Fatigue Crack Growth Model Research Articles

Quasi-static and fatigue crack growth simulation in co-consolidated thermoplastic joints containing crack arrest features

In the present article, quasi-static and fatigue crack growth in co-consolidated thermoplastic Crack-Lap Shear (CLS) specimens containing two different Crack Arrest Features (CAFs) have been numerically simulated. The substrates have been manufactured from unidirectional T700 carbon fiber reinforced Low-Melt PAEK thermoplastic material. The Friction Stir Spot Welding (RFSSW) and the Induction Low Stir Friction Riveting (ILSFSR) CAFs were studied. Crack growth simulation has been based on the cohesive zone modeling method and has been implemented via the LS-Dyna FE software. Both static and fatigue crack growth models have been successfully validated against results from respective mechanical tests. Both CAFs have been proven capable of delaying crack growth, especially for fatigue loading. An evaluation of various installation parameters of the two features, such as the diameter, the distance to the crack tip, and the installation depth, was performed for the quasi-static loading cases. All parameters have been found to affect the crack stopping efficiency, but the most important effect comes from the diameter of the CAF. Furthermore, a series of quasi-static and fatigue simulations have been run on a mono-stiffener element, representative of an aeronautical structural assembly, in order to evaluate numerically the efficiency of the CAFs at a higher scale. The results showed no crack stopping for the ILSFSR and a low crack stopping for the RFSSW for fatigue loading.

A Literature Review of Incorporating Crack Tip Plasticity into Fatigue Crack Growth Models.

This paper presents an extensive literature review focusing on the utilisation of crack tip plasticity as a crucial parameter in determining and enhancing crack growth models. The review encompasses a comprehensive analysis of various methodologies, predominantly emphasising numerical simulations of crack growth models while also considering analytical approaches. Although experimental investigations are not the focus of this review, their relevance and interplay with numerical and analytical methods are acknowledged. The paper critically examines these methodologies, providing insights into their advantages and limitations. Ultimately, this review aims to offer a holistic understanding of the role of crack tip plasticity in the development of effective crack growth models, highlighting the synergies and gaps between theoretical, experimental, and simulation-based approaches.

Prediction of Fatigue Crack Growth in Vacuum-Brazed Titanium Alloy

The assessment of fatigue is a crucial concern in welded components and structures. This study investigates the fatigue properties and models for predicting fatigue crack growth in Ti-6Al-4V titanium alloy when processed by vacuum brazing with TiCuNi filler. Fatigue properties and the impact of the stress ratio were determined through constant amplitude fatigue tests. By utilizing the results obtained from variable amplitude fatigue tests, various prediction models for fatigue crack growth were examined: modifications for load interaction, residual stress, and crack closure. The results indicate that the microstructures in the brazed zone consist of numerous fine, elongated needle-like Widmanstätten structures. In terms of cycle counting methods, the rainflow method outperforms the simple-range method. In the stable crack growth rate region, fatigue crack growth rate increases with the rise in stress ratio in a manner similar to high-strength steels. The Paris model without any modification obtains good predictions. For models modified with crack closure, the Elber model yields slightly better prediction results than the Schijve model. Among fatigue crack growth prediction models, the Willenborg model with residual stress modification produces the best results. Fracture surfaces within fatigued specimens’ brazed zones exhibit ductile failure characteristics, where fatigue striations and secondary cracks were observed.

Phase field modeling of thermal fatigue crack growth in elastoplastic solids and experimental verification

It is challenging to simulate thermal fatigue crack growth in elastoplastic solids, meanwhile, the phase field model is very attractive for simulating complex cracking problems. A thermal-elastoplastic phase field model for thermal fatigue was developed, and its accuracy and availability were verified by typical examples. Then a verified thermal fatigue experiment of the V-notch specimen was carried out and the crack growth was simulated based on the phase field model. The results indicate that the process of thermal fatigue crack in elastoplastic solids from initiation to propagation is effectively simulated by the proposed phase field model. As the regularization length increases, the simulated crack has a longer length and stronger diffusivity. The appropriate regularization length needs to be determined based on experimental results.

Mechanistic modeling of fatigue crack growth in asphalt fine aggregate matrix under torsional shear cyclic load

Fatigue crack growth in asphalt pavements under vehicle load may primarily occur within the asphalt fine aggregate matrix (FAM) phase of the mixture. This study aims to predict fatigue crack growth in FAM by developing a mechanistic-based fatigue crack characterization model and fatigue crack growth model under torsional shear cyclic load. Initially, a fatigue crack characterization indicator, fatigue damage density, was derived using principles of torque and dissipated strain energy equivalence. Afterwards, a fatigue crack growth model was established based on the pseudo J-integral Paris’ law. Finally, the viscoelastic damage constitutive model was further constructed by coupling the fatigue crack growth model with a viscoelastic model, which was subsequently implemented in COMSOL Multiphysics. The results show that the fatigue damage density can be determined by the initial shear modulus and phase angle, as well as shear modulus and phase angle under fatigue conditions. Additionally, a logarithmic-linear correlation exists between the fatigue crack growth rate and the dissipated pseudo strain energy rate. The parameters of the fatigue crack growth model exhibit minimal variation across different shear strain levels and temperatures. Overall, the proposed numerical model can effectively simulate damaged torsional shear cyclic tests of FAM.

