Fatigue Life Estimation Research Articles

Quantitative Review of Critical Plane Criteria and Stress Analysis Approaches for Multiaxial Fatigue of Welded Joints

ABSTRACTThis quantitative review evaluates the effectiveness of stress‐based critical plane criteria, specifically Findley's criterion, the approach due to Carpinteri–Spagnoli (CS), and the Modified Wöhler Curve Method (MWCM), in assessing fatigue strength in aluminum and steel welded joints subjected to constant amplitude (CA) and variable amplitude (VA) multiaxial loading. These criteria were analyzed alongside stress analysis approaches, including nominal stress (NS), hot‐spot stress (HSS), effective notch stress (ENS), and the Theory of Critical Distances–Point Method (TCD PM). Results confirm that all criteria effectively estimate fatigue life for steel welded joints under CA loading, with MWCM combined with HSS proving most accurate. For aluminum joints, estimations showed greater conservatism and scatter, highlighting the need for further experimental data to improve accuracy. Experimentally calibrated constants significantly enhanced prediction reliability. Future research should refine these criteria for diverse aluminum grades and thicknesses, ensuring accurate estimations and robust alternatives to established codes.

Propagation of a Fatigue Crack Through a Hole.

The stop-hole technique is a well-known strategy to extend the fatigue life of cracked components. The ability to estimate fatigue life after the hole is important for safety reasons. The objective here is to develop strategies for the accurate prediction of initiation and propagation life ahead of the stop-hole. Experimental work was developed in a Compact-Tension (CT) specimen made of 7050-T7451 aluminium alloy and with a 3 mm diameter hole. A total number of 625,000 load cycles were required to re-initiate the crack after the hole. Crack initiation life after the hole was estimated using the Theory of Critical Distances combined with the Smith-Watson-Topper parameter. A value of a0 = 31.83 µm was obtained for El Haddad parameter, which was used to define the critical distance. The predicted life was found to be only 4% lower than the experimental value. The fatigue crack growth (FCG) rate was calculated using a node release strategy, assuming that cyclic plastic deformation is the main damage mechanism and that cumulative plastic strain is the crack driving parameter. A good agreement was found between the numerical predictions of da/dN and the experimental results. The main result, however, is the proposed methodology, which allows predicting the initiation and propagation lives in notched components.

Improving Fatigue Life Prediction of Natural Rubber Using a Physics‐Informed Neural Network Model

ABSTRACTTraditional physical models and purely data‐driven approaches often struggle with small sample sizes and the complex effects of strain ratios. To overcome these challenges, this study integrates physical principles with machine learning techniques to improve fatigue life predictions for natural rubber (NR). A uniaxial fatigue test on NR was performed, generating data to construct a physical model. A physics‐informed neural network (PINN) model was subsequently developed, utilizing the fatigue life predicted by the physical model, along with engineering strain amplitude and strain ratio as input variables, whereas the experimentally observed fatigue life served as the output variable. The accuracy of the physical model, a data‐driven model, and the proposed PINN model was evaluated by comparing their predictions against measured fatigue life data. The findings demonstrate that the PINN model significantly enhances prediction accuracy, with its fatigue life estimates consistently falling within 1.5 times the measured values.

Analysis of Inertial Influence and Damping of Mooring Lines on Fatigue Damage

The high demand for oil has driven its exploration into increasingly deeper water depths, which required significant scientific and technological advancements. In this context, the floating production and offshore system is a type of platform, based on ship, anchored by mooring lines arranged by chains/steel cables and polyester cables with the objective to restrict the platform’s movements in a design region. Offshore platforms are exposed to environmental loads of waves, wind, and currents, which are responsible for generating hull motions and tension variation in the mooring lines. This tension history, in turn, is directly associated with fatigue failure of the lines. Despite efforts to estimate the fatigue life of mooring lines to ensure their integrity throughout the platform’s operation, premature failures in the mooring system have been observed over the past decades. This serves as an alert that the fatigue damage estimated during the design phase may be less than the actual damage occurring in the field. Several factors influence the initial estimation of fatigue life, for instance, the analysis method used to represent the lines behavior, such as quasi-static and dynamic analysis. The first one, that ignore the inertial and damping effects, was widely used in design of mooring lines in the 90s and the beginning of this century due its low computational cost, while the dynamic analysis, that represents rigorously the mooring line dynamic behavior, is used increasingly nowadays. The use of these two different approaches can affect the fatigue damage. Therefore, the present work aims to evaluate the influence of the inertia and damping of moorings in the fatigue damage, comparing the quasi-static and dynamic approaches studied with a floating unit numerical model, with 910m water depth, that uses a conventional catenary mooring system. In this way, a critical analysis is carried out based on the comparison between the fatigue life resulting from the two forms of analysis.

