Fatigue Crack Length Research Articles

Second harmonic generation at fatigue cracks by low-frequency Lamb waves: Experimental and numerical studies

Abstract This paper presents experimental and theoretical analyses of the second harmonic generation due to non-linear interaction of Lamb waves with a fatigue crack. Three-dimensional (3D) finite element (FE) simulations and experimental studies are carried out to provide physical insight into the mechanism of second harmonic generation. The results demonstrate that the 3D FE simulations can provide a reasonable prediction on the second harmonic generated due to the contact nonlinearity at the fatigue crack. The effect of the wave modes on the second harmonic generation is also investigated in detail. It is found that the magnitude of the second harmonic induced by the interaction of the fundamental symmetric mode (S 0 ) of Lamb wave with the fatigue crack is much higher than that by the fundamental anti-symmetric mode (A 0 ) of Lamb wave. In addition, a series of parametric studies using 3D FE simulations are conducted to investigate the effect of the fatigue crack length to incident wave wavelength ratio, and the influence of the excitation frequency on the second harmonic generation. The outcomes show that the magnitude and directivity pattern of the generated second harmonic depend on the fatigue crack length to incident wave wavelength ratio as well as the ratio of S 0 to A 0 incident Lamb wave amplitude. In summary, the findings of this study can further advance the use of second harmonic generation in damage detection.

Wyznaczanie dystrybuant długości pęknięcia zmęczeniowego metodą Monte Carlo

Described is the determination of random distributions of the fatigue crack length by the Monte Carlo method and the Bogdanov–Kozin model. Input data needed to determine the distributor were obtained by simulation of fatigue crack growth using the Paris–Erdogan model.

Detectability of Crack Lengths from Acoustic Emissions Using Physics of Wave Propagation in Plate Structures

This paper presents a study to understand the physical nature of fatigue crack growth as an acoustic emission source and detectability of the crack length form the recorded acoustic emission signal in plate structures. For most of the thin walled engineering structures, the acoustic emission detection through sensor network has been well established. However, the majority of the research is focused on prediction of the acoustic emission due to fatigue crack growth using stochastic methods. Where, stochastic models are used to predict the criticality of the damage. The scope of this research is to use predictive simulation method for acoustic emission signals and extract the damage related information from acoustic emission signals based on physics of material. This approach is in contrast with the traditional approach involving statistics of acoustic emissions and their relation with damage criticality. In this article, first, we present our approach to understand fatigue crack growth as source of acoustic emission using physics of guided wave propagation in FEM. Then, using this physical understanding, we present our investigation on detectability of crack lengths directly from crack-generated acoustic emission signals. Finally, we present our method to extract fatigue crack length information from acoustic emission signals recorded during fatigue crack growth.

Material property controlling non-propagating fatigue crack length of mechanically and physically short-crack based on Dugdale-model analysis

Non-propagating fatigue crack lengths were analytically calculated under stress control conditions using plasticity-induced crack closure analysis with the Dugdale model. In addition, a non-dimensionalization method was applied in terms of the Burgers vector and a monotonic plastic zone size under small-scale yielding conditions, which was validated for various initial crack lengths and material properties. When the yield strength was increased, the non-propagating fatigue crack lengths were found to increase for a short crack and decrease for a long crack. The non-dimensionalization enabled the analytical derivation of a generalized non-propagating fatigue crack length, which can be utilized for fatigue designs. The material property controlling the threshold stress intensity factor range of mechanically and physically short-crack was discussed.

