Fatigue Theory Research Articles

Метод реконструкции остаточных напряжений в призматическом образце с надрезом полукруглого профиля после опережающего поверхностного пластического деформирования

The stress-strain state in a surface-hardened bar (beam) with a stress concentrator of the semicircular notch type is investigated. A numerical method for calculating the residual stresses in the notch region after an advanced surface plastic deformation is proposed. The problem is reduced to the boundary-value problem of fictitious thermoelasticity, where the initial (plastic) deformations of the model are simulated by temperature deformations in an inhomogeneous temperature field. The solution is constructed using the finite element method. For model calculations, experimental data on the distribution of residual stresses in a smooth beam made of EP742 alloy after ultrasonic mechanical hardening were used. The effect of the notch radius and beam thickness on the nature and magnitude of the distribution of the residual stress tensor components in the region of the stress concentrator is studied. For the normal longitudinal component of the residual stress tensor, which plays an important role in the theory of high-cycle fatigue, it was found that if the radius of a semicircular notch is less than the thickness of the hardened layer (area of material compression), an increase (in modulus) of this component of residual stresses occurs in the smallest section of the part (in the volume immediately adjacent to the bottom of the concentrator). If the depth of the notch is greater than the thickness of the hardened layer, then a decrease (in magnitude) of this value is observed in comparison with a smooth hardened sample. It is shown that in a reinforced notched beam, the deflection value due to induced self-balanced residual stresses is less than in a smooth beam. Experimental verification of the developed numerical method is done for a surface-hardened smooth beam made of EP742 alloy.

On the theory of scale structural fatigue of metals at the proportional loading

The probabilistic multi-level model of metal fatigue at proportional loadings is presented. A system of hypotheses about the step-by-step grow of metal defects on micro-, meso- and macroscale levels is formulated. Here are proposed constitutive relations for the failure probability and a system of fatigue curves and equations of multilevel damage. The amplitude of the maximum principal stress is chosen as a variable, the material functions are determined according to fatigue tests, taking into account the results of physical research of brittle crack grow and in accordance with experimentally valid criteria of fatigue strength. It is shown the correlation between predicted fatigue strength and experimental data for steel 12XH2A, S135 and some ductile steel at combined tension and torsion.

Precision Retaining Time Prediction of Machining Equipment Based on Operating Vibration Information

The precision of machining equipment is the main factor that affects the reliability of the manufacturing system. The failure of equipment function which affects the efficiency of manufacturing system is often caused by out-of-tolerance of precision. In this research, the precision degradation was connected to the stress and frequency of the external load, and a method was proposed to predict the precision retention time (PRT) of machining equipment, in which the traditional fatigue theory was combined with the monitoring technology of the operating vibration information. The calculation method of vibration energy was derived based on the principle of mechanical dynamics. Combined with signal processing technology, the complex loads were expressed by energy spectrum in frequency domain. According to the characteristics of S-N curve and the historical test data, the F-E-T surface reflecting the relationship among load frequency, vibration energy and precision retention time was obtained. The surface was used to predict the PRT of the equipment under a certain processing task, and the effectiveness of the method was verified by a case study.

Unsteady performances of a parked large-scale wind turbine in the typhoon activity zones

Numerous large-scale wind turbines have been built in tropical cyclone zones in China during the last decades. However, considerable failures of parked wind turbines have been reported in typhoon activity zones each year. Many researches have been conducted to investigate the failure using theories of meteorology, fatigue, vibration, flutter and buckling. However, in the most studies, the aerodynamics of wind turbines were analyzed in analytical or simplified manner. To figure out the unsteady performances of a parked wind turbine in typhoon activity zones, a wind model is established by various wind speeds, directions and turbulence intensities, based on the observation data of super typhoons. The unsteady aerodynamics of a parked wind turbine, consists of three blades and a tower, were then investigated through numerical simulation. It has been found that the wake interaction between the blades and the tower can strongly affect the aerodynamic forces on the wind turbine, which highly depends on the wind direction. Critical directions for wind load were found to be E, W, NW, and NE directions.