Multiscale finite element modelling of dynamic subsea power cables in bending

Abstract This paper proposes a multiscale finite element modelling strategy for dynamic offshore power cables which allows for detailed analysis of individual components. The challenge of modelling the intricate power cores within the cable is addressed by considering a separate repeated unit cell (RUC) of the power core to define its stiffness, where the power cores themselves are then discretised with beam elements in the dynamic cable model. Periodic boundary conditions allowing for geometric non-linearity are employed at both the power core and dynamic cable scale. This means the model size can be reduced to the smallest possible RUC while still permitting non-linear material behaviour. The resulting model is capable of detailed stress analysis of individual components required for fatigue life estimation. The model is validated against existing experimental data showing strong agreement. The proposed multiscale approach may therefore be used to augment existing fatigue analysis methods for dynamic offshore cables where the stress state at individual wires is required.

A comparative study on combined high and low cycle fatigue life prediction model considering loading interaction

Fatigue life estimation of aero-engine turbine components under combined high and low cycle fatigue (CCF) is of significance for guaranteeing the structural reliability during operation. According to the investigations on damage evolution process, a nonlinear damage accumulation method is proposed for life prediction under CCF loadings, and the interaction effect between high cycle fatigue (HCF) and low cycle fatigue (LCF) is considered by integrating the interaction factor and stress ratio of CCF. Furthermore, experimental results of alloys and turbine blades are utilized to validate the proposed method and conduct a comparative analysis among Miner’s rule and other two typical nonlinear cumulative damage methods under combined loading conditions. Comparative results demonstrate that the developed model holds better prediction robustness and accuracy than those of others.

Structural analysis and fatigue prediction of harrow tines used in Canadian prairies

The Canadian prairies are renowned for their substantial agricultural contributions to the global food market. Harrow tines are indispensable in farming equipment, especially for soil preparation and weed control before planting crops. During operation, these tines are exposed to repetitive cyclic loading, which eventually causes fatigue failure. Commercially available three different harrow tines named 0.562HT, 0.625HT, and 0.500HT undergo an experimental fatigue evaluation and are validated through Finite Element Analysis (FEA). Fatigue life estimation for different deflections under various real-field deflections was carried out where 0.562HT showed groundbreaking life compared with others. The study results showed that the fatigue life is highly dependent on geometry, number of coils, pitch angle, leg length, and coil diameter. The 0.354HT model, developed to investigate the effect of wire diameter, closely resembles the 0.500HT model. The harrowing ability of the four different harrow tine models against identical deflections has been analyzed. Experimental fractured surfaces went through morphological investigation. This research has an impeccable impact on prairies’ agricultural acceleration by saving time and mitigating unpredictable fatigue failure often faced by farmers. Even the observed failure phenomena can serve as motivation to develop more reliable and durable harrow tines, which could increase agricultural efficiency.

Experimental results for fatigue damage growth in laminated fiber reinforced cross-ply laminates

In this paper, experimental results for fatigue damage growth behavior of a single-edge notched cross-ply laminate obtained using Digital Image Correlation (DIC), thermography, and supplemented by prior X-ray computed microtomography (mCT) data, are presented. These experimental results are used to develop a novel multi-scale fatigue life estimation model, whose details are reported elsewhere [1].

A Review of Fatigue Failure and Life Estimation Models: From Classical Methods to Innovative Approaches

This review paper encompasses a comprehensive exploration of fatigue failure and fatigue life estimation techniques which spans from the classical methods to new and innovative approaches. The paper looks into the limitations and advancements of these techniques and highlights their respective strengths and areas for improvement. Some of the models such as artificial neural networks and genetic algorithms exhibit clear advantages in terms of processing speed, accuracy, and adaptability to diverse materials and loading scenarios. For instance, in estimating fatigue life under multiaxial loading, the stress scale factor model emerges as a viable alternative to the critical plane-based approach, as this technique offers superior efficiency under both constant and variable amplitude loadings. Additionally, optimization algorithms such as artificial neural networks and genetic algorithms show promising potential in efficiently estimating fatigue life due to their rapid computational capabilities. Despite the notable successes achieved by these techniques, none of them can be ascribed as a universal model capable of accurately estimating the fatigue life of all materials across diverse operating conditions as each of the techniques possesses its unique strengths and weaknesses, thus, necessitating the study for a better understanding of their applicability. Hence, this paper serves as a valuable compilation of various fatigue analysis techniques, targeted at paving the way towards the development of a universal model capable of handling different materials and loading conditions.

