Fatigue Crack Growth Process Research Articles

Machine Learning Based Prognostics of Fatigue Crack Growth in Notch Pre-cracked Aluminum 7075-T6 Rivet Hole

Constant stress amplitude fatigue tests were conducted on the notch pre-cracked Aluminum 7075-T6 rivet hole dog-bone coupons. Monitoring of visible surface crack length by special surface engraving using digital microscope images and by ultrasonic sensors signals was carried out to yield fatigue crack length measurements in relation to number of fatigue cycles applied. The experimental results provide ultrasonic sensor validation for fatigue crack length measurements. Fracto-graphic examination of failed fatigue surfaces has provided further confirmation of notch pre-crack length, crack initiation process, and crack growth marker bands. These experimental inputs were used in NASGRO and AFGROW software fatigue crack growth simulations. The simulation results did not match the crack initiation fatigue life measured by experiments. However, there was good agreement with crack growth simulations of larger cracks. Hence, we plan to develop a machine learning application that will learn the fatigue crack initiation and crack growth processes from data obtained from our own experiments and other fatigue data available from AFGROW databases. Nonlinear AutoRegressive models with eXogenous input (NARX) artificial neural network were used to predict crack growth longer than 5.0-mm. Particle filtering modeling with Bayesian updating was applied to these experimental data for prognostics of fatigue crack growth. A concept design and preliminary implementation results will be presented.

Energy response of S355 and 41Cr4 steel during fatigue crack growth process

In this research, a novel approach of the fatigue crack growth rate description has been proposed. Based on theoretical and experimental approach, the mean stress effect expressed by R-ratio is present in classical da/dN–Δ K diagram. According to energy approach – based on the irrevocably dissipated energy accumulated in material (hysteresis loop) during fatigue process – the mean stress effect can be minimalized. Experimental validation of the proposed model was performed using results of fatigue crack propagation data for S355 and 41Cr4 steels in terms of strain energy density parameter Δ S or cyclic J-integral range –Δ J. In contrast to the force approach based on Kmax (or Δ K), the energy parameters Δ S or Δ J represent unambiguously the fatigue crack propagation rate, without influence of mean stress effect – R-ratio. However, in near threshold range of kinetic fatigue fracture diagram, the energy parameter displays a slight dispersion of the experimental data. According to the crack closure theory and its U-Elber parameter, the dispersion of experimental data is decreased. Therefore, the crack closure effects have a high significance in energy model – similar to the ‘force approach’ based on Δ K concept.

Probabilistic Fatigue Crack Initiation and Propagation Fields Using the Strain Energy Density

The fatigue crack growth (FCG) has been widely studied by the scientific community. There are several proposed FCG models, the best known being the Paris relation. The fatigue crack initiation and propagation have been studied separately, however, researchers have made an effort to study the relationship between these two fatigue phenomena. In this sense, several fatigue crack growth models based on local approaches have been proposed, the UniGrow model being well-known. The fatigue crack growth process is assumed a succession of crack re-initiations considering a certain elementary material size. Recently, Huffman developed a strain energy density based on Walker-like stress life and fatigue crack growth behavior. In this paper, the Huffman model based on local strain energy density is used to predict the fatigue crack initiation and propagation for the P355NL1 pressure vessel steel. This model is combined with the generalized probabilistic fatigue model proposed by Correia aiming the generation of probabilistic fatigue crack initiation and propagation fields. In this study, the local stress and strains at the crack tip were obtained combining linear-elastic and elastoplastic analyses. The probabilistic fatigue crack growth rates fields for several stress R-ratios are estimated considering strain, SWT, and equivalent stress amplitude damage parameters. A comparison between the experimental FCG data and the generated probabilistic FCG fields is made with very satisfactory correlations being found.

Effect of cavitation intensity on degradation of X6CrNiTi18-10 stainless steel

An influence of cavitation intensity on degradation mechanism of X6CrNiTi18-10 stainless steel has been presented. Investigations have been carried out at various inlet and outlet pressures in a chamber with a system of barricades. Regardless of the test conditions, erosion of the tested steel started with high erosion rate and then decreased indicating on very aggressive cavitating flows. The minimum erosion rate was within a very narrow range, showing little dependence on the inlet pressure, but showing dependence on other processes: the phase transformation and/or the work-hardening process. After 600 min of exposition, the steel was in various erosion stages which were related to the inlet pressure. Degradation of X6CrNiTi18-10 steel was dominated by the process of fatigue crack growth in the surface layer. Slip bands and cracks, as well as voids and dimples were formed, which reduced strength of the exposed surface layer. Hydrodynamic cavitation causes uneven distribution of the erosion over the steel surface, which has been demonstrated by roughness measurements. Roughness measurements also enable visualization of the location, shape and topography of the aggressive and non-aggressive zones. The experimental data shows that the volume loss in a cavitation test fulfills the Paris-Erdogan law in a following form: ∆V(t)=C′(t)∙(v−v0)n(t), where C’(t) and n(t) are the time-dependent functions related to the degradation of the surface layer, v is the flow velocity during the test, v0 is the flow velocity, at which cavitation erosion is initiated.