Crack‐like effectiveness of some discontinuities in AA2024

AbstractMaintaining aircraft airworthiness to ensure the fleet's safe operation and maintain its readiness is critically dependent on accurate modelling and reliable predictions of fatigue crack growth. In this process, a knowledge of the representative initial discontinuity sizes that cause fatigue crack nucleation and early growth in aircraft is essential. Here the effective pre‐crack size of aluminum alloy 2024, from samples of aircraft production material and tested under aircraft spectra, are considered.

Crack growth-based life prediction for additively manufactured metallic materials considering surface roughness

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

Spectral fatigue analysis of ship structures based on a stochastic crack growth state model

Fatigue life estimation in ship structures is a very complex problem, because of the stochasticity in the wave loading experienced by the hull and the inherent variability in the material and geometric parameters. On an effort to quantify such aleatoric uncertainties, this work integrates in a novel setting the spectral approach to loading description into a probabilistic fatigue crack growth model. The proposed framework effectively models both the randomness in the experienced sea states and the corresponding random sequence of the sea states that are encountered by the ship and contribute to the fatigue accumulation. The spectral approach eventually allows for the construction of potential crack growth path instances from a single realization of an effective random stress range that is applied for a corresponding realization of number of cycles. The obtained bundle of stochastic crack paths is further used in order to perform reliability estimations in the entire life cycle. Initially the proposed method is presented formally and algorithmically and its application is demonstrated through a numerical case study of a cracked plate where we are interested in estimating its remaining useful life along with the time distribution of the probability of failure.

Microstructure relevant fatigue short crack propagation behavior of Al0.3CoCrFeNi high entropy alloy: in-situ SEM study

The microstructure effects on fatigue short crack propagation behavior of Al0.3CoCrFeNi high entropy alloys (HEAs) were studied by in-situ fatigue testing under scanning electron microscope (SEM). The experimental results indicated that fine grain (FG) specimens had better fatigue crack propagation resistance and higher fatigue life compared with coarse-grain (CG) specimens. Fatigue short crack propagation followed transgranular mode, associated with octahedral slip. The fatigue small crack growth is primarily microstructurally sensitive, showing evident fluctuations related to the blocking effects of grain boundaries and twin boundaries. Furthermore, a modified fatigue crack growth model has been proposed, which can successfully evaluate the crack growth rates of HEAs with different grain microstructures under different fatigue stresses.

A novel energetic approach for predicting fatigue crack growth in pseudoelastic NiTi alloys

A novel strain energy-based method for analyzing fatigue crack growth (FCG) in pseudoelastic Nickel-Titanium (NiTi) -based shape memory alloys (SMAs) is proposed. It uses the dissipated energy to predict the FCG. This parameter can be computed either by volume integration of near-crack-tip strain energy or by the force–displacement hysteresis measured at the loading pins of the sample. Eccentrically-loaded single Edge Crack tension samples (ESE(T)) were used for FCG tests. High resolution Digital Image Correlation (DIC) was used to capture near-crack-tip displacement and strain fields. DIC data were also used to estimate the effective stress intensity range by regressing the William’s expansion series. Furthermore, a constitutive model for SMAs was used for FE simulations of ESE(T) samples, and the evolution of the dissipated energy during FCG tests was computed. Experimental FCG rate, plotted against the cyclic dissipated energy, are well fitted by a power law equation (R2 = 0.99). This result would open new perspectives to develop predictive models for FCG in SMAs considering intricate thermomechanical coupling mechanisms and material non-linearities.

