Fretting fatigue crack initiation lifetime predictor tool: Using damage mechanics approach

Fretting fatigue is a combination of two complex mechanical phenomena. Fretting appears between components that are subjected to small relative oscillatory motions. Once these connected components undergo cyclic fatigue load, fretting fatigue occurs. In general, fretting fatigue failure process can be divided into two main portions, namely crack initiation and crack propagation. Fretting fatigue crack initiation characteristics are very difficult to detect because damages such as micro-cracks are always hidden between two contact surfaces.In this paper Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Analyses (FEA) is used to find a predictor tool for fretting fatigue crack initiation lifetime. For this purpose an uncoupled damage evolution law is developed to model fretting fatigue crack initiation lifetime at various fretting condition such as contact geometry, axial stress, normal load and tangential load. The predicted results are validated with published experimental data from literature.     

钢丝微动疲劳裂纹萌生寿命预测研究*

钢丝微动疲劳过程中,钢丝裂纹萌生特性直接影响其裂纹扩展特性,进而制约钢丝微动疲劳寿命,因此开展钢丝微动疲劳裂纹萌生寿命预测研究具有重要意义。基于有限元法、摩擦学理论和断裂力学理论,运用Smith-Watson-Topper（SWT）多轴疲劳寿命准则建立考虑磨损的钢丝微动疲劳裂纹萌生寿命预测模型,基于多种不同的钢丝疲劳参数估算方法对钢丝的微动疲劳裂纹萌生寿命进行了预测,并探究接触载荷、疲劳载荷、交叉角度及钢丝直径等微动疲劳参数对钢丝微动疲劳裂纹萌生寿命的影响规律。结果表明：基于中值法的预测结果最接近实际值;在微动疲劳过程中,钢丝微动疲劳裂纹萌生寿命主要与接触载荷和疲劳载荷相关。通过引入微动损伤参数建立简化的适用于钢丝绳的钢丝微动疲劳裂纹萌生寿命预测模型,通过与考虑磨损的预测模型计算结果进行对比验证了该模型的准确性。     

Numerical Investigation into the Effect of Contact Geometry on Fretting Fatigue Crack Propagation Lifetime

Fretting fatigue is a phenomenon in which two contact surfaces undergo a small relative oscillatory motion due to cyclic loading. There is a need to analyze the effects of contact geometry on crack propagation under fretting fatigue conditions. In this investigation, a finite element modeling method was used to study the effects of different contact geometries along with crack–contact interaction on crack propagation lifetime. Different contacts geometries—that is, cylindrical on flat and flat on flat—along with different contact span widths were analyzed. In addition, the effects of different contact spans on stress distribution at the contact interface were investigated. The computed crack propagation life was compared with experimental results. It was found that the crack initiated near the contact trailing edge for all contact geometries, which agreed with experimental observations. In terms of crack propagation for different contact spans, the fretting fatigue life for a two-based cylindrical pad was shorter than that for a two-based flat pad. By increasing the contact span width for both flat and cylindrical pads, the crack propagation lifetime increased. A comparison between the experimental and numerical results demonstrated a difference of about 18% in crack propagation lifetime.     

带有微动磨损缺口钢丝的疲劳特性

在自制的微动磨损试验机上进行钢丝的微动磨损试验,将微动磨损后的钢丝试样在液压伺服疲劳试验机上进行不同应力比和不同应力幅下的疲劳试验。结果表明,钢丝的微动磨损深度随微动时间和接触载荷的增加而增加,磨损缺口处的应力集中使其成为了裂纹萌生源,也使钢丝试样的疲劳寿命大大降低,微动磨损后钢丝试样的疲劳寿命和磨损深度呈反比关系。通过钢丝疲劳断口的SEM形貌分析了其疲劳断裂机制,断口对应不同的疲劳阶段,可分为裂纹萌生区、裂纹扩展区和裂纹瞬断区。     

Life estimation of Ti-6Al-4V specimens subjected to fretting fatigue and effect of surface treatments

Suitability of different multi-axial parameters in predicting fretting fatigue life of Ti-6Al-4V specimens has been investigated. Ameliorating effect of surface treatments on fretting fatigue has been studied. In simple uni-axial/multi-axial fatigue tests, nucleation as well as propagation of cracks occur under the influence of identical stresses. Hence nucleation accounts for most of the total life. Fretting fatigue crack nucleation occurs due to very large contact stresses, effect of which is felt only close to the surface (due to steep gradients). Propagation mostly occurs due to lower stresses in the bulk of the material (negligible influence of contact tractions) and forms a significant portion of total life. Total life has to be taken as sum of initiation life calculated from different multi-axial fatigue parameters and propagation life from conventional fracture mechanics approach. Steep stress gradients necessitate the adoption of a statistics based approach to predict the crack initiation life, based on an assumed distribution of flaws. The quality of comparison between predicted and experimentally observed failure lives provides confidence in the notion that conventional fatigue life prediction tools can be used to assess fretting fatigue failure. Effect of surface treatments like shot-peening with or without additional surface coatings on total life of the specimen and on friction coefficient has been studied.     