Fatigue crack sizing in rail steel using crack closure-induced acoustic emission waves

The acoustic emission (AE) technique is a promising approach for detecting and locating fatigue cracks in metallic structures such as rail tracks. However, it is still a challenge to quantify the crack size accurately using this technique. AE waves can be generated by either crack propagation (CP) or crack closure (CC) processes and classification of these two types of AE waves is necessary to obtain more reliable crack sizing results. As the pre-processing step, an index based on wavelet power (WP) of AE signal is initially established in this paper in order to distinguish between the CC-induced AE waves and their CP-induced counterparts. Here, information embedded within the AE signal was used to perform the AE wave classification, which is preferred to the use of real-time load information, typically adopted in other studies. With the proposed approach, it renders the AE technique more amenable to practical implementation.Following the AE wave classification, a novel method to quantify the fatigue crack length was developed by taking advantage of the CC-induced AE waves, the count rate of which was observed to be positively correlated with the crack length. The crack length was subsequently determined using an empirical model derived from the AE data acquired during the fatigue tests of the rail steel specimens. The performance of the proposed method was validated by experimental data and compared with that of the traditional crack sizing method, which is based on CP-induced AE waves. As a significant advantage over other AE crack sizing methods, the proposed novel method is able to estimate the crack length without prior knowledge of the initial crack length, integration of AE data or real-time load amplitude. It is thus applicable to the health monitoring of both new and existing structures.

Probability of the Critical Length of a Fatigue Crack Occurring at the Tooth Foot of Cylindrical Geared Wheels of the Drive System of a Fiomax 2000 Ring Spinner

In the present paper, we describe a method of determination of the probability of reaching the critical crack length at the tooth root of the cylindrical geared wheels of the drive system of the Fiomax 2000 ring spinner. The Paris-Erdogan formula was utilised for calculations of the fatigue crack length depending on the number of load cycles. Experimental investigations were performed on cylindrical geared wheels. The wheel specimens were manufactured from 1.6523 steel (UE) according to a technical specification relevant to the drive system of the ring spinner. The experiments were performed using a professional pulsator (pulsating test machine). Based upon the experiments (series of 12 tests), material constants and were calculated. These parameters were utilised in the Paris law of crack propagation for further calculations. Moreover it was also ascertained that these unknowns are related via the deterministic relationship. Therefore a function allowing for approximation of constant in dependence on exponent m was derived. In the next step, for the values of parameter chosen – belonging to the variability interval, established from experimental data – we determined the times of reaching the critical length of the fatigue crack. It was stated that the best approximation distribution describing the simulated random values of times of reaching the critical length of the tooth crack for the drive system of the ring spinner is the asymptotic Gumbel’s distribution. Knowing the distribution and number of cycles until reaching the critical crack length at the tooth root, one can evaluate the fatigue life of the damaged wheel in the ring spinner (Fiomax) drive system for the assumed probability. The goal of the present paper is evaluation of the working time of the elements of the drive system of a ring spinner until the occurrence of damage. The highest fatigue life of geared wheels was achieved within the interval (4.3 – 4.5)x 105 cycles. However, it is recommended to change of the geared wheel in case of the spotting of early symptoms of defect. For the stretching apparatus, the authors of the present paper suggest the exchange of the idler geared wheels at least once per year.

Strain modal analysis and fatigue residual life prediction of vibrating screen beam

The displacement and strain modal analysis of vibrating screen beam is carried out, the results show that the relative deviation of the modal frequencies between intact and damaged beam is small, the displacement mode shapes of the damaged beam have no obvious variation, but the strain mode shapes have mutation peaks at the damaged location for the damaged beam. Therefore, a damage index is defined as the rate of strain modal change between damaged and intact beam. The rate of strain modal change increases with the increasing damage extent of the beam. The initial fatigue crack length is related to the damage extent of the beam; the fatigue crack propagation residual life of the beam is predicted by the Paris law. The results show that the rate of strain modal change is a sensitive and reliable damage index for indicating the damage location and damage extent. The predictions of the damage extent and the crack propagation residual life of the vibrating screen beam are beneficial to dynamic optimization design, which can improve the service life of the vibrating screen.

