Fatigue Crack Growth Law Research Articles

Study on the synergistic effect of welding residual stress and hydrogen diffusion on fatigue crack growth of X80 steel pipeline

During the service of X80 high-strength pipeline steel, the combined effects of welding residual stress, cyclic loading, and hydrogen complicate the prediction of pipeline fatigue life. This article combines ABAQUS and FRANC3D finite element software to analyze the fatigue crack growth laws of the X80 pipeline with thickness of 22 mm under the combined condition. After heat treatment, the fatigue life of pipelines with annular and axial cracks increased by 19 % and 83 %, indicating that post-weld heat treatment significantly improves the fatigue life of the pipeline. When the crack grows to the outer surface of the pipeline, the fatigue life of a pipeline with a 10 % hydrogen doping ratio is reduced by 77 % compared to one with a 1.5 % hydrogen doping ratio. These findings indicate that toughness of the crack front region is significantly reduced by hydrogen concentration, the crack propagation rate is accelerated, and the fatigue life of the pipeline is significantly reduced.

Comparison of fatigue crack growth design curves on GMAW and EBW joints of high strength steels

There is a growing demand in the industrial sector for the use of high-strength structural steels (HSSSs), which can achieve a significant weight reduction in structures. These structural steels are usually produced by quenching and tempering (Q + T) or thermomechanical treatment (TM), and their applications in welded structures pose several challenges for the users. In industrial practice, gas metal arc welding (GMAW) is basically the most commonly used fusion welding process, which has a relatively high heat input. However, at HSSSs, there is a need for low heat input but, at the same time, productive welding processes. High-energy density welding processes, e.g., electron beam welding (EBW), offer a unique opportunity to weld these steels. The widespread use of HSSSs is also hampered by the fact that the benefits of high strength can be exploited primarily under static loading. At the same time, different welded structures made of HSSSs are often subjected to cyclic loading, and possible weld defects and material discontinuities are major risks in this case. During our experiments, GMAW and autogenous EBW processes were applied to make welded joints from S960 Q + T and TM structural steels. The fatigue resistance of the welded joints was characterized by fatigue crack growth (FCG) tests, considering the increased crack sensitivity of HSSSs. A statistical approach was followed both in the design of the experiments and in the evaluation of their results. Based on the test results fatigue crack propagation design curves were determined for the investigated GMAW and EBW welded joints. The design curves were compared with each other, with design curves of lower strength material (S690QL) and with the recommended fatigue crack growth laws of BS 7910.

Experimental, Analytical, and Computational Studies on the Fatigue Crack Growth Behavior of a Titanium Alloy under Cold-Turbistan Spectrum Loads

Abstract The fatigue crack growth (FCG) behavior of Ti-6Al-4V alloy subjected to spectrum loads was experimentally determined and compared with predicted behavior by analytical and computational methods. In the experimental method, a compact tension (CT) specimen of Ti-6Al-4V was tested under standard cold-Turbistan spectrum loads to determine crack propagation behavior. Spectrum fatigue tests were conducted with triangular waveform at 2 Hz. In the analytical predictive method firstly, constant amplitude FCG tests were conducted at several stress ratios and a unified FCG law based on crack driving force, K* was derived for Ti-6Al-4V alloy. Then, the crack growth for every rainflow-counted fatigue load cycle in the cold-Turbistan sequence was determined using the derived FCG law. In the computational method, a global and a local model of the CT specimen of Ti-6Al-4V were created in HYPERMESH and FRANC3D, respectively. The FCG behavior under the cold-Turbistan spectrum was then predicted using FRANC3D and MSC NASTRAN. The required materials constants for the FCG law in the FRANC3D software were derived from the experimental constant amplitude FCG rate data of Ti-6Al-4V alloy. It was observed that both methods of FCG predictions, i.e., analytical and computational methods, although conservative, compared quite well with experimental results.

