In situ analysis and modeling of crack initiation and propagation within model fretting contacts using polymer materials

Crack initiation and growth under fretting-fatigue and fretting-wear contact conditions have been investigated using model epoxy materials which allowed an in situ visualization of damage processes within the contact zone. A fretting-fatigue predictive model has been used to analyze these experiments on the basis of an accurate determination of the contact conditions and knowledge of the bulk fatigue properties of the epoxy materials. A special emphasis has been directed towards crack nucleation and early growth during Stage I and Stage I-to-Stage II transition, Stage II crack growth. Photoelastic experiments especially showed that crack propagation under fretting-fatigue loading was strongly dependent upon the complex cyclic micro-sliding behaviour of the crack faces. Under a fretting-wear condition, the constancy of the local contact conditions within the gross slip regime allowed the derivation of realistic estimates of the crack initiation times from the theoretical model.     

New results for the fretting-induced stress concentration on Hertzian and flat rounded contacts

Recent work on fretting fatigue has emphasized the role of stress concentration on fretting damage, while previous work had concentrated on empirical parameters to assess influence of fretting on fatigue life. In particular, analogies with fatigue in the presence of a crack or a notch have been noticed, suggesting that the stress field induced by frictional contact per se may explain the reduction of fatigue life due to fretting.In the paper, new analytical and numerical solutions are produced for the stress concentration induced in typical fretting contacts involving the Hertzian geometry or the flat punch with rounded corners in view of application to the dovetail joints. Normal and tangential load (in the Cattaneo–Mindlin sense) is considered with “moderate” or “large” bulk stresses.     

The fatigue endurance limit of a high strength CrNi steel in a fretting dominated regime

In many assemblies of moving components, contact problems under various lubrication conditions are lifetime-limiting. There, relative motion of contacting bodies, combined with high loads transmitted via the contact surface lead to fretting fatigue failure. For a reliable prediction of in service performance load type, different damage and failure mechanisms that may be activated during operation have to be known.In this contribution selected results of a currently conducted research project are presented. The aim of this study was to examine the material behavior of a surface stressed steel. The influence of the fretting regime on fatigue properties has been investigated.     

随机载荷循环作用下的机械结构疲劳寿命预测模型

基于名义应力法建立了随机载荷循环作用下的结构疲劳寿命预测模型。分析了结构所受循环载荷作用的不确定性特征,在以循环载荷作用次数为寿命度量指标框架下,运用概率加权法和线性Miner累积损伤法则,分别建立了疲劳寿命与应力之间关系分别服从指数函数和幂函数两种形式时,随机载荷循环作用下的结构疲劳寿命预测模型,并运用所建立的模型对某转动轴的疲劳寿命进行了预测研究。     

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。     

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.     

车轮滚动接触疲劳与磨耗耦合关系数值模拟

滚动接触疲劳和磨耗是车轮失效的主要方式。通过三维弹性体非赫兹滚动接触理论得到接触斑内的法向、切向应力和材料上不同深度处的最大切应力分布,以CL60钢和贝氏体车轮钢为例,基于"layer"滚动接触疲劳失效模型和Zobory车轮磨耗模型,分析LM型车轮踏面和75 kg.m–1钢轨型面匹配时轮轨接触条件和车轮材质对车轮滚动接触疲劳和磨耗竞争关系的影响。计算结果表明,摩擦因数为0.3时,CL60钢在小蠕滑条件下会发生滚动接触疲劳损伤,在大蠕滑条件下只有轴重大于30 t时才会出现滚动接触疲劳损伤,而贝氏体车轮钢只有在大蠕滑条件且轴重为30 t时,载荷循环次数小于1×105的情况下才会出现滚动接触疲劳损伤;摩擦因数为0.6时,CL60钢和贝氏体车轮钢在各种工况下的滚动接触疲劳损伤速度都小于相同条件下的磨耗速度。     

Some observations on the CLNA model in fretting fatigue

Using the Atzori–Lazzarin criterion, the author has recently proposed a unified model for Fretting Fatigue denominated Crack-Like Notch Analogue—CLNA model, considering only two possible behaviours: either “crack-like” or “large blunt notch”. In a general FF condition, the former condition is treated with a single contact problem corresponding to the MIT Crack Analogue (CA) improved in some details also by the author. The latter, with a simple peak stress condition, i.e. a simple Notch Analogue model, simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical condition of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions are immediately written, and the CLNA model permits to collapse the effect of the contact loads on a single closed form equation (differently from many other models which do not permit this flexibility). For not too large contact areas (“crack-like” contact) no dependence at all on geometry is predicted, but only on 3 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 size-effect disappear, but the dependence on all other factors including geometry remains. The model compares favourably with some experimental results in the literature. In this paper, some aspects of the CLNA model are further elucidated.     

Cyclic tangential loading of dissimilar elastic bodies

A two-dimensional fretting fatigue problem involving normal and tangential loading of dissimilar elastic bodies in contact is analyzed. The bodies are brought into contact by a monotonic normal load and then a cyclic tangential load is superimposed with the normal load held constant. The Hertz half plane assumption is retained for each body and the region of contact is divided into a central zone of stick and two external regions of micro-slip in each of which the Amontons-Coulomb law of sliding friction is assumed to apply. The effect of the interaction between the normal and shear stresses due to the mismatch in elastic constants is quantified by comparing the present rigid-elastic numerical solution (extreme case) to the Cattaneo-Mindlin closed form solution for elastically identical materials.     

Investigation into effects and interaction of various fretting fatigue variables under slip-controlled mode

Fretting fatigue behavior of unpeened and shot-peened Ti–6Al–4 V was investigated using a dual-actuator test setup which was capable of applying an independent pad displacement while maintaining a constant cyclic load on the specimen. The fretting regime was identified based on the shape of the hysteresis loop of tangential force versus relative slip range and the evolution of normalized tangential force. The fretting regime changed from stick to partial slip and then to gross slip with increasing relative slip range, and the transition from partial to gross slip occurred at a relative slip range of 50–60 μm regardless of the applied cyclic load, surface treatment, contact load and contact geometry. The fretting fatigue life initially decreased as the relative slip range increased and reached a minimum value, and then increased with increase of the relative slip range due to the transition in fretting regime from partial slip to gross slip. Shot-peened specimens had longer fatigue life than unpeened specimens at a given relative slip range, but the minimum fatigue life was found to be at the same value of relative slip range for both shot-peened and unpeened specimens. Tangential force was directly related to relative slip and this relationship was independent of other fretting variables.     

Elastic–plastic spherical contact under combined normal and tangential loading in full stick

The behavior of an elastic–plastic contact between a deformable sphere and a rigid flat under combined normal and tangential loading with full stick contact condition is investigated theoretically. Sliding inception is treated as a plastic yield failure mechanism, which allows static friction modeling under highly adhesive conditions. Several contact parameters such as: junction tangential stiffness, static friction force and static friction coefficient are extensively investigated. The phenomenon of junction growth and the evolution of the plastic zone in the contact region are briefly described. It is found that at low normal dimensionless loads the static friction coefficient decreases sharply with increasing normal load, in breach with the classical laws of friction. As the normal load further increases the static friction coefficient approaches a constant value that is about 0.3 for many material properties combinations.     

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.     

起重机箱型梁疲劳裂纹与寿命预估

起重机疲劳裂纹是起重机破坏的主要形式之一,根据断裂力学与损伤力学,给出了单一裂纹的线弹性与弹塑性的应力强度因子和恒幅载荷与无级变幅载荷下的疲劳裂纹扩展公式,推导出了在无级变幅载荷下多裂纹的应力强度因子公式.运用起重机数据记录仪测得的数据,结合峰值计数法,得出起重机箱形梁的应力谱.结合实例对1台在役起重机箱型梁疲劳裂纹进行分析,实例表明,推导出的疲劳裂纹公式能够正确快捷地求出箱型梁的疲劳寿命;对特种设备检验以及减少起重机疲劳事故的发生具有重要的工程价值.     

