Elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra

Most fatigue loaded components or structures experience a variety of stress histories under typical operating loading conditions. In the case of constant amplitude loading the fatigue crack growth depends only on the component geometry, applied loading and material properties. In the case of variable amplitude loading the fatigue crack growth depends also on the preceding cyclic loading history. Various load sequences may induce different load-interaction effects which can cause either acceleration or deceleration of fatigue crack growth. The recently modified two-parameter fatigue crack growth model based on the local stress–strain material behaviour at the crack tip [1,2] was used to account for the variable amplitude loading effects. The experimental verification of the proposed model was performed using 7075-T6 aluminum alloy, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data shows the ability of the model to predict the fatigue life under different types of variable amplitude loading spectra.     

A modification of UniGrow 2‐parameter driving force model for short fatigue crack growth

In this paper, a modification of the UniGrow model is proposed to predict total fatigue life with the presence of a short fatigue crack by incorporating short crack propagation into the UniGrow crack growth model. The UniGrow model is modified by 2 different methods, namely the “short crack stress intensity correction method” and the “short crack data‐fitting method” to estimate the total fatigue life including both short and long fatigue crack propagations. Predicted fatigue lives obtained from these 2 methods were compared with experimental data sets of 2024‐T3, 7075‐T56 aluminium alloys, and Ti‐6Al‐4V titanium alloy. Two proposed methods have shown good fatigue life predictions at relatively high maximum stresses; however, they provide conservative fatigue life predictions at lower stresses corresponding high cycle fatigue lives where short crack behaviour dominates total fatigue life at lower stress levels.     

Application of a modified Wheeler model to predict fatigue crack growth in Fibre Metal Laminates under variable amplitude loading

This paper presents the investigation regarding fatigue crack growth prediction in Fibre Metal Laminates under variable amplitude fatigue loading. A recently developed constant amplitude analytical prediction model for Fibre Metal Laminates has been extended to predict fatigue crack growth under variable amplitude loading using the modified Wheeler model based on the Irwin crack-tip plasticity correction and effective stress intensity factor range (ΔK_eff). The fatigue crack growth predictions made with this model have been compared with crack growth tests on GLARE center-cracked tension specimens under selective variable amplitude loading as well as flight simulation loading. The accuracy of the model is discussed in comparison with the experimental fatigue crack growth data.     

Fatigue crack growth simulation of aluminium alloy under spectrum loadings

Fatigue crack growth in structure components, which is subjected to variable amplitude loading, is a very complex subject. Studying of fatigue crack growth rate and fatigue life calculation under spectrum loading is vital in life prediction of engineering structures at higher reliability. The main aim of this paper is to address how to characterize the load sequence effects in fatigue crack propagation under variable amplitude loading. Thus, a fatigue life under various load spectra, which was predicted, based on the Austen, Forman and NASGRO models. The findings were then compared to the similar results using FASTRAN and AFGROW codes. These models are validated with the literature-based fatigue crack growth test data in 2024-T3 Aluminium alloys under various overload, underload, and spectrum loadings. With the consideration of the load cycle interactions, finally, the results show a good agreement in the behaviour with small differences in fatigue life compare to the test data.     

Method of analysis and prediction for variable amplitude fatigue crack growth

Fatigue crack growth behavior of structure subjected to variable amplitude loading is very complex. Both the truncation and the load sequence have been shown to have a significant influence on the test results because of the load level interaction effects. To understand these interaction effects and the possible influence they can have on the results obtained a test program was performed. Fatigue crack growth tests were conducted on the program using 7075-T6 and 2024-T3 aluminum and titanium 6A1-4V mill anneal.

Using the test data, an analysis method was developed. In this analysis method the crack growth rate is evaluated for each load cycle using a modification of the fracture mechanics correlation technique. The crack growth for each cycle was evaluated as a function of the stress intensity factor excursion with a correction factor for the maximum and minimum peak stress levels in the test spectrum. The fatigue crack growth correction for the peak stresses in the spectrum is given as a growth rate correction factor r. The relationship for r, is termed the ‘fatigue crack growth rate interaction model’.

For verification, the interaction model was applied to test data from spectrum loading tests. The correlation obtained for the example, indicated that the model properly predicts the interaction effects and its use could significantly improve the accuracy of crack growth life calculations for programmed spectrum tests.     