Fretting fatigue behaviour of Ti–6Al–4V alloy under plane bending stress and contact stress

Fretting fatigue tests for Ti–6Al–4 V alloy were conducted by use of the plate fatigue specimen with bolt-tightened shoe on both sides of the plate. It was clarified that the repeated bending stress at the contact area where fretting fatigue failure starts linearly decreased as stress over the contact area increased. Fretting fatigue crack starts from the pit where stress concentrate. The pit initiates when fretting debris were removed from the surface striation formed due to the contact slip movement. The fretting fatigue crack initiation mode was transgranular, while the fretting fatigue crack propagation mode was striation.     

Fretting fatigue crack initiation and propagation behavior of Inconel 690 alloy

Several studies have been conducted on the fretting fatigue limit characteristics of Inconel alloy tube material used in steam generators of nuclear power plants. Nevertheless, additional research on fretting fatigue crack initiation and propagation behavior is necessary in order to evaluate its fretting fatigue life more accurately. In this study, crack growth tests of fretting fatigue are conducted, and the characteristics of fatigue crack initiation and propagation are analyzed on Inconel 690 alloy. Also, plain fatigue crack growth tests are performed on the same material, and the results are compared with those of fretting fatigue crack growth tests. From both of the plain and fretting fatigue crack growth test results, the ΔK-da/dN diagrams are obtained and the crack growth rates are compared. It is found that the crack growth rate for fretting fatigue tests is faster than that for plain fatigue tests under a certain value of DK. However, over this value of DK, the crack growth rate for fretting fatigue tests becomes slower than that for plain fatigue tests due to debris which is produced by fretting and trapped in the propagated cracks. Finally, the fracture surfaces examined by an optical microscope, and the initiation angles of the oblique cracks are determined under various applied stresses. Also, the microstructure of the fracture surfaces is observed by a Scanning electron microscopy (SEM).     

含夹杂物轴承钢中裂纹的萌生与扩展

针对轴承钢中夹杂物周围应力集中导致的疲劳剥落,建立了一种结合连续损伤力学的内聚力模型,用于模拟滚动接触循环加载下的裂纹萌生与扩展。基于内聚力模型的损伤起始准则和损伤演化规律,利用VUMAT子程序结合连续损伤力学构造了新的损伤演化方式,实现循环加载下的损伤累积,建立了基于内聚力模型的疲劳损伤累积失效模型,对含夹杂物模型的疲劳裂纹萌生与扩展进行了模拟,并研究了载荷条件和接触区摩擦因数对裂纹萌生与扩展以及疲劳寿命的影响。研究结果揭示了微观裂纹的萌生与扩展过程,为认识滚动接触疲劳提供了基础。     

Fretting fatigue of single crystal nickel at 600 °C

An experimental setup has been developed to conduct fretting fatigue tests at 610 °C and fretting fatigue lives are characterized for the contacting pair of IN100 and single crystal nickel subjected to a range of loading conditions. A well characterized set of experiments have been conducted to obtain the friction coefficient in the slip zone. A robust quasi-analytical approach, based on solution to singular integral equations, has been used to analyze the contact stresses. Different multi-axial fatigue parameters have been investigated for their ability to predict the initiation life of the specimens. An estimation of crack propagation life was made using conventional fracture mechanics approaches, after making certain assumptions to simplify the problem. Total life was predicted using nucleation life from different parameters and propagation life from conventional fracture mechanics approach. These predicted lives were compared with experimentally observed failure lives. The quality of the comparison provides confidence in the notion that conventional life prediction tools can be used to assess fretting fatigue at elevated temperatures.     