An energy dissipation-based fatigue crack growth model

This paper presents a local approach to analyze the fatigue crack growth rate (FCGR) through the characterization on the dissipative process of fatigue crack tip zone. An energy dissipation-based FCGR model is established, and a dedicated thermographic method for dissipated energy assessment in the cyclic plastic zone is developed. Fatigue crack growth tests are conducted on the 316L steel under the varied stress ratios. The results demonstrate that the fatigue crack growth process can be well characterized by the near-tip energy dissipation. The proposed FCGR model shows, however, an unexpected stress-ratio-dependence. This dependence is analyzed by the crack closure effect, and the FCGR model is improved by introducing an effective energy dissipation rate concept.

Fatigue crack growth in a compressor stage of a turbofan engine by FEM-DBEM approach

In this work, the fatigue crack-growth process in a rotating disk of an aircraft gas turbine engine has been simulated. The considered crack nucleated in the attachment between a blade and the disk of a compressor stage, both made of a two-phase titanium alloy.The fatigue crack-growth process of such crack has been simulated by means of two codes, ABAQUS and BEASY, based on Finite Element Method (FEM) and Dual Boundary Element Method (DBEM) respectively. In particular, a variant of the submodelling technique, based on the superposition principle, has been used for coupling the two codes in order to exploit simultaneously their peculiar strength points. The FEM code has been used to compute the global stress field whereas the DBEM code has been used to calculate the fracture parameters, useful to predict the crack-growth evolution. The J-integral method and the Minimum Strain Energy Density Criterion (MSED) have been used for calculating K values and predicting crack kinking respectively.In this work, the FEM-DBEM crack path is compared with both the path obtained by a full-scale experimental test and the path predicted via a full FEM approach: having in an initial stage considered the only centrifugal load, with no allowance e.g. for the fluid pressure on the blades and for the blade dynamic behaviour, some discrepancies are found between numerical and experimental results.The computational advantages of the proposed submodelling approach are highlighted, in addition to a preliminary fatigue assessment provided for the considered compressor disk (further analyses are under development).

An accurate and efficient algorithm for the simulation of fatigue crack growth based on XFEM and combined approximations

This study aims to reduce the computational cost in the simulation of fatigue crack growth process. Extended finite element method and combined approximations (CA) are integrated to form an efficient algorithm for such analysis. In the CA approach, binomial series are used as high quality basis vectors for the reduced basis expression and then crack propagation path can be predicted without solving the complete set of system equations. The validity of presented algorithm is fully investigated through several numerical examples. From these results, it is shown that the presented algorithm is very accurate and can save huge amounts of computational effort.

Effect of Low-Cycle Fatigue on Fracture Mechanics Parameters According to Speckle Interferometry

Evolution of parameters of fracture mechanics at various stages of low-cycle damage is studied. The developed approach is based on elaboration of optical interference measurements of the deformation response to a small crack length increment. Three sequential symmetrical notches simulate the fatigue crack growth process across the cumulative fatigue damage zone caused by low-cycle fatigue. The values of tangential components of displacement that are measured at several points on cut edges by electronic speckle interferometry are initial experimental information. The coefficients of stress intensity (SIC) and T strains are determined on the basis of the Williams solution. Values of opening and coefficients of stress intensity (SIC) and T strains for cracks of different length with fixed values of preloading cycles Nc equal 0, 100, 1000, 1800, 2500, and 3300 are obtained. The dependences of the parameters of fracture mechanics for cracks of the fixed length on Nc are constructed.

Fatigue crack growth modeling and prediction with uncertainties via stochastic perturbation series expansion method

The fatigue crack growth process is characterized by uncertainties inherent to the variations in geometrical properties, material properties, and operating conditions. This paper proposes a novel stochastic perturbation series expansion method for predicting fatigue crack growth evolution which accounts for uncertain parameters. Unlike the deterministic method, the parameters of the crack growth model are considered to be stochastic with perturbation terms. The solution to the crack growth equation is then transformed into a perturbation series after introducing said small parameters. A series of modified differential equations for predicting the stochastic characteristics of the crack length history are derived via first-order Taylor series expansion method. The initial crack length under perturbation can be expressed via the artificial small parameter method per the measurement errors. Further, by substituting the initial conditions into the modified stochastic equations, variations in the mean value and standard deviation as well as the probabilistic region of crack length history can be successfully obtained. The performance of the proposed method is evaluated through two examples. Comparison against experimental and Monte-Carlo simulation data confirm that the proposed method is indeed feasible and effective for predicting fatigue crack growth evolution with consideration of stochastic uncertainties.

