High Cycle Fatigue Range Research Articles

Crack growth based tooth root life prediction model—an influence quantity analysis

One of the key challenges of epicyclic gearboxes in turbo gearbox applications is the high number of load cycles reached by the gearbox components. Standards such as ISO 6336 deliver design guidelines for bending strength up to a limiting number of NG = 3∙106 and AGMA up to 107 load cycles which is far less than the expected lifetime of turbo gearbox applications.To design gears for geared turbofans safely and weight-optimized, the tooth root load capacity in the very high cycle fatigue (VHCF) range must be known as precisely as possible. Most VHCF SN-curve concepts show a continuously decreasing fatigue strength, so that a consideration of a constant fatigue strength level does not meet the material behavior. A life prediction model can be used to determine the specific load that can be carried for each number of load cycles.In this paper, the nasgro crack growth equation is applied to gears to determine the tooth root life in the VHCF range. A lifetime for surface and sub-surface induced fractures is calculated, resulting in a stepped SN-curve. Most of the cycles until fracture occur during crack initiation and micro crack growth, while the macro crack is a small part of the total number of load cycles until tooth root fracture. The nasgro equation is able to represent micro and macro crack growth and is extended by further approaches to the threshold of crack initiation Kth, which also consider the characteristics of short and long crack growth. In addition, the tooth root stress depth curve (via FEM), the hardness depth curve, the residual stress depth curve and the defect distribution will be included in the life-time prediction as important influencing variables of the VHCF tooth root load capacity. The influence of the inputs is determined in an influence quantity analysis. In the future the lifetime prediction model is validated with rig tests up to the VHCF range.

LCF and HCF of Short Carbon Fibers Reinforced AE42 Mg Alloy.

Lightweight magnesium alloys and magnesium matrix composites have recently become more widespread for high-efficiency applications, including automobile, aerospace, defense, and electronic industries. Cast magnesium and magnesium matrix composites are applied in many highly moving and rotating parts, these parts can suffer from fatigue loading and are consequently subjected to fatigue failure. Reversed tensile-compression low-cycle fatigue (LCF) and high-cycle fatigue (HCF) of short fibers reinforced and unreinforced AE42 have been studied at temperatures of 20 °C, 150 °C, and 250 °C. To select suitable fatigue testing conditions, tensile tests have been carried out on AE42 and the composite material AE42-C at temperatures of up to 300 °C. The Wohler curves σa (NF) have shown that the fatigue strength of the reinforced AE42-C in the HCF range was double that of unreinforced AE42. In the LCF range at certain strain amplitudes, the fatigue life of the composite materials is much less than that of the matrix alloys, this is due to the low ductility of this composite material. Furthermore, a slight temperature influence up to 150 °C has been established on the fatigue behavior of the AE42-C. The fatigue life curves Δεtotal (NF) were described using the Basquin and Manson-Coffin approaches. Fracture surface investigations showed a mixed mode of serration fatigue pattern on the matrix and carbon fibers fracturing and debonding from the matrix alloy.

Very high cycle fatigue properties at 973 K of additively manufactured and conventionally processed intermetallic TiAl 48-2-2 alloy

The fatigue lives of 2nd generation γ-TiAl alloy Ti–48Al–2Cr–2Nb manufactured both by additive manufacturing using electron beam powder bed fusion (EB-PBF) as well as conventional casting process by vacuum arc remelting for comparison (REF) were investigated. Both batches (EB-PBF and REF) were subject to the common treatment process, i.e. hot isostatic pressing and heat treatment to achieve a duplex microstructure. As a result, a fine- and a coarse-grained microstructure consisting of γ-grains and colonies of α2/γ lamellae have evolved for the EB-PBF and conventionally cast material, respectively. Uniaxial fatigue tests were performed in the very high cycle fatigue (VHCF) range up to 109 cycles at a load ratio of R = −1 using ultrasonic fatigue testing equipment at an elevated temperature of 973 K. The SN data of both batches were discussed with respect to the influence of microstructure and temperature on the processes of crack initiation and propagation. The additive manufactured material showed superior fatigue strength compared to the conventional material due to its smaller grain size. It was shown that the fine-grained duplex microstructure of the batch EB-PBF is particularly appropriate to decrease short crack propagation at elevated temperatures due to its microstructural characteristics.

Crack initiation and propagation analysis for fisheye failures in high-strength gears

Lightweight design has had an important role to play in recent gear developments. One way of reducing gear weight is to apply a shot-peening process in addition to the usual case-hardening because the higher compressive residual stresses within the material mean that the same torque values can be transmitted with smaller gears. However, due to the compressive residual stresses, fisheye failures at non-metallic inclusions can occur, which have an effect on the endurance fatigue strength of high-strength gears, especially in the very high cycle fatigue range. This paper presents a detailed FEM simulation of the stress state at a non-metallic inclusion in the tooth root fillet of such high-strength gears. The aim is to explain certain fracture characteristics, which differ from fisheye failures of standard specimens. With the results of the simulation und taking into consideration the fracture characteristics determined in a SEM, a fracture analysis for fisheye failures in the tooth root fillet of high-strength gears is carried out that links different theories found in the literature. Subsequently, this analysis and the influence of residual stresses are compared with data and further fracture analyses from experimental investigations found in the literature.

A Competitive Study of the Static and Fatigue Performance of Flax, Glass, and Flax/Glass Hybrid Composites on the Structural Example of a Light Railway Axle Tie

The most common studies in the literature are those analyzing fatigue life under cyclic loading for flax fiber-reinforced composites. A novel type of staple fiber yarn made from flax tow with almost unidirectional fiber orientation and a quasi-unidirectional fabric was developed for composite applications. Additionally, a hybrid material made of flax and glass was produced for a demonstrator component (an axle tie of a narrow-gauge railway). For such an application, the investigation of fatigue strength is of particular importance. Therefore, the fatigue behavior of flax, glass, and hybrid flax/glass composites was investigated in the high cycle fatigue range. A total of 106 load cycles were carried out. From about 7³ to 8³ loading cycles, the flax laminate was found to have higher fatigue strength than the glass fiber-reinforced composite. The hybrid materials tend to show a higher fatigue strength than the glass type from approximately 2 × 105 load cycles. Results based on a finite element method also demonstrate better fatigue properties at an increased number of load cycles for flax-based composites than the glass fiber-reinforced component. The flax/glass component’s fatigue strength ranged between the flax values and the glass fiber-reinforced composites. Overall, the hybrid material shows significantly better static bending and impact characteristics than flax and considerably better fatigue properties than the glass fiber-reinforced composite making the hybrid material attractive for an application in an axle tie.

МЕТОД ВИЗНАЧЕННЯ ХАРАКТЕРИСТИК НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ЛОНЖЕРОНА РЕГУЛЯРНОЇ ЧАСТИНИ ЛОПАТІ НЕСