Fatigue Crack Growth Model Research Articles

A Multi-Scale Model for Predicting Physically Short Crack and Long Crack Behavior in Metals.

The fatigue behavior of metal specimens is influenced by defects, material properties, and loading. This study aims to establish a multi-scale fatigue crack growth model that describes physically short crack (PSC) and long crack (LC) behavior. The model allows the calculation of crack growth rates for uniaxial loading at different stress ratios based on the material properties and specimen geometry. Furthermore, the model integrates the Gaussian distribution theory to consider material heterogeneity and the experimental measurement errors that cause fatigue scatter. The crack growth rate and fatigue life of metal specimens with different notch geometry were predicted. The curves generated by the multi-scale model were mainly consistent with the test data from the published literature at the PSC and LC stages.

An improved phase-field model for fatigue crack growth considering constraint effects

The phase field model is a promising method for simulating fatigue crack growth (FCG) behavior. However, the conventional phase field (PF) model may not adequately account for constraint effects, where fracture toughness is affected by geometries. Therefore, stress triaxiality is incorporated into the PF model by modifying the fracture energy release rates to consider constraint effects. The model successfully simulates the FCG behavior of different geometries, such as CT, SENB, and MT specimens, as well as the mixed-mode FCG behavior of CTS specimens and other complex geometries. All simulations agree well with experiments, proving that our model is capable to capture the constraint effects in FCG behavior. These findings indicate that stress triaxiality is important to capture the constraint effects.

A crystal plasticity phase-field model for microstructure sensitive fatigue crack growth in a superalloy

In this work, a dislocation density-based crystal plasticity phase-field model (CP-PFM) is developed to simulate fatigue crack growth in nickel-based superalloys. Through normalization validation, the plastic dissipation work and crystallographic work are shown to be consistent with the fatigue indicator factors (FIPs), cumulative equivalent plastic strain and cumulative shear strain, and the two energies are computed as the main driving forces of the phase field. Both driving force models are able to obtain fatigue crack growth in close approximation to the experimental rate. However, the model with crystallographic work as the main driving force obtains crack growth paths that are in better agreement with electron backscattering pattern (EBSD) observations, which is attributed to its greater ability to characterize the microstructural susceptibility of fatigue crack growth. Specifically, the model is able to capture the tendency of cracks to crack along the close-packed planes and the hindering effect of grains with large misorientation angles on fatigue crack growth, which together contribute to the curved morphology of fatigue cracks. The combination of large grains or grains with small misorientation angles favors persistent slip band (PSB) formation and leads to softening of the crack tip, which results in lower fatigue crack growth rates.

An adaptive fatigue crack growth model at the welded joints of steel bridge

Under the influence of random loads such as those from vehicles, the welded details in steel bridges tend to gradually develop into macrocracks, typically originating from manufacturing defects or stress concentration points. As the service life of the steel bridge increases, the continuous generation and propagation of fatigue cracks lead to a decline in the bridge's service performance, potentially resulting in catastrophic failures such as bridge collapse. Accurately analyzing the fatigue crack growth patterns at welded joints is a prerequisite for reliably assessing the structural service performance. The analysis of fatigue crack propagation depends on both the crack growth step size and the cyclic stress–strain response at the welded joint under loading. Considering the complexity of the material properties and stress concentration at the welded joint, which leads to a lack of analytical solutions for the cyclic stress–strain characteristics at the crack tip, numerical analysis was employed to obtain the cyclic stress–strain response at the crack tip of the welded joints. Using the size of the cyclic plastic zone at the crack tip as an adaptive crack growth step size, a model for fatigue crack growth was developed based on the plastic strain energy of the cyclic plastic zone. Fatigue test specimens extracted from the welded toe of cruciform welded joints were tested, providing cyclic stress–strain (Ramberg-Osgood material parameters) and fatigue damage characteristics (Manson-Coffin material parameters) of the material at the welded toe. High-cycle fatigue tests using cruciform welded joint specimens determined a good correlation between the crack propagation characteristic dimensions obtained from the adaptive numerical analysis model and the experimental results. The experimental findings confirmed the applicability of the established adaptive numerical analysis model for studying fatigue crack growth in cruciform welded joints. The parameters introduced in this model are physically meaningful, easy to obtain, and suitable for engineering applications.

