Recent developments in the understanding of fretting fatigue

Considerable progress has been made in the understanding of fretting fatigue over the last decade. Experiments have become more standardised and carefully controlled and this has provided the data necessary for development of methods for predicting fretting fatigue performance. This paper reviews a number of recent developments, starting with attempts to apply multiaxial initiation criteria to the fretting problem. The importance of the size effect is highlighted and an analogy is made between fretting and notch fatigue. Methods for characterising crack initiation using asymptotic analysis are discussed, together with short crack arrest concepts which provide a means of predicting fretting fatigue limits from plain fatigue data.     

Experimental and numerical study on crack initiation under fretting fatigue loading

Press-fitted railway axles and wheels are subjected to fretting fatigue loading with a potential hazard of crack initiation in press fits. Typically, the resistance against crack initiation and propagation in press fits is investigated in full-scale tests, which procedure is both costly and time consuming. In this context, combined experimental and numerical approaches are of increasing practical importance, as these may reduce the experimental effort and, moreover, provide a basis for the transferability of experimental results to different axle geometries and materials. This study aims at evaluating stress–strain conditions under which fretting fatigue crack initiation is likely to occur. Experiments on small-scale specimens under varying fretting fatigue load parameters and their finite-element modelling to characterize the resulting stress–strain fields are performed. Subsequently, different multiaxial fatigue parameters are applied to predict crack initiation under fretting fatigue conditions.     

Applications of crack analogy to fretting fatigue

In literature the most common approach to investigate fretting fatigue is based on contact mechanics. Crack initiation parameters of fretting fatigue are developed using elastic solution of two contacting bodies. Even though contact based parameters has been used extensively, they could not fully capture crack initiation mechanism due to the complexities of the fretting fatigue damage process, which depends on pad geometries, surface properties, material properties, and mechanical loading conditions. This has instigated fretting fatigue researcher to investigate other approaches. Recently, taking advantage of the similarities between contact mechanics and fracture mechanics lead to the development of crack analogy methodology (CAM), which defines the stress intensity factor as a fretting fatigue crack initiation parameter. CAM has shown a great potential investigating fretting fatigue. However, it has not been applied to wide range of fretting fatigue scenarios. The scope of this paper is not to focus on analytical development of CAM as much as validating its ability to analyze various fretting fatigue scenarios. Based on CAM, the present study introduces the crack analogy fretting parameter (CAF-parameter) to investigate crack initiation of fretting fatigue, which is equivalent to the change of mode II stress intensity factor at the contact surface, since the change in the stress intensity factor reflects the cyclic mechanism of fatigue. Further, a modification to the CAM is adopted to include various indenter-substrate geometries. Also, CAF-parameter-life curve, similar to the stress-life S-N curve, will be developed as a prediction tool to crack initiation for various geometric configurations using experimental data. This is consistent with presenting fatigue data. The results show similar pattern to plain fatigue with lower damage tolerance. It also shows scatter and dependency on the pad configuration as expected. Finally, the CAF-parameter shows potentials in effectively analyzing/predicting the complex mechanism of fretting fatigue.     

Multiaxial fretting fatigue testing and prediction for splined couplings

This paper presents a combined experimental and computational methodology for fretting fatigue life prediction of aeroengine splined couplings under combined loading cycles involving cyclic torque and axial load, as well as rotating bending and fluctuating torque. The experimental method is based on the concept of a simplified representative test, which mimics the multiaxial fretting conditions between spline teeth via biaxial loading of specially-designed bridge pads and a fatigue specimen. The numerical method is based on a three-dimensional finite element model of the test rig assembly, including frictional contact effects, along with a multiaxial, critical-plane fatigue parameter for crack nucleation followed by crack growth prediction in the Paris regime using El Haddad small crack correction. The prediction methodology is shown to successfully capture the effect of the key fretting fatigue stress, which mimics the spline rotating bending moment, on total fatigue life.     

A general model to estimate life in notches and fretting fatigue

Fatigue in notched specimens and fretting fatigue are two different phenomena but they have in common the existence of a stress gradient. In these cases fatigue life estimation is usually considered as a superposition of an initiation and propagation phase. One of the main problems to estimate the fatigue life is to define the crack length where one phase finishes and the other begins. The model employed in this paper combines both phases without defining a priori the separation between them. The proposed model is applied to uniaxial and multiaxial fatigue in specimens with stress gradient: a group of fretting fatigue tests with spherical and cylindrical contact and another group of tests with notched specimens. The comparison between life estimations and experimental results allows checking the validity of the model in different conditions.     