Non‐destructive evaluation of fatigue damage and fatigue crack initiation in type 316 stainless steel by positron annihilation line‐shape and lifetime analyses

AbstractRotating bending fatigue tests were conducted using type 316 stainless steel. The fatigue tests were periodically terminated, and fatigue damage and fatigue crack initiation were non‐destructively and sequentially evaluated by positron annihilation line‐shape and lifetime analyses. The counter‐jig and anticoincidence methods were used for positron annihilation line‐shape and lifetime analyses, respectively, to enhance the analytical precision. The fatigue crack lengths were monitored by a plastic replication technique, and related to the parameters in both analyses. S‐parameter obtained in the line‐shape analysis increased with increasing fatigue damage, while it was difficult to detect fatigue crack initiation and subsequent small fatigue crack growth. That was because the precision of line‐shape analysis was limited. On the other hand, both fatigue damage and fatigue crack initiation were successfully detected by lifetime analysis. Positron annihilation lifetime also increased with increasing fatigue damage, and lifetime was longer at the notch root with fatigue crack than at the smooth section without crack. It was considered that the precision of lifetime analysis was high enough to detect high dislocation density areas at the fatigue crack tips.

Dynamic Model for Fatigue Evolution in a Cracked Beam Subjected to Irregular Loading

The coupling of vibration and fatigue crack growth in a simply supported uniform Euler–Bernoulli beam containing a single-edge crack is analyzed. The fatigue crack length is treated as a generalized coordinate in a model for the mechanical system. This coupled model accounts for the interaction between the beam oscillations and the crack propagation dynamics. Nonlinear characteristics of the beam motion are introduced as loading parameters to the fatigue model to match experimentally observed failure dynamics. The method of averaging is utilized both as an analytical and numerical tool to: (1) show that, for cyclic loading, our fatigue model reduces to the Paris' law and (2) compare the predicted fatigue damage accumulation with the experimental data for chaotic and random loadings. A utility of the fatigue model is demonstrated in estimating fatigue life under irregular loadings.

Mechanical-probabilistic evaluation of size effect of fatigue life using data obtained from single smooth specimen: An example using Fe-30Mn-4Si-2Al seismic damper alloy

Abstract A recently developed high Mn austenitic steel damper was found to show an excellent low-cycle fatigue resistance, irrespective of specimen size. To explain the robustness against specimen size, this study proposes a probabilistic prediction method for the effect of specimen size on fatigue life. In the present study, a Fe-30Mn-4Si-2Al model austenitic alloy that shows a superior low-cycle fatigue property was used as a case study. The prediction method is based on the measurement results of the rate of fatigue subcrack propagations, which are separated into two parts: small and large fatigue crack propagations. An important aspect of the prediction is the scatter characteristics of the small and large fatigue crack propagations; the former showed a large scatter in the propagation rate data, while the latter did not show large scatter data. Based on the scatter, two characteristic crack lengths were introduced in the probabilistic analyses: a) a boundary, l 0 , for small and large fatigue crack propagations, and b) a critical fatigue crack length for fracture, l f . Moreover, the effect of specimen size on the small fatigue crack propagation scatter was estimated using a Poisson distribution. The effect of specimen size on the large fatigue crack propagation part was estimated by an exponential approximation of the relationship between fatigue crack length and number of cycles after the l 0 . In addition, the boundary condition between the fatigue crack propagation and the fracture was determined using the critical fatigue crack length for fracture obtained from a fractograph. According to our prediction model, the small fatigue crack propagation lives decreased with an increase in the specimen size, and the large crack propagation lives increased with an increase in the specimen size.

Stochastic modelling and optimum inspection and maintenance strategy for fatigue affected steel bridge members

This paper presents a method for stochastic modelling of fatigue crack growth and optimising inspection and maintenance strategy for the structural members of steel bridges. The fatigue crack evolution is considered as a stochastic process with uncertainties, and the Gamma process is adopted to simulate the propagation of fatigue crack in steel bridge members. From the stochastic modelling for fatigue crack growth, the probability of failure caused by fatigue is predicted over the service life of steel bridge members. The remaining fatigue life of steel bridge members is determined by comparing the fatigue crack length with its predetermined threshold. Furthermore, the probability of detection is adopted to consider the uncertainties in detecting fatigue crack by using existing damage detection techniques. A multi-objective optimisation problem is proposed and solved by a genetic algorithm to determine the optimised inspection and maintenance strategy for the fatigue affected steel bridge members. The optimised strategy is achieved by minimizing the life-cycle cost, including the inspection, maintenance and failure costs, and maximizing the service life after necessary intervention. The number of intervention during the service life is also taken into account to investigate the relationship between the service life and the cost for maintenance. The results from numerical examples show that the proposed method can provide a useful approach for cost-effective inspection and maintenance strategy for fatigue affected steel bridges.

