A finite element analysis of fretting fatigue crack growth behavior in Ti-6Al-4V

There is a need for methodology(ies) to analyze the crack growth behavior under fretting fatigue condition since its experimental determination is a challenging task. A finite element sub-modeling method was used to estimate the crack propagation life in titanium alloy, Ti-6Al-4V specimens. Two contact geometries, cylinder-on-flat and flat-on-flat, were analyzed. The computed crack propagation lives were combined with the results of an experimental study where total fatigue lives were measured. The combined numerical-experimental approach provided the crack initiation lives. The crack propagation life increased with increasing applied cyclic bulk stress in similar manner for both contact geometries. Almost 90% of the fretting fatigue life was spent during the crack nucleation and initiation phases in the high cycle fatigue regime. A parametric study was also conducted to investigate the effects of contact load, coefficient of friction and tangential force on the crack growth behavior. The crack propagation life decreased with increase of these three parameters. This decrease was similar for the contact load and the tangential force in both contact geometries, however, the decrease in the case of coefficient of friction was relatively more in the cylindrical pad than in the flat pad.     

Effect of various surface conditions on fretting fatigue behavior of Ti–6Al–4V

An experimental investigation was conducted to explore the fretting fatigue behavior of Ti–6Al–4V specimens in contact with varying pad surface conditions. Four conditions were selected: bare Ti–6Al–4V with a highly polished finish, bare Ti–6Al–4V that was low-stress ground and polished to RMS #8 (designated as ‘as-received’), bare Ti–6Al–4V that was grit blasted to RMS #64 (designated as ‘roughened’) and stress relieved, and Cu–Ni plasma spray coated Ti–6Al–4V. Behavior against the Cu–Ni coated and as-received pads were characterized through determination of a fretting fatigue limit stress for a 10⁷ cycle fatigue life. In addition, the behavior against all four-pad conditions was evaluated with S-N fatigue testing, and the integrity of the Cu–Ni coating over repeated testing was assessed and compared with behavior of specimens tested against the as-received and roughened pads. The coefficient of friction, μ, was evaluated to help identify possible crack nucleation mechanisms and the contact pad surfaces were characterized through hardness and surface profile measurements.

An increase in fretting fatigue strength of 20–25% was observed for specimens tested against Cu–Ni coated pads as compared to those tested against as-received pads. The experimental results from the S-N tests indicate that surface roughness of the coated pad was primarily responsible for the increased fretting fatigue capability. Another factor was determined to be the coefficient of friction, μ, which was identified as ˜0.3 for the Cu–Ni coated pad against an as-received specimen and ˜0.7 for the bare as-received Ti–6Al–4V. Specimens tested against the polished Ti–6Al–4V pads also performed better than the specimens tested against as-received pads. Fretting wear was minimal for all cases, and the Cu–Ni coating remained intact throughout repeated tests. The rougher surfaces got smoother during cycling, while the smoother surfaces got rougher.     

The effect of contact pad hardness on the fretting fatigue behaviour of AZ61 magnesium alloy

In the present study, the effect of hardness of contact material on fretting fatigue strength was experimentally investigated as a function of stress ratio. AZ61 magnesium alloy used in defense and transportation industries was used as the material for both the specimen and the contact pad. Two levels of hardness of contact material, 55.3 Vickers Hardness (HV) and 83.3 HV, were prepared by heat treatments. According to the results, with increasing hardness, the fretting fatigue strength decreased. The relative slip amplitude increased with increasing hardness, while the tangential force amplitude was not influenced by the hardness. It was speculated that because the local tangential stress at the contact edge increases with increasing hardness, the fretting fatigue strength decreases with increasing hardness.     

Influence of pad span on fretting fatigue behaviour of AISI 304 stainless steel

The present work deals with the influence of pad span on fretting fatigue behaviour of AISI 304 stainless steel. Relative slip is one of the three primary variables influencing fretting fatigue behaviour. The relative slip can be modified by changing the pad span and/or cyclic stress. In the present study, the effect of relative slip was studied at different cyclic stress levels and by using fretting pads with three different pad span values (15, 20 and 30 mm). The relative slip increased with an increase in pad span and cyclic stress. Samples tested with fretting pads having longer pad span (30 mm) exhibited longer lives. Though the specimens tested with pads having longer pad span experienced higher frictional stress and tangential force coefficient compared with those tested with pads having smaller pad span (15 or 20 mm), the relative slip values were larger in the former. Due to larger relative slip values it was assumed that small cracks initiated by fretting fatigue would have been worn away due to wear damage. Due to this the specimens tested with pads having longer pad span exhibited enhanced fretting fatigue lives. More deformation-induced martensite formed in the samples tested with pads having longer pad span owing to longer lives.     