Statistical distribution for initial crack and number of loading in fatigue crack growth process

Statistical distribution for initial crack and number of loading in fatigue crack growth process

Residual stress effects of a fatigue crack on guided lamb waves

Structural health monitoring has focused on the use of computational models to capture the effect of crack-like discontinuities on the behaviour of acoustic-ultrasonic signals. However, few models have taken into account the effect of geometric complexity in combination with residual stresses generated during the fatigue crack growth (FCG) process. In this study, a finite element analysis model of a C-channel type aeronautical structure is evaluated under a pitch-catch scenario. Three different finite element model configurations were considered in order to understand the effects that residual stresses of a fatigue crack emanating from a through-hole have on the guided Lamb wave propagation behaviour. The results demonstrate that numerical modelling is able to capture the change in amplitude and the effect of a phase shift on the guided Lamb wave behaviour due to the presence of the discontinuity and the stress field generated during the FCG process.

Effects of transitional functions on multiscale fatigue crack growth

Transitional functions are the reflection of combined effects of material, loading and geometry through the process of fatigue crack growth. They are incorporated in the segmented multiscale model. Based on the formulated multiscale fatigue crack growth model, effects of transitional functions on the crack growth behaviors of superalloys are discussed. Considering the inevitable assumption on the three transitional functions, the uncertainties of coefficient variation remains to be clarified. Material, loading and geometry effects are separately studied on the basis of collected test data of 2024-T3 Al sheet. Consequently, three transitional functions are optimally determined. These findings offer a new perspective of combined material, loading and geometry effects on crack growth behaviors of superalloys.

Kinetics of fatigue crack growth and crack closure effect in long term operating steel manufactured at the turn of the 19th and 20th centuries

In this paper the fatigue crack growth behaviour in structural components from the old 19th century structures (e.g. bridges) has been investigated. The delivered material for investigation was extracted from a beam made of puddled iron, commonly used in the 19th century. The obtained results from several ancient railway metallic bridges (located in Lower Silesia, Poland) have shown the presence of microstructural degradation processes in puddled iron. The kinetic fatigue fracture diagrams (KFFD) have been obtained for post-operated steel. The problem of crack closure has been involved in fatigue crack growth process during the experiments and its understanding is fundamental for the analysis of stress ratio effects on KFFD. An experimental and numerical approach has been considered for the evaluation of the crack closure/opening forces based on the hysteresis loop deformation. The implemented algorithm in the numerical environment gives promising results in the description of the kinetics of fatigue crack growth of the old metallic materials with consideration of crack closure effects. The problem of fatigue crack growth rate description from the energy point of view has been presented and discussed. The Universal Graph method (based on Dimensional Analysis approach) was used for phenomenological formulation of the kinetic equation.

A multiscale approach for modeling fatigue crack growth in concrete

A linearized stress intensity factor (SIF) is derived for concrete through a multiscale approach by considering the predominant process zone mechanisms such as aggregate bridging and microcracking. This is achieved by considering a bridging zone and a microcrack at the macrocrack tip. The bridging zone resists the crack growth through aggregate bridging mechanism. The SIF thus derived is further used in developing an analytical model which predicts the entire crack growth curve for plain concrete by making use of the concepts of dimensional analysis and self similarity in conjunction with the human population growth model. This model is validated using experimental data reported on normal strength, high strength and self consolidating concrete. Through sensitivity analyses it is shown that the specimen size plays an important role in the fatigue crack growth process of concrete.

Energy description of fatigue crack growth process - theoretical and experimental approach

The aim of the paper is the presentation of the energy methods in description of the fatigue crack growth rate (FCGR) process in structural steel components. In the literature and engineering practice, the ΔK – approach is preferred in construction of the FCGR diagrams. One of the main disadvantages of force approach, is a mean stress effect, reflected in a well-known stress R-ratio effect on FCGR. The second disadvantage seems to be inconsistency in closure estimation with ΔK and description only in the linear-elastic range. In this paper, two energy approaches are presented – ΔH and ΔJ. The kinetic equations based on energy parameters, describe synonymously the kinetics of fatigue crack growth under uniaxial fatigue loading. It has been demonstrated, that the energy description – based on dissipated strain energy density – ΔH is independent from R-ratio. All theoretical and numerical calculations based on ΔJ, ΔH strain energy density parameters were compared with experimental results obtained for different type of alloys.