Correlating stress ratio effects on the fatigue crack growth rate behavior of a nickel-based superalloy GTM718

Damage tolerance evaluation under service loads requires a unified constant amplitude fatigue crack growth law for the material which takes care of stress ratio effects. Several types of crack driving force parameters have been proposed in the past to correlate stress ratio effects on fatigue crack growth rates. In the present investigation, a unified crack growth law is derived for a nickel-based superalloy by considering various crack driving force parameters to eliminate stress ratio effects. Initially, the constant amplitude fatigue crack growth rate (FCGR) behavior of GTM718 alloy was experimentally determined at various stress ratios, R ranging from R = 0.1 to 0.7. As expected, increasing the stress ratio, increased crack growth rates, and decreased threshold stress intensity factor range, ΔKth. The conventional crack growth rate, da/dN vs stress intensity factor range, ΔK data was then modified and re-plotted as a function of different crack driving force parameters viz., (a) Elber’s parameter, ΔKeff, (b) Walkers’ parameter, Kw (c) Kujawski’s parameter, K*, (d) Forman’s parameter, Kf, and (e) Two-parameter crack driving force, ΔK*. It was observed that Kf and ΔK* crack driving force parameters were correlating stress ratio effects better than other models in all three regimes of crack growth rates. Further, a unified crack growth law was derived based on the Kf and ΔK* crack driving force parameters which is useful in predicting FCG behavior under service loads.

Fatigue crack growth behaviour of wire arc additively manufactured steels

Combining welding technology with robotics, wire arc additive manufacturing (WAAM) is emerging as a viable method of construction. To facilitate its wider application, in particular with structural integrity in mind, an improved understanding of the fatigue properties of WAAM materials is needed. Hence, an experimental investigation into the fatigue crack growth (FCG) behaviour of WAAM plates made of normal- and high-strength steels has been conducted and is reported herein. Following material characterisation, FCG tests on 13 machined compact tension specimens were undertaken, extracted in different directions from WAAM plates built using a parallel deposition strategy. Fractography of the tested specimens was also performed to analyse the mechanisms of crack growth. The material testing demonstrated an approximately proportional relationship between the hardness and ultimate strength. From the FCG tests, Paris’ law constants were derived for the WAAM normal- and high-strength steel specimens, revealing consistently lower material constants m for the latter. Similar FCG behaviour to that of equivalent, conventionally-produced steels, with no significant anisotropy, was found. The observed response was shown to be generally well captured by the FCG laws given in BS 7910, with the recommended curve for unwelded steels providing a close match to the experimental data and the recommended curve for welded steels providing conservative predictions. Additional FCG data on WAAM steels printed using the parallel and oscillatory deposition strategies were collected and analysed. It was shown that the two deposition strategies led to similar crack growth rates for WAAM normal-strength steels, but distinct FCG behavioural trends for WAAM high-strength steels. Finally, the fractographic analysis showed that the WAAM specimens exhibited principally brittle behaviour during FCG but somewhat ductile behaviour before fracture.

Adaptive modeling of vibrations and structural fatigue for analyzing crack propagation in a rotating system

This study is concerned with adaptive modeling of vibrations and structural fatigue in a rotating system with a propagating crack. The system consists of a Jeffcott rotor with a transverse surface crack at mid-span. It undergoes low and high cycle loadings due to an unbalance force. The high cycle loading (HCL) and the consequent high cycle fatigue (HCF) can accelerate crack growth, structural degradation and occurrence of mechanical failure. Therefore, accurate modeling is critical for lifetime prediction and prognostics requirements. There is a significant difference between the time constants of the rotor’s dynamic behavior and that of crack growth. Hence, in most of the prior studies, it has been assumed that the crack depth is constant, which implies that the system undergoes low cycle loading (LCL). In some studies that do focus on HCL, the loading scenario is assumed to be a summation of LCL steps with constant length. This study shows that assuming constant and pre-defined length for these steps can significantly affect the accuracy of the model leading to inaccurate lifetime prediction and poor prognostics in general. Hence, in this study, a novel approach is proposed in which the LCL step length is variable and adaptive. Considering different relationships proposed for modeling the fatigue crack growth, fluctuation of stress intensity factor (SIF) is the most important factor for driving the crack growth. Hence, an index is defined based on the rate of SIF fluctuation. Critical thresholds of this index are set at rapid and slow crack growth conditions. The level of proximity to these thresholds determines each LCL step length, which is hence determined adaptively. The equations governing the rotor motion and crack growth are formulated using Newton’s second law of motion and Paris–Erdogan’s fatigue crack growth law, respectively. The equations are solved numerically using the Runge–Kutta method. It is shown that this novel adaptive approach makes the modeling process realistic and computationally efficient while providing high accuracy. The results of this study could be of significance in decision making processes that would require lifetime prediction and prognostics of crack growth.

