Fatigue Crack Growth Assessment Research Articles

A strain-interfaced digital twin solution for corner fatigue crack growth using Bayesian inference

This paper introduces a digital twin solution for corner fatigue crack growth assessment. The digital twin comprises three core features: (1) diagnosis, (2) prognosis and (3) updating. The diagnosis arm performs remote crack size measurement via strain data collected from strategically identified locations. The prognosis component postulates the fatigue life across both linear-elastic and elasto-plastic loading regimes through a fatigue crack growth power law with the cyclic J-integral, ΔJ, as the crack driving force. Uncertainty in power law parameters, however, may result in differences between the prognosis and observed fatigue life. Hence, the digital twin completes the feedback loop via Bayesian updating of the power law parameters, thereby mirroring its physical counterpart closely. An improved estimation of the remaining useful life follows. The proposed digital twin solution validates against three specimens under constant amplitude loading and a single specimen under variable amplitude loading. The successful application of the approach marks a significant step toward operational digital twins within practical settings.

Measuring fatigue crack growth using microscale specimens: Si-modified Inconel 939 alloy processed by laser powder bed fusion additive manufacturing

Quantitative assessment of fatigue crack growth (FCG) in a Si-modified Inconel 939 alloy, processed by laser powder bed fusion additive manufacturing (L-PBF AM), was conducted through cyclic bending of pre-notched cantilevers with a characteristic cross-sectional dimension of 25 μm × 25 μm. To the best of our knowledge, this work is the first to show that cyclic bending of such pre-notched microscale cantilevers can sense both the threshold regime and the Paris-law regime of FCG quantitatively, despite the small specimen size. The deliberate fabrication of such microscale test specimens enables control of the direction of fatigue crack propagation with respect to a given microstructure, while avoiding the inclusion of volumetric defects within the test volume. Significant differences in FCG behavior were observed when the direction of crack propagation was switched from being parallel to the AM build direction to being perpendicular to it. The present work demonstrates the efficacy of FCG assessment using microscale specimens, which can enhance our understanding of the influence of a given microstructure on crack growth behavior.

Assessment of fatigue crack growth in metro cast manganese steel frogs and inspection strategy

Fatigue cracking is one of the notable failure mechanisms of railway turnout frogs due to high contact forces induced by the wheel-rail impact. However, the treatments specific to the frogs of cast high manganese steel to prevent sudden failure are rarely provided and are independent of the crack conditions, which can significantly affect the fatigue crack growth rate. To address this shortcoming, the fatigue crack growth in a cast high manganese steel frog is computationally investigated with varied wheel and crack conditions. The dynamic wheel-frog impact is first simulated to obtain the distribution of contact pressure imposed on the frog, and the propagation of the fatigue crack is then predicted using the finite element formulation in fracture mechanics. The simulation results show that the train speed and axle load can change the maximum contact stress. Nevertheless, when representing the growth rate in terms of the cumulative passing axle load, the effect of axle load and train speed on the crack growth is minimal and moderate, respectively. In contrast, the initial crack conditions, including the location and angle, have an overweighted influence. As a result, an inspection scheduling strategy for identified cracks with different conditions is proposed to consider both safety and operational efficiency.

Zone‐based failure risk assessment of fatigue crack growth caused by initial defects in powder turbine disc

AbstractIn this research, A zone‐based failure risk assessment (FRA) method of fatigue crack growth (FCG) caused by initial defects in the FGH96 alloy turbine disc is developed. Firstly, the initial defects distribution in the FGH96 alloy turbine disc is calculated based on the defect data. Subsequently, a probabilistic short FCG life model is established, taking into account the dispersion in grain size. Meanwhile, a probabilistic long FCG life model is established, incorporating the life dispersion factor. To calculate the Stress Intensity Factor (SIF) at any position of the disc, the general weight function method and the rectangular plate model are established. Finally, the zoning process is established, enabling a FRA that considers the FCG due to initial defects. The results indicate that the number of cycles corresponding to a 0.13% failure probability of the turbine disc is 7150, and the percentage of failures in each zone is analyzed.