Prediction of fatigue crack growth in notched members under variable amplitude loading histories

A technique for estimating fatigue crack propagation in notched plates subjected to variable amplitude loading is outlined in this paper. An elastic-plastic finite element model is used to determine the effect of notch geometry and the residual plastic deformations. The analytic model for crack growth is based on an effective stress intensity concept. All of the calculations are based on constant amplitude materials data. Results of this procedure are compared to tests on a modified compact tension specimen. The program consisted of predicted propagation lives for forty-five (45) tests on two structural steels, three load histories and, at least, three maximum load levels.     

Experimental investigation and numerical prediction of fatigue crack growth of 2024-T4 aluminum alloy

Compact specimens were employed to study fatigue crack growth of 2024-T4 aluminum alloy under constant/variable amplitude loading. Apparent R-ratio effect under constant amplitude loading was identified with the nominal stress intensity factor range. Fatigue crack growth rates predicted by a unified model agreed with the experimental data well. Single tensile overload resulted in significant retardation of crack growth which was fully recovered after propagating out of overload-affected zone. Retarded crack growth induced by three-step sequence loading was heavily dependent on two sequence loading parameters. The influence of variable amplitude loading on crack growth was reasonably characterized by Wheeler’s model.     

FEM analysis of crack closure and delay effect in fatigue crack growth under variable amplitude loading

An analysis of fatigue crack closure under variable amplitude loading was made by using the finite element technique. Two basic types of variable amplitude loading were selected for the analysis; constant amplitude loading with a single overload and block loading. A characteristic variation of a crack closure level was found to exist for both types of loading: the trace of the crack closure level vs crack length rose to a maximum value and then decreased asymptotically. The characteristic behavior was explained in terms of the residual stress which had been induced by an overload or a load preceding to the variation. The predicted fatigue crack growth behavior which was obtained analytically was consistent with the experimental results, and it was concluded that the retardation and acceleration phenomena are closely correlated with the crack closure.     

Fatigue crack closure analysis of bridged cracks representing composite repairs

This article presents an analytical and numerical study of the fatigue crack‐closure behaviour of a bridged crack representing a crack that has been repaired by a composite patch. It is shown that, provided that the plate stress beneath the patch is less than 40% of the material’s yield stress, the crack‐closure stress of a patched crack is approximately equal to that of an unbridged crack under small‐scale yielding, depending only on the stress ratio. Furthermore, it is shown that the transient crack‐closure behaviour of a patched crack subjected to variable amplitude loading can be determined by analysing an unpatched crack subjected to the same stress intensity factor history. Based on these findings, it is proposed that the fatigue crack closure of a patched crack can be determined by analysing an unpatched centre crack subjected to an adjusted stress, for which an explicit expression is given. Predictions based on the proposed method are shown to correlate very well with experimental results obtained under two aircraft loading spectra.     

Influence of loading path on fatigue crack growth under multiaxial loading condition

In this study, the specimens made of carbon steel S45 with an initial surface straight edge notch were subjected to combined cyclic axial‐torsion loading at room temperature. The fatigue life, surface crack extension direction and crack length were experimentally investigated. The effects of loading path, stress amplitude ratio and phase angle on the crack growth behaviour were also discussed. The results showed that, under the combination of cyclic axial and torsion loading, the tension stress amplitude had more effect on the initial crack growth path than the latter. The shear stress amplitude contributed mainly to the latter crack extension. The crack extension path was mainly determined by the stress amplitudes and the ratio of the normal stress to the shear stress, and almost independent of the mean stresses. The increase of the tension stress amplitude and shear stress amplitude would both accelerate the crack growth rate.     

Flight-by-flight fatigue crack growth life assessment

Conventionally, fatigue crack growth in aircraft structures under flight spectrum loading is often analysed and predicted based on crack growth rates obtained from constant-amplitude crack growth testing with cycle-by-cycle life prediction methods or models. Because the mechanism of fatigue crack growth under spectrum loading is yet to be fully understood, no matter how closely the models are able to account for the load interaction effects, the predictions generally have to be subjected to the validation by fatigue crack growth tests using either representative specimens or real structures under the representative flight spectrum. In view of this fact, it is not difficult to deduce that the predictions should be much more reliable if the predictions are made directly based on the flight spectrum crack growth data. Therefore, a new approach to fatigue crack growth life assessment has been proposed in this paper based on the analysis of flight-by-flight fatigue crack growth data measured by quantitative fractography for several common aircraft structural materials under various fighter aircraft flight spectra. Quantitative fractography was successfully used for titanium coupons to generate crack growth curves under flight spectrum loading. The crack growths were also shown to be exponential. As a demonstration, the flight-by-flight approach was used to determine fatigue crack growth lives of aircraft aft fuselage frames under a fighter aircraft usage.     