An improved constitutive model for rapid fatigue properties evaluation based on fatigue damage entropy

A constitutive model, which reflects the non-linear response association between microstructural motion and thermodynamic entropy production, is improved in this study. Two critical stress amplitudes associated with two microstructural movement mechanisms are considered in the improved constitutive model. The determination procedures for the parameters of the presented model are developed. Entropy generation data from three materials computed by two calculation methodologies, collected from the experiment and literature, are used to validate the improved model. Subsequently, a rapid fatigue life estimation method is proposed by using the accumulated entropy corresponding to fatigue damage, i.e. FFE, related to irreversible inelastic microstructural motion. Fatigue tests of welded joints fabricated by Q310NQL2 and Q345NQR2 steels, Q235 steel specimens, as well as experimental data, stainless steel specimens, collected from the literature, are employed to determine the values of the parameters of the developed model. The model is then used to forecast the S–N curve of butt joints with a 50% survival probability, and on this basis, the S–N curve with a certain confidence level is well estimated by the improved statistical method. This enhanced model may offer a fast forecast of the P–S–N curve at a certain confidence level within a limited set of tested data ranges.

Stress fracture of bone under physiological multiaxial cyclic loading: Activity-based predictive models

While it is known that excessive accumulation of fatigue damage from daily activities contributes to fracture, a model of bone failure under physiologically relevant multiaxial cyclic loading needs to be developed in order to develop effective management strategies for stress or fatigue fractures. The role of strain-induced damage from repetitive loading is a strong candidate for such a model, as cycles of mechanical loading leading to failure can be measured directly. However, this approach has been limited by the restrictions of uniaxial loading models, which often overestimates the fatigue life of bone and suggests that bone will only break well beyond the realistic limits of exercise. To address this gap and develop a physiologically relevant model, our study leverages the power of four commonly used engineering failure criteria as a model for multiaxial loading using a cohort of human tibiae from cadaveric donors (age range 21–85 years old). Four failure criteria (Von Mises, Tsai-Wu, Findley critical plane, and maximum shear strain) were found to be effective in vitro models of tibial fracture when age groups of donors were combined (r2 > 0.84) and stratified (younger: 21–52-years-old versus older: 57–85-years-old) (r2 > 0.83) (p < 0.001). Each failure criterion displayed distinctly lower fatigue curves for the older age group. The maximum shear strain model was used to determine the efficacy of this approach to predict fatigue fractures in humans using published in vivo data from human volunteers. Consistent with in vivo observations in general population, the model demonstrated failure at 5000 to 200,000 loading cycles depending on activities such as jumping, sprinting, and walking, with a 3-fold reduction of fatigue life in older donors. These findings dramatically improve estimates of fatigue life under repetitive loading and demonstrate how age-related changes in bone significantly increase its propensity for fatigue-induced fractures.

A generalized machine learning framework to estimate fatigue life across materials with minimal data

In this research, a generalized machine learning (ML) framework is proposed to estimate the fatigue life of epoxy polymers and additively manufactured AlSi10Mg alloy materials, leveraging their failure surface void characteristics. An extreme gradient boosting algorithm-based ML framework encompassing Synthetic Minority Over-sampling TEchnique (SMOTE), categorical data encoding, and external loop cross-validation is developed to evaluate the fatigue life across materials. The influence of different training strategies based on materials, input features, encoding method, and data standardization on the model performance is explored. Additionally, the importance of anti-data-leakage and anti-overfitting measures over the ML model performance is addressed. The result shows that the data-leakage-free, external loop cross-validated model can estimate the fatigue life of selective epoxy polymers and metal alloys with an average R2 of 0.71 ± 0.06 using a mere 12 to 27 experimental data points per material category. Whereas the model trained with data-leakage and overfitting results in high R2 of 0.9.

