Prediction of fretting fatigue behavior under elastic-plastic conditions

Fretting fatigue generally leads to the degradation of the fatigue strength of a material due to cyclic micro-slip between two contacting materials. Fretting fatigue is regarded as an important issue in designing aerospace structures. While many studies have evaluated fretting fatigue behavior under elastic deformation conditions, few have focused on fretting fatigue behavior under elastic-plastic deformation conditions, especially the crack orientation and fatigue life prediction for Ti-6Al-4V. The primary goal of this study was to characterize the fretting fatigue crack initiation behavior in the presence of plasticity. Experimental tests were performed using pad configurations involving elastic-plastic deformations. To calculate stress distributions under elastic-plastic fretting fatigue conditions, FEA was also performed. Several parametric approaches were used to predict fretting fatigue life along with stress distribution resulting from FEA. However, those parameters using surface stresses were unable to establish an equivalence between elastic fretting fatigue data and elastic-plastic fretting fatigue data. Based on this observation, the critical distance methods, which are commonly used in notch analysis, were applied to the fretting fatigue problem. In conclusion, the effective strain range method when used in conjunction with the SMSSR parameter showed a good correlation of data points between the pad configurations involving elastic and elastic plastic deformations.     

微动疲劳寿命的估算方法研究

着重分析了零构件由于微动磨损而造成的疲劳失效机制 ,说明了在这种微动疲劳模式下疲劳寿命的组成情况 ,用门槛值应力公式估算了当磨蚀坑根部萌生扩展性裂纹时蚀坑的临界深度尺寸 ,并分析了微动裂纹尖端的应力强度因子 ,得出了计算微动裂纹萌生尺寸的表达式 ,最后用上述方法计算了螺纹联接件的微动磨损寿命与裂纹萌生尺寸 ,用局部应力应变法计算了微动裂纹的萌生寿命 ,所得到的估测寿命与试验值相符 ,由此可见 ,该微动疲劳寿命的估测方法是合理的、有效的     

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.     

Mean stress effects in fretting fatigue life estimation method using fatigue damage gradient correction factor

In our previous study, we developed a fretting fatigue life estimation method that considers stress gradient effect [Journal of Mechanical Science and Technology 28 (2014) 2153–2159]. In this method, fatigue damage value at the cracking location is corrected with the factor that is a function of fatigue damage gradient, and the corrected value is treated as the fatigue damage value in plain fatigue for life estimation. In the present study, we examined the effect of mean stress on fatigue damage gradient correction function, because the reliability of the developed method was only verified at a stress ratio (R) of ?1 in previous studies. Fretting fatigue experiments were conducted to obtain the fatigue life data of three different fretting pad shapes with R values ranging from ?1.0 to 0.3. Finite element analyses were then conducted to evaluate the fatigue damage parameter in the cracking region. The results revealed that fretting fatigue life decreases at increased stress ratio. Furthermore, the fatigue damage gradient correction function was unaffected by the stress ratio, although it is affected by plastic deformation at the cracking location. Thus, a correction function for the occurrence of plastic deformation and another for the absence of plastic deformation are necessary. The developed method was demonstrated to predict the fretting fatigue life at various levels of stress ratio with the use of plain fatigue data.     

Characterization of fretting wear behavior of Cu–Al coating on Ti–6Al–4V substrate

Fretting wear and fretting fatigue are two commonly observed material damages when two contacting bodies with a clamping load are under the oscillatory motion. In this study, fretting wear damage of Cu–Al coating on titanium alloy, Ti–6Al–4V substrate was investigated using the dissipated energy approach. Fretting tests were conducted with either no fatigue load or the maximum fatigue load of 300 MPa and stress ratio of 0.1 on the substrate (specimen). In order to investigate the effect of contact load and contact size, different pad sizes and contact loads were used in the tests. Accumulated dissipated energy versus wear volume data showed a linear relationship regardless of fatigue loading condition on specimen with the smaller pad size. However, two separate linear relationships were observed based on the fatigue loading condition with the larger pad size, such that a relatively more dissipated energy was required for a certain amount of wear with fatigue load on the specimen. The linear relationship between the accumulated dissipated energy and wear volume for both pad sizes extended from partial to gross slip regimes and was not affected by the applied contact load. Further, fretting tests with and without fatigue load resulted in different shapes of fretting loops when the larger pad size was used.     