Fretting of glass

Fretting damage to a glass surface in contact with a steel ball was investigated. In the initial stage of fretting, severe wear occurred on the steel ball and considerable wear debris was transferred to the glass surface. The coefficient of friction increased during this stage by 80%. Fatigue cracks were observed on the glass surface under conditions of high normal load and tangential force. The mechanism of fretting fatigue and fretting wear is discussed in relation to a brittle material. Finally the effect of thin metal foil inserts in reducing fretting damage is described.     

基于泊松随机过程的风力发电机叶片疲劳寿命估算

疲劳寿命决定了正常工况下工程结构服役期限的长度,对其进行准确预测对于零部件疲劳强度设计至关重要。由于机械零部件在工作期间经常会受到随机变幅载荷的作用,载荷间相互作用效应现象十分显著,导致单次循环载荷对材料所造成的疲劳损伤量发生变化,若忽略该效应会影响疲劳寿命估算的准确性。针对当前研究中的疲劳损伤累积法则无法考虑该效应的问题,提出一种将非齐次泊松随机过程函数与伴随损伤理论相结合来估算零部件疲劳寿命的方法,解决了由于载荷间相互作用效应所带来的载荷作用顺序的问题,并以随机加载试验为例验证了该方法的准确性。将其应用于风力发电机叶片的疲劳寿命估算过程中,结果表明该方法可靠、有效,为风力机叶片的疲劳可靠性设计提供了新的路径。     

Some Observations on Frictional Force During Fretting Fatigue

Frictional force behavior during fretting fatigue and its interdependence on other fretting variables are investigated. Both coefficient of static friction and the normalized frictional force (i.e., the ratio of frictional force and normal contact load) increase during the earlier part of a fretting fatigue test and then both reach to a stabilized value. The variation of temperature in the contact region and normalized frictional force with increasing cycle numbers and bulk stress show similar trend implying that normalized frictional force represents the average friction in the contact region during a fretting fatigue. An increase in bulk stress, relative slip, and hardness of pad material results in an increase of the normalized frictional force, while an increase in contact load, frequency and temperature decreases the normalized frictional force. The normalized frictional force is also affected by the contact geometry. On the other hand, coefficient of static friction increases with an increase in the hardness of mating material, temperature and roughness from shot-peening treatment, but is not affected by contact geometry and displacement rate. Further, the normalized frictional force is not affected by the contact geometry, roughness and applied bulk stress level when fretting fatigue test is conducted under slip controlled mode, however it increases with increasing applied relative slip and decreasing contact load in this case.     

Modelling of fretting fatigue in a fracture-mechanics framework

The use of fracture mechanics as an alternative to (Cauchy) stress-based fatigue criteria is illustrated in this paper, using the “crack analogue” concept to deal with crack initiation in a fracture mechanics framework. A very simple model, based entirely on independently derived parameters, is shown to be able to capture the qualitative effects of the normal and tangential loads of fretting-fatigue performance. The accuracy of the total life predictions is also satisfactory. Examples of how to account for residual stresses and size effect with such a model are discussed.     

应变疲劳可靠性理论与方法的新进展

介绍概率应变疲劳试验法、评价模型和损伤随机演化机制方面的新进展。突破经典极大似然法在参考试验载荷之外的单试样限制，提出新的广义极大似然疲劳试验法。新发现随机循环应力—应变响应现象并建立其概率模型。新发展概率疲劳应变一寿命模型。概率模型参数由称为广义极大似然法的方法确定，在整体数据层面综合考虑数据分散性规律与样本量对概率评价的影响。考虑随机应力—应变关系反映“随机应变载荷”、随机应变—寿命关系揭示材料的“应变强度”，提出随机应变载荷—强度干涉恒幅可靠性模型，与Keciguliu的递推法结合可进行变幅和应变载荷谱下的可靠性分析，形成了应变疲劳可靠性理论和方法的新体系。进一步根据有效短裂纹准则，揭示疲劳性能随机及演化性的本质原因源于主导有效短裂纹萌生区域及其裂尖区域微观结构扩展条件的差异及演化性；随机疲劳裂纹扩展、应变—寿命和应力—应变关系是3个关联的随机疲劳关系；疲劳损伤是一个由初始混沌状态，到独立无关的随机状态，然后到史相关随机状态的演化过程。