Stress intensity factors and fatigue crack growth law of cracked submarine special-shaped pipe under earthquake load

The strength of the elastic stress fields next to crack tip is usually measured by the stress intensity factor (SIF). Unfortunately, There will be different stress singular fields next to corner cracks tip of the special-shaped pipe under earthquake load. J2 integral can only solve the SIFs of same singular stress fields and cannot satisfactorily guide the anti-crack propagation design. Accordingly, based on the bending theory and elementary mechanics, a method of calculating the SIFs of the different stress singular fields and the corner crack growth law of the special-shaped pipe are established in this article. The method would provide a unique view to the calculation of SIFs for similar cracked structures and the design of anti-crack propagation of pipes under earthquake load.

A study on the fatigue crack growth behaviour of GTM718 nickel based super alloy under cold-TURBISTAN spectrum loads

In this study, the fatigue crack growth (FCG) behavior of GTM718 nickel base super alloy subjected to cold-TURBISTAN spectrum load sequence was determined by three different methods i.e., (i) Experimental, (ii) Analytical prediction using cycle-by-cycle method and, (iii) Prediction by finite element analysis (FEA). In the experimental method, a standard compact tension (CT) specimen was prepared and pre-cracked to produce a sharp fatigue crack at the notch root. Then, the specimen was subjected to spectrum load blocks repeatedly and crack growth was measured as a function of applied number of flights. Two such tests were carried out in a servo-hydraulic universal test machine with triangular waveform and at an average frequency of 2 Hz. In the second analytical method, the individual load cycles in cold-TURBISTAN spectrum block were separated through rain flow cycle counting method. For each of this counted cycle, the crack extension was determined using crack growth law which was based on two-parameter crack driving force, ΔK*. An in-house MATLAB code was written and used to determine the FCG behavior by cycle-by-cycle method. In the third FEA method, a global model of CT specimen of GTM718 was created in HYPERMESH and a local model with a pre-crack was created in FRANC3D. The FCG behavior under spectrum load was determined using FRANC3D in conjunction with MSC NASTRAN. Two different types of ‘FCG law - stress ratio effect’ combinations were employed i e., Paris’-Walker (P-W) and Bi-linear-Walker (B-W). The required constants for these laws were derived from the available experimental data of the material. It was observed that the predicted FCG behavior by analytical and FEA methods, although conservative, were fairly good when compared to experimental results.

Predictive fatigue crack growth law of high-strength steels

The fatigue resistance of metallic materials is generally attributed to both strength and toughness. Unfortunately, these properties are mutually exclusive in most materials. Classical theories like Paris’ law only provide some data correlation schemes rather than a predictive capability, which cannot satisfactorily guide the anti-fatigue design. In this study, for the first time, the predictive fatigue crack growth rate law is proposed by considering the effects of both strength and toughness. Accordingly, a quantitative criterion is established for judging the fatigue crack resistance of high-strength steels. The predictive law would provide a unique view to the quantitative anti-fatigue design of metallic materials.

An inverse method to reconstruct crack-tip cohesive zone laws for fatigue by numerical field projection

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loadings, but the functional form of such phenomenological models does not have a strong micromechanical basis. While numerical techniques have been developed to extract the crack-tip cohesive zone law for monotonic fracture from experimental strain information, elucidating the unloading-reloading hysteresis representing accumulated and irreversible damage under fatigue cycling is still challenging. Here, we introduce a novel field projection method (FPM) to reconstruct the cohesive zone laws for steady-state fatigue crack growth from elastic strain field information at various loading and unloading stages within a single steady-state fatigue cycle. The method is based on the Maxwell-Betti’s reciprocal theorem, which considers the material response to be linear elastic during loading and unloading, albeit with a reciprocity gap to account for the inhomogeneous residual elastic strain accumulated at the end of each fatigue cycle. Through numerical experiments, we demonstrate that this FPM is capable of accurately extracting the crack-tip cohesive tractions and separations, along with the elusive unloading-reloading hysteresis, which constitute the cohesive zone law for fatigue crack growth. We discuss the errors and uncertainties associated with this inverse approach.