Stress ratio effect on fatigue crack growth assessment via thermoelastic stress analysis

The fatigue performance of welded joint is strongly dependent on welding residual stresses as well as the local geometry of the weld toes. To ensure the structural integrity over time of such components, fine predictive models must be proposed together with efficient experimental methods for their assessment.This study introduces a model based on linear elastic fracture mechanics to forecast fatigue life in service of high strength steel welded joints. This model considers the effect of the local stress ratio (dependent on stabilized residual stresses) on the crack growth rate through the definition of an effective stress range. The use of Thermoelastic Stress Analysis (TSA) is used to perform in-situ monitoring of fatigue cracks on welded joints to experimentally characterize the crack-closure phenomenon at different load ratios. Indeed, under adiabatic conditions, the temperature's first harmonic at the surface of a structure submitted to cyclic loading is proportional to the stress tensor's first invariant's amplitude. As a result, the presence of a surface crack and the non-linearity induced by the alterative opening and closing within one loading cycle can be observed in the immediate temperature response. This phenomenon is used to evaluate a crack-opening rate that is related to the fatigue life of the welded joints.

Fatigue crack growth and life assessment of full penetration U-rib welded joints considering residual stresses

The combination of cyclic stresses and welding residual stresses (WRS) can significantly contribute to fatigue cracking in steel bridge decks. This study aims to investigate the effect of WRS on the fatigue life and crack propagation of single-sided and full penetration double-sided U-rib welded joints through experimental and numerical methods. Fatigue tests were conducted to study fatigue crack initiation and propagation behavior. Utilizing the ABAQUS software, a thermoelastic-plastic finite element method was employed to determine the residual stress distribution. Subsequently, based on linear elastic fracture mechanics (LEFM), fatigue crack propagation and life assessment were performed using ABAQUS and FRANC3D software under the coupling of residual stresses and external cyclic stresses. Findings reveal that WRS play a crucial role in fatigue life by altering the effective stress ratio during fatigue crack growth. The effective stress ratio ranges from 0.15 to 0.57, while the changing trends differ between single-sided and double-sided U-rib welded joints. The fatigue crack growth rate of double-sided U-rib welded joints is lower compared to single-sided U-rib welded joints with the same deck thickness. Furthermore, the introduction of WRS induces a mixed mode I, II, and III fracture at the outer weld toe of the U rib, with mode I fracture predominating, which leads to a deviation in the crack propagation path. The fatigue life prediction results agree well with experimental findings when considering WRS. Importantly, these predictions tend to be conservative, thereby ensuring safety and reliability in engineering applications.

Characterization of Fatigue Crack Growth Based on Acoustic Emission Multi-Parameter Analysis.

In engineering structures that are subject to cyclic loading, monitoring and assessing fatigue crack growth (FCG) plays a crucial role in ensuring reliability. In this study, the acoustic emission (AE) technique was used to monitor the FCG behavior of 2.25Cr1Mo0.25V steel in real-time. Specifically, an AE multi-parameter analysis was conducted to qualitatively assess the crack growth condition and quantitatively correlate the crack growth rate with AE. Various AE parameters were extracted from AE signals, and the performances of different AE parameters were analyzed and discussed. The results demonstrated that four stages of FCG, which correspond to macrocrack initiation, stable crack growth with low crack growth rate, stable crack growth with high crack growth rate, and unstable crack growth, are distinctly identified by several AE time domain parameters. The sudden and continuous occurrence of many AE signals with high count (>100) and high energy (>40 mV·ms) can provide early and effective warning signs for accelerated crack growth before final failure occurs. Moreover, linear correlations between crack growth rate and different AE parameters are established for quantifying crack growth. Based on the AE multi-parameter analysis, it was found that the count, energy, and kurtosis are superior AE parameters for both qualitatively and quantitatively characterizing the FCG in 2.25Cr1Mo0.25V steel. Results from this research provide an AE strategy based on multi-parameter analysis for effective monitoring and assessment of FCG in engineering materials.

