Fatigue Curves Research Articles

The design of responsible details of an axial piston hydraulic machine improving

Methods of improving the designs of the most complex details of the axial piston hydraulic machine (APHM), cylinder block (CB) and face distributor (FD) are proposed in order to increase their strength. The possibility of modernization is demonstrated by the example of APHM 210.25 with a CB inclined. For samples of CB material, bronze CuSn12, tests were performed and fatigue curves are constructed. Based on the results of these tests, the endurance limit of the CB is determined using the theory of similarity fatigue fracture. The calculation of the BC by the finite element method showed that maximum stresses arise in its inter-cylinder wall (jumper). With conserved CB dimensions, a decrease in the maximum stress level by 30% is achieved if the axial cylinders are shifted in the peripheral direction by 2 … 3 mm. In the proposed design of the CB the calculated stresses became lower than its endurance limit. For FD an increase in the thickness of its peripheral zone was proposed, which also made it possible to reduce stresses by 12%. As a result, the level of acting stresses turned out to be 5.3% lower than the FD endurance limit. The achieved reduction in stress level for the considered details and an increase in their durability is a factor that growing the environmental safety of APHM.

The Critical Distance Method to estimate the fatigue strength of notched additively manufactured titanium alloys

The present investigation deals with the problem of performing the fatigue assessment of notched components made of 3D-printed titanium alloy Ti6Al4V when it is used in the as-manufactured condition. The notch fatigue strength of this additively manufactured metallic material was investigated by testing under axial loading a large number of specimens containing geometrical features of different sharpness. This experimental programme was designed to investigate also the effect of non-zero mean stresses, so that the experimental results were generated under a load ratio not only equal to -1, but also equal to 0.1. Being supported by the experimental evidence, the hypothesis was formed that the mechanical response of the 3D-printed titanium alloy being investigated could be modelled effectively by treating it as a material that is linear-elastic, homogenous and isotropic. This simplifying hypothesis allowed the Theory of Critical Distances to be employed also to assess the notch fatigue strength of 3D-printed titanium alloy Ti6Al4V weakened by geometrical features of different kind. The validation exercise based on the experimental results being generated demonstrates that this theory is highly accurate, with its use leading to predictions falling mainly within the scatter bands associated with the fatigue curves used for calibration. This level of accuracy is certainly satisfactory especially because the Theory of Critical Distances can be employed in situations of engineering relevance by making use of the results obtained by solving standard linear-elastic Finite Element models.

Evaluation of the Effect of the TIG-Dressing Technique on Welded Joints through the Strain Energy Density Method

Among the various techniques employed to increase the fatigue strength of a welded joint, the TIG dressing technique acts on the weld geometry re-melting the welding toe to eliminate the presence of sharp V-notches. The main aim of this work is to investigate the effect of the TIG dressing technique on the fatigue behavior of welded joints summarizing the results of experimental tests taken from the literature through the Strain Energy Density method. The experimental tests considered were performed both on as-welded and TIG-dressed joints in order to better understand the improvement that such a technique leads to the welded joints. Finally, the data were summarized through the Strain Energy Density technique to show that the same fatigue curve, defined in terms of Strain Energy Density versus number of cycles, obtained for the as-welded joints could be used also for the TIG-dressed joints being the method not dependent on the geometry considered.

СТОХАСТИЧЕСКИЙ РАСЧЕТ РЕСУРСА ДЕТАЛЕЙ МЕТАЛЛИЧЕСКИХ КОНСТРУКЦИЙ ПО РОСТУ МИКРОДЕФЕКТОВ

A stochastic approach has been developed to evaluate fatigue strength using elements of the fracture mechanics. The article presents a method for determining the initial parameters of statistical distributions. It also considers the method for constructing a fatigue curve for a component of any size and configuration with any given probability of failure.