Similarities of stress concentrations in contact at round punches and fatigue at notches: implications to fretting fatigue crack initiation

A linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines. The asymptotic forms for the stress fields in the vicinity of a rounded punch-on-flat substrate are derived for both normal and tangential loading, using both analytical and finite element methods. Under the action of the normal load, P , the ensuing contact is of width 2 b which includes an initial flat part of width 2 a . The asymptotic stress fields for the sharply rounded flat punch contact have certain similarities with the asymptotic stress fields around the tip of a blunt crack. The analysis showed that the maximum tensile stress, which occurs at the contact boundary due to tangential load Q , is proportional to a mode II stress intensity factor of a sharp punch divided by the square root of the additional contact length due to the roundness of the punch, Q /(√( b − a )√ π b ). The fretting fatigue crack initiation can then be investigated by relating the maximum tensile stress with the fatigue endurance stress. The result is analogous to that of Barsom and McNicol where the notched fatigue endurance stress was correlated with the stress intensity factor and the square root of the notch-tip radius. The proposed methodology establishes a 'notch analogue' by making a connection between fretting fatigue at a rounded punch/flat contact and crack initiation at a notch tip and uses fracture mechanics concepts. Conditions of validity of the present model are established both to avoid yielding and to account for the finite thickness of the substrate. The predictions of the model are compared with fretting fatigue experiments on Ti–6Al–4V and shown to be in good agreement.     

The effect of angle on dovetail fretting experiments in Ti-6Al-4V

The objective of this work was to compare the fretting fatigue performance of Ti‐6Al‐4V dovetail specimens on Ti‐6Al‐4V pads having various contact angles typical of engine hardware; 35°, 45° and 55° dovetail angles were considered. The dovetail fixtures were instrumented with strain gages so that the local normal and shear contact forces could be calculated. The contact force hysteresis loops were recorded showing the stick‐slip history. At R= 0.1, gross slip was observed for several thousand cycles followed by partial slip after the average coefficient of friction increased. At R= 0.5, gross slip was present only during the first half cycle. During partial slip, the slope of the shear versus normal force was a function of the dovetail angle. The local contact loads, therefore, differed for the same remotely applied force. Despite this, the fretting fatigue life depended primarily on the remotely applied load not dovetail angle.     

Computational fretting fatigue maps for different plasticity models

This paper presents qualitative elastoplastic simulations and analyses of fretting fatigue. Three hardening constitutive models are considered, and their effects on stick–slip conditions and lifetime prediction are compared. The computational analysis consists of the estimation of the shakedown limit cycle and the fatigue prediction using Dang Van or Crossland criterion. A particular configuration, the interaction of a flat pad with rounded corners in contact with a flat substrate made, respectively, of Inconel In718 and Titanium Ti64 alloys, is studied. The shakedown state is analysed using the cyclic and ratcheting equivalent strain concepts already discussed in the literature. In the paper, different fretting maps, based on slip, shakedown and fatigue regimes, are numerically produced and analysed. A new variable, the global slip percentage, is proposed for the characterization of the stick–slip regimes. Analyses of a series of slip maps show that the different hardening models do not introduce significant changes in the stick–slip conditions. Using finite element method simulations combined with fatigue limit criteria (Dang Van and Crossland), fretting fatigue maps are qualitatively reproduced. The main contribution of this work is a comparative discussion on the influence of the hardening models complexity on such maps.     

An apparatus for quantitative fretting testing

The design and construction of an apparatus for performing quantitative fretting fatigue experiments is described. The device allows accurate measurement and control of normal contact force, tangential contact force, relative displacement between contacting surfaces and bulk fretting loads, as well as measurement of average friction coefficients. Its design is simple, and includes interchangeable fretting contact pads, allowing the use of various pad geometries without major adjustment. The device incorporates many points of adjustment for alignment and compliance, making it a robust frame for a wide variety of fretting fatigue conditions involving different materials. The capabilities of this device are also verified by results of fretting fatigue experiments conducted on a 7075-T6 aluminium alloy.     