Mechanics of two-stage crack growth in fretting fatigue

Motivated by experimental observations, we carry out a numerical analysis of the two-stage crack growth under fretting fatigue by using an efficient and accurate boundary element method. To start with, the variation of stress field during a loading cycle is analyzed. Various values of friction coefficient in the contact zone are considered, which is shown to considerably affect the stress field. Then, by assuming crack initiation to occur in the shear mode, a surface-breaking crack is introduced to the specimen at the location of highest shear-stress amplitude. The crack-tip stress intensity factors (SIFs) are calculated for various crack lengths and at various crack angles ranging from 25° to 45° about the contact surface. It is shown that, for a loading ratio of 0.5, the cyclic mode-II SIF amplitude decreases with increasing crack length, whilst its mean value increases. It suggests that the (first-stage) shear crack would sooner or later become dormant, or switch to another mode that can provide continuous support of growth. Then, the first-stage shear crack is manually kinked into a second-stage opening crack, and the follow-on driving force is analyzed. It is shown that the kinking event is only favored after the first-stage crack has grown to a certain length. The present study thus provides insights in the mechanics of two-stage crack growth that has been frequently observed in a typical dovetail joint under fretting fatigue. It also suggests an improved experimental setup to quantitatively investigate the fretting fatigue in dovetail joints.     

Fretting fatigue crack analysis in Ti–6Al–4V

A study was conducted to verify the efficacy of a fracture mechanics methodology to model the crack growth behavior of fretting fatigue-nucleated cracks obtained under test conditions similar to those found in turbine engine blade attachments. Experiments were performed to produce cracked samples, and fretting fatigue crack propagation lives were calculated for each sample. Cracks were generated at 10⁶ cycles (10%-of-life) under applied stress conditions previously identified as the fretting fatigue limit conditions for a 10⁷ cycle fatigue life. Resulting cracks, ranging in size from 30 to 1200 μm, were identified and measured using scanning electron microscopy. Uniaxial fatigue limit stresses were determined experimentally for the fretting fatigue-cracked samples, using a step loading technique, for R=0.5 at 300 Hz. Fracture surfaces were inspected to characterize the fretting fatigue crack front indicated by heat tinting. The shape and size of the crack front were then used in calculating ΔKth values for each crack. The resulting uniaxial fatigue limit and ΔKth values compared favorably with the baseline fatigue strength (660 MPa) for this material and the ΔKth value (2.9 MPa√m) for naturally initiated cracks tested at R=0.5 on a Kitagawa diagram.Crack propagation lives were calculated using stress results of FEM analysis of the contact conditions and a weight function method for determination of ΔK. Resulting lives were compared with the nine million-cycle propagation life that would have been expected in the experiments, if the contact conditions had not been removed. Scatter in the experimental results for fatigue limit stresses and fatigue lives had to be considered as part of an explanation why the fatigue life calculations were unable to match the experiments that were modeled. Analytical life prediction results for the case where propagation life is observed to be very short experimentally were most accurate when using a coefficient of friction, μ=1.0, rather than for the calculations using μ=0.3     

The model of the residual life time estimation of tribojoint elements by formation criteria of the typical contact fatigue damages

A two-dimensional theoretical model is proposed for investigation of the fracture processes and assessing residual contact durability of solids subjected to cyclic contact. The model is based on the step-by-step calculation of fatigue crack propagation paths in the contact region which includes the criteria of local fracture of materials under complex stress–strain state, characteristics of fatigue crack growth resistance of materials and also presupposes the possible change of fracture mechanisms (transversal shear – normal opening fracture mechanisms). Within the frames of the model the peculiarities of formation of such typical contact fatigue damages like pits, spalls, squat (“dark spot”) and cracking (“checks”) in rolling bodies and edge cracks growth in the elements of fretting couples under conditions of sliding/sticking between them are investigated. Examples of assessing the life time by damages formation (pitting and spalling) in the contact region are presented.     

Fatigue crack initiation and growth on a steel in the very high cycle regime with sea water corrosion

This paper is devoted to the effect of corrosion on the gigacycle fatigue strength of a martensitic-bainitic hot rolled steel used for manufacturing offshore mooring chains for petroleum platforms. Smooth specimens were tested under fully reversed tension between 10⁶ and 10¹⁰ cycles in three testing conditions and environments: (i) in air, (ii) in air after pre-corrosion and (iii) in air under real time artificial sea water flow. The fatigue strength at greater than 10⁸ cycles is reduced by a factor more than five compared with non-corroded specimens. Fatigue cracks initiate at corrosion pits due to pre-corrosion, if any, or pits resulting from corrosion in real time during the cyclic loading. It is shown that under sea water flow, the fatigue life in the gigacycle regime is mainly governed by the corrosion process. Furthermore, the calculation of the mode I stress intensity factor at hemispherical surface defects (pits) combined with the Paris-Hertzberg-Mc Clintock crack growth rate model shows that fatigue crack initiation regime represents most of the fatigue life.     

Corrosion fatigue behavior of extruded magnesium alloy AZ31 in sodium chloride solution

In the present study, corrosion fatigue experiments were done using the extruded magnesium alloy AZ31 in the 3% sodium chloride solution to clarify the corrosion fatigue characteristics of the material. Corrosion fatigue lives greatly decreased as compared with those in laboratory air. It was also clarified that most of the corrosion fatigue life (70–80%) at the lower stress amplitude is occupied with the period of the corrosion pit growth. Corrosion fatigue lives were evaluated quantitatively by dividing the corrosion fatigue process into the following two periods, i.e. (1) the corrosion pit growth period preceding the crack initiation from the pit and (2) the crack growth period before the specimen failure. In the analysis, the law of the corrosion pit growth proposed by authors was used to deal with the above first period. The evaluated results corresponded well to the experimental results.     