Automated fatigue strength assessment of arc-welded structures according to the Peak Stress Method

The Peak Stress Method (PSM) is an approximate, FE-oriented application of the notch stress intensity factor (NSIF) approach to fatigue design of welded joints. This approach is based on the singular linear elastic peak stresses calculated from coarse FE models. The PSM was calibrated by using 2D, four-node plane quadrilateral elements; 3D, eight-node brick elements and 3D, four-node or ten-node tetra elements. By adopting the averaged Strain Energy Density (SED) as a fatigue strength criterion, a design stress, the so-called equivalent peak stress, has been defined and adopted in conjunction with a reference design fatigue curve to estimate the fatigue life of welded structures. The equivalent peak stress has successfully been adopted to assess the fatigue strength of arc-welded joints made of either structural steels or aluminum alloys and subjected to axial, torsion or multiaxial fatigue loadings. In the present work, a subroutine, named ANSYS-PSM, has been developed in the post-processing environment of ANSYS® FE code to automate the PSM for 2D or 3D FE models. After having briefly recalled the theoretical background of the PSM and the procedure to apply it step by step, the paper presents the adopted programming languages and the workflow of the developed subroutine.

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.

Fatigue damage of the heel joint of welded roof truss

The investigation of the welded roof truss behavior under the complex influence of static and cyclic loads is carried out. The truss is made of the shaped pipes and its size is 24000x2400 mm. The technique of computer simulation experiment by means of SolidWorks Simulation software is used. It is found that the maximum stresses are formed in the area of thermal impact from the weld in the truss heel joints. During the truss operation, these stresses initiate the emergence of fatigue cracks and their growth until the structure ultimate state. The fatigue curve for the investigated structure is constructed. It is determined that the design service life of the truss under operational load modes is going to be 52 years.

Damage analysis four-point bending fatigue tests on stone matrix asphalt using dissipated energy approaches

Four-point bending tests under strain-controlled mode were conducted on a stone matrix asphalt. Fatigue properties were evaluated by comparing indexes and fatigue curves at different frequencies, temperatures, and strain levels. The results show the effects of temperature and strain level are more significant than that of frequency. The fatigue life is much longer under the conditions of high temperature or low strain level than those under other conditions. Stiffness ratio curve can be fitted well by the Weibull equations. The damage model expressed as a power exponential function for dissipated energy provides a reliable method for evaluating fatigue damage.

Fatigue curve of microscale single-crystal copper: An in situ SEM tension-compression study

A series of quantitative in situ tension-compression fatigue experiments in SEM are performed to investigate the fatigue curve of microscale single-crystal copper specimens with a test part of 1 × 1 × 2 μm under various strain amplitudes. The variation of resolved shear stress on the primary slip plane (τB4) and the corresponding evolution of crystallographic slips in each cycle are analyzed and in situ observed, respectively. The variation of τB4 during fatigue shows that, (i) the variation of τB4 clearly includes the early stage, the saturation stage, and the final fracture of the specimen; (ii) apparent cyclic hardening and softening appear in the early stage of all specimens; (iii) τB4 shows a strain-dependent variation in the saturation stage. Continuous cyclic softening and secondary cyclic hardening occur in specimens with relatively higher strain, while only slight cyclic hardening emerges in the specimen with the minimum strain. Based on in situ SEM observations, the variation trend of τB4 is interpreted from the evolution of geometrical characteristics of slip traces. Finally, we obtain the fatigue curve of microscale single-crystal coppers. The fatigue life is apparently dependent on the strain amplitude, while insensitive to the frequency of cyclic loading. Moreover, the fatigue lives of microscale single-crystal Cu are much shorter than those of bulks, indicating a significant size effect. The difference in fatigue lives of microscale and bulk ones reduces from about 360 to only 7 times with the decrease of applied strain, revealing the strain-dependence of size effect of fatigue life for microscale single-crystal coppers.

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.

Shot peening intensity effect on bending fatigue strength of S235, S355 and P460 structural steels

In this study, the effect of shot peening intensity of the structural steel specimens on the bending fatigue strength was investigated. Three structural steels S235JRG2, S355J2+N, P460NH were shot-peened with three levels of intensity. The results of fatigue tests were compared with non-peening processed samples. S-N curves in fatigue were determined in cyclic bending fatigue. The novel attempt to evaluate the bending fatigue, which relies on the 3D optical profiler measurement of the side-area of fractures, was proposed. All investigated steels present ferritic-pearlitic structure. Moreover, due to the peening process, refinement of the grains size was observed. Also, fractures were analysed with the 3D profiler. In the presented results of research, the highest level of peening gave the greater increase in fatigue life. For all types of investigated steels, shot-peening gave superior results of fatigue bending performance compared with unpeened specimens.