Improvement of the fatigue crack growth resistance in long term operated steel strengthened with CFRP patches

The maintenance of the old steel structures is one of the main challenges in engineering practice – mainly due to the lack of the experimental data performed for existing old steel structures erected at the turn of the 19th and 20th centuries. In this paper the fatigue crack growth behavior in structural components from the old 19th (and early 20th) centuries structures (e.g. bridges) has been investigated. The delivered material for investigation was extracted from a beam made from puddled iron and mild rimmed steel, commonly used 100 years ago. It has been confirmed in author's experimental works, that the fatigue crack growth rate in this ancient type of steel is higher than in its modern equivalent. One of the fundamental engineering task is the problem of the extension of the pre-critical fatigue crack growth in such a type of steel. One of the promising approach is hybrid approach (experimental-numerical) based on the additional energy dissipation mechanisms in fatigue crack growth process. One of the successful strengthening method is the CFRP (Composite Fiber Reinforced Polymer) patching along the fatigue crack paths. The presented approach has been studied and discussed in this paper on the background of the numerical and experimental data. As it was expected, the proposed strengthening method is efficient and promising in case of the “immediate” repairs of critical members with cracks

Multiple Failure Modes Reliability Modeling and Analysis in Crack Growth Life Based on JC Method

The fatigue crack growth (FCG) phenomenon generally exists in large mechanical structures. Due to the influences of varied kinds of random factors, the safety evaluation of structure in FCG is under great uncertainty. In this paper, based on the reliability theory, the limit state equations of fracture failure and static strength failure were derived firstly, and the parameters in those equations were regarded as random variables that follow the normal distribution or log‐normal distribution. According to the limit state equations, the JC method (equivalent normalizing method) was used to calculate the reliability indexes under the different failure modes of structure in every stress cycle. Based on the reliability indexes and correlation of the two failure modes, the joint failure probability was obtained. In the end, a specific computation example was given, and the curve of joint failure probability in multiple failure modes was used for comparison with the result of single failure mode. The results indicated that the reliability analysis based on multiple failure modes was more reasonable, and the evaluation of reliability could be obtained in fatigue crack growth process.

Non-destructive observation of the internal fatigue crack initiation and growth process in Ti-6Al-4V using synchrotron radiation micro-CT

Non-destructive observation of the internal fatigue crack initiation and growth process in Ti-6Al-4V using synchrotron radiation micro-CT

Fatigue crack growth modelling for pipeline carbon steels under gaseous hydrogen conditions

A corrosion-crack correlation model is proposed for the hydrogen embrittlement (HE) influenced fatigue crack growth modelling of pipeline carbon steels under gaseous hydrogen conditions. The model is developed primarily based on the correlation of environment-affected zone (EAZ) and plastic zone. In the model, fatigue crack growth rate is predicted by Forman equation to take into account the influence from fracture toughness. The critical frequency and the “transition” stress intensity factor (SIF) are derived based on stress-driven hydrogen diffusion and Hydrogen-Enhanced De-cohesion (HEDE) hypothesis, which provides reasonable explanation on the frequency dependence of fatigue crack growth for pipeline carbon steels in hydrogen gas. Furthermore, an approximation formula involving threshold the SIF range and the stress ratio is established to describe the phenomenon of crack growth rate plateau. In addition, a formula is proposed to estimate the equilibrium fracture toughness according to the equilibrium between crack growth and hydrogen delivery rates. A series of experimental data from different grades of carbon pipeline steels (including high-strength grades such as X70 and X80) are utilized for demonstrate the validity of the proposed formulae and model effectiveness. The comparison between model predictions and experimental data shows that the proposed model is capable of capturing the essence of pipeline carbon steels’ fatigue crack growth process under gaseous hydrogen conditions.

Fatigue crack growth in an aluminum alloy-fractographic study

A two-fold approach was adopted to understand the fatigue crack growth process in an Aluminum alloy; fatigue crack growth test of samples and analysis of fractured surfaces. Fatigue crack growth tests were conducted on middle tension M(T) samples prepared from an Aluminum alloy cylinder. The tests were conducted under constant amplitude loading at R ratio 0.1. The stress applied was from 20,30 and 40 per cent of the yield stress of the material. The fatigue crack growth data was recorded. After fatigue testing, the samples were subjected to detailed scanning electron microscopic (SEM) analysis. The resulting fracture surfaces were subjected to qualitative and quantitative fractographic examinations. Quantitative fracture analysis included an estimation of crack growth rate (CGR) in different regions. The effect of the microstructural features on fatigue crack growth was examined. It was observed that in stage II (crack growth region), the failure mode changes from intergranular to transgranular as the stress level increases. In the region of intergranular failure the localized brittle failure was observed and fatigue striations are difficult to reveal. However, in the region of transgranular failure the crack path is independent of the microstructural features. In this region, localized ductile failure mode was observed and well defined fatigue striations were present in the wake of fatigue crack. The effect of interaction of growing fatigue crack with microstructural features was not substantial. The final fracture (stage III) was ductile in all the cases.