Corrosion fatigue crack growth model for aluminum alloys in jet fuel

AbstractAluminum alloys are primary structural materials in aircraft fuel systems, where jet fuel can influence the fatigue crack growth (FCG) behavior of materials. This paper presents a model for calculating the FCG rate of aluminum alloys in jet fuel environment. The model is based on elastoplastic fracture mechanics and revises the interaction terms in the linear superposition model by accounting for the corrosive environment and the crack closure effect. The derivation process of the model is discussed in detail. To validate the efficacy of the model, FCG tests were conducted on three types of aviation aluminum alloys, namely, 2524‐T3, 7050‐T7451, and 7075‐T62 in the jet fuel. The experimental results were compared with FCG rates in the laboratory air environment. Findings indicate that the proposed model effectively captures the primary trends observed in the experimental data. In addition, the failure surfaces of the specimens were observed using a super‐depth‐of‐field optical microscopy system.

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

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

Isothermal and thermomechanical fatigue crack growth behavior and modelling of 316LN stainless steel with the superposition of HCF loading

This work comparatively investigates the effect of superposition of high-cycle fatigue (HCF) loading on the crack growth behavior of 316LN stainless steel in isothermal fatigue (IF) and thermomechanical fatigue (TMF) tests. Results show that a deflection of the crack growth rate is observed in the tests without HCF loading. The superposition of HCF loading leads to a marked increase of crack growth rate in IF and out-of-phase TMF tests while a minimal variation in in-phase TMF test. Moreover, the crack growth rate in in-phase TMF test is smaller than the IF and out-of-phase TMF tests due to the different shape and evolution behavior of plastic zone at crack tip. Finally, the model based on the cumulative damage rule of time-dependent and cycle-dependent components is proposed, which considers the characteristics of plastic zone size and grain size and leads to a satisfactory prediction result.

Merging Data with Modeling: An Example from Fatigue.

It is well known that errors are inevitable in experimental observations, but it is equally unavoidable to eliminate errors in modeling the process leading to the experimental observations. If estimation and prediction are to be done with reasonable accuracy, the accumulated errors must be adequately managed. Research in fatigue is challenging because modeling can be quite complex. Furthermore, experimentation is time-consuming, which frequently yields limited data. Both of these exacerbate the magnitude of the potential error. The purpose of this paper is to demonstrate a procedure that combines modeling with independent experimental data to improve the estimation of the cumulative distribution function (cdf) for fatigue life. Subsequently, the effect of intrinsic error will be minimized. Herein, a simplified fatigue crack growth modeling is used. The data considered are a well-known collection of fatigue lives for an aluminum alloy. For lower applied stresses, the fatigue lives can range over an order of magnitude and up to 107 cycles. For larger applied stresses, the scatter in the lives is considerably reduced. Consequently, modeling must encompass a variety of conditions. The primary conclusion of the effort is that merging independent experimental data with a reasonably acceptable model vastly improves the accuracy of the calibrated cdfs for fatigue life, given the loading conditions. This allows for improved life estimation and prediction. For the aluminum data, the calibrated cdfs are shown to be quite good by using statistical goodness-of-fit tests, stress-life (S-N) analysis, and confidence bounds estimated using the mean square error (MSE) method. A short investigation into the effect of sample size is also included. Thus, the proposed methodology is warranted.

Heterogeneity induced fracture characterization of concrete under fatigue loading using digital image correlation and acoustic emission techniques

Understanding the fatigue failure mechanisms in concrete is complex and remains an area of ongoing investigation. Material heterogeneity, along with the size effect, plays a significant role in specifying the crack propagation behaviour and fatigue life in case of repetitive loading conditions. In this study, the influence of material heterogeneity on the fatigue behaviour of concrete has been examined. Three different-size beam specimens with varying heterogeneity (aggregate sizes) have been considered to investigate various fracture characteristics under repetitive load conditions. Acoustic emission and digital image correlation techniques have been employed to analyse crack growth behaviour. The results revealed that stiffness degradation and crack propagation rates are faster for the specimens with smaller aggregate sizes compared to the larger aggregate size specimens of the same depth. Moreover, the fatigue life and effective crack length at failure are also higher in the case of larger aggregate sizes compared to smaller ones. Therefore, a heterogeneity-adjusted, analytical model of fatigue crack growth has been proposed. Further, the AE parameters have been utilized to characterize the tensile and shear crack dominance in different stages of fatigue crack propagation. The outcome of this study can be utilized to anticipate the crack propagation behaviour and residual fatigue life for any combination of specimen size and aggregate size.

