with appropriate fatigue design curves. An Ansys® Mechanical extension has been developed to achieve full automated implementation of the tasks and calculations necessary to apply the PSM to welded structures. The tool allows to identify and analyse all the V-notch tip edges of the structure and perform fatigue life estimation on each analysed node. As an output, fatigue life results can be visualized through dedicated tabular data, graphs and contour results generated over the edges of the model. In this work, common-to-complex 3D geometries taken from the literature and related to aluminium alloys welded joints subjected to uniaxial as well as multiaxial fatigue loads have been analysed by comparing two design approaches: (i) manual application of the PSM, (ii) automated implementation of the PSM. The tool developed in Ansys® Mechanical allows to significantly contain the time and effort required to analyse welded structures according to the PSM.

Viscoplastic constitutive model considering strain rate sensitivity under multiaxial thermomechanical fatigue loading

AbstractStrain rate sensitivity will change the cyclic mechanical response of materials under multiaxial thermomechanical fatigue loading; thus, it will lead to errors in fatigue life prediction if strain rate sensitivity is not considered in constitutive simulation. In order to more accurately express the time/rate dependence of viscoplastic behavior, a strain rate sensitivity factor is proposed to modify the viscoplastic function of Chaboche model first. On this basis, a viscoplastic constitutive model considering strain rate sensitivity under multiaxial thermomechanical fatigue loading is proposed, which can describe the varying influence of strain rate sensitivity on cyclic mechanical behavior. Meanwhile, the exponential isotropic hardening rule with the linear term is adopted to characterize the initial rapid softening and subsequent stable softening of the material under fatigue loading at elevated temperature. Moreover, the material‐dependent nonproportional hardening coefficient and the loading path‐dependent rotation factor are used in the kinematic hardening rule to consider the effect of nonproportional additional hardening on the cyclic mechanical behavior of materials. Finally, the proposed method is verified by the stress–strain data of titanium alloy TC4 and Ni‐based superalloy GH4169 under uniaxial and multiaxial thermomechanical fatigue loadings, and a good agreement is obtained.

On material-agnostic fatigue life prediction using Buckingham Pi Theorem

A robust, quantitative analysis is needed to prevent frequent, catastrophic failure of components in powerplants and aircraft, to cite but two examples, due to cyclic loading that could lead to fatigue failure. The model presented in this research will be useful in the reliable design and safe operation of components and equipment. A fatigue life (the dependent variable) prediction model, which employs both stress-based, and stress–strain based criteria is presented that uses the Buckingham Pi Theorem with the experimental parameters influencing fatigue behaviour taken as the independent variables. The validation of the model is done using reliable, frequently used uniaxial fatigue data, culled from the NIMS (National Institute for Materials Science, Tsukuba, Japan) fatigue database on important industrial alloys that experience fatigue loading in service. (No reliable data on such a scale were available to test the validity of this model under multi-axial fatigue loading conditions.) It is demonstrated that the model predicts the experimental results accurately. The accuracy of prediction is examined for every case and compared with that of some other existing methods. Moreover, the potential applicability of this analysis in areas not yet validated is examined.

Glass laminate aluminum reinforced epoxy under non-proportional multiaxial fatigue loading: Experimental testing and new fatigue apparatus development

Predominately, the structures and components in aeronautic, automotive and other important implementations suffer from non-proportional multi-axial fatigue loading. One of the best selected materials to fabricate these structures and components are fiber metal laminates (FML). In this research, fatigue crack-propagation in glass-laminate aluminum reinforced-epoxy (GLARE) specimen under the effect of special case of multi-axial fatigue loading (constant shear with repeated tensile stresses) has been studied analytically, numerically and experimentally. GLARE_2 A 2/1 specimen was fabricated using vacuum assisted resin transfer molding technique after special preparation aluminum surface procedure. New multi-axial fatigue apparatus including mechanical, hydraulic and control systems was manufactured to investigate crack growth experimentally. Analytical model using Paris relation was adopted to predict crack growth through aluminum layers of GLARE specimen. The rate of crack propagation is related to the mixed-mode equivalent stress intensity factor, which is estimated by the superposition for both fiber-bridging and far-field stress intensity factors. The crack opening contour, distribution of fiber-bridging stress, delamination growth and its shape were evaluated in simultaneous manner to find the fiber-bridging stress intensity factor. ABAQUS 2021 software has been used to simulate crack and delamination growth in GLARE specimen with the aforementioned fatigue loading. The extracted results from analytical and numerical models such as crack growth, crack opening, delamination shape and crack angle have been compared with that measured experimentally. The comparison indicates that there is good agreement between the calculated and measured results (with maximum deviation of 8.74% for crack growth).