TC4合金微动疲劳损伤研究

研究了TC4合金在柱面-平面接触务件下的微动疲劳行为，分析了其微动疲劳损伤机制。结果表明：在试验务件下，微动区边缘的损伤特征以粘着磨损为主，而微动区中部则以磨粒磨损和接触疲劳为主。疲劳裂纹易于在微动区．特别是在蚀坑处萌生和扩展。促使微动疲劳裂纹萌生的因素：一是法向应力和切向摩擦力引起的材料表层塑性变形，二是微动磨损破坏了材料的表面完整性，造成了缺口应力集中效应。     

轧机油膜轴承锥套接触疲劳损伤的机理分析

研究了油膜轴承锥套与辊颈接触表面在轧制载荷作用下发生微动疲劳损伤的力学机理。在分析油膜轴承油膜压力分布特征的基础上,采用有限元法给出了锥套与辊颈接触区边缘产生接触应力集中和微滑移的分布规律,阐明了弹性结合连接的锥套与辊颈接触表面产生微动疲劳损伤的原因。利用断裂力学裂纹尖端应力场与接触边缘区域应力局部渐近场的等效原则,给出了疲劳裂纹自点蚀处萌生与扩展的力学条件。上述结果为锥套和辊颈的实际损伤状态及模拟试验所验证。     

Fracture mechanics approach to fretting fatigue and problems to be solved

A large number of research works have been devoted to fretting fatigue from both mechanical and metallurgical viewpoints. In the present paper, fracture mechanical approaches for evaluating fretting fatigue life and strength have been briefly reviewed. Furthermore, a new approach based on a singular stress field near the contact edge and on fracture mechanics has been proposed. The directions of crack initiation and propagation as well as fretting fatigue life, which have coincided with the experimental results, could be estimated according to the new approach, in which singular stress near the contact edge and mixed mode crack growth have been taken into consideration. In the application of the new method to predict the fretting fatigue behavior, there are still several problems to be clarified, which have also been discussed in detail.     

Fretting damage modeling of liner-bearing interaction by combined finite element – discrete element method

This paper presents a methodology to study the fretting damage behavior by combined finite element-discrete element method based on FFD method and cut boundary displacement method. A discrete element modeling technique is developed. An inter-element contact constitutive model and its microscopic parameters are determined and calibrated to reproduce continuous and discontinuous behaviors of material in DEM. A crack visualization technique is developed to display cracks according to their failure mode and time dependency. The effect of fretting condition on crack initiation and propagation as well as fretting damage is studied. The mechanism of fretting wear is investigated.     

Characterisation of fretting fatigue damage using synchrotron X-ray micro-tomography

The fretting fatigue damage of mechanical joints is studied experimentally by considering the following scenario: first, the crack nucleation in the joint is investigated via fretting tests. Second, the propagation of the fretting cracks under cyclic uniaxial tensile loading is carried out and analysed. Synchrotron radiation X-ray micro-tomography is used to image for the very first time the three-dimensional shape of the initial fretting cracks as well as that of the propagating cracks at different stages of the fatigue life, thanks to a dedicated set-up. This technique brings new experimental data on the influence of the local microstructure on fretting fatigue damage, initiation and growth.     

Ti-6Al-4V燕尾榫结构微动疲劳裂纹萌生及扩展行为研究

针对Ti-6Al-4V钛合金燕尾榫连接结构在不同载荷下的微动疲劳现象,采用榫形微动疲劳试验进行研究,并对裂纹萌生扩展、微动磨损及断口进行分析。结果表明,微动疲劳使构件疲劳寿命显著降低约70%;疲劳载荷对微动裂纹扩展的影响比对裂纹萌生的影响更大;微动疲劳裂纹起始于接触面边缘,与接触表面约成45°角,裂纹扩展到60~150μm后转向与接触表面垂直;微动疲劳断口形貌表面在微动磨损区具有多个裂纹源点,但只有一个主裂纹形成。     

Modeling of geometry effects in fretting fatigue

The stress field that results from two bodies in contact is an important aspect that governs the fretting fatigue behavior of materials. Applied loads as well as contact geometries influence the contact stresses. The profile of an indenter and the boundary conditions provide sufficient information from which the surface tractions and the corresponding subsurface stresses have been calculated in a semi-infinite halfspace using singular integral equations. In this investigation, a numerical subroutine was developed to calculate the surface tractions and the corresponding surface and subsurface stresses of an arbitrary finite thickness infinite plate subjected to loading through a random indenter. The results from the detailed stress analysis of the contact region are required by both an initiation and fracture mechanics approach. While initiation criteria involving stress gradient fields, such as sharp notches and edges of contact in fretting fatigue, are not well established or agreed upon, stress intensity factor calculations using tools such as weight functions are more reliable. The stress intensity analysis, which is used to determine whether an initiated crack will continue to grow if it is above the threshold, depends on many variables in the stress analysis such as pad and specimen geometry, loading configuration and friction coefficient. The contact stress analysis has been used to determine equivalent stress parameters that are related to the initiation of a crack. Similarly the numerical subroutine for the contact stresses is used in conjunction with the stress intensity analysis to determine the influence of the geometry, loading configuration and friction coefficient on the stress intensity factor. Results from high-cycle fretting fatigue experiments are used to determine the threshold stress intensity factor for a given configuration. The combination of the numerical and experimental analysis is then used to develop a tool for high-cycle fretting fatigue based on a threshold approach involving a go–no go criterion.     