Measuring stress intensity factors during fatigue crack growth using thermoelasticity

Thermoelastic stress analysis has been developed in recent years as a direct method of investigating the crack tip stresses in a structure under cyclic loading. This is a consequence of the fact that stress intensity factors obtained from thermoelastic experiments are determined from the cyclic stress field ahead of a fatigue crack, rather than inferred from measurement of the crack length and load range. In the present paper the results of fatigue crack growth tests performed on welded ferritic steel plates are reported. From the results it can be observed that the technique is sensitive to the effects of crack closure and the presence of tensile and compressive residual stresses due to welding.     

Fatigue crack growth in railway axles: Assessment concept and validation tests

Railway axles are safety relevant components which are usually designed for up to 30 years of service. Besides the experience based definition of inspection intervals, the application of fracture mechanics tools is currently being introduced as an appropriate method. Basic fatigue crack growth data both in the range of stable crack propagation and near the threshold have been experimentally determined for the heat-treated railway axle steels 25CrMo4 (EA4T) and 34CrNiMo6+QT under constant and variable amplitude loading at relevant stress ratios (predominantly fully reversed load cycles, R = −1). For the computational modelling of fatigue crack propagation, a generally applicable stress intensity factor solution has been derived by finite-element analyses. The results are employed for predicting fatigue crack growth in a reference railway axle within the shaft and in the fillet zone near a press fit. Additionally, the influence of press fitting on the crack propagation behaviour in a fillet is discussed. Finally, fatigue crack growth curves experimentally determined on 1:3 and 1:1 scaled axles at constant and variable amplitude loading are compared to the test results for standard M(T) specimens, as well as to respective analytical predictions.     

Influence of foreign object damage on fatigue crack growth of gas turbine aerofoils under complex loading conditions

Foreign object damage (FOD) has been identified as one of the main life limiting factors for aeroengine blades, with the leading edge of aerofoils particularly susceptible. In this work, a generic edge ‘aerofoil’ geometry was utilized in a study of early fatigue crack growth behaviour due to FOD under low cycle fatigue (LCF), high cycle fatigue (HCF) and combined LCF and HCF loading conditions. Residual stresses due to FOD were analyzed using the finite element method. The longitudinal residual stress component along the crack path was introduced as a nodal temperature distribution, and used in the correction of the stress intensity factor range. The crack growth was monitored using a nanodirect current potential drop (DCPD) system and crack growth rates were correlated with the corrected stress intensity factor considering the residual stresses. The results were discussed with regard to the role of residual stresses in the characterization of fatigue crack growth. Small crack growth behaviour in FODed specimens was revealed only after the residual stresses were taken into account in the calculation of the stress intensity factor, a feature common to LCF, HCF and combined LCF + HCF loading conditions.     

Random fatigue crack growth with retardation

On basis of a study of the literature concerning empirical findings in fatigue crack growth in metal specimens under constant amplitude loading with occasional overloads, the paper summarizes the reported qualitative effects of the overloads. The great scatter of the observations and the difficulty of setting up a clear physical mechanism, which in deterministic terms explains the crack growth retarding effects of the overloads, motivates attempts to formulate stochastic process models of phenomenological type. The paper shows that birth processes have features that make them applicable in modelling fatigue crack growth processes. In fact, this process type allows a time transformation that reduces the case of variable amplitude loading to the case of constant amplitude loading. The mean growth curve defined as the mean time of growth to a given crack length as function of this crack length may in the constant load amplitude case be calibrated to the Paris-Erdogan law. For the case of occasional overloads it may be further calibrated to the empirical results reported in the form of the Wheeler model of crack retardation based on the concept of a strengthening plastic zone at the crack tip caused by the overload.     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

Characteristics of fatigue crack growth in GFRP laminates

Multiple fatigue crack growth behaviour has been studied in quasi-isotropic GFRP laminates under constant amplitude fatigue loading conditions. Characteristics of fatigue crack growth in off-axis plies have been described and comparisons have been made between quasi-static and fatigue crack growth behaviour. Careful monitoring of individual fatigue cracks reveals three distinct stages of crack growth including initiation, steady-state crack growth (SSCG) and crack interaction and saturation. Stress redistribution due to matrix cracking and the associated stiffness reduction have been simulated using finite element models. Strain energy release rates associated with the off-axis matrix cracking have also been obtained and correlated with the measured fatigue crack growth rates.     

Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic-plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K_max are simulated. In comparison with a fixed K_max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.