Fatigue cracking detection in steel bridge girders through a self-powered sensing concept

Development of fatigue cracking is affecting the structural performance of many of welded steel bridges in the United States. One of the main sources of fatigue cracking is out-of-plane distortion occurring at connections of transverse structural members and longitudinal girders. Distortion-induced fatigue cracks mostly occur in older bridges with members prone to fatigue. Prediction of secondary stresses in these members is difficult using conventional design specifications. This limitation suggests the necessity of utilizing new strategies to analyze the damage caused by distortion-related cracking. This study presents a new approach for detection of distortion-induced fatigue cracking of steel bridges based on the interpretation of the data provided by a newly developed self-powered piezo-floating-gate (PFG) sensor. The PFG sensors are empowered using piezoelectric transducers through harvesting energy from the mechanical loading experienced by the structure. In order to assess the performance of the proposed sensing system, three-dimensional finite element models were developed and the structural response of the girder was subsequently obtained. The fatigue life of the girder was determined based on J-integral concept and Paris Law. Several damage states were defined by extending the fatigue crack lengths. Thereafter, features representing the PFG sensor output were extracted from the strain data for different sensing nodes to detect the damage scenarios. Furthermore, a new data fusion concept based on the effect of group of sensors was proposed to improve the damage detection performance. The results indicate that the proposed method is capable of detecting different damage progression states. This is specifically evident for the sensors that are located close to the damage location. The acceptable performance of the proposed sensing system implies its applicability for other modalities of infrastructure/structural health monitoring (I/SHM).

Experimental determination of J-resistance curves of nuclear steam generator tubes

The experimental determination of room temperature J-resistance curves of thin walled Incoloy 800 nuclear steam generator tubes was studied. Different non-standard specimens’ geometries were considered, including circumferential and longitudinal trough-wall cracks. J-integral values were estimated using the η-factor method from the experimental load vs. LLD and CMOD displacement records. Circumferential cracks led to higher J-resistance curves than longitudinal cracks indicating a degree of anisotropy in the fracture properties. Low constraint conditions promoted by predominant tensile loadings gave higher J-resistance curves than bending configurations. Details associated with the fatigue pre-cracking procedure and crack length monitoring along the tests are presented.

Analysis of fatigue behaviour of stainless steels under hydrogen influence

Three stainless steels – ASTM 304, 316 and 316L - used in hydrogen utilization equipment are under investigation at conditions of tension-compression, rotating-bending and fretting fatigue. Fatigue tests are carried out with hydrogen charged and uncharged specimens. Hydrogen charging includes cathodic type of charging and exposure to high pressure hydrogen gas. The experiments under rotating bending and tensioncompression fatigue are conducted under different frequencies in three different laboratories: at The University of Chemical Technology and Metallurgy, Sofia, Bulgaria; at Sandia National Laboratory, California and The University of Tufts, Medford, Massachusetts, USA; The HYDROGENIUS Institute at Kyushu University, Japan. The fretting fatigue tests are presented by The HYDROGENIUS Institute at Kyushu University, Japan. The obtained results are presented in Wohler curves complemented by plots Short fatigue crack length– Number of cycles and “Tangential force coefficient–Stress amplitude”. The found fatigue characteristics are analyzed and compared at different loading conditions, showing the best performance of Steel 316L.