Thermal Fatigue Fracture Behavior of Sintered Ag Nanoparticles under Equibiaxial Thermal Stress

An equibiaxial thermal fatigue test of die-attach materials that reproduces the same stress state as the power cycle was proposed, and the fatigue fracture behavior of Ag sintered die-attach materials under equibiaxial thermal stress was investigated. Thermal fatigue tests under equibiaxial stress showed that vertical cracks were observed throughout the sintered Ag nanoparticles. Thermal fatigue fracture was out-of-phase type, in which crack initiation and opening were driven by equibiaxial tensile stress during temperature drop. It is suggested that the fatigue crack growth in the die-attach joint during power cycling can be predicted by the fatigue crack growth law at high temperatures obtained by mechanical fatigue tests.

Damage Tolerance Behavior of a Nickel-Based Super-alloy GTM718 Under Cold-TURBISTAN Variable Amplitude Loads

In this study, the damage tolerance behavior in terms of fatigue crack propagation behavior of an aero-engine material under a standard variable amplitude load sequence was predicted and compared with experimental results. The constant amplitude (CA) fatigue crack growth rate (FCGR) behavior of GTM718, a nickel-based super-alloy, was determined at various stress ratios R = σmin/σmax ranging from R = 0.1 to 0.7. The empirical fatigue crack growth law was derived from this data in terms of two-parameter crack driving force, ΔK*. Then, the fatigue crack propagation behavior of GTM718 under a standard cold-TURBISTAN variable amplitude load sequence was predicted using cycle-by-cycle approach and using the CA fatigue crack growth law. Also, experimental fatigue crack growth behavior under the same cold-TURBISTAN variable amplitude load sequence was determined and compared with predicted results. A fairly good correlation was observed with predicted and experimental results.

Fatigue crack growth behaviour of a nickel base super alloy GTM720 under cold-TURBISTAN spectrum load sequence

Damage tolerance concept is widely used in aerospace industry for designing structural components against fatigue. In this study, an attempt is made to predict fatigue crack growth behavior in an aero-engine material under a standard spectrum load sequence using a closure independent crack driving force parameter, K* and compare with experimental results. Initially, constant amplitude (CA) fatigue crack growth rate (FCGR) behavior of GTM720, a nickel based super alloy was determined at stress ratios, R = σmin/σmax ranging from R = 0.1 to 0.7. Then, empirical fatigue crack growth law was derived from this CA-FCGR data in terms of two parameter crack driving force, K*. Further, the fatigue crack growth behavior was predicted through cycle-by cycle approach in a pre-cracked compact tension (CT) specimen of GTM720 alloy under standard cold-TURBISTAN spectrum load sequence using K* as the crack driving force. Also, experimental fatigue crack growth behavior under the same load sequence was determined in a CT specimen and compared with predicted results. A fairly good correlation was observed with predicted and experimental results. Predicted fatigue crack growth life was conservative and the fatigue crack growth life ratio, Npred/Nexpt was about 0.92.

Two-stage physics-based Wiener process models for online RUL prediction in field vibration data

Due to most failure mechanisms, such as fatigue crack growth and fatigue spall, the degradation process of rotating machinery commonly exhibits two-stage features in engineering practice. Other minor factors are also the key issues affecting the health evolution process, including the component structure, assembly accuracy, and working environment. Ignoring such a mechanism may lead to imprecise in degradation modeling, life prognostic, and ultimately lead to safety risk. Besides, achieving high accuracy of prognostic emphasizes the influence of random effect in the degradation process. The contribution of this study lies in addressing this issue by proposing two-stage physics-based Wiener process models integrating: (a) fatigue crack mechanism and crack growth law, and (b) other minor factors. A general prognostic framework is formulated by jointly employing the online change point detection, parameter estimation, and remaining useful life (RUL) prediction, which has good statistic inference and applicability in two general nonlinear systems, i.e., power-law and exponential-law. A joint implement of offline two-step parameter estimation method and the online Bayesian update method is executed, making full advantage of historical and in-service data, based on which the RUL prediction transcends into an imperative PHM module. A practical case study on the vibration dataset of wheel treads demonstrates the practically implement ability of the proposed method in achieving high accuracy of RUL prediction.