Prediction of fatigue life of a bolted joint in railway steel arch bridge using multiaxial fatigue criteria

Fatigue represents a critical condition for infrastructure subjected to repeated cyclic loads, such as steel railway bridges. The literature offers several methods to estimate fatigue life, consisting of three main phases: cycle counting, fatigue damage criterion, and damage accumulation criterion. Applying S–N curves might not be conservative in the case of railway bridges subjected to traffic because the stress-time history is complex and cannot be reduced to a sinusoidal history. Additionally, the presence of a multiaxial stress state must be considered. Therefore, this work compares eight multiaxial fatigue damage criteria for evaluating fatigue life in a scenario between high and low-cycle fatigue. Specifically, the authors considered four low-cycle fatigue criteria, namely Smith–Watson–Topper (SWT), Kandil, Brown and Miller (KBM), Glinka, Fatemi and Socie (FS), and four high-cycle fatigue criteria, Crossland, Basquin and the methods recommended by Eurocode 3 and British Standard. The rainflow counting method in ASTM E1049-85 (2011) and Miner’s rule for damage accumulation were used. The Polcevera railway steel bridge was selected as a case study. A 3D numerical model was developed for this purpose using Midas Civil software, taking into account the material non-linearity of the bridge’s elements. Once the area with the highest stress concentration was identified, a detailed analysis was conducted to estimate the stress and strain time histories induced by train traffic. A sensitivity analysis was conducted after critically comparing the eight methods for predicting fatigue life to assess the impact of traffic parameters, train velocity, axle load, and convoy length on fatigue life. It has been found that the criteria considering axial stress tend to overestimate the number of fatigue cycles to failure compared to the criteria, including the effect of shear stress components.

Method for assessing the durability of structures under stationary and non-stationary random loading using variational mode decomposition (VMD)

In the era of digital transformation, most devices are equipped with a variety of sensors, which provide information to be used in developing intelligent models for predicting the fatigue life. The development of digital models of real objects for fatigue life estimation faces the lack of algorithms for performing such an estimation. The problem arises in the adaptive and automatic analysis of signals from real sensors installed on the object and their subsequent processing to estimate the fatigue life of the object. We propose a new method for assessing the fatigue life of structures based on application of the adaptive method of variational mode decomposition to signals gained from sensors, including non-stationary ones. Variational mode decomposition involves decomposition of an initial complex random process into simpler random processes (modes) that are stationary and narrowband. An original method of summarizing damage resulted from the action of the modes obtained as a result of the decomposition is used. The developed method can be used as an algorithmic support for the generation of digital doubles of the residual lifetimes of natural products. The proposed method is compared with the «rainflow» method in the time domain. Different realizations of random stationary and non-stationary signals with different bandwidths are compared numerically. In addition, the traditional frequency methods of Dirlik and Benasciutti have been compared with the «rainflow» method. The analysis showed good results for the proposed method, i.e., the error was smaller compared to traditional frequency methods, especially for non-stationary processes.

Design of an Overhead Crane in Steel, Aluminium and Composite Material Using the Prestress Method

The present research describes a design of an overhead crane using different materials with a prestress method, which corresponds to an external compression force with the aim of reducing the displacement of the beam due to the external load. This study concerns a bridge crane with a span length of 10 m, with a payload equal to 20,000 N and an estimated fatigue life of 50,000 cycles. Three different materials are studied: steel S355JR, aluminium alloy 6061-T6 and carbon fibre-reinforced polymer (CFRP). These materials are analysed with and without the contribution of the prestress method. In reference to the prestressed steel solution (which has a weight equal to 79% of the non-prestressed configuration), this study designed an aluminium solution that is 50.7% of the weight of the steel one and a composite solution that is always 20.3% of the steel configuration. In combining the methods, i.e., the materials and prestress, compared to the non-prestressed steel solution with a weight evaluated to be 758 kg, the weight of the aluminium configuration is equal to 40% of the traditional one, and the composite value is reduced to 16%, with a weight of 121 kg.

Modeling Stress Concentration Factors for Fatigue Design of KT-Joints Subjected to In-Plane Bending Loads Using Artificial Neural Networks

Stress concentration factor (SCF) is an important parameter for the fatigue design of offshore joints. There are many empirical equations for quick estimation of SCF in tubular joints, based on experimental and numerical investigations. However, most of these equations apply at the crown and saddle points only, even though the maximum SCF may not always occur at these points, resulting in overestimated fatigue life. As the maximum SCF location varies due to multiplanar loads, damage, or reinforcement of joints, its location and magnitude are critical for a realistic fatigue life estimation. However, conventional statistical tools cannot approximate the complex behavior of SCF around the brace axis. On the other hand, artificial neural networks (ANN) can efficiently approximate complex phenomena. This study uses ANN to develop empirical models for determining SCF around the weld toe of KT-joints subjected to in-plane bending (IPB) loads. Eighteen hundred and fifty-eight (1858) designs were simulated using finite element analyses to generate data for training the ANN. Two IPB load conditions were focused on, and empirical equations were proposed for SCF around the chord side of the central brace-chord interface. These equations approximate maximum SCF with less than 5% error. This methodology applies to other joints and load configurations also.