A two-surface contact model for DEM and its application to model fatigue crack growth in cemented materials

This paper proposes a modelling approach that combines the discrete element method (DEM) and a novel bonded contact model to characterise the fatigue response of cemented materials. While DEM is commonly used to simulate bonded materials undergoing cracking, the centrepiece of the present method is the development of the novel bonded fatigue model. This new model couples damage mechanics and bounding surface plasticity theory to capture fatigue crack growth in cement bridges between aggregates. Thanks to the incorporation of the bounding surface plasticity, the proposed model provides a smooth transition from static to fatigue damages and vice-versa in a unified manner, making it more flexible to capture damage responses of cemented materials under different loading conditions (i.e. monotonic and cyclic loadings). Moreover, the proposed approach automatically captures the hysteretic response in cement bridges between aggregates under fatigue loadings without ad-hoc treatments. More importantly, by removing the direct dependence of the fatigue damage variable on the number of loading cycles, the modelling approach can be applied to simulate the fatigue behaviour of cemented materials under cyclic variable load amplitudes. The proposed modelling approach is evaluated against several strength tests to examine its predictive capability. Satisfactory agreements with fatigue experiments are achieved for flexural modulus degradations, lifetimes and sensitivity of stress levels under constant and variable amplitude cycles. This result suggests that the proposed discrete modelling approach can be used to conduct numerical experiments for insights into the fatigue behaviour of cemented materials.

A novel multiscale model for mixed-mode fatigue crack growth in laminated composites

A multiscale model is developed to predict mixed-mode fatigue crack growth (FCG) behavior in laminated composites by considering the micromechanical effects of fiber bridging. The proposed model consists of a micromechanical part dedicated to the fiber bridging mechanism near the crack tip, a macroscopic FCG model based on the maximum principal strain criterion, and an effective crack tip processing zone (i.e., an equivalent critical distance) connecting the two parts of the model. The core novelty of the presented model is to connect two scales (micro and meso) through a measurable physical quantity – called equivalent critical distance – accounting for various micromechanical as well as macroscopic phenomena occurring at both scales. The suggested model is validated against FCG test data available in the literature for laminated glass fiber composites under mode I, mode II, and mixed mode I/II conditions. It is found that the proposed framework is superior to its conventional (pure macroscopic) version, which eliminates fiber bridging effects, in the prediction of the cyclic mixed-mode crack propagation behavior in laminated composites. The multiscale nature of the proposed FCG model offers less complexity than fully micromechanical approaches while providing higher accuracy as compared to pure macroscopic models that ignore micromechanical phenomena occurring at the fiber scale.

Probabilistic damage tolerance assessment method based on the multi-scale crack growth model

The probabilistic damage tolerance analysis method, which combines the theory of damage tolerance and probabilistic fracture mechanics, can significantly improve the reliability and safety of engineering structures. In this study, the stress intensity factors under different crack sizes of experimental specimens were simulated by the finite element method, and the damage tolerance evaluation effects of three fatigue crack growth models were compared. Then, based on the multi-scale fatigue crack growth model and the first-order second-moment (FOSM) method, the reliability under the specified fatigue crack growth life was obtained. Finally, considering the uncertainty of initial crack and fracture toughness, the probabilistic damage tolerance assessment map based on the multi-scale fatigue crack growth model is established. The map provides a basis for developing a more reasonable model and establishing a more perfect and reliable damage tolerance assessment method.

A mixed-mode fatigue crack growth model for co-consolidated thermoplastic joints

In this work, a mixed-mode fatigue crack growth model for simulating interfacial fracture of co-consolidated thermoplastic joints was developed. The model is based on the cohesive zone modeling approach and was specifically designed to account for any I + II mode-mixity, requiring only pure mode I and II loading data as input. The fatigue crack growth rate is constantly updated using a function of the energy release rates and the computed mode-mixity ratio. A linear mode-mixity law is applied. Both force-controlled and displacement-controlled loads can be modeled in specimens ranging from coupon-scale sizes to larger structural elements. Implementation of the model was done for the low-melt polyaryletherketone (LM-PAEK) material by developing a user-defined subroutine in the LS-Dyna FE software. To feed the model, mode I and mode II fatigue tests were conducted using double-cantilever beam and end-notch flexure specimens, respectively, while to validate the model mixed-mode single lap shear (SLS) tests were conducted. The model reproduces accurately the mode I and II fatigue crack growth while it predicts also accurately the mixed-mode fatigue crack growth of the SLS specimens.

Stochastic selection of fatigue crack growth model for a damaged bridge gusset plate

Damage tolerance-based fatigue assessment of operational structures is often rationalized by integrating the simple Paris model with fixed parameters, which often do not represent the unique geometrical, boundary, and loading conditions of the structure. This paper has implemented a stochastic approach which involves different crack growth models, from the simple Paris model to the complex NASGRO model, and estimates the parameters which truly fit the structural condition and crack propagation models. The case study for this paper is a steel riveted railway bridge, where an edge fatigue crack was observed in one of the gusset plates. The most suitable models are recognized at different damage states of the plate and the influence of the measurement uncertainties on the model selection process is highlighted.

