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 multiaxial fretting fatigue test for spline coupling contact

A novel fretting fatigue experimental methodology is presented for mimicking the salient fretting variables for arbitrary axial locations within a complex spline coupling geometry, under combined torque, axial loading and rotating bending moment. The approach permits the simulation, in a simplified test arrangement, of the superimposed multiaxial fretting conditions between the spline teeth. This is achieved via the combination of a low frequency in-plane cyclic normal clamping load and a higher frequency out-of-plane cyclic fatigue stress. The latter is known from spline fatigue tests to play a critical role, along with torque and axial loads, in fretting fatigue cracking of splines.     

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.     

Lifetime estimation of mechanical assemblies under constant amplitude fretting fatigue loading

In the present paper, a new analytical methodology to estimate both crack path and lifetime of metallic structural components under fretting fatigue elastic partial slip loading condition is proposed. Such a methodology consists in the joint application of (a) the criterion by Carpinteri et al for metallic structures under multiaxial constant amplitude fatigue loading in high‐cycle fatigue regime, (b) the critical direction method by Araújo et al, and (c) the critical distance method by Taylor, in the form of the line method. The accuracy of the above methodology is evaluated through experimental tests available in the literature, performed employing two cylindrical fretting pads pressed with a constant normal load against a dog‐bone type test specimen subjected to a cyclic axial load. All these components are made of Al 7075‐T651 aluminium alloy.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.     

Two methods for predicting the multiaxial fatigue limits of sharp notches

In this paper the problem of the multiaxial fatigue limit estimation of sharply notched components has been addressed using two different methods: a critical distance method and a method involving modified Wöhler curves. These two methods had been previously developed by the authors, but required modification for use in conjunction with finite element stress analysis of sharply notched specimens subjected to multiaxial loadings. Initially, it was demonstrated mathematically that these methods are equivalent in terms of multiaxial stresses near the notch tip. Subsequently, by employing some well‐known uniaxial notch fatigue concepts, some assumptions have been made in order to extend the use of these methods to in‐phase multiaxial notch fatigue situations. Experimental data were obtained from tests conducted on V‐notched specimens subjected to in‐phase mixed Mode I and Mode II loadings. Both methods were successful in giving fatigue limit predictions with an error usually less than 15%. This is interesting because the two methods make quite different assumptions about the nature of fatigue crack growth in the vicinity of the notch.     

A study on the combined effect of notch and fretting on the fatigue life behaviour of Al 7075-T6

In this study, an investigation was conducted on the fatigue performance of Al 7075-T6 plates in the presence of stress raisers (notch, fretting, and a combination of notch and fretting). Fretting situation was induced on the surface of the aluminium plate through steel contacting pads under two different clamping forces of 2 kN and 5.6 kN. The fatigue tests revealed a more dominant effect from stress concentrators originating from geometrical discontinuities such as the tested notch compared to the fretting wear conditions. Therefore, no noticeable differences were found between the fatigue lives of the notched specimens and the combined notch and fretting condition. A finite element stress analyses of the notched model under the contacting fretting pads agreed with the experimental results. The stress distribution at the clamped area introduced tensile stresses at the edge of the contact region, however, the stress at the notch tip was observed to be higher when an axial tensile load was applied to the end of the plate. Fractographic analyses confirmed the presence of cracks initiating from the fretting damaged surface for most of the combined notch and fretting fatigue test specimens particularly at the high cycle fatigue (HCF) zone.     

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.     

On the prediction of high-cycle fretting fatigue strength: Theory of critical distances vs. hot-spot approach

This paper summarises the results we obtained when applying both the theory of critical distances (TCD) and the hot-spot approach to predict high-cycle fretting fatigue strength. In particular, the accuracy of such approaches was checked considering some experimental results taken from the literature and ad hoc generated to explicitly investigate the size effect in fretting fatigue. According to the well-known experimental outcome that initiation and initial growth of fretting fatigue cracks is mainly mixed-mode dominated, both the TCD and the hot-spot approach were used in conjunction with two different multiaxial fatigue criteria: the so-called modified Wöhler curve method (MWCM), that is, a conventional critical plane approach, and the well-known mesoscopic criterion due to Dang Van. Considering cylindrical-on-flat contacts tested under partial slip conditions, it was seen that the TCD is successful in predicting the size effect in fretting fatigue, resulting in more accurate predictions than those obtained by applying the classical hot-spot approach. Moreover, the present study revealed that the overall best accuracy is obtained when applying the TCD along with the MWCM. This result is very promising, especially in light of the fact that such a design methodology can be employed by simply post processing linear-elastic FE results, making it suitable for being used to assess real mechanical assemblies without the need for carrying out time-consuming elasto-plastic analyses.     