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.     

Fretting fatigue life estimations based on fretting mechanisms

Generally the fretting fatigue S-N curve has two regions: one is the high cycle (low stress) region and the second is the low cycle (high stress) region. In a previous paper we introduced the fretting fatigue life estimation methods in high cycle region by considering the wear process; with this estimation method the fretting fatigue limit can be estimated to be the crack initiation limit at the contact edge. In this paper we estimate the low cycle fretting fatigue life based on a new critical distance theory, modified for a high stress region using ultimate tensile strength σ_B and fracture toughness K_IC. The critical distance for estimating low cycle fretting fatigue strength was calculated by interpolation of the critical distance on the fretting fatigue limit (estimated from σ_w0 and ΔK_th) with critical distance on static strength (estimated from σ_B and K_IC). By unifying this low cycle fretting fatigue life estimation method with the high cycle fretting fatigue life estimation method, which was presented in the previous paper, we can estimate the total fretting life easily. And to confirm the availability of this estimation method we perform the fretting fatigue test using Ni-Mo-V steel.     

Analysis of Fretting Fatigue of Cavitation Shotless Peened Ti–6Al–4V

Fretting fatigue behavior of cavitation shotless peened titanium alloy, Ti–6Al–4V coupons was investigated using finite element method and a critical plane-based multi-axial fatigue parameter. Cavitation shotless peening (CSP)-induced compressive residual stress, which was larger at the contact surface than its counterpart from the shot peening (SP). However, compressive residual stress decreased more sharply with distance from the contact surface in CSP than in SP. Analysis using a critical plane-based multi-axial fatigue parameter demonstrated that the crack initiation would occur inside the cavitation shotless peened specimen which matched with the experimental observations. On the other hand, crack initiation would occur on the contact surface in the shot peened specimen which again was in agreement with experiments. The analysis also showed that the crack propagation part of the total fretting fatigue life was longer in the shot peened specimen than in the cavitation shotless peened specimen while the crack initiation part was almost equal from both peening methods. Therefore, CSP could not improve the fretting fatigue life/strength as much as the SP did but it improved relative to the un-peened specimen.     

A fretting-fatigue damage threshold concept

Fretting fatigue studies were conducted on Ti-6Al-4V and 7075-T6 aluminum specimens cycled in axial fatigue loading at a fatigue ratio (R) of +0.1. Axial fatigue loading was applied at a frequency of 30 Hz in a laboratory environment with the fretting applied to the specimen central section through a fretting pad made of the same material as the fatigue specimen. Tests were conducted at various maximum axial fatigue loads and normal pressures.The fretting damage that occurred resulted in a significant reduction in fatigue life. The reduction in fatigue strength was greater for both materials studied in the long life region. A fretting fatigue damage threshold that results from the fretting was found to exist for both materials. At all load levels a given amount of fretting damage is required before any fatigue life reduction occurs. Presumably the damage leads to the development of cracks in the fretted areas. The concept of the fretting damage threshold is related to the development of an initial crack that causes the local stress intensity to exceed the threshold value at a much smaller number of applied cycles. Thus, the concepts of fracture mechanics are related to the “initiation” of fretting damage.     

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。     

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.     

