Investigations on fatigue crack growth under variable amplitude loading in wheelset axles

The present paper summarizes the results of fatigue crack growth simulations for hollow wheelset axles. Within the scope of this paper different influencing factors of the remaining lifetime have been identified. Therefore different simulations using NASGRO have been performed with different initial crack depth as well as aspect ratios. Moreover the influence of press fitting on the remaining lifetime has been pointed out. Preliminary experimental studies using standardized fracture mechanical specimens have been used in order to optimize time- and cost-consuming component testing.     

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.     

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.     

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.     

A mathematical model of fatigue crack propagation under variable amplitude loading

A mathematical model of fatigue crack propagation based on the crack closure concept is proposed. It allows prediction of fatigue crack growth under complex loading sequences on the basis of data obtained under constant amplitude and simple Low-High, High-Low loading sequences. The model explains the influence of single and multiple positive overloads and the interaction of positive and negative overloads. An algorithm for cycle-by-cycle calculation of crack growth is proposed.     

Estimating fatigue damage under variable amplitude multiaxial fatigue loading

The present paper is concerned with the use of the modified Wöhler curve method (MWCM) to estimate both lifetime and high‐cycle fatigue strength of plain engineering materials subjected to complex load histories resulting, at critical locations, in variable amplitude (VA) multiaxial stress states. In more detail, when employed to address the constant amplitude (CA) problem, the MWCM postulates that fatigue damage reaches its maximum value on that material plane (i.e. the so‐called critical plane) experiencing the maximum shear stress amplitude, fatigue strength depending on the ratio between the normal and shear stress components relative to the critical plane itself. To extend the use of the above criterion to those situations involving VA loadings, the MWCM is suggested here as being applied by defining the critical plane through that direction experiencing the maximum variance of the resolved shear stress. Such a direction is used also to perform the cycle counting: because the resolved shear stress is a monodimensional quantity, stress cycles are directly counted by the classical rain‐flow method. The degree of multiaxiality and non‐proportionality of the time‐variable stress state at the assumed critical sites instead is suggested as being measured through a suitable stress ratio which accounts for the mean value and the variance of the stress perpendicular to the critical plane as well as for the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear stress. Accuracy and reliability of the proposed approach was checked by using several experimental results taken from the literature. The performed validation exercise seems to strongly support the idea that the approach formalized in the present paper is a powerful engineering tool suitable for estimating fatigue damage under VA multiaxial fatigue loading, and this holds true not only in the medium‐cycle, but also in the high‐cycle fatigue regime.     

Short surface fatigue cracks growth under constant and variable amplitude loading

This paper deals with the fatigue strength of S355NL steel, of a common use within the shipbuilding industry, under uniaxial constant and variable loading. Indeed, ship structures are subjected to variable loading due to various sea states, wind and waves. As a consequence, a better knowledge of fatigue behavior under real loading conditions is needed. This study aims at analyzing the influence of loading conditions (load ratio and variable amplitude loading) on the short crack behavior and last, with a proposed model to assess the fatigue crack life. The tools used to prepare inspections in critical areas only take into account the long crack behavior. The results from the proposed model were compared to the assessments these tools are providing with.     

An efficient variable amplitude loading scheme for three-dimensional fatigue crack

The finite element alternating method (FEAM) is an extremely useful and efficient scheme for the accurate calculation of stress intensity factors in complex three dimensional structures. This approach involves the combination of an analytical solution for a crack in an infinite body with a finite element solution for the uncracked component. Previously a three-dimensional fatigue crack growth algorithm has been incorporated into the alternating method for the case of constant amplitude loading. The major accomplishment outlined in this paper is the implementation of an additional numerical scheme for the more difficult case of variable amplitude loading. Test cases, with an emphasis on components taken from the aerospace industry, are used to validate the revised alternating method computer program. Results reveal excellent levels of correlation with existing packages and highlight the suitability of the finite element alternating method for fatigue crack growth analyses in a wide variety of components such as aircraft components, pipelines, offshore structures, pressure vessels, ships, etc.     