Safety assessment of external defects in the nozzle-head intersection of a nuclear steam generator

The nozzle-head intersection of a nuclear steam generator (SG) has gained great attention due to its special location and prone to cracks. For the purpose of estimating and ensuring the integrity of the SG structure, the fracture evaluation of nozzle-head intersection after a period of operation needs to be analyzed under a variety of loading conditions. In this paper, stress intensity factors (SIFs) of external surface cracks postulated at the nozzle-head intersection of a SG subjected to pressure, bending, and thermal loadings are evaluated using finite element method. Comparing to the SIFs of cracked pipe described in the RSE-M code, it is found that SIF calculation method of cracked pipe can be conservatively applied to the external surface cracks at the nozzle-head intersection of the SG. Using the conservative SIF solution, the fatigue crack growth and fracture assessment of the postulated cracks are evaluated according to the RSE-M code considering the material aging. Finally, the critical crack size and allowable initial crack size for the life of 40 years are given for the nozzle-head intersection of the SG.

Thoughts on the durability and damage tolerance assessment of adhesively-bonded joints

This paper first discusses the accuracy of the standard adhesively-bonded joint design code, the analytical A4EI code, that is used in the aircraft industry to determine the strain-energy density in a complex step-lap joint under shear loads. This joint geometry is then used to assess the ability of the A4EI code, and a standard finite-element analysis, to meet the static design requirement that there be no yield at 115% of the design limit load. Secondly, the analysis tools needed for the durability and damage tolerance (DADT) assessment of adhesively-bonded airframes are discussed. This study demonstrates the significant advantages of now adopting a Harman-Schijve approach, which considers a fatigue crack growth rate approach to DADT assessment. Indeed, this study reveals how very different approaches are required to assess the static versus the DADT performance of adhesively-bonded joints. A key finding is that, if a valid DADT assessment of fatigue crack growth in adhesively-bonded structures is to be performed, then the aspect of the fatigue crack growth data associated with the growth of small cracks in bonded joints needs to be resolved, together with the question of what is the value of the fatigue threshold associated with such small, naturally-occurring cracks in bonded structures.

Assessment of fatigue crack growth based on 3D finite element modeling approach

Fatigue crack growth life assessment enables manufacturers to quantify damage tolerance capability of high-risk components. Reduced order models that are based on simple geometries (i.e. surface crack in a plate, corner crack at a bolt hole) and on the assumption that cracks maintain an elliptical shape during propagation, are commonly employed in the damage assessment. A more comprehensive modeling process should consider the component geometry, service loading conditions and, eliminate assumptions related to crack front shape or planarity of the crack growth path. A 3D finite element-based approach is evaluated in this study as a more accurate alternative to reduced order models. For verification purposes, an analytical solution-based model was developed and implemented in MATLAB to predict fatigue crack growth life and crack front evolution for three different crack types: surface, corner and internal. The analytical model solutions are compared against 3D finite element (FE) based approach implemented in SimModeler Crack. The 3D FE modelling approach has been further tested and validated against experimental fatigue crack growth measurements from two Al 2024-T3 specimens containing multiple cracks. The verification and validation data presented herein show that the 3D FE-based modelling approach provides an accurate and effective modelling tool for crack propagation life assessment of structural components.

Crack growth modeling and simulation of a peridynamic fatigue model based on numerical and analytical solution approaches

Fatigue crack growth assessment of 2024-T3 aluminum alloy is carried out on the basis of a recently developed peridynamic fatigue model. The governing remaining-life equation of the peridynamic fatigue model has been solved by two different approaches i.e. numerical and analytical approaches to perform fatigue-crack growth simulations for 2024-T3 aluminum specimen with a pre-existing crack. Remaining-life parameters of the numerical and analytical solution approaches are determined by calibrating with the experimental crack growth data. Fatigue crack growth predictions, and associated material deformation of the specimen under various loading conditions are simulated by the two approaches. Predicted results show that the numerical approach has shortcomings in accurate predictions of crack growth rates for the application of different loading conditions, while the analytical approach can be applied for a wide range of loading conditions with good prediction accuracy and stable simulations of the material deformation with a growing crack. Furthermore, it is found that the computational time of the analytical approach is considerably shorter in comparison with the numerical approach.

A simplified analytical model for the investigation of contact acoustic nonlinearity in pipe structures

A simplified analytical model of contact acoustic nonlinearity (CAN) in pipe structures was established and verified by finite element modelling to analyse the multimode second harmonic waves induced by a breathing crack. The analytical model was developed from plate to pipe structures with S-parameter formulation applied for the investigation of second harmonic generation where pure longitudinal wave mode excitation was used. A numerical simulation model with the same excitation condition was developed to confirm the results from the theoretical analysis. Multimode second harmonic waves were obtained in both analytical and simulation models and the proportion of different modes in terms of axial amplitude was also studied. A new nonlinear index was finally proposed for the quantitative assessment of fatigue crack growth in pipe structures.

