Fatigue life estimation of MD36 and MD523 bogies based on damage accumulation and random fatigue theory

Bogies are one of the multifunctional parts of trains which are extremely subjected to random loads. This type of oscillating and random excitation arises from irregularities of the track including rail surface vertical roughness, rail joints, variance in super-elevation, and also wheel imperfections like wheel flats and unbalancy. Since most of the prementioned sources have random nature, a random based theory should be applied for fatigue life estimation of the bogie frame. Two methods of fatigue life estimation are investigated in this paper. The first approach which is being implemented in time domain is based on the damage accumulation (DA) approach. Using Monte-Carlo simulation algorithm, the rail surface roughness is generated. Finite element (FE) model of the bogie is subjected to the generated random excitation in the first approach and the stress time histories are obtained, and consequently the fatigue life is estimated by using the rain-flow algorithm. In the second approach, the fatigue life is estimated in frequency domain. Power spectral density (PSD) of the stress is obtained by using the FE model of the bogie frame and the fatigue life is estimated using Rayleigh technique in random fatigue theory. A comprehensive parametric study is carried out and effects of different parameters like the train speeds and level of the rail surface vertical roughness on the estimated fatigue life are investigated. This paper was recommended for publication in revised form by Associate Editor Hong Hee Yoo Davood Younesian received his MSc and PhD in Mechanical Engineering, both from Sharif University of Technology, Iran. He joined the Iran University of Science and Technology in 2005 as an Assistant Professor in the School of Railway Engineering. Dr Younesian’s research area is mainly focused on non-linear and random vibrations, optimal control of vibrations, dynamics and vibration of structures and railway vehicle systems. He has published more than 75 papers in international journals and conference proceedings in the areas of his research. Ali Solhmirzaei received his BSc in Railway Engineering (Rolling Stock) from Iran University of Science and Technology and his MSc in Mechanical Engineering from K.N.T University of Technology, Iran. His research is mainly focused on finite elements, railway vehicle dynamics and fatigue analysis of railway structures. Alireza Gachloo received his BSc in Railway Engineering (Rolling Stock) from Iran University of Science and Technology, Iran. His research is mainly focused on random vibration, railway vehicle dynamics and random fatigue.     

A new method for the two-dimensional analysis of bone structure in human iliac crest biopsies

A new method is described for the analysis of the two-dimensional structural pattern of trabecular bone in human iliac crest biopsies. 8 μm thick undecalcified sections stained with the von Kossa technique were examined at a magnification of ×9. Using an Ibas II image analyser, the ratio of nodes to free ends and the length of different strut types (cortex to free end, node or cortex, free end to free end and node to node, loop or free end) expressed as a percentage of total strut length were assessed. The reproducibility of the method was good for most of the measured indices but inter-observer and inter-section variation were greater. Comparison of biopsy sections obtained from eleven young healthy control subjects and eleven patients with hepatic osteoporosis revealed a significantly higher node to free end ratio, node to loop and node to node strut length and significantly lower cortex to free end and free end to free end strut length in the controls. No significant differences were seen in node to free end, cortex to cortex or cortex to node strut length. This approach to trabecular bone structure analysis should prove useful in determining patterns of bone loss in health and disease and in examining the effects of treatment on bone structure in osteoporosis.     

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.     

A study on fatigue damage modeling using neural networks

Fatigue crack growth and life have been estimated based on established empirical equations. In this paper, an alternative method using artificial neural network (ANN) -based model developed to predict fatigue damages simultaneously. To learn and generalize the ANN, fatigue crack growth rate and life data were built up using in-plane bending fatigue test results. Single fracture mechanical parameter or nondestructive parameter can’t predict fatigue damage accurately but multiple fracture mechanical parameters or nondestructive parameters can. Existing fatigue damage modeling used this merit but limited real-time damage monitoring. Therefore, this study shows fatigue damage model using backpropagation neural networks on the basis of X-ray half breadth ratioB/B ₀ , fractal dimensionD _f and fracture mechanical parameters can estimate fatigue crack growth rateda/dN and cycle ratioN/N _f at the same time withinengineering limit error (5%).     