Energy based damage model for low-cycle fatigue of ductile materials

A uniaxial material model for fatigue damage accumulation, established on the connection of unit elements, is presented in this paper. Although these units are regarded as micro-elements in the proposed model, they are based on a hysteretic operator that enables calculating hysteretic energy loss as an analytical expression. Further, this unit element represents a mechanical model with elastoplastic damage behavior in function of strain. The second level of modeling is defined by the connection of these units (micro-elements) with different values of total energy dissipated at failure. By changing the distribution of dissipated energy limit, various fatigue damage evolution laws are developed. Calculation of total and hysteretic energy loss in one loading cycle is also affected by fatigue damage as the varying number of unit elements are been eliminated when their maximum dissipation energy is reached. Material parameters for the model were defined based on the experimental monotonic and cyclic stress-strain tests, still, detailed comparison was not performed as the main advantage and aim of the paper was the development of the method for assessment of damage evolution in fatigue analysis. On the other hand, the number of cycles to failure ( Nf) and total heat dissipation are compared in both qualitative and quantitative aspects with experimental results. Finally, based on the proposed model, mean strain and load sequence effect diagrams were constructed. It is shown that the proposed model can provide a reliable estimation of fatigue life in the low-cycle regime of loading. The maximum error for the calculated Nf was 3% for constant strain loading for experiments with strain amplitude less than 5%. In load sequence fatigue life estimation, the proposed model demonstrated good accuracy, with a maximum error of 34%. Further, obtained results were achieved with different types of damage evolution that could be defined for the same material and fatigue life.

Estimation of residual fatigue life of high-strength steel welded joints based on diffuse ultrasound

Fatigue significantly affects the durability and capacity of high-strength steel welded joints (WJs) in engineering. Despite the capability of ultrasonic-based methods to issue early warnings for fatigue crack initiation and effectively monitor crack expansion, estimating residual life before surface cracks poses a considerable challenge. This study introduces a novel method that relies on the correlation coefficient of the ultrasonic energy density, α, to estimate the residual life of WJs before surface cracks become evident. The fatigue damage of 20 butt- and cross-WJs of Q690qENH and Q960E, subjected to different fatigue stresses, was monitored using α. The results revealed a cubic polynomial relationship between α and the number of fatigue cycles when a sample experienced early fatigue damage. Consequently, we introduced an α-N early fatigue damage monitoring curve. The zero value of its second derivative functioned as an early warning indicator, and the corresponding life of the sample was recorded as ζ. Finally, a warning of 20%–50% of the fatigue life for WJs made of two high-strength steels was attainable. A linear relationship between ζ and fatigue stress, denoted as the ζ-S curve, facilitated residual life estimation before surface cracks developed. The blind test produced an approximately ±10% error with 4 samples.

Correction: Artificial neural networks for fatigue life estimation of glass-carbon/epoxy hybrid composites

Correction: Artificial neural networks for fatigue life estimation of glass-carbon/epoxy hybrid composites

Fatigue and corrosion‐fatigue behavior of the β‐metastable Ti‐5Al‐5Mo‐5V‐3Cr alloy processed by laser powder bed fusion

AbstractWe performed rotating bending tests and axial (tension‐compression) load‐increase and constant amplitude high‐cycle fatigue tests in air and Hanks' balanced salt solution (HBSS) on the β‐metastable titanium alloy Ti‐5Al‐5Mo‐5V‐3Cr, processed by laser powder bed fusion (LPBF‐M), solution‐treated and aged, and shot‐peened. Rotating bending loading in air revealed a strong influence of process‐induced flaws on fatigue endurance. Especially in the high‐cycle fatigue range and the transition region, the stochastic distribution of the flaws and flaw sizes led to a high scatter of the number of cycles to failure. The axial load‐increase tests yielded a good fatigue life estimation, with a negligible difference between air and HBSS. The cyclic deformation behavior in HBSS was also strongly influenced by the local microstructure and defect distribution, and, thus, by crack formation and propagation. Plastic deformation and microcrack growth interact, and their relative amount resulted in different progressions of the plastic strain amplitude over the number of cycles for different specimens. Changes in the free corrosion potential and the corrosion current were highly sensitive indicators for fatigue‐induced damage on the rough surfaces, which was correlated to the microscopic examination, fracture surface features, and the fatigue crack development.