Uncertainty theory based reliability modeling for fatigue

The study of the fatigue crack growth law is usually carried out by the fatigue crack growth experiments (FCGE), and is expressed by the fatigue crack growth model. Epistemic uncertainties exist in FCGE with small samples. Generally, Bayesian method, interval probability method, and fuzzy probability method are presented to quantify the epistemic uncertainty in the case of small samples. However, the expression of the epistemic uncertainty in most studies is greatly influenced by subjective information, and there are interval expansion problems in the calculation. Therefore, the problem of how to quantify the epistemic uncertainties in FCGE with small samples has not been well solved. Under such circumstance, a novel uncertain measure is used to quantify such epistemic uncertainty in this paper, which is belong to uncertainty theory proposed by Prof. Baoding Liu. Firstly, the fatigue crack growth model proposed by Zhang is introduced as the foundation of modeling. Then, the sources of uncertainties in FCGE are analyzed and the uncertainties are quantified based on the uncertainty theory. Finally, a belief reliability model of fatigue crack growth is proposed, in which the associated reliability function is derived, and the uncertain statistics for the parameter estimations is presented. The case study illustrates the proposed methodology and the corresponding discussions show that the uncertainty theory contributes to more stable reliability evaluation than probability theory when quantifying the epistemic uncertainty, and the influence of the material scatter on fatigue reliability should be emphasized.

Regression Analysis of Stochastic Fatigue Crack Growth Model in a Martingale Difference Framework

In the present paper, we are mainly concerned with the degradation mechanism that arises in fatigue crack growth (FCG). The crack evolution mechanism is modeled by a first order stochastic differential system, composed by a deterministic FCG equation perturbed by a stochastic process. The main purpose is to investigate the estimators of the model parameters and establish some asymptotic properties by transforming the initial equation into a regression model. To this purpose, least squares estimation (LSE) is applied in the framework of the errors being martingale differences. The parametric conditional LSE are proved to be consistent. Our results are obtained in the general case and specified for the linear case with focus on a particular application model derived from the most widely used FCG law in fracture mechanics, i.e., the Paris model. We derive the asymptotic normality of the LSE for the nonlinear case with discussion for the linear case. Finally, we provide a numerical example to illustrate the performance of the proposed methodology, on a particular version of the stochastic model.

Influence of crack driving force on correlating stress ratio effects in fatigue crack growth rate of a nickel base super alloy IN720

Damage tolerance evaluation under service loads requires a unified constant amplitude fatigue crack growth law for the material with nullified stress ratio effects. Several types of crack driving force parameters have been proposed in the past to correlate stress ratio effects on fatigue crack growth rates in various materials. In the present investigation, an effort was made to use four different crack driving force parameters to eliminate stress ratio effects in a nickel base super alloy IN720. Constant amplitude fatigue crack growth rate of Inconel 720 (IN720) was experimentally determined at various stress ratios, R ranging from R = 0.1 to 0.7. All the tests were performed at room temperature and in laboratory air condition in a 100-KN servo-hydraulic test machine using compact tension specimen and following ASTM test standard procedures. As expected, increasing the stress ratio increased crack growth rates and decreased threshold stress intensity factor range, ΔKth. The conventional crack growth rate, da/dN versus stress intensity factor range, ΔK data was modified and re-plotted as a function of four different crack driving force parameters, viz., (a) Kujawski’s K*, (b) two parameter ΔK*, (c) Walker’s ΔKw and (d) Foreman’s ΔKf. It was observed that Kujawski’s crack driving force parameter, K*, was correlating stress ratio effects better than all other models in all the three regimes of crack growth rates in this material. Further, all these models were employed to predict fatigue crack growth behaviour under a truncated FALSTAFF spectrum load sequence. It was observed that the total fatigue crack growth life estimated varied from about 25 blocks to about 75 blocks. Thus, the use of appropriate crack growth model appears to influence accuracy of life prediction under spectrum loads.