Study on characteristics of fatigue strength of ARALL composite in constructive elements

Due to Fatigue Testing fatigue life of specimens made of various materials and with various flange types was estimated. Specimens with dish-shaped and ring-shape flanges were tested. Specimens were made of aluminum alloy D16chATV sheets (thickness 1.2 mm) and of ARALL with a thickness of 1.2 mm based on aluminum layers of 0.5 mm thickness. Specimens were tested under 3 levels of cyclic stress: σmax=120, 100, 80 MPa with minimum stress of σmin=20 MPa. Some of ARALL specimens were tested only under σmax=100 MPa stress level. Under each stress level were tested 5 – 6 specimens. According to the results of all specimen tests the authors plotted plotted fatigue curves. Using the Finite Element Method the stress state of specimens during cyclic stress tests was analyzed. Calculations of fatigue life of specimens were made on the basis of the offered method. Full-element and numerical experiments revealed that fatigue resistance of monolithic alloy specimens with dish-shaped flange under all stress levels is higher than of specimens with a ring-shaped flange. ARALL specimens with dish-shaped and ring-shaped flanges both according to test results have a higher fatigue resistance than monolithic alloy specimens.

Modification and Extension of Screening Criteria for Fatigue Analysis

Abstract ASME Code VIII-2-2019 and previous versions provided three screening criteria for fatigue analysis. From edition 2004 to 2019, the design factor for material allowable stress decreased and the considered range of permissible cyclic number for design fatigue curve extended. However, screening criteria are almost unchanged except one restriction: If the specified number of cycles is greater than 106, then the screening criteria are not applicable and a fatigue analysis is required. In this paper, percentage limit of the design pressure in method A is modified and the specified number of cycles is extended. Some revision suggestions are also proposed to broaden the applicable range of the screening criterion.

Weibull and Bootstrap-Based Data-Analytics Framework for Fatigue Life Prognosis of the Pressurized Water Nuclear Reactor Component Under Harsh Reactor Coolant Environment

AbstractIn general, the fatigue life of a safety critical pressure component is estimated using best-fit fatigue life curves (S-N curves). These curves are estimated based on underlying in-air condition fatigue test data. The best-fitting approach requires a large safety factor to accommodate the uncertainty associated with large scatter in fatigue test data. In addition to this safety factor, reactor component fatigue life prognostics requires an additional correction factor that in general is also estimated deterministically. This additional factor known as the environmental correction factor Fen is to cater the effect of the harsh coolant environment that severely reduces the life of these components. The deterministic Fen factor may also lead to further conservative estimation of fatigue life leading to unnecessary early retirement of costly reactor components. To address the above-mentioned issues, we propose a data-analytics framework which uses Weibull and Bootstrap probabilistic modeling techniques for explicitly quantifying the uncertainty/scatter associated with fatigue life rather than estimating the lives based on a best-fit based deterministic approach. We assume the proposed probabilistic approach would provide the first hand information for assessing the maximum and minimum effects of pressurized water reactor water on the reactor component. In the discussed approach, in addition to the probabilistic fatigue curves, we suggest using a probabilistic environment correction factor Fen. We assume the probabilistic fatigue curve and Fen would capture the S-N data scatter associated with the bulk effect of material grades, surface finish, strain rate, etc. on the material/component fatigue life.