Fractographic analysis of fatigue damage in 7000aluminium alloys

In this paper, an attempt is made to correlate the fatigue damage in 7000 aluminium alloys with different impurity contents to the microstructural features and to explain their interdependence through fractographic observations. The Paris constants of these alloys in the form of hot‐forged plates subjected to the overaged T73 temper are evaluated and differences in the fatigue crack growth rate described by striation spacing measurements. Scanning electron microscopy analysis of fatigue fracture surfaces revealed that the type and morphological parameters of coarse intermetallic particles play a critical role in fatigue crack growth behaviour. The elemental distribution determined by means of energy‐dispersive spectroscopy analysis showed that the fractured particles accelerating the crack advances are larger particles of Fe‐rich phases. The fatigue crack growth rate increases considerably with increasing amounts of these particles. The smaller η, S and Mg₂Si particles contribute beneficially to fatigue life.     

车轴轮座微动损伤对车轴疲劳寿命的影响

使用有限元软件ANSYS计算轮座损伤对车轴疲劳寿命的影响.首先计算车轴的稳态受力,这时主要考虑两种栽荷:过盈应力和额定载重应力,关键是考虑两种载荷的复合作用效应.采用外推方法获得车轴材料的S-N曲线,然后将其导入有限元程序进行计算.计算结果表明:有微动损伤的车轴疲劳寿命比无微动损伤的疲劳寿命明显减少.     

疲劳损伤状态的模糊等效性试验研究

针对复杂载荷下以等效损伤假设为基础的材料疲劳寿命的估算误差较大的问题,基于模糊理论并结合耦合损伤概念提出模糊等效损伤假设,考虑加载顺序对疲劳损伤累积的影响来回避等效损伤假设。利用45钢材料进行了L-H和H-L加载顺序两级应力下的疲劳损伤累积规律验证,并选取16Mn材料的疲劳试验数据验证基于Miner线性损伤法则和本假设对材料疲劳寿命预测的准确性。结果表明,根据本假设计算的损伤量在两种加载顺序下均与试验值吻合良好,疲劳寿命估算结果比较接近于试验值,该假设以模糊理论为依据,为疲劳分析和寿命预测提供了一定的理论参考。     

Kinetics of damage accumulation in pearlitic rail steels under contact fatigue

The kinetics of damage accumulation in specimens of rail steels with the pearlitic structure manufactured by various companies has been studied in contact fatigue tests. The parameters of damage to the steels, such as the number, dimensions, and area of defects, the angular coefficients of cumulative size statistical distributions of the defects, as well as the velocity of propagation and the attenuation coefficient of ultrasonic waves, have been assessed. New criteria have been proposed to characterize the evolution of damage under contact fatigue. A linear interrelation between the number of surface defects and the number of subsurface defects in the zone of contact has been established, which can serve as a basis for continuously monitoring the condition rail steels and for assessing their current and remaining service lives.     

Prevention of fluttering fatigue damage in a tilting pad journal bearing

Tilting pad journal bearings have been widely used to support high-pressure/fast rotating turbine rotors owing to their inherent dynamic stability characteristics. However, fatigue damage in the upper unloaded pads and the break of locking pins by pad fluttering continuously take place in actual steam turbines. The purpose of this paper is to develop a bearing model that can prevent bearing problems effectively using pad fluttering in a tilting pad journal bearing. A developed bearing model with a wedged groove is suggested from studies of a fluttering mechanism performed in previous research. The fluttering characteristics of the upper unloaded pad are studied experimentally in order to verify the reliability of the bearing model. It was found that very little pad fluttering nearly occurs in the bearing model under various experimental conditions. In addition, no type of bearing failures by pad fluttering was detected in applications involving actual steam turbines.     