A unified formulation for fatigue crack onset and growth via cohesive zone modelling

This paper presents a unified cohesive zone formulation for describing the fatigue-driven crack onset and propagation in quasi-brittle materials. This approach is based on formulating a modified traction-displacement law involving linear softening, which accounts for the onset of fatigue failure described by materials S-N curves. The fatigue crack propagation in a steady-state regime is described as a sequence of initiation stages that progressively take place within the process zone ahead of the “zero-stress” fracture tip. It is demonstrated that the damage distribution within the process zone under cyclic load is governed by a non-linear Fredholm integral equation of the second kind, which is solved numerically using an iterative scheme. It is also shown that the Paris-Erdogan law for fatigue crack growth can be directly obtained from engineering S-N curves via the linear traction displacement model introduced here. The Paris-Erdogan propagation regime is attained when the crack propagation rate is much smaller that the length of the process zone. The exponent of the Paris-Erdogan law is equal to half the inverse of that characterising the material S-N curve. The main advantage of the cohesive zone model introduced here is that it does require neither ad-hoc additional parameters nor calibration constant to obtain the Paris-Erdogan law from material S-N data. It is also proved that the cohesive zone length in fatigue depends on the exponent of the S-N curve and it always shorter than its static counterpart. The unified cohesive zone model is validated against experimental data for the specific cases of mode I and mode II fatigue delamination growth in the carbon/epoxy composite material IM7/8552. Finally, an analysis of the role played by size effects is presented, with emphasis on the influence of the laminate thickness on the fatigue damage accumulation within the process zone and the ensuing propagation rates of cohesive cracks.

Fatigue crack growth in compacted and spheroidal graphite cast irons

The present paper focuses on the fatigue life of a Compacted Graphite cast Iron (CGI) as compared to a Spheroidal Graphite cast Iron (SGI). Fatigue crack growth laws have been determined with digital image correlation. Main difference between the materials is that cracks propagate faster in the CGI than in the SGI. X-ray tomography was also used in order to assess graphite morphologies and crack shapes. A complex morphology was observed for the vermicular graphite with rounded edges that limit notch effects. The crack spreads easily in CGI via a quasi cleavage mechanism and by propagating through graphite mainly by breaking the vermicules.

Influence of fillet end geometry on fatigue behaviour of welded joints

This paper presents a fatigue analysis of a type of fillet welded joint representative of one main joint of the steel box girder of the Alcácer do Sal railway bridge. From previous studies, it was found that the welded joint between the box girder diagonal and the central hanger gusset is one of the most stressed details of the bridge. This welded joint was not fully manufactured according to current construction procedures, as regards the fillet weld end configuration. In order to assess the fatigue behaviour of such welded joint, the present study combines an experimental campaign and numerical analysis. A total of four welded joint series were produced in order to allow the comparison of the fatigue performance of similar type of welded joint of the Alcácer do Sal bridge with welded joints produced according to existing recommendations, such as EC3. Since scale-down specimens were considered, two different thicknesses were included in this study for each joint configuration, to allow the verification of any thickness effect. Concerning the numerical analyses, two main numerical tools were used: the standard Finite Element Method (FEM) with ANSYS and the eXtended Finite Element Method (XFEM) with ABAQUS. Fatigue life predictions were performed including both fatigue crack initiation and fatigue crack propagation phases. The number of cycles to initiate a fatigue crack was computed using local notch strain-life approaches, and the number of cycles for fatigue crack propagation was computed by integrating the Paris fatigue crack growth law with stress intensity factors computed with ANSYS (virtual crack closure technique) and ABAQUS (contour integral method, 3D XFEM model). Experimental tests demonstrated little influence of fillet weld end geometry on fatigue behaviour of welded joints and plate thickness effects were also reduced as also confirmed by the similar fatigue crack propagation rates. Both numerical simulations provided very accurate predictions of the experimental S-N curves, however the XFEM modelling opens new possibilities for mix-mode fatigue crack propagation simulations.