Calculation of KII in crack face contacts using X-FEM. Application to fretting fatigue

In this work, the modeling of LEFM problems that imply crack face closure and contact using the extended finite element method (X-FEM) is presented aiming at its application to fretting fatigue problems. An assessment of the accuracy in the calculation of K_II is performed for two different techniques to model crack face contacts in X-FEM: one is based on the use of additional elements to establish the contact and the other on a segment-to-segment (or mortar) approach. It is concluded that only the segment-to-segment approach can lead to optimal convergence rates of the error in K_II. The crack face contact modeling has also been applied to a fretting fatigue problem, where the estimation of K_II under crack closure conditions plays an important role in the stage I of fatigue crack propagation. The effect of the crack face friction coefficient has been studied and its influence on the range of K_II has been ascertained during loading and unloading cycles.     

Deterministic surface tractions in rough contact under stick–slip condition: Application to fretting fatigue crack initiation

A robust approach for the deterministic prediction of pressure distribution in dry rough-line contact configuration considering the elastic-fully plastic asperity effects is presented. Adopting Civarella–Jager approach, a procedure for calculation of the tangential traction distribution for cyclic loading condition in stick–slip regime is also described in detail. The effect of surface roughness on the pressure and tangential traction distribution and sub-surface stress field is evaluated. To illustrate the utility of the approach, the crack initiation risk in a stick–slip (fretting) contact is investigated for different surface roughness values. The methodology is conceptually simple and can be easily implemented in a computer code.     

On low cycle fatigue life of nickel-based superalloy valve membranes under non-proportional cyclic loading

A numerical model for low cycle fatigue damage analysis of valve membranes is presented in this paper. The isotropic and non-linear kinematic hardening laws of Lemaître–Chaboche, which define both the cyclic hardening and the ratchetting phenomenon, are adopted. The model for prediction of the number of cycles to crack initiation is based on a combination between Manson–Coffin relationship and Jiang–Sehitoglu fatigue parameter. The applied cyclic loading consists in a load pressure imposed to the internal face of the membrane and a vertical displacement of its hub section. The experimental results and numerical simulation predictions in terms of number of cycles to failure turned out to be in good concordance. Thus, numerical predictions are confirmed by microscopic observations made on membranes failed during testing.     

Stress gradient effect on the crack nucleation process of a Ti–6Al–4V titanium alloy under fretting loading: Comparison between non-local fatigue approaches

This study focuses on the stress gradient effect regarding the crack nucleation of a cylinder/plane Ti–6Al–4V titanium alloy contact under low cycle fatigue (LCF) fretting loading. Several local and non-local analytical approaches were compared to predict experimental results. The first part of the study presents fretting nucleation boundaries for three different cylinder radii in the partial slip regime. In the next part, the Crossland and Papadopoulos multi-axial fatigue criteria are computed and compared. Finally, local and non-local fatigue approaches are compared. Square constant volume, critical distance and weighted function approaches have been compared.The methodology used covers a large range of stress gradients. The impact of varying the stress gradients is that the larger the stress gradient, the larger the difference between experiments and local stress fatigue predictions. A Crossland local form was applied to confirm that a local stress fatigue analysis cannot predict the fretting cracking risk. Three non-local approaches were carried out, and the results allowed the proper prediction of the empirical thresholds with a 3–5% margin of error. The positive results obtained helped to select a multi-axial fatigue criterion and a non-local approach which take into account the gradient effect of contact fretting behavior.     

Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes

This paper is focused on the VHCF behavior of aeronautical titanium alloy under tensile and torsion fatigue loadings. Tensile tests were carried out with two different stress ratios: R = −1 and R = 0.1. Both surface and subsurface crack initiations were observed. In the case of subsurface crack initiation several fatigue life controlling mechanisms of crack initiation were found under fully-reversed loading conditions: initiation from (1) strong defects; (2) ‘macro-zone’ borders; (3) quasi-smooth facets and (4) smooth facets. Tests with stress ratio R = 0.1, have shown that initiation from the borders of ‘macro-zones’ becomes the dominant crack initiation mechanism in presence of positive mean stress. Like for the tensile results, surface and subsurface crack initiations were observed under ultrasonic torsion in spite of the maximum shear stress location on the specimen surface. But the real reason for the subsurface crack initiation under torsion was not found.     

Four-point bending fatigue behaviour of an iron-based laser sintered material

New material processing methods such as laser sintering of metal powder necessitates new knowledge and characterization of the material to support its implementation in technical applications. Fatigue behaviour of a laser sintered FeNiCu-alloy was studied with emphasis on crack path, initiation and propagation. Fatigue crack growth was investigated by surface replication in four-point bending fatigue tests. The fatigue behaviour was controlled by the complex layered structure. Pores on or under the surface were preferable places for crack initiation. Crack linkage and deflection occurred due to crack tip interaction with microstructure and sinter layers where microcracks initiated at pores adjacent to the advancing crack tip. Crack growth rate and stress intensity factor were calculated from surface replicas and showed an oscillating behaviour.