Effect of mean stress on fretting fatigue of Ti-6Al-4V on Ti-6Al-4V

Fretting fatigue tests of Ti‐6Al‐4V on Ti‐6Al‐4V have been conducted to determine the influence of stress amplitude and mean stress on life. The stress ratio was varied from R=−1 to 0.8. Both flat and cylindrical contacts were studied using a bridge‐type fretting fatigue test apparatus operating either in the partial slip or mixed fretting regimes. The fretting fatigue lives were correlated to a Walker equivalent stress relation. The influence of mean stress on fretting fatigue crack initiation, characterized by the value of the Walker exponent, is smaller compared with plain fatigue. The fretting fatigue knockdown factor based on the Walker equivalent stress is 4. Formation of fretting cracks is primarily associated with the tangential force amplitude at the contact interface. A simple fretting fatigue crack initiation metric that is based on the strength of the singular stress field at the edge of contact is evaluated. The metric has the advantage in that it is neither dependent on the coefficient of friction nor the location of the stick/slip boundary, both of which are often difficult to define with certainty a priori.     

FRETTING FATIGUE OF AN AUSTENITIC STAINLESS STEEL IN SEAWATER

Abstract— Fretting fatigue tests of an austenitic stainless steel used for a propeller tail shaft were carried out in seawater and in air. In seawater, fretting significantly reduced the fatigue strength, however, the fretting fatigue lives at higher levels of stress were longer than those in air. The tangential force coefficient (defined as the ratio of the frictional force amplitude and the contact load) in seawater was much lower than that in air and varied in the range from 0.3 to 0.5 during the fretting fatigue tests. The lower tangential force coefficient in seawater seems to be the main reason for the longer fretting fatigue life in seawater. The prediction of fretting fatigue life was made on the basis of elastic-plastic fracture mechanics, where the frictional force between the specimen and the contact pad was taken into consideration. The predicted fatigue lives agreed well with the experimental results in both air and seawater.     

Application of fracture mechanics to estimate fretting fatigue endurance curves

This paper presents approximations to fatigue curves in fretting conditions with spherical contact in the alloy Al 7075. The curves are defined for a specific contact geometry and loads applied in the tests (axial load on the specimen, the normal and tangential contact forces). In order to obtain a curve of this type it is necessary to fix all parameters except for one and analyse its influence on life. The method used to estimate life in fretting fatigue combines initiation with propagation. Different approaches to the growth of short cracks are employed and in some cases a fretting fatigue limit is predicted. Various groups of fretting tests have been analysed, evaluating the suitability of each approximation.     

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.     

Prediction of fretting crack propagation based on a short crack methodology

Fretting tests have been conducted to determine the maximum crack extension under partial slip conditions, as a function of the applied tangential force amplitude. An analytical elastic model representing a fretting-induced slant crack has been implemented and combined with the Kitagawa-Takahashi short crack methodology. This approach provides reasonable qualitative agreement between experimental and predicted maximum fretting crack lengths as long as the global response of the interface remains elastic. It confirms the stability of the crack arrest approach to predict the fretting fatigue endurance. It is, however, observed that the model is systematically conservative when significant plastic deformations are generated in the interface. A discussion of the appropriate fundamental parameters when dealing with steep stress gradients such as those present in fretting, and which are difficult to interpret in the context of the Kitagawa-Takahashi method, is presented. It is also shown that the maximum crack length evolution under plain fretting wear test conditions can be used to calibrate fretting fatigue predictions.     

Fretting–fatigue behavior of steel wires in low cycle fatigue

The effect of strain amplitude on fretting–fatigue behavior of steel wires in low cycle fatigue was investigated using a fretting–fatigue test rig which was capable of applying a constant normal contact load. The fretting regime was identified based on the shape of the hysteresis loop of tangential force versus displacement amplitude. The variations of the normalized tangential force with increasing cycle numbers and fretting–fatigue lives at different strain amplitudes were explored. The morphologies of fretting contact scars after fretting–fatigue tests were observed by scanning electron microscopy and optical microscopy to examine the failure mechanisms of steel wires. The acoustic emission technique was used to characterize the fretting–fatigue damage in the fretting–fatigue test. The results show that the fretting regimes are all located in mixed fretting regimes at different strain amplitudes. The increase in strain amplitude increases the normalized tangential force and decreases the fretting fatigue life. The abrasive wear, adhesive wear and fatigue wear are main wear mechanisms for all fretting–fatigue tests at different strain amplitudes. The accumulative total acoustic emission events during fretting–fatigue until fracture of the tensile steel wire decrease with increasing strain amplitude. An increase of the strain amplitude results in the accelerated crack nucleation and propagation and thereby the decreased life.     