Fatigue crack growth under variable amplitude loading Part I: experimental investigations

During use, a component or a structure is exposed to variable amplitude loading, which influences the lifetime. Within the scope of this work, systematic investigations of different loading situations are carried out by means of experimental studies (part I) as well as analytical and numerical studies (part II). The experimental investigations show that overloads lead to retardation effects, which are influenced by several factors, e.g. the overload ratio, baseline‐level loading, number of overloads or the fraction of mixed mode. In a high–low–high block loading, both retarded and accelerated crack growth can be obtained, which is also influenced, e.g. by the block loading ratio and the length of the block. Moreover, experimental studies have been performed with load spectra, like FELIX/28, CARLOS vertical and WISPER. They have been applied in original form as well as in counted and reconstructed sequences.     

Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions

Service conditions experienced by rubber components often involve cyclic loads which are more complex than a constant amplitude loading history. Consequently, a model is needed for relating the results of constant amplitude characterization of fatigue behaviour to the effects of variable amplitude loading signals. The issue is explored here via fatigue crack growth experiments on pure shear specimens conducted in order to evaluate the applicability of a linear crack growth model equivalent to Miner's linear damage rule. This model equates the crack growth rate for a variable amplitude signal to the sum of the constant amplitude crack growth rates associated with each individual cycle. The variable amplitude signals were selected to show the effects of R-ratio (ratio of minimum to maximum energy release rate), load level, load sequence, and dwell periods on crack growth rates. In order to distinguish the effects of strain crystallization on crack growth behaviour, two filled rubber compounds were included: one that strain crystallizes, natural rubber, and one that does not, styrene-butadiene rubber. The linear crack growth model was found to be applicable in most cases, but a dwell effect was observed that is not accounted for by the model.     

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.     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

A review of some aspects of fatigue crack growth under variable amplitute loading

The literature on some aspects of the influence of variable amplitude loading on fatigue crack growth has been reviewed. In particular the importance of residual stresses, fatigue crack closure, microstruture, geometry and environment on the fatigue crack growth of long, through-thickness cracks following overloads, underloads and overload-underload combinations in Mode 1 opening have been identified. Other behaviour, including the influence of temperature, frequency and the effects of mixed-mode loading, is beyond the scope of this review. Areas of work requiring further investigation have been proposed.     

Fatigue crack growth under variable amplitude loading Part II: analytical and numerical investigations

In part I, the effects of variable amplitude loadings on the fatigue crack growths were illustrated by means of experimental results. Within the scope of part II, systematic analytical and numerical investigations are presented. Using different analytical concepts it can be shown that the lifetime depends both on the concept used and on the loading sequence. Also, the influence of the parameters that must be fitted by experimental data for all analytical prediction models has been investigated. By means of detailed elastic–plastic finite element simulations it becomes obvious that not only the crack opening caused by large plastic deformations subsequent to overloads and block loadings, but also the stress field in the ligament is an indicator for the retardation effect. If the σ_y‐stresses both at maximum and minimum loading are identical with the σ_y‐stress distribution of an appropriate constant amplitude (CA) loading, one can assume that the interaction effect is annihilated.     

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.     

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial K _II /K _I mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small K _II /K _I ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

Dugdale crack closure analysis of fatigue cracks under constant amplitude loading

Fatigue fracture mechanics which means structural analysis including crack propagation and crack closure in conjunction with a local failure criterion provides detailed insight into mechanisms of cyclic loaded crack sheets. Using the Dugdale method and rigid-perfectly plastic strip material law the infinite sheet with colinear cracks was parametrically investigated in respect of: SSY limits, crack closure occurrence, formation of contact stresses and displacements, influences of material parameters, $\text{R-}\text{ratio}$ and maximum load on effective stress ratio. Rationales for the load ratio, mean load and maximum load dependence and the form of $\text{da/dN-}\text{curves}$ are given based on crack closure analysis.