Fretting fatigue in hydrogen gas

To clarify the effect of hydrogen gas on fretting fatigue strength of the materials, which supposed to be used for hydrogen utilization machines, fretting fatigue tests were conducted in hydrogen gas. It is important to take fretting fatigue into account in strength design, because many fatigue failure accidents have occurred at joints or contact parts between components. As a part of the experiments, an austenitic stainless steel was focused in this paper. The material was SUS 304. Fretting fatigue strength in hydrogen gas decreased compared with that in air. Tangential force coefficient increased in the reverse order of fretting fatigue strength. Therefore, one of the reasons of the decrease of fretting fatigue strength was that tangential force was different depending on the environment. Absorption of hydrogen occurred during fretting in hydrogen gas was detected. The absorption could be considered as one of the causes of the decrease of fretting fatigue strength, since fretting fatigue life of pre-charged specimen was decreased and also the crack propagation threshold of short fatigue crack was reduced by hydrogen charge.     

The effect of rubber contact on the fretting fatigue strength of railway wheel tire

The cause of the ICE train derailment, which occurred in 1998 at Eschede, was fatigue failure originating on the inside of the wheel tire. Rubber-sprung resilient wheels were used for the trailer cars. The wheel tire is mounted on the wheel disc. Thirty-four rubber pads were arranged between the wheel disc and the wheel tire. It was postulated that fretting fatigue between the rubber block and the inner side of the tire might have an influence on the initiation of the incipient crack. In order to clarify the influence of the rubber contact on the fatigue strength of the tire, fretting fatigue experiments under rubber contact conditions were performed. During the fundamental fretting fatigue test using bridge pads and small size carbon steel specimens, no typical fretting damage such as fretting wear and minute cracks were observed due to contact of the rubber. Stress conditions of the rubber-sprung wheel under vertical and lateral wheel loads were evaluated by a three-dimensional elastic stress analysis. Since the rubber is a super-elastic material, the Mooney-Rivlin model was used in the FEM calculation. It was found that the wheel tire is subjected to a cyclic stress during one revolution of the wheel and the maximum stress occurred at the center of the inner surface of the tire where the fatigue crack initiated. Fatigue strength of the wheel tire was determined by the rotating bending fatigue testing of specimens taken from the tire. It was found that the tire with an 862 mm diameter at a wheel load of 80 kN had a safety factor more than 3.5 from a fatigue limit diagram with a failure probability of 0.01. To confirm the fretting damage under the rubber contact and the result of the fatigue strength evaluation, fatigue tests of a full size wheel were made. After 20 million cycles at the wheel load of 280 kN, which was just below the endurance limit estimated by the endurance limit diagram, no fretting damage and no fatigue cracks were observed. The wheel was, however, fractured at 1.56 million cycles under the maximum load of 308 kN, which was just above the endurance limit. The estimation of the safety factor of 3.5 estimated from the endurance diagram was confirmed by the full size fatigue testing. It was concluded that there was no effect of fretting due to the rubber contact on the fatigue strength of the rubber-sprung single-ring railway wheel.     

Effect of contact pressure on fretting fatigue of austenitic stainless steel

The effect of contact pressure on fretting fatigue in solution-treated austenitic stainless steel was studied. With an increase in contact pressure, fretting fatigue life was almost unchanged at low contact pressures, however it decreased drastically at high contact pressures. At low contact pressures, stress concentration due to fretting damage occurred at the middle portion of the fretted area and the main crack responsible for failure was initiated there. At high contact pressures, concavity was formed at the fretted area without accompanying heavy wear. The main crack was initiated at the outer edge corner of the concavity which probably acted as a notch. Plain fatigue prior to the fretting fatigue test increased the fretting fatigue life at high contact pressures since the concavity formation was suppressed by the cyclic strain hardening.