Modeling of crack tip fields and fatigue crack growth in fcc crystals

Predicting the mechanical behavior of polycrystalline materials containing a crack under both monotonic and cyclic loading conditions is crucial for accurately assessing the integrity of engineering materials. This study focuses on the deformation characteristics of face-centered cubic (fcc) grains within the crack tip field and their significant role in governing the driving force for fatigue crack growth during cyclic loading. We employ a cyclic crystal plasticity finite element (CPFE) model to analyze the mechanical response of austenitic 316L stainless steel polycrystals by accounting for nonlinear kinematic hardening effects. Through CPFE simulations, we investigate the deformation fields in 316L grains at the crack tip, considering two different grain orientations under plane strain conditions. Our CPFE results under monotonic loading align consistently with previous theoretical and experimental findings, particularly in comparing CPFE-simulated and experimentally observed plastic sectors consisting of different slip traces on the specimen surface near the crack tip. Based on a critical plastic work criterion for crack advancement, cyclic CPFE simulations are used to determine the fatigue crack growth rate as a function of stress intensity factor range for the two crack tip grain orientations in stainless steel. The simulated Paris law exponent matches experimental values. Furthermore, we compare cyclic CPFE results with those from cyclic J2 plasticity finite element simulations. This study demonstrates a cyclic CPFE approach for determining crack tip fields, accounting for crystallographic effects on plastic deformation of crack tip grains. Our approach can be applied to effectively evaluate fatigue crack growth rates in fcc polycrystalline metals.

Modelling Fatigue Crack Growth in High-Density Polyethylene and Acrylonitrile Butadiene Styrene Polymers.

Prior studies into fatigue crack growth (FCG) in fibre-reinforced polymer composites have shown that the two methodologies of Simple-Scaling and the Hartman-Schijve crack growth equation, which is based on relating the FCG rate to the Schwalbe crack driving force, Δκ, were able to account for differences observed in the measured delamination growth curves. The present paper reveals that these two approaches are also able to account for differences seen in plots of the rate of crack growth, da/dt, versus the range of the imposed stress intensity factor, ΔK, associated with fatigue tests on different grades of high-density polyethylene (HDPE) polymers, before and after electron-beam irradiation, and for tests conducted at different R ratios. Also, these studies are successfully extended to consider FCG in an acrylonitrile butadiene styrene (ABS) polymer that is processed using both conventional injection moulding and additive-manufactured (AM) 3D printing.

A combined cyclic viscoplasticity and entropy generation approach for modelling fatigue crack growth behavior of a nickel-based superalloy at high temperature

This paper developed an entropy-based approach to estimate the fatigue crack growth (FCG) behavior of GH4169 at high temperature. Firstly, systematic FCG experiments of GH4169 at 650 °C were conducted to obtain the experimental data. Then, a finite element analysis combined with Chaboche viscoplasticity and node release technology was developed to obtain cyclic stress–strain responses and entropy generation fields. Based on thermodynamic analysis, numerous discrete material elements as sub-systems were divided along the crack growth direction in simplified representative 2D middle section. Fracture process zone (FPZ) was defined equal to the size of discrete material elements (ρ) which can be determined by distribution of normal stress perpendicular to the crack plane. Subsequently, an effective cyclic entropy generation related to ρ was defined as the crack driving force. Effective cumulative entropy generation was calculated when crack increment was ρ and the results indicated that effective cumulative entropy generation float within a certain range. The average of all effective cumulative entropy generation values was defined as crack growth entropy. Finally, an entropy-based FCG rate model was established to estimate the FCG behavior of GH4169, and a good correlation between experimental results and model predictions are achieved for all the high temperature FCG tests.