基于能量密度法预测微动疲劳寿命

通过接触界面的应力应变场和临界平面法计算了能量密度损伤参数,结合疲劳试验得到了能量密度损伤参数-寿命关系曲线中的材料常数,建立了LZ50钢微动疲劳寿命的预测公式。根据裂纹萌生寿命预测效果,将Chen损伤值作为裂纹萌生控制参数。分析了摩擦因数、微动桥半径、循环载荷和微动桥压力对LZ50车轴钢的Chen损伤值的影响,以及CRH2型动车组空心车轴裂纹萌生的位置及寿命。     

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。     

The effects of laser peening and shot peening on fretting fatigue in Ti-6Al-4V coupons

This paper describes testing of Ti-6Al-4V coupons in fretting fatigue and compares the effects of mechanical surface treatments on performance. Fretting fatigue tests were performed using a proving ring for fretting load, bridge-type fretting pads, and applied tension-tension cyclic fatigue stress. As-machined (AM), shot peened (SP), and laser peened (LP) coupons were evaluated, and data generated to compare residual stress, surface condition, lifetime, and fractographic detail encountered for each. Near-surface residual stress in SP and LP coupons was similar. The layer of compressive residual stress was far deeper in LP coupons than in SP coupons and, consequently, subsurface tensile residual stress was significantly greater in LP coupons than in SP coupons. SP coupons exhibited a rough surface and had the greatest volume of fretting-induced wear. LP coupons exhibited a wavy surface and had a small volume of wear localized at wave peaks. SP coupons had the greatest fretting fatigue lifetime, with significant improvement over AM coupons. Lifetimes of LP coupons were similar to those for SP coupons at high fatigue stress, but fell between AM and SP coupons at lower fatigue stress. Fractographic evaluation showed that fractures of AM samples were preceded by initiation of fretting-induced cracks, transition of a lead fretting crack to mode-I fatigue crack growth, and crack growth to failure. SP and LP samples exhibited behavior similar to AM samples at high fatigue stress, but in coupons tested at low stress the lead crack initiated subsurface, near the measured depth of maximum tensile residual stress, despite the presence of fretting-induced cracks. The level of fatigue stress above which lead cracks were initiated by fretting was higher for LP than for SP, and was predicted with good accuracy using an analysis based on linear elastic fracture mechanics, the fatigue crack growth threshold stress intensity factor range, and superposition of measured residual stress and applied fatigue stress.     

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).     

Numerical Estimation of Fretting Fatigue Lifetime Using Damage and Fracture Mechanics

Fretting fatigue is a complex tribological phenomenon that can cause premature failure of connected components that have small relative oscillatory movement. The fraction of fretting fatigue lifetime spent in crack initiation and in crack propagation depends on many factors, e.g., contact stresses, amount of slip, frequency, environmental conditions, etc., and varies from one application to another. Therefore, both crack initiation and propagation phases are important in analysing fretting fatigue. In this investigation, a numerical approach is used to predict these two portions and estimate fretting fatigue failure lifetime under a conformal contact configuration. For this purpose, an uncoupled damage evolution law based on principles of continuum damage mechanics is developed for modelling crack initiation. The extended finite element method approach is used for calculating crack propagation lifetimes. The estimated results are validated with previously reported experimental data and compared with other available methods in the literature.     

微动疲劳寿命预测方法的探讨

进行激动疲劳和普通疲劳的对比分析，找出它们的差异和共性。根据已有的研究成果，本文提出根据微动作用确定疲劳裂纹萌生和扩展点的位置，在该位置用普通的疲劳理论和计算方法计算微动疲劳寿命的方法。该方法具有一定的准确性，可用来进行微动疲劳寿命的初步估算。     

Correlation between fretting and plain fatigue using fatigue damage gradient

Fretting fatigue is correlated with plain fatigue in order to develop a method to estimate fretting fatigue life from plain fatigue data. Fretting fatigue experiments as well as plain ones were conducted to obtain fatigue life data at various conditions. Finite element analyses were conducted to evaluate the Smith-Watson-Topper (SWT) fatigue damage parameter around crack initiation location. It is revealed that the SWT in fretting fatigue decays exponentially away from the surface. Moreover, a correlation function exists that relates the gradient of normalized SWT at the surface to the maximum SWT ratio of plain fatigue to fretting fatigue at the same life. It is demonstrated that equivalent SWT for fretting fatigue, which is determined from the correlation function, can be compared directly with plain fatigue data for estimation of fretting fatigue life.     

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.     

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.