Determination of Paris' law constants and crack length evolution via Extended and Unscented Kalman filter: An application to aircraft fuselage panels

Prediction of fatigue crack length in aircraft fuselage panels is one of the key issues for aircraft structural safety since it helps prevent catastrophic failures. Accurate estimation of crack length propagation is also meaningful for helping develop aircraft maintenance strategies. Paris' law is often used to capture the dynamics of fatigue crack propagation in metallic material. However, uncertainties are often present in the crack growth model, measured crack size and pressure differential in each flight and need to be accounted for accurate prediction. The aim of this paper is to estimate the two unknown Paris' law constants m and C as well as the crack length evolution by taking into account these uncertainties. Due to the nonlinear nature of the Paris' law, we propose here an on-line estimation algorithm based on two widespread nonlinear filtering techniques, Extended Kalman filter (EKF) and Unscented Kalman filter (UKF). The numerical experiments indicate that both EKF and UKF estimated the crack length well and accurately identified the unknown parameters. Although UKF is theoretical superior to EKF, in this Paris' law application EKF is comparable in accuracy to UKF and requires less computational expense.

Development of fatigue prediction model for steel bridges based on characteristics of variable stress spectra

The fatigue life prediction of steel bridges depends on the amplitude, stress ratio, stress interaction (stress order), and frequency of variable stress spectra. The stress interaction is always altering the crack growth rate under the application of variable stress spectra. The random nature of variable stress spectra makes it difficult to model all these influential parameters correctly. In this study, the fatigue prediction model of steel bridges based on linear elastic fracture mechanics was developed by using measured variable stress spectra of three steel bridges. Variable stress spectra data are used to calculate and analyze the entropy index of stress interaction and crack severity index (CSI) of the effective stress associated with the characteristics of the variable stress spectra. Using these results, the results of fatigue analysis, and multiple regression, we develop prediction models for entropy index–CSI–fatigue crack length, average daily truck traffic (ADTT)–CSI–fatigue crack length, and ADTT-entropy-fatigue crack length. These models can predict the fatigue life of a bridge structure, and this information can be used to plan lifetime maintenance for similar bridges with variable stress spectra.

Fatigue Crack Growth in Specimens with Rectangular Section under Torsion and Bending with Torsion

The paper presents the test results on the fatigue crack growth under torsion and proportional bending with torsion in the aluminium alloy EN AW-2017A-T4. The tests were performed at the fatigue test stand MZGS-100 at the constant amplitude of moment MB = MT = MBT = 15.84 N⋅m and stress ratio R = -1. Plane specimens with stress concentrators in form of the external one-sided blunt notch were tested. The results of experiments were described on graphs of the fatigue crack length „a” versus numbers of cycles N. A non-uniform fatigue cracks growth on both lateral surfaces of specimens was observed during experimental tests.

Experimental examination of fatigue life of welded joint with stress concentration

This paper presents results of experimental examinations of stress concentration influence to fatigue life of butt welded joints with K-groove, produced from the most frequently used structural steel S355J2+N. One group of experiments comprised examinations carried out on the K-groove specimens with stress concentrators of edged notch type. Specimens with short cracks (limited length of initial crack), defined on the basis of the experience from fracture mechanics by the three points bending examinations, have been examined according to standard for the determination of S-N curve, and aimed to determine fatigue strengths for different lengths of initial crack and Relationship between fatigue strength and crack length. Other group of experiments comprised examinations of specimens with edge notch, prepared in accordance with ASTM E 399 for three points bending, in order to establish regularity between crack growth and range of exerted stress intensity factor aimed to determine resistance of welded joint to initial crack growth, namely fatigue threshold

Effect of Carbon on the Microstructural Evolution and Thermal Fatigue Behavior of a Ni-Base Superalloy

The effect of carbon content on the microstructural evolution and thermal fatigue behavior of Ni-Cr-Fe-Mo alloy with different carbon content was carried out at temperature ranging from 20°C to 920°C. The microstructure evolution was detected and the length of thermal fatigue cracks was measured. The results revealed that all the alloys are mainly composed of γ phase and carbides. With the increase of carbon content, the volume fraction of carbides increase and the morphology varies from blocky to script-like and sheet-like. The microstructural features exert influence on the thermal fatigue cracks of the alloys with different carbon content. Considering the thermal fatigue properties, the optimum carbon content of the Ni-Cr-Fe-Mo alloy superalloy should be below 0.08wt.%.

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.