Fatigue design of metallic railway bridges in France at the end of the nineteenth century

Among more than 25 000 bridges and viaducts in the French railway network, more than 2000 metallic bridges have been in service for over a century, and they need adapted measures for their maintenance. Due to the increase in rolling speed and axle load, the understanding of the behaviour of this type of connection becomes of utmost importance. In order to understand better how old bridges behave, a specific aggressiveness index has been defined, and it enables comparison of the effects of different rolling stocks on the mechanical behaviour of stringers. This index has been determined for different French historical standard trains. For these calculations, a set of real iron stringers has been considered, including different periods of construction, different spans and different inertias. Since fatigue is one of the main phenomena to take into account in order to extend the safe service life of metallic bridges, a fatigue design criterion has been considered. Regarding historical calculation methods, an allowable fatigue stress has been chosen using the Societé Suisse des Ingénieurs et des Architectes fatigue curve, assuming Δσ c = 80 MPa. The method for determining the allowable stress in stringers presented in this paper shows a good agreement with the National Society of French Railways historical inventory of repairs.

Effect of geometric parameters and combined loading on stress distribution of tubular T-joints

Steel tubular structures are widely used in the construction of offshore platforms and T-type junctions are extensively used in this domain. The tubular members are welded, which generates significant stress concentrations at the edges. The stress levels reached in these critical places are used to assess lifetimes based on fatigue curves from tests conducted on standard samples. This study is devoted to the modeling and analysis of T-type welded tubular structures for the determination of hot spots stresses (HSS) at the chord/brace intersection, A numerical analysis was carried out to study the effect of a combined loading composed of an axial loading and a continuation of rational bending, that best assimilate real conditions, as well as the effect of normalized geometric parameters α, β, g on the distribution of stress concentration (area and values) of T-joints. The mechanical behaviour has been modeled in 2D using quadrangular and triangular thin-shell elements by the finite element method (FEM). It is the most appropriate approach because it considers all geometric complexities and singularities of the structure, while the efforts as well as the computation time are considerably reduced compared to an experimental study or to complex FE models implementing solid elements. In this study, we use the COMSOL-MULTIPHYSICS® software...

The reliability calculation method for aviation frames by refining of the static finite elements calculation results

In the article is describes the method of calculating of the element reliability by refining the results of static calculations. The calculation was made on the effect of the overloads that operate during the ground-air-ground cycle. By the static calculations of the wing model, the conditions of the schematized overloads were simulated. By means of computer-aided design, the necessary typical operations of calculating reliability were consistently implemented: determination of a critical point by static or modal calculation, reduction of the spatial load to uniaxial, reduction of the asymmetric load to symmetric, determination of the coefficient of fatigue quantity, building of the fatigue curve of the material recalculation, determination of limit fatigue cycles, determination of damage from each overloads separately. The Huber-Mises-Genka, Serensen-Kinasoshvili, Nadai-Lode criteria’s was implemented. A simplified expression is proposed and justified for calculating loads in a rib with an arrow-shaped wing. The expression allows you to select the ribs before the creating of a wing contour model and significantly save time for modeling. The contour model of the aircraft wing and its ribs are used in the calculations. The models are built on the theoretical surface of the wing. An example of calculation is provided. An example of the calculation of the reliability of the force frame of the wing and ribs of the aircraft type AN-24 is given. The calculated resource is the same as the maintenance period for the selected aircraft specified in the operational documentation. The calculation was carried out in the MSN Nastran finite element package and the Mathcad Express mathematical package.

Influence of Loading Frequency on Fatigue of Construction Materials

Investigations have been carried out in respect of structural steel and titanium alloy fatigue at various cyclic loading frequencies and these investigations have made it possible to reveal regularities in changes of parameters pertaining to fatigue resistance and stability behaviour of the tested materials. A change in cyclic loading frequency affects duration of a single (during one cycle) stay of the material in the loaded state and it has an impact on its durability. In addition, with an increase in frequency of load cycles, deformation rate becomes higher, and stress build-up time is decreasing, while distortion of a crystal lattice is increasing due to reduction of time for development of a weakening process. This process is accompanied by an increase in intensity of grain crushing into fragments and blocks, and their disorientation. Tests on cyclic strength of the studied material samples have been carried out at various frequencies and at a room temperature according to the following loading schemes: cantilever cyclic transverse bending of a flat sample; cantilever bending with rotation of a cylindrical sample; axial tension on a pulsating cycle. Quantitative estimates of a fatigue resistance index in the form of slope tangent in a left branch of the fatigue curve to a cycle axis have been used in order to analyze and evaluate performance and stability of the tested materials. Methods for mathematical statistics have been applied to process the obtained results. Graphic dependences of fatigue curves have been plotted in logarithmic coordinates that allowed to obtain straightening of approximating lines for experimental data. The investigations have revealed that loading frequency has an ambiguous effect on fatigue resistance due to some differences in materials in respect of their reaction to changes in a load spectrum within different areas of the fatigue process, but at the same time it has been found that an increase in fatigue strength leads to a slope decrease in the fatigue curve regardless of a decrease or an increase in a load frequency. The paper proposes a new approach to assess a cyclic strength and durability of materials, and it comprises a system of parameters including a relative coefficient of limited endurance, a correlation coefficient and a slope tangent of the fatigue curve. Behavior dynamics for real machine parts and structures made of these alloys under operating conditions has been indicated in the paper.