A full-stage fatigue crack growth model for metallic materials

In this study, based on the understanding of blunting and re-sharpening to micro-void coalescence mixed mechanism, a new full-stage fatigue crack growth model is proposed by exploiting the energy distribution concept. As the crack growth rate increases, the transformation efficiency of three types of mechanisms exhibited different trends. The parameter m in the Paris’ law, derived from the new model, is in accordance with the experimental results. The new model is accurately verified by considering some engineering materials, including steels, titanium and aluminum alloys, which would be further applied to other innovative materials such as composites and high-entropy alloys.

A robust probabilistic fatigue crack growth model based on walker’s crack growth rate equation for metallic materials

The fatigue crack growth data inherits statistical variation despite carefully controlled test procedures. The available probabilistic models rely extensively on fatigue crack growth test data of the coupon material under replicate loading conditions. In view of the often unavailability of such a database, this work proposes a new probabilistic model based on Walker’s crack growth rate equation and considers the variability in both the stress intensity factor range, ΔK and stress ratio, R. The optimum estimates of the model parameters are established using the maximum likelihood estimation (MLE) method. The model is examined using selected sets of measured fatigue crack growth curves of 7075-T6 and 2024-351 aluminum alloys. It demonstrates acceptable predictions for fatigue crack growth data on replicate and variable R-ratio loadings with failure probabilities in the range of 0.10 ≤pF≤ 0.90. The error on the observed fatigue crack growth rate data is normally distributed. The criterion of the minimum number of replicate tests for a valid probabilistic assessment of the fatigue crack growth data is established. Based on the mean squared error (MSE) parameter, the model provides a better representation of the mean fatigue crack growth rate behavior of the material for fatigue loading with variable R-ratios.

Fatigue life prediction of stud shear connectors under corrosion-fatigue coupling effect

Based on the three-stage fatigue crack growth model, a corrosion fatigue life prediction method considering the coupling effect of corrosion and fatigue is proposed in this paper. In this case, stress factor amplitude was claimed considering the coupling effect of corrosion and fatigue. Three push-out tests in corrosion conditions were conducted to study the failure mode of studs. The crack propagation of studs, obtained through the push-out tests, was simulated in FRANC 3D to establish a library of adequate stress factor amplitude. According to the corrosion degree of the specimens, the corrosion dissolution rate formula was formed, and the corrosion fatigue life of the specimen was predicted. Results show that the error between the predicted and experimental values is approximately 25%.

Modelling of time‐dependent fatigue crack growth of hydrogels

AbstractThe service life of hydrogel‐based devices is strongly influenced by the anti‐fatigue capability of hydrogels. While recent advancements in the synthesis of hydrogels have improved their fatigue resistance, the underlying mechanisms that dominate the time‐dependent fatigue crack growth of hydrogels are still poorly understood. In this study, a computational method is developed to predict the fatigue crack of hydrogels. A physics‐based poro‐visco‐hyperelastic model is developed within the framework of the Theory of Porous Media at finite strains to describe the mechanical behaviour of hydrogels. A Bell model‐based chain evolution law is adopted to describe the time‐dependent breaking/reforming kinetics of physical chains. An energy‐based fatigue crack growth model is proposed to predict the fatigue crack growth of hydrogels. The averaged elastic energy density surrounding the crack tip is calculated as the driving force of fatigue crack growth. The effects of viscoelasticity, physical chain kinetics and fluid transport on the fatigue crack growth are analysed. The results indicate that these time‐dependent mechanisms cannot be ignored in predicting the fatigue crack behaviour of hydrogels.

Comparison of Monte Carlo and bootstrap analyses for residual life and confidence interval

Abstract Failure starts with creation of a crack, then the propagation of the crack and eventually the fracture of the material. Furthermore, material selection, geometry, processing and residual stresses are critical factors that may contribute to uncertainty and prospective failure mechanisms in engineering. These issues may also arise in computational analysis, a problematic model, for instance, a three-dimensional surface fracture that may necessitate numerous degrees of freedom during analysis. However, considering the multiple incidents of material failure, detailed analysis and efforts to prevent premature material failure for safety and engineering integrity can be carried out. Thus, the objective of this study is to model crack growth in a surface-cracked structure. Aluminium alloy 7075-T6 was the material of interest in this study. The S-version finite element method (SFEM) was used to study fracture propagation. The numerical approach developed in this research was the probabilistic SFEM. Instead of mesh rebuilding, a typical finite element approach, the SFEM uses global–local element overlay method to create a fatigue crack growth model, which was then used for crack research. Empirical computation and previous experimental data were used to evaluate the stress intensity factor (SIF), surface crack growth and fatigue life. The SIF was determined using a virtual crack closure method (VCCM). In addition, the probabilistic approach is also a critical method to generate random parameters, such as Monte Carlo and bootstrap methods. The SIF, fatigue life and surface crack growth were validated and deemed to be within the acceptable range.