Magnification Factor Mk and its Parametric Solutions for Fatigue Crack Growth Assessment of Flaws at Weld Root Toes in Girth Welds

Abstract To account for the effect of the stress concentration factor (SCF) at the weld toe on stress intensity factor range ΔK, a magnification factor Mk is used. The existing Mk solutions given in BS 7910 were developed for the fatigue assessment of flaws at the toes of fillet and butt welds and may not be suitable for assessing flaws at single-sided girth weld root toes, where fatigue cracking often initiates and the weld width is relatively small. Finite element (FE) modeling was performed to determine a 2D Mk solution for engineering critical assessment (ECA) of a flaw at the weld root bead toe. The weld root bead profile was uniquely characterized by five variables including weld root bead width, weld root bead height, hi-lo, weld root bead angle, and weld root bead radius. Following a parametric sensitivity study, defect size, weld root bead height, and hi-lo were identified as the governing parameters. A total of 6000 FE simulations was performed, covering different combinations of weld root bead height and hi-lo. A series of automation scripts were developed in the python programming language and the Mk solution for each type of defect model was developed and provided in a parametric equation. The accuracy of the 2D Mk solutions was confirmed by the experimental data. It was found that the methods and Mk solutions currently recommended in BS 7910 and DNVGL-RP-F108 are inappropriate for assessing a flaw at a girth weld root toe.

Assessment of mixed mode fatigue crack growth under biaxial loading using an iterative technique

Crack growth is investigated numerically in a cruciform specimen with an inclined center crack subjected to biaxial fatigue loading. The mixed-mode fatigue crack growth was examined using a parametric study both on the biaxial stress ratio and the initial crack angle. A fatigue crack growth code for two-dimensional problems was developed to investigate the mixed-mode behavior of fatigue crack growth under biaxial loading. The effects of initial crack angle and the biaxial stress ratio on the specimen fatigue life are explored using finite element analysis and the results are discussed.

Fatigue crack growth assessment method subject to model uncertainty

Fatigue crack growth (FCG) is an important degradation process of many critical mechanical equipment. Probabilistic FCG models are often used to account for the variability among FCG process conditions. In the well-known model of Yang and Manning, a deterministic FCG model is randomized by multiplying the crack growth rate with a random multiplier assumed to obey a lognormal distribution and unknown parameters are jointly estimated through Maximum likelihood estimation. By so doing, the modeling error due to inappropriate choice of the deterministic FCG model and that due to unsuitable assignment of the probability distribution of the random multiplier cannot be distinguished. Besides, the model uncertainty of the random multiplier is not explicitly considered. In this paper, a two-step least-square estimation method is proposed, which estimates the unknown parameters in the deterministic FCG model at first, and generates a sample set for the estimation of the random multiplier considering model uncertainty by way of Bayesian model selection. In Bayesian model selection, three types of Bayes factor are considered to select the appropriate candidate model and a simulation experiment is carried out to guide their selection. The effectiveness and feasibility of the proposed method are illustrated through two case studies using the real FCG datasets.

Fatigue Crack Growth Thresholds at Negative Stress Ratio for Ferritic Steels in ASME Code Section XI

Thresholds of fatigue crack growth rates are important characteristics for fatigue crack growth assessment for the integrity of structural components. ASME Code Section XI provides fatigue crack growth thresholds for ferritic steels in air and water environments. The threshold is given as a constant value under a negative stress ratio. However, the thresholds are not clearly defined in the range of negative stress ratios. The definition seems to be maximum stress intensity factors. Besides, the thresholds expressed by the maximum stress intensity factors decrease with decreasing stress ratios. This means that the thresholds under negative stress ratios become unconservative assessments. The objective of this paper is to discuss the definition of fatigue crack growth threshold and to propose the threshold equation for the ASME Code Section XI, based on experimental data obtained from a literature survey.