A fretting damage correction factor applicable to the McDiarmid criterion of plain high-cycle fatigue

This paper presents an assessment of the performance of a set of multi-axial high-cycle fatigue criteria on the basis of a series of fretting fatigue experiments. We carried out tests on a creep-resistant chromium steel material used for steam-turbine blades. The first type of experiment employed the classical cylinder-on-flat geometry with flat dog-bone specimens. The second set of experiments adopted dovetail geometry. Various loads were applied in order to capture a wide range of contact slip amplitudes. A set of eight plain multi-axial fatigue criteria was applied to the numerically simulated stress response in the contacts during a single load cycle. Methods, which originated in the so-called theory of critical distances, were used for correcting the results in order to take the stress gradient effect into account. A simple factor based on slip amplitudes is introduced in order to consider the surface damage and is calibrated for the McDiarmid method. This criterion provided the best estimates of the most probable cracking sites.     

Investigation into relative slip during fretting fatigue under partial slip contact condition

A finite element analysis based methodology was developed to compute local relative slip on contact surface from the measured global relative slip away from contact surface. A set of springs was included in finite element model to simulate fretting fatigue test system. Compliance of springs was calibrated by comparing experimental and computed global relative slips. This methodology was then used to investigate local relative slip during fretting fatigue in cylinder‐on‐flat contact configuration under partial slip contact condition for unpeened and shot‐peened titanium alloy, Ti–6Al–4V. Relative slip on contact surface is significantly smaller (about one order) than the measured global relative slip by using a conventional extensometer near the contact surface. Effects of coefficient of friction, rigidity of fretting fatigue system and applied stress to specimen on the global and local relative slips were characterized. Coefficient of friction and contact load have considerable effect on local relative slip, and practically no effect on global relative slip. Gross slip condition can develop at some locations on contact surface in spite of overall partial slip condition. Increase in rigidity of fretting fatigue system increases local relative slip but decreases global relative slip. Finally, fatigue life diagrams based on relative slip on contact surface are established for both unpeened and shot‐peened titanium alloy. These show the same characteristics as of the conventional S–N diagram where fatigue life decreases with increase of relative slip.     

A fracture mechanics approach to high cycle fretting fatigue based on the worst case fret concept – II. Experimental evaluation

This is Part II of a series of two papers that describe the development and evaluation of a fracture-mechanics based life-prediction methodology for treating fretting fatigue in structural alloys. In Part I, the development of a life-prediction methodology based on the worst case fret (WCF) concept is presented with parametric calculations to illustrate the capability of the method. In this paper, the results of an experimental program designed to evaluate the applicability of the WCF model to treating high-cycle fretting fatigue in Ti-6Al-4V are described. High-cycle fretting fatigue tests were performed on Ti-6Al-4V at ambient temperature and at 2100 Hz. A flat pad with rounded edges or a cylindrical pad on rectangular specimens was fretted using either single or multiple cyclic load steps. Each load step was conducted for 10⁷cycles before the cyclic load range was increased. This process repeated until fretting fatigue specimen failed. The existence of nonpropagating cracks was identified using metallography and fractography. The experimental results were used to assess the accuracy of the WCF methodology.     

EFFECT OF RELATIVE SLIP AMPLITUDE ON FRETTING FATIGUE OF HIGH STRENGTH STEEL

Abstract— The effect of relative slip amplitude on fretting fatigue in high strength steel was studied at various contact pressures using fretting pads of various lengths. Under a given contact pressure, the fretting fatigue life showed a minimum at a certain relative slip amplitude. Under a fixed pad length, the life also showed a minimum at a certain contact pressure. A map of fretting fatigue life versus contact pressure and relative slip amplitude was obtained using the data of this study. The map indicated that both the phenomena which showed a minimum life in relation to slip dependence and contact pressure dependence were the same, as were the underlying mechanisms. The minimum life was interpreted in terms of local stress concentration at the fretted area.     

INFLUENCE FUNCTIONS FOR INCLINED EDGE CRACKS

A theoretical technique is developed for determining both KI and K_II from influence functions for angled edge cracks subjected to arbitrary distributions of normal and tangential contact stresses. Numerical results are presented which indicate the effect of crack length and crack angle on four influence functions, from which KI and K_II can be readily determined for specified distributions of tangential or normal contact stresses. In order to illustrate the use of the influence functions, a worked example is presented which shows the variation of KI and K_II with crack length and crack angle calculated for an assumed parabolic distribution of tangential stress under a fretting pad. Corresponding values of KI and K_II for other distributions of tangential and normal stresses may be determined by the same simple summation techniques used in this report.