Fretting fatigue failure mechanism of automotive shock absorber valve

Fretting fatigue is a complex mechanical failure phenomenon, in which two contact surfaces undergo a small relative oscillatory motion due to cyclic loading. This study proposes a methodology to analyze the fretting fatigue failure mechanism of automotive shock absorber valve by means of experimental and numerical approaches. A servo hydraulic test set-up is used to simulate fretting fatigue under real working conditions. Moreover, a 3-D finite element model is developed to analyze the contact status and stress distribution at contact interface between connected components, i.e. washer-disc contact. The experimental test results depict that fretting damage appears at contact interface between washer and disc, which causes the initial crack nucleation and advancing the crack up to the final fracture of valve disc. Stress field, obtained by numerical simulation, is used to monitor some fretting fatigue features such as the distribution of relative slip amplitude, contact pressure and different stress fields at contact interfaces. Eventually, the crack initiation site is estimated by monitoring variation of equivalent multiaxial damage stress at contact interface.     

基于局部应变能密度法的缺口多轴疲劳寿命评估

本文提出了包括实验和数值工作在内的综合分析,阐明了缺口行为对比例多轴疲劳寿命的影响。方法对45钢和45QT钢进行了考虑缺口半径和开口角的多轴疲劳试验,基于平均应变能量密度理论的多轴疲劳分析的分析和计算框架进行了研究,以处理能量梯度。结果显示,大量新的疲劳数据首先通过法向应力和剪应力进行汇总,然后通过凹口尖端周围受控体积中的局部应变能密度重新分析。结论缺口角度对比例载荷下多轴疲劳数据的影响较小,而缺口半径是影响疲劳寿命的主要因素。     

A 'crack-like' notch analogue for a safe-life fretting fatigue design methodology

Various analogies have recently been proposed for comparing the stress fields induced in fretting fatigue contact situations, with those of a crack and a sharp or a rounded notch, resulting in a degree of uncertainty over which model is most appropriate in a given situation. However, a simple recent approach of Atzori–Lazzarin for infinite‐life fatigue design in the presence of a geometrical notch suggests a corresponding unified model also for fretting fatigue (called Crack‐Like Notch Analogue model) considering only two possible behaviours: either ‘crack‐like’ or ‘large blunt notch.’ In a general fretting fatigue situation, the former condition is treated with a single contact problem corresponding to a Crack Analogue model; the latter, with a simple peak stress condition (as in previous Notch Analogue models), simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical situation of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions can be readily stated. Not only is the model asymptotically correct if friction is infinitely high or the contact area is very small, but also remarkably accurate in realistic conditions, as shown by excellent agreement with Hertzian experimental results on Al and Ti alloys. The model is useful for preliminary design or planning of experiments reducing spurious dependences on an otherwise too large number of parameters. In fact, for not too large contact areas (‘crack‐like’ contact) no dependence at all on geometry is predicted, but only on three load factors (bulk stress, tangential load and average pressure) and size of the contact. Only in the ‘large blunt notch’ region occurring typically only at very large sizes of contact, does the size‐effect disappear, but the dependence is on all other factors including geometry.     

Prediction methods of fatigue critical point for notched components under multiaxial fatigue loading

Two methods based on local stress responses are proposed to locate fatigue critical point of metallic notched components under non‐proportional loading. The points on the notch edge maintain a state of uniaxial stress even when the far‐field fatigue loading is multiaxial. The point bearing the maximum stress amplitude is recognized as fatigue critical point under the condition of non‐mean stress; otherwise, the Goodman's empirical formula is adopted to amend mean stress effect prior to the determination of fatigue critical point. Furthermore, the uniaxial stress state can be treated as a special multiaxial stress state. The Susmel's fatigue damage parameter is employed to evaluate the fatigue damage of these points on the notch edge. Multiaxial fatigue tests on thin‐walled round tube notched specimens made of GH4169 nickel‐base alloy and 2297 aluminium‐lithium alloy are carried out to verify the two methods. The prediction results show that both the stress amplitude method and the Susmel's parameter method can accurately locate the fatigue critical point of metallic notched components under multiaxial fatigue loading.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

A procedure for estimating the total life in fretting fatigue

ABSTRACT This paper proposes a procedure for estimating the total fatigue life in fretting fatigue. It separately analyses the fatigue crack initiation and propagation lives. The correlation between crack initiation and propagation is made considering a non‐arbitrary crack initiation length provided by the model. The number of cycles to initiate a crack is obtained from the stress distribution beneath the contact zone and a multiaxial fatigue crack initiation criterion. The propagation of the crack is considered using different fatigue crack propagation laws, including some modifications in order to take the short crack growth into account. The results obtained by this method are compared with the fatigue lives obtained in various fretting fatigue tests under spherical contact with 7075‐T6 aluminium alloy.     

A unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings

This paper proposes an engineering method suitable for predicting the fatigue limit of both plain and notched components subjected to uniaxial as well as to multiaxial fatigue loadings. Initially, some well‐known concepts formalized by considering the cracking behaviour of metallic material under uniaxial cyclic loads have been extended to multiaxial fatigue situations. This theoretical extension allowed us to form the hypothesis that fatigue limits can be estimated by considering the linear–elastic stress state calculated at the centre of the structural volume. This volume was assumed to be the zone where all the main physical processes take place in fatigue limit conditions. The size of the structural volume was demonstrated to be constant, that is, independent from the applied loading type, but different for different materials. Predictions have been made by Susmel and Lazzarin's multiaxial fatigue criterion, applied using the linear–elastic stress state determined at the centre of the structural volume. The accuracy of this method has been checked by using a number of data sets taken from the literature and generated by testing notch specimens both under uniaxial and multiaxial fatigue loadings. Our approach is demonstrated to be a powerful engineering tool for predicting the fatigue limit of notch components, independently of material, stress concentration feature and applied load type. In particular, it allowed us to perform predictions within an error interval of about ±25% in stress, even though some material mechanical properties were either estimated or taken from different sources.     

A notch critical plane approach of multiaxial fatigue life prediction for metallic notched specimens

An approach based on the local stress response is proposed to locate the fatigue critical point for metallic blunt notched specimens under multiaxial fatigue loading. According to the stress analysis, both stress gradient and gradient of loading nonproportionality exist at notch root. The plane in the vicinity of the notch that passes through the fatigue critical point and experiences the maximum shear stress amplitude is defined as the critical plane for notch specimens (CPN). Furthermore, the Susmel's fatigue damage parameter is modified to assess fatigue life of notched components by combining CPN and the theory of critical distance (TCD). The multiaxial fatigue test of the thin‐walled round tube specimens made of Ni‐base alloy GH4169 is carried out to verify the above approaches. In addition, test data of two kinds of materials are collected. The results show that the maximum absolute error of the fatigue critical point is 9.6° and the majority of the predicted life falls within the three‐time scatter band.     

Proportional/nonproportional constant/variable amplitude multiaxial notch fatigue: cyclic plasticity,non‐zero mean stresses,and critical distance/plane

This paper deals with the formulation and experimental validation of a novel fatigue lifetime estimation technique suitable for assessing the extent of damage in notched metallic materials subjected to in‐service proportional/nonproportional constant/variable amplitude multiaxial load histories. The methodology being formulated makes use of the Modified Manson‐Coffin Curve Method, the Shear Strain–Maximum Variance Method, and the elasto‐plastic Theory of Critical Distances, with the latter theory being applied in the form of the Point Method. The accuracy and reliability of our novel fatigue lifetime estimation technique were checked against a large number of experimental results we generated by testing, under proportional/nonproportional constant/variable amplitude axial‐torsional loading, V‐notched cylindrical specimens made of unalloyed medium‐carbon steel En8 (080M40). Specific experimental trials were run to investigate also the effect of non‐zero mean stresses as well as of different frequencies between the axial and torsional stress/strain components. This systematic validation exercise allowed us to demonstrate that our novel multiaxial fatigue assessment methodology is remarkably accurate, with the estimates falling within an error factor of 2. By modelling the cyclic elasto‐plastic behaviour of metals explicitly, the design methodology being formulated and validated in the present paper offers a complete solution to the problem of estimating multiaxial fatigue lifetime of notched metallic materials, with this holding true independently of sharpness of the stress/strain raiser and complexity of the load history.     

The use of multiaxial fatigue models to predict fretting fatigue life of components subjected to different contact stress fields

This work describes the application of multiaxial fatigue criteria based on critical plane and mesoscopic (Dang Van, 1973, Sciences et Techniques de lÁrmement, 47 , 647—722) approaches to predict the fatigue initiation life of fretted components. To validate the analysis, several tests under closely controlled laboratory conditions are carried out in a Ti‐6Al‐4V alloy. These classical Hertzian tests reveal a size effect where fretting fatigue lives vary with contact size. Experimentally available data for fretting fatigue of an Al‐4Cu alloy are also used to assess the models. Neither the critical plane models nor the mesoscopic criterion considered can account for the effects of different contact stress fields on the initiation life, if the calculation is based only on highly stressed points on the surface. It is shown, however, that satisfactory results can be achieved if high values of the fatigue parameters are sustained over a critical volume.     

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.