РАСЧЕТНО-ЭКСПЕРИМЕНТАЛЬНАЯ МЕТОДИКА ОЦЕНКИ ОСТАТОЧНОГО РЕСУРСА ГАЗОПРОВОДА ПО УСТАЛОСТНОЙ ПРОЧНОСТИ

Актуальность. В реальных эксплуатационных условиях газопроводы работают при переменном уровне давления, которое в общем случае является величиной случайной, с неизвестным законом распределения. Также случайной является и температура окружающей среды. Вследствие отмеченных условий напряжения, возникающие в стенках трубы, не могут быть описаны законами, исследованными в рамках теории параметрической статистики. Основой прогнозирования ресурса газопровода является кривая усталости материала трубы, связывающая амплитуду действующих напряжений не со временем работы испытываемых до разрушения образцов, а с числом циклов их деформирования. Для определения в процессе эксплуатации газопровода остаточного ресурса во времени необходимо оценивать накопление в его материале усталостных повреждений при любом законе распределения напряжений независимо от его сложности. В настоящее время методики прогнозирования остаточного ресурса газопроводов, учитывающие фактический спектр изменения внешних нагрузок и процессы накопления от них усталостных повреждений в стенке трубы, отсутствуют. Поскольку газопроводы являются потенциально опасными объектами, определение их остаточного ресурса по времени эксплуатации является задачей важнейшей. Цель: определение во временном диапазоне остаточного ресурса газопровода с заданной вероятностью неразрушения, подвергающегося в процессе эксплуатации воздействию случайного спектра внешних нагрузок независимо от сложности спектра, с учетом процессов накопления усталостных повреждений в газопроводе. Методы: кинетическая теория механической усталости, методы непараметрической статистики, измерение циклических деформаций с помощью датчиков деформаций переменной чувствительности. Результаты. Разработана расчетно-экспериментальная методика, основанная на комплексном использовании: кинетической теории механической усталости, учитывающей накопление повреждений в процессе циклического деформирования изделий; методов непараметрической статистики, обеспечивающих восстановление функции плотности распределения напряжений независимо от сложности закона их изменения в процессе эксплуатации газопровода; оригинальных средств измерения циклических деформаций – датчиков деформаций переменной чувствительности. Рассмотрены основные этапы реализации методики. По зафиксированной в процессе эксплуатации газопровода на датчике величине перемещения границы его реакции (первых «темных пятен») на основе разработанных в рамках кинетической теории усталости уравнений получены математические зависимости решения задачи определения эквивалентных по повреждающему воздействию чисел циклов нагружения для восстановления длительности ступеней блока напряжений, расчета эквивалентных по повреждающему воздействию напряжений. На примере реализации методики установлена зависимость остаточного ресурса газопровода в зависимости от величины реакции на датчике, позволяющая оперативно оценивать остаточный ресурс различных участков газопровода в условиях эксплуатации. Показан вариант использования результатов реализации методики для определения влияния коррозионного дефекта газопровода на его остаточный ресурс.

Fatigue life prediction of the wire rope based on grey theory under small sample condition

The fatigue life prediction of wire rope has the characteristics of large sample size required and many uncertain factors. In this paper, the 40 6 × 31SW FC type wire rope is taken as the research object. Under the condition of fatigue life data of small sample size, the fatigue life prediction of wire rope under different load conditions is realized based on gray theory. As a first step, for the problems existing in the current fatigue life prediction of wire rope, this paper constructs an improved GM (1,1) model and predicts the reliability life data of wire rope under small sample size condition. Subsequently, based on this, combined with the equivalent alternating stress of the critical locations of wire rope during the fatigue test, the reliability stress-life curve of the critical locations of wire rope is determined; Finally, the fatigue life prediction model of wire rope is obtained by combining with the cumulative damage theory of fatigue. The fatigue life of wire rope under different loads is predicted and compared with the experimental value. The results show that the proposed method has high accuracy in predicting the small sample fatigue life of wire rope under single and combined loading conditions, which proves the effectiveness of this method.

Reliability-Based Mechanical Design, Volume 2: Component under Cyclic Load and Dimension Design with Required Reliability

A component will not be reliable unless it is designed with required reliability. Reliability-Based Mechanical Design uses the reliability to link all design parameters of a component together to form a limit state function for mechanical design. This design methodology uses the reliability to replace the factor of safety as a measure of the safe status of a component. The goal of this methodology is to design a mechanical component with required reliability and at the same time, quantitatively indicates the failure percentage of the component. Reliability-Based Mechanical Design consists of two separate books: Volume 1: Component under Static Load, and Volume 2: Component under Cyclic Load and Dimension Design with Required Reliability. This book is Reliability-Based Mechanical Design, Volume 2: Component under Cyclic Load and Dimension Design with Required Reliability. It begins with a systematic description of a cyclic load. Then, the books use two probabilistic fatigue theories to establish the limit state function of a component under cyclic load, and further to present how to calculate the reliability of a component under a cyclic loading spectrum. Finally, the book presents how to conduct dimension design of typical components such as bar, pin, shaft, beam under static load, or cyclic loading spectrum with required reliability. Now, the designed component will be reliable because it has been designed with the required reliability. The book presents many examples for each topic and provides a wide selection of exercise problems at the end of each chapter. This book is written as a textbook for senior mechanical engineering students after they study the course Design of Machine Elements or a similar course. This book is also a good reference for design engineers and presents design methods in such sufficient detail that those methods are readily used in the design.