材料非稳态疲劳损伤智能模型可靠性分析仿真方法

材料的疲劳损伤是一非稳态过程,难以用传统的数学函数准确表达。摒弃了能量均匀耗散及线性累积损伤理论假设,采用神经网络技术准确描述其与材料性能、载荷应力间复杂的非线性映射关系,真实描述了材料疲荧损伤过程;建立了疲劳失效动态准则,综合考虑了材料疲劳性能及载荷的随机性,能够正确反映两者的个体性能及相互关系,并运用离散事件仿真原理,构造了材料疲劳可靠性分析的智能仿真系统,用于准确地进行疲劳寿命可靠性分析。经正火35钢随机载荷疲劳实验验证,其可靠性分析精度较高。     

Stress analysis of two-dimensional cellular materials with thick cell struts

Finite element analyses (FEA) were performed to thoroughly validate the collapse criteria of cellular materials presented in our previous companion paper. The maximum stress (von-Mises stress) on the cell strut surface and the plastic collapse stress were computed for two-dimensional (2D) cellular materials with thick cell struts. The results from the FEA were compared with those from theoretical criteria of authors. The FEA results were in good agreement with the theoretical results. The results indicate that when bending moment, axial and shear forces are considered, the maximum stress on the strut surface gives significantly different values in the tensile and compressive parts of the cell wall as well as in the two loading directions. Therefore, for the initial yielding of ductile cellular materials and the fracture of brittle cellular materials, in which the maximum stress on the strut surface is evaluated, it is necessary to consider not only the bending moment but also axial and shear forces. In addition, this study shows that for regular cellular materials with the identical strut geometry for all struts, the initial yielding and the plastic collapse under a biaxial state of stress occur not only in the inclined cell struts but also in the vertical struts. These FEA results support the theoretical conclusion of our previous companion paper that the anisotropic 2D cellular material has a truncated yield surface not only on the compressive quadrant but also on the tensile quadrant.     

Fretting fatigue in 2XXX series aerospace aluminium alloys

This research investigated the effects of microstructural characteristics on the fretting response in 2XXX series aerospace aluminium alloys. Fretting fatigue tests were conducted to determine the influence of slip character, alloy purity, grain structure and yield strength on fretting crack nucleation and growth. Crack length measurements and micrographs of the specimens indicated there was no significant difference in the fretting response of these alloys based on their microstructural characteristics. Results also showed that fretting caused cracks to nucleate in the first 1–5% of total life which resulted in much shorter fatigue lives. Additionally, fretting normalized the nucleation time in all alloys, eliminating the differences in intrinsic fatigue nucleation resistance. This resulted in the alloys with the highest stress-life (S–N) fatigue properties exhibiting a greater reduction in fatigue strength under fretting conditions. The total fretting fatigue life appeared to be primarily determined by the fatigue crack propagation resistance of the alloys.     

Rolling contact fatigue in lubricated contacts

This work presents and discusses the results of rolling contact fatigue tests (IP-300) with six different lubricants using a four-ball E.P. lubricant tester. These results tended to confirm the mechanism for rolling fatigue proposed by Jin and Kang. The lubricants tested were two mineral oils (SN 350 and SN 600) and four synthetic oils (PAG-9, PAG-12, PAO 6, and PAO X), the test machine used was a Four-Ball E.P., and the IP 300/87 standard was applied. The results indicated that: 1) lubrication has an important influence on the rolling fatigue life of mechanical components; 2) normally, in oils of the same family, the higher the viscosity is, the higher the rolling fatigue life is; 3) besides viscosity, other lubricant properties such as the pressure–viscosity coefficient (α), compressibility (B), and the EHL friction coefficient (γ), should all be taken into account for lubricated contact design.     

Propagation in fretting fatigue from a surface defect

This paper analyses the growth of cracks in fretting fatigue from an initial flaw at the surface. Different crack growth laws are used in order to take into consideration the particular behaviour of short cracks. This methodology is applied to estimate life in various fretting fatigue tests with spherical contact characterized by two different geometries. The material used in the experiments is Al7075. The two geometries present significant differences in the evolution of the stresses, crack growth, etc. which are discussed. The approaches used to model short crack growth give different results, some of them being in good agreement with the experiments.     