Normalized characterization method for fatigue behavior of cement-treated aggregates based on the yield criterion

The objective of this paper is to propose a normalized characterization method based on the yield criterion to eliminate the impacts of different stress models on the fatigue behaviors characterization of cement-treated aggregates. Based on the theory of octahedral shear stress strength and yield surface mode, the yield surface of cement-treated aggregates was established with four-point bending, compression, and indirect tensile strength value under different loading rates. Then, the fatigue stress and corresponding ultimate strength could be characterized by the yield surface, uniformly and uniquely. In the yield surface space (I1, J2), the fatigue stress growth route from initial stress to ultimate strength was identified as fatigue stress path. Based on the fatigue stress path, the fatigue stress ratios related to loading rate and stress model were calculated. With these stress ratios, the conventional S-N fatigue equation was modified, on the basis of which a normalized characterization method of fatigue behavior was proposed to characterize the fatigue behavior of cement-treated aggregates. Compared with the traditional characterized method, the normalized characterization method has considered the influence of loading rate and stress model on strength and fatigue test results. The test results demonstrated that different strength and fatigue test results were obtained under distinct stress model and loading rates. All strength values have been expressed indiscriminately in the yield surface. With the normalized characterization method, a unique fatigue curve was gained for cement-treated aggregates under different loading rates and stress models. Therefore, findings of this work realized the normalization characterization of fatigue behavior of cement-treated aggregates.

Fatigue Resistance Changes of Structural Steels at Different Load Spectra

Fatigue strength of widely used engineering structural steels was studied at various loading frequencies according to the cantilever bending scheme of rotating cylindrical samples. The inclination angle tangent of the fatigue curve to the axis of durability was taken as the fatigue resistance index. It has been established that 40 and 45 grade steels (UNS G10400/G10420 and G1044/G1045) belong to the group of materials in which a decrease in the loading frequency leads to cyclic softening and a decrease in the fatigue resistance, which is numerically expressed by the increase in the slope of the fatigue curve. Test samples made of 40Cr grade steel (UNS G51400) have shown that the increase in the frequency of loading cycles leads to a noticeable decrease in the fatigue curve slope parameter, i.e., leading to an increase in the fatigue resistance. The decrease in the fatigue resistance parameter is associated with the enhanced hardening of the material of the samples’ surface layers, which reduces the fatigue damage to the surface itself. The tangent dependence of the fatigue curve slope is shown on the surface damage rate when the loading cycles change frequency. Regardless of the frequency, the damage rate of the material’s surface layers increases along the fatigue curve slope. For each of these groups, mathematical relations have been defined. A correlation coefficient that shows the degree of convergence of experimental results and the constructed fatigue curve is adopted as a criterion of the cyclic behavior stability of steels. An increase in the behavior stability of 40Cr steel is observed with the increasing cyclic deformation rate. 45 grade steel tests have shown that a decrease in the cyclic strength with an increasing loading frequency does not affect the material’s fatigue stability. Experimental results showed increased dispersion for 40 grade steel at a low loading frequency despite high values of the cyclic strength at a given loading frequency. Based on the experiments, the behavior dynamics of real machine parts and structures subjected to cyclic loads within the studied loading spectrum has been established.