Entropy-Based Approach for Fatigue Crack Growth Rate of Dual-Phase Steel

This paper presents an entropy-based approach for the fatigue crack growth of dual-phase steel under a constant amplitude loading. According to the degradation-entropy generation theorem, the degradation coefficient can be derived from the correlations of entropy and crack propagation. The temperature evolutions induced for the duration of the fatigue crack growth tests on the as-received and dual-phase steel till it failed were measured to ensure their validity. The results of the present model and the calculated Paris-regime crack growth data were analysed to reach the conclusion that the temperature at the surface of a specimen during a fatigue crack growth test can be used for the assessment of fatigue crack growth by the intensity of the degradation coefficient. The predicted results showed that the present model could accurately predict the fatigue crack growth rate of dual-phase steel with a regression value (R2) of 0.9952.

Assessment of fatigue crack growth in 316LN stainless steel based on acoustic emission entropy

This paper presents an investigation of assessment of fatigue crack growth (FCG) of 316LN stainless steel using the acoustic emission (AE) monitoring technique. A new AE parameter, i.e. AE entropy, was used for accurate assessment of fatigue damage and prediction of fatigue crack length. The effects of peak load on both FCG and AE behaviors were also discussed by fractographic observations and AE parameter analyses. The results showed that AE entropy is effective for accurately identifying the point of crack initiation and assessing the fatigue damage during FCG of 316LN stainless steel under high noise loading environment. Moreover, two distinct damage stages were distinguished by the characteristics of AE entropy. The source mechanisms of AE entropy for stage 1 were fatigue crack initiation and small crack growth, while the mechanisms responsible for stage 2 were the plastic activities in plastic zone at the crack tip, the formation of micro-voids and the ligaments shearing between these micro-voids. The results also indicated that AE entropy is available for identifying the transition in stress condition from plane strain to plane stress state of specimens under high peak load. In addition, a probabilistic model based on the quantitative relationship between the crack growth size and cumulated entropy was proposed for prognosis of crack growth. Bayesian inference was used to estimate the model parameters and the posterior predictive distribution of crack length. The predictive results showed that the model could accurately predict the measured crack growth lengths in all cases. The proposed model is applicable to stable long crack growth and can be applied under high noise loading environment.

Fatigue Crack Growth in an Al-Mg-Si Alloy under Negative Load Ratio

The usual approaches for Fatigue Crack Growth (FCG) assessment are based on semi-empirical models that consider the stress intensity factor range of fracture mechanics, ΔK, as the governing driving force for crack propagation. However, FCG data incorporating compressive loads have brought discussions and controversies. The compressive loads are not taken into account in the usual life prediction codes and the negative portion of the loading cycle is neglected. In the present work, constant amplitude fatigue crack growth tests with load ratios-1 and 0 are performed, for two diferent stess levels, in AA 6005 alloy centre-notched middle tension M(T) specimens and the obtained results are discussed. It is shown that the crack closure concept, that usually work well for positive ratios, is not enough to satisfactorily explain the negative load ratio effects. The results also showed how the negative part of the load affected the propagation rate of the crack, mainly for larger cracks and smaller loads. Finally, it is shown that a previously proposed expression for the stress distribution ahead of the crack can shed some light on this question.

Stochastic fatigue crack growth analysis of metallic structures under multiple thermal–mechanical stress levels

This paper proposes an analytical–empirical framework for stochastic assessment of fatigue crack growth. The study offers solutions for drastic problems in studying fatigue field including dispersion and scarcity of fatigue data, and impact of several factors on fatigue crack growth. The research composes of two complementary phases. The first phase analyses the behavior of fatigue models under probabilistic conditions. The propagation of uncertainty is studied in fatigue models in this phase under cyclic loads. The research is based on two fundamental deterministic fatigue models: Walker and Forman correlations. The second phase employs probabilistic distributions for stochastic assessment of fatigue crack growth. A new approach is introduced to simulate fatigue crack growth stochastically under the effects of different variables through combining lognormal distribution and stress life models. Bayesian approach is applied for parameter estimation. The final presented models offer the ability of predicting fatigue crack length with desirable probability under multiple stress levels. Although the method is examined on an automotive application, the presented approach is universal and applicable for other industries dealing fatigue damage with multiple impacting factors.