Time-domain calculation method for structural fatigue life under multi-axis correlation random excitation

Based on the typical aerospace frame structure, the fatigue life law of the structure under multi-axis correlation time-domain random excitation is studied. By constructing multi-axis time-domain random excitation with different correlation coefficients, multi-axial fatigue theory and structural vibration fatigue life time-domain method are used to calculate the fatigue life of the structure under different excitations; by constructing the structural finite element model in MSC. Pastran and nCode-DesignLife, and Co-simulation calculates the structural fatigue life. The results show that there is a negative correlation between the correlation coefficient of the applied multi-axis time-domain random excitation and the structural fatigue life, that is, the larger the correlation coefficient, the shorter the fatigue life.

Crack initiation characteristics of ring chain of heavy-duty scraper conveyor under time-varying loads

Crack initiation characteristics of ring chain of heavy-duty scraper conveyor under time-varying loads were investigated in this study. The dynamic tension of ring chain of the heavy-duty scraper conveyor was obtained using the time-varying dynamic analysis. Finite element analyses of three-dimensional contacts between adjacent chain rings at straight and bending segments were carried out to explore three-dimensional stress distributions of chain rings. The crack initiation life of chain ring was predicted employing the multiaxial fatigue theory. The results show that the ring chain is subjected to time-varying dynamic tensions during operation. During tension-tension contact fatigue, as compared to the straight segment of ring chain, the bending segment engaging in the sprocket presents an overall lower (or higher) equivalent stress distribution in the case of flat (or vertical) chain ring, respectively. Maximum equivalent stresses at the contact regions of adjacent chain rings both present time-varying dynamic characteristics similar to evolutions of dynamic tension. During tension-torsion contact fatigue, an increase in torsion angle level causes unobvious difference between equivalent stress distributions at contact regions of adjacent rings. Predicted crack initiation lives of chain rings during tension-tension contact fatigue indicates more severe fatigue damages of the vertical chain ring at the straight segment and of the flat chain ring at the right bending segment.

A viscoelastic damage constitutive model for asphalt mixture under the cyclic loading

Taking into consideration the shortcomings of traditional fatigue theory in addressing fatigue cracking distress in asphalt pavement, this paper attempts to investigate the fatigue damage characteristic of asphalt mixture through the fatigue damage theory, which demonstrates fatigue damage’s mechanism, and mainly focuses on the theory’s pivotal content --- the damage constitutive model. First, this paper couples the Burgers viscoelastic model with a modified Chaboche damage model, using classical mechanics of viscoelastic materials as well as strain equivalent principle of damage mechanics, to establish a viscoelastic damage constitutive model that can reflect the effect of cyclic loading or loading frequency on mixture’s stress-strain characteristic. Then, some indirect tensile fatigue tests were conducted to collect the data for strain progress, damage development, and the fatigue life of mixtures under different loading conditions, so as to obtain the value of model parameters that fit these test data. Finally, a comparison of the cumulative strain, damage variable, as well as the fatigue life verified the model’s effectiveness and accuracy. Results showed that the proposed model can better reflect the damage evolution law and stress-strain characteristics of asphalt mixture under the cyclic loading, as well as the effect of loading frequency or load level on mixture’s fatigue damage characteristics. The model is worthy of further application and promotion in the area of fatigue damage research for asphalt pavement.

Analysis and Study of FBG Sensor in Crack Monitoring of Aircraft Structure

Based on the FBG sensing principle, the stress of each test point was measured by fatigue test with the change of tensile time using the strain sensitivity characteristics of FBG (fiber Bragg grating) sensor, and the experimental results were compared with the fatigue theory, FBG sensor can not only monitor the various stages of the crack growth, but also can effectively determine the time of occurrence of fatigue cracks and the top of the general location. This will provide a strong basis for the further application of FBG sensors in aircraft structural health monitoring.