Retardation mechanisms and modeling of fatigue crack growth of a high-strength steel after single overload

This study investigated the retardation mechanisms and modeling methodology for the fatigue crack growth (FCG) of a high-strength Q500qE steel after a single overload. Different stress ratios (R = 0.1, 0.3, and 0.5) and overload ratios (OLR = 1.5, 2.0, and 2.5) were considered as key parameters. The digital image correlation (DIC) testing technique was used to capture the deformation at the crack tip during the tests. The crack closure response in the crack wake region was investigated using a virtual extensometer. The results show that, under an identical stress ratio, the fatigue life was increased as the OLR increased. The FCG was completely arrested when OLR reached 2.5 when R ≥0.3. Under an identical stress ratio, the residual strain before the crack tip and the residual deformation in the crack wake region increased with the rise of the overload ratio after a single overload. It’s found that the FCG was retarded or completely arrested due to the constraint of the crack tip plastic zone caused by single overload. Finally, a modified Wheeler model was proposed to predict the FCG rate based on the measured plastic zone size at the crack tip, and the predicted results agree well with the experimental findings.

Representation of the microstructure of pearlitic steels for DEM simulations of fatigue

The fatigue behavior of pearlitic steels in wheel-rails is correlated to the microstructure. However, existing models do barely take this correlation into account. In this work, we propose a hierarchical meshing to describe the microstructure of pearlitic steels. The mesh includes grain and block/colony boundaries, lamellae orientations, and orientation perpendicular to lamellae. We use the Voronoi Tessellation method to generate elements with the specific area fraction distribution for pearlite colony areas. The colony and block information is obtained from SEM and EBSD measurements of R260 steel to construct the mesh that represents the microstructure. Finally, we obtained the deformed microstructure via simple geometrical shearing. This meshing method is the first step for modeling fatigue crack growth anisotropy due to plastic deformation.

A Comparative Analysis of 3D Software for Modeling Fatigue Crack Growth: A Review

Fatigue crack growth modeling is critical for assessing structural integrity in various engineering applications. Researchers and engineers rely on 3D software tools to predict crack propagation accurately. However, choosing the right software can be challenging due to the plethora of available options. This study aimed to systematically compare and evaluate the suitability of seven prominent 3D modeling software packages for fatigue crack growth analysis in specific applications. The selected software tools, namely ABAQUS, FRANC3D, ZENCRACK, LYNX, FEMFAT, COMSOL Multiphysics, and ANSYS, were subjected to a comprehensive analysis to assess their effectiveness in accurately predicting crack propagation. Additionally, this study aimed to highlight the distinctive features and limitations associated with each software package. By conducting this systematic comparison, researchers and engineers can gain valuable insights into the strengths and weaknesses of these software tools, enabling them to make informed decisions when choosing the most appropriate software for their fatigue crack growth analysis needs. Such evaluations contribute to advancing the field by enhancing the understanding and utilization of these 3D modeling software packages, ultimately improving the accuracy and reliability of structural integrity assessments in relevant applications.

High-cycle and low-cycle fatigue life prediction under random multiaxial loadings without cycle counting

A novel fatigue life prediction method under random multiaxial loadings is proposed in this paper. One unique benefit of the proposed method is that it is based on the time-derivative fatigue crack growth formulation and does not need cycle counting under arbitrary loadings. First, a brief review of subcycle fatigue crack growth (FCG) analysis and the equivalent initial flaw size (EIFS) concept for life prediction is introduced. Next, the existing subcycle fatigue crack growth model is extended to near-threshold conditions. An intrinsic fatigue threshold of the material is introduced, and a hypothesis is proposed that the crack only grows when the local stress intensity factor is beyond the intrinsic threshold. Following this, the analogy of stress intensity factor and strain intensity factor is used to extend the fatigue life prediction model to strain-based fatigue analysis. Correction for large plastic deformation is included to handle low-cycle fatigue life prediction. The novelties of this model are that it considers the FCG at the threshold and near-threshold region and it is able to predict both HCF and LCF conditions using FCG-based life prediction. Following this, extensive in-house and literature data for AL-7075-T6 under uniaxial and multiaxial, constant, and random loadings are used for model validation. Discussions for the effect of model parameters are provided based on parametric analysis. Conclusions and future work are mentioned. Code and data are released in public cloud service for interested readers.