Maximum principal tensile stress and fatigue crack origin for compression springs

Contrary to the traditional concepts, for helical compression springs with a large coil radius to wire radius ratio, the most highly stressed region is at the outer surface of the helix rather than inside. The likely fatigue crack origin is also located on the outer surface of the helix where the maximum amplitude of the principal tensile stress was calculated during cyclic loading. An equation is proposed for the maximum tensile stress from loading of a helical spring, and a method is presented to calculate the likely fatigue crack origin. It is demonstrated that for high-stressed springs, fatigue design should be based on the range of the maximum principal tensile stress. The influence of the shot peening on the location of the fatigue crack origin is also investigated.     

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.     

A study on residual fatigue bending strength and damage behavior of CFRP composites subjected to impact loadings

This paper evaluates the static and fatigue bending strengths of CFRP (carbon-fiber reinforced plastic) laminates having impact damages, e.g., foreign object damages (FOD). Composite laminates used in this experiment are CF/EPOXY and CF/PEEK orthotropy laminated plates with two-interfaces [0°₄/90°₄]_s A steel ball launched by an air gun collides against the CFRP laminates to generate impact damages. The damage growth during a bending fatigue test is observed by a scanning acoustic microscope (SAM). When the impacted side is compressed, the residual fatigue bending strength of CF/PEEK specimen P is greater than that of CF/EPOXY specimen B. On the other hand, when the impacted side is in tension, the residual fatigue bending strength of CF/PEEK specimen P is smaller than that of CF/EPOXY specimen B. In the case of impacted-side compression, the fracture is propagated from the transverse crack generated near the impact point. In the case of impacted-side tension, however, the fracture develops toward the impact point from the edge of interface-B delamination.     

一种疲劳试验数据处理的仿真方法

由于疲劳寿命试验具有难度较大,其实验数据具有分散性强的特点,如果直接用灰色预测模型（ＧＭ（１,１））作预测,其预测值与真实结果的误差较大。在此提出一种试验仿真的新方法。首先将数据处理成对数据序列,以降低低其数据分散性;然后再用灰色预测模型进行预测。     

Effective elastic constants of two-dimensional cellular materials with deep and thick cell walls

In order to analyse the elastic constants of cellular materials with deep and thick cell walls, finite element analysis using two kinds of unit cell approach (stiffness matrix method and compliance matrix method) is performed which is applicable to any orthotropic cellular materials. Comparison between results from the FEA, the theories presented in this paper and experiments of previous investigators indicate that the elastic constants of cellular materials with thick cell walls depend not only on the relative density but also on the joint stiffening effect. Approximate formulae under generalised plane strain conditions are also presented for the purpose of obtaining the effective elastic constants for cellular materials with deep and thick cell walls. A satisfactory agreement was found with experimental results obtained on a deep and thick cellular material. The results indicate that the previous models in which the wall of cellular materials is treated as a simple beam are not adequate to evaluate the effective elastic constants of cellular materials with deep and thick cell walls. In addition, considerable attention needs for the measurement of effective Young's modulus of square cellular materials in the two soft directions because it is strongly affected by misalignment errors.     

Surface fatigue of brittle polymers in rolling line contact

The two-disc machine was used to study surface fatigue in polymethylmethacrylate (PMMA) specimens in rolling line contact. A notch was introduced to the specimen to study the crack growth rate. The form of damage in PMMA disc ranges from the appearance of small cracks on the contact path, leading to the formation of pits and initiation, growth and failure of crazes. A degree of sliding was introduced into the contact between the two discs to study the effect of the tangential force on surface fatigue and crack propagation. The creation of crazes was observed in both rolling and rolling/sliding configurations, but the time of initiation, the appearance, their size and the time to failure were different. An optical microscope and SEM were used to study the morphology of the failure produced. The growth rate in the artificially induced crack was monitored and appeared to be stable with an initial burst of crack extension.