Fatigue damage evolution model of asphalt mixture considering influence of loading frequency

In view of shortcomings for the traditional fatigue theory in addressing fatigue cracking distress of asphalt pavement, this paper attempts to adopt fatigue damage theory, which is more consistent with the essence of pavement fatigue distress, to study the fatigue damage characteristic of asphalt mixture, and mainly focuses on its pivotal content—damage evolution model. Considering the important influence of loading frequency on the fatigue life and damage evolution characteristics of asphalt mixture, a new damage evolution model is constructed by introducing the influence of loading frequency into the classical Chaboche damage evolution model, as well as the theoretical analysis and laboratory tests are used to analyze and verify the model proposed in the paper. The results show that the calculated results of the model agree well with the measured, which can not only reflect the basic law of damage evolution and accumulation for asphalt mixture, but also reflect the influence of loading frequency on fatigue damage characteristics of mixture. Consequently, it is worthy of further application and promotion in the research of fatigue damage of asphalt pavement.

Multiaxial fatigue reliability assessment using a differential ant-stigmergy algorithm

This study presents a process of establishing a multiaxial Weibull model to assess S45C steel reliability and high-cycle fatigue. The proposed model includes multiaxial stress state, stress gradient and component size factors, and the probability of failure. The model was based on multiaxial fatigue theory, where the expressed damage parameter is a single value for one cycle of the multiaxial stress state, combined with the weakest link concept. Through the maximum likelihood method (MLE), a probabilistic stress-life (P-S-N) curve that reflects both failure and right-censored data was plotted; whereas optimal Weibull parameters were estimated via the differential ant-stigmergy algorithm (DASA). The completed multiaxial Weibull model was then applied to S45C steel tension-compression (TC) and zero-tension (ZT) fatigue test data, both of which agreed well. Afterward, the model was cross-checked with torsion fatigue test data results for validity.

A multi-scale failure-probability-based fatigue or creep rupture life model for estimating component co-reliability

The American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC) Committee has recently developed a new Section XI (Nuclear Components Inspection) Division 2 Code named “Reliability and Integrity Management (RIM)." RIM incorporates a new concept known as “System-Based Code (SBC)" originally due to Asada and his colleagues (2001–2004), where an integrated approach from design to service inspection is introduced using an overall statistical quantity known as “reliability index,” or, “co-reliability target.” In this paper, we develop a new theory of fatigue and creep rupture life modeling for metal alloys at room and elevated temperatures such that the co-reliability target can be estimated from fatigue and creep rupture test data. To illustrate an application of this new modeling approach, we include two numerical examples using (a) the fatigue failure data of six AISI 4340 steel specimens at room temperature (Dowling, N. E., 1973) and (b) the creep rupture time data of 37 specimens of 1.3Mn-0.5Mo-0.5Ni steel plates at 500 C (NRIM, 1987). Significance and limitations of this new fatigue and creep rupture life modeling approach are presented and discussed.

Estimation of Service Life of Mechanical Engineering Components

The paper is aimed to the methodology for estimation of service life of mechanical engineering components in the case of elastic-plastic contact of surfaces. Well-known calculation methods depending on physics, theory of probability, the analysis of friction pair’ shape and fit include a number of parameters that are difficult or even impossible to be technologically controlled in the manufacturing of mechanical engineering components. The new approach for wear rate estimation using surface texture parameters as well as physical-mechanical properties and geometric parameters of components is proposed. The theoretical part of the calculations is based on the 3D surface texture principles, the basics of material fatigue theory, the theory of elasticity and the contact mechanics of surfaces. It is possible to calculate the service time of the machine, but the process of running-in of the components is relatively short (less than 5%), therefore, the service time is mainly determined by a normal operating period, which also was used to evaluate this period. The calculated input parameters are technologically and metrologically available and new method for calculating the service time can be used in the design process of the equipment. The results of approbation of the method for estimation service time of mechanical engineering, which prove the applicability of mentioned method, are offered as well.

On the cavitation resistance of deep rolled surfaces of austenitic stainless steels

In the present work, two austenitic stainless steels (AISI 304 and AISI 316) were evaluated in cavitation tests with deep rolling treatments (DRT) on their surfaces. The results show that both steels exhibited better behaviour after the deformation process than in untreated conditions; however, the wear rate did not stabilize for the deformed surfaces due to the gradient of properties, attributed mainly to hardness profile of the material after DRT. A correlation between the cavitation erosion resistance and the fatigue strength is presented, with the cavitation wear rate and incubation time showing a good correlation with the fatigue strength coefficient in the case of high-cycle fatigue. In the case of low-cycle fatigue, a good correlation was established for the cavitation wear rate considering the Manson-Coffin theory of strain fatigue, assuming that the cavitation wear rate is inversely proportional to the fatigue life and using a fracture strain equal to the fatigue-ductility coefficient. In this case, a proportional constant around of 103 was found to establish the correlation for both steels. On the other hand, a linear correlation between the cumulative mass loss and surface roughness was separately established for steels under DRT conditions and untreated conditions. In addition, it was demonstrated that DRT is a great possible method for reducing the cost by wear.