Experimental investigation and phenomenological modeling of fatigue crack growth in X80 pipeline steel under random loading

Ocean structures are subjected to random environmental loads during their service life. Under the action of random loads, fatigue crack growth within pipeline steel exhibits transient behaviors such as retardation or acceleration. This poses significant challenges in predicting the fatigue life of ocean structures under random loadings. To establish a predictive model for fatigue crack growth in X80 pipeline steel under random loadings, this study first conducts fatigue crack growth experiments under constant amplitude and random loading conditions. Then, based on deep learning methods and the fracture yield zone theory, a phenomenological model is developed to predict fatigue crack growth in X80 pipeline steel under random loading conditions. The results show that under random loading conditions, the fatigue crack growth curve of X80 pipeline steel maintains a relatively clear logarithmic-linear feature during the stable crack growth stage. However, due to the continuous variation of stress ratio with loading sequence, the fatigue crack growth curve exhibits strong fluctuation characteristics; The phenomenological model established in this study for predicting fatigue crack growth under random loading conditions can relatively accurately reflect the overall trend of fatigue crack growth under random loadings, with a maximum prediction error of less than 10%.

Analytical modeling of fatigue crack growth in plastically pre‐strained steels

AbstractΑ fatigue crack growth analysis to simulate the effect of plastic pre‐straining on fatigue crack growth by taking into account the cyclic material properties is presented. A critical energy concept is implemented, which correlates the critical energy for failure under low cycle fatigue with the critical energy at the crack tip from the SED criterion, using an appropriate scaling factor. The fatigue damage process area controlling the crack increment is defined by the cyclic plastic zone. Analytical fatigue crack growth rates in plastically pre‐strained steels are verified and compared with experimental data in the S355MC and S460MC HSLA steels showing good agreement.

Modelling of Fatigue Delamination Growth and Prediction of Residual Tensile Strength of Thermoplastic Coupons.

Thermoplastic composites are continuously replacing thermosetting composites in lightweight structures. However, the accomplished work on the fatigue behavior of thermoplastics is quite limited. In the present work, we propose a numerical modeling approach for simulating fatigue delamination growth and predicting the residual tensile strength of quasi-isotropic TC 1225 LM PAEK thermoplastic coupons. The approach was supported and validated by tension and fatigue (non-interrupted and interrupted) tests. Fatigue delamination growth was simulated using a mixed-mode fatigue crack growth model, which was based on the cohesive zone modeling method. Quasi-static tension analyses on pristine and fatigued coupons were performed using a progressive damage model. These analyses were implemented using a set of Hashin-type strain-based failure criteria and a damage mechanics-based material property degradation module. Utilizing the fatigue model, we accurately foretold the expansion of delamination concerning the cycle count across all interfaces. The results agree well with C-scan images taken on fatigued coupons during interruptions of fatigue tests. An unequal and unsymmetric delamination growth was predicted due to the quasi-isotropic layup. Moreover, the combined models capture the decrease in the residual tensile strength of the coupons. During the quasi-static tension analysis of the fatigued coupons, we observed that the primary driving failure mechanisms were the rapid spread of existing delamination and the consequential severe matrix cracking.

Dual boundary element method for comparative studies on fatigue crack growth models

Fatigue crack growth studies require models that accurately predict component life with low uncertainty. Despite the large number of proposed models, there is no clarity on their applicability, which justifies a comparative analysis between some of them. The dual boundary element method (DBEM) was applied for cracked bodies, whereby the stress intensity factors (SIF), the growth rate, and the number of cycles were computed. Three crack increment models were studied under constant amplitude fatigue loads: the Paris, the Klesnil-Lucas, and the Forman models. Results were validated with experimental literature and through the finite element method, indicating that each model represents a specific zone of the crack growth curve. Klesnil-Lucas model reproduces the region near the fracture threshold, Paris fits the controlled crack growth zone, whereas Forman’s model recreates the unstable fracture zone, i.e., when the stress intensity factor approaches the material’s fracture toughness. The J-integral with stress field decomposition gave errors below 0.8% for mode I. Results were similar for the propagation path and the number of cycles to those obtained with the finite element method, with errors of about 3% considering different K-effective approaches. Klesnil-Lucas accurately predicts the number of cycles with an error margin below 3%, considering the curved region in the growth rate at the propagation onset, while the Paris model becomes very conservative, predicting values up to 50% lower than experimental data. The Klesnil-Lukas model is advised for simulating the entire crack propagation.