Pathophysiological and cognitive mechanisms of fatigue in multiple sclerosis

Fatigue is one of the most common symptoms in multiple sclerosis (MS), with a major impact on patients’ quality of life. Currently, treatment proceeds by trial and error with limited...

An Airfield Soil Pavement Design Method Based on Rut Depth and Cumulative Fatigue

The structure and damage modes of soil pavement, as well as existing problems in current design methods, were comprehensively analyzed, and a new design method for airfield soil pavement was proposed. The proposed method avoids the use of the “designed aircraft” concept and instead adopts the cumulative fatigue theory widely used in permanent airfield design at present. Moreover, in view of the lack of aircraft wheel trajectory distribution data, an approximate method for calculating the wheel trajectory distribution considering the side slip distance of the aircraft was proposed and the equivalent width of the wheel tread was calculated by introducing the modulus ratio. Finally, the pass-to-coverage ratio was obtained. According to the characteristics and damage modes of airfield soil pavement, rut depth was determined to be the unique factor affecting soil pavement damage, and resilient modulus was used as the control variable to improve the adverse impact of the empirical method. Furthermore, according to the rut prediction formula for airfield soil pavement put forward by the US Army Engineer Research and Development Center, a fatigue equation based on the resilient modulus was proposed to calculate the allowable number of repetitions. To verify the reliability of the design method, a test section was constructed at a test center in Jining, China, and the theoretical maximum allowable repetitions on the soil runway were calculated by the currently used California bearing ratio test, the β-fatigue equation, and the proposed method. Aircraft traffic tests were carried out on the test section. Finally, the theoretical and test results were compared and the values calculated via the proposed method were found to be consistent with experimental values, thereby validating the reliability of the method.

Fatigue life assessment of crankshaft with increased horsepower

PurposeThe purpose of this paper is to analyze the fatigue life of the crankshaft in an engine with increased horsepower.Design/methodology/approachThe applied load on the powertrain components was calculated through a dynamic analysis. Then, to estimate the induced stress in every crank angle, the calculated loads in different engine speeds were applied on the crankshaft. Finally, the critical plane fatigue theories in addition to URM standard were used to estimate the damage and fatigue life of the crankshaft with the increased power.FindingsIt was found that a simultaneous increase of gas pressure and engine speed by 30 percent will cause an increase of maximum applied load on the crankshaft by 25 percent. It was also found that while the results of finite element (FE) method predict an infinite life for the crankshaft after increasing the power, the URM method predicts an engine failure for the increased power application. In this study, the crankpin fillet is introduced as the most critical area of the crankshaft.Originality/valueIncreasing the power of the internal combustion engines without changing its main components has been of high interest; however, the failure associated with the increased load as the result of increased power has been a big challenge for that purpose. Moreover, although URM standard provided an efficient practice to evaluate a crankshaft fatigue life, using FE analysis may provide more reliability.

A model for hybrid bearing life with surface and subsurface survival

Hybrid bearings have rings made of steel and rolling elements made of bearings grade silicon nitride ceramic. Due to the higher modulus of elasticity of ceramic compared to steel, the ellipse of the Hertzian contact is slightly smaller than that in a conventional bearing. This results in about a 12% increase in the contact pressure between the ceramic ball and the raceway. Following the standard Rolling Contact Fatigue theory, a higher contact pressure leads to a reduction of the dynamic load-carrying capacity and service life of the bearing. However, long experience in the use of hybrid bearings shows that, in most applications, hybrid bearings clearly outperform traditional bearings made entirely out of steel.This paper addresses this issue by applying a novel approach to Rolling Contact Fatigue. Central to the new method is the survival probability of the raceway surface which is explicitly formulated into the basic life equations of the rolling contact. This allows tailoring the contribution of the stress system close to the rolling surface to better represent the ceramic-steel interaction, which has been proven to be substantially more favourable in the case of a hybrid ceramic-steel contact. The comparison between experimentally obtained hybrid bearings fatigue lives and lives predicted using the new calculation model indicates good agreement.It is found that an increase of the fatigue resistance of the raceway surface of hybrid bearings can, in most cases, compensate for the additional stress present in the subsurface region of the rolling contact. The new methodology, by providing a direct account of the survival probability of the ceramic-steel interface gives a better representation of the expected performance of hybrid bearings, opening new opportunities for the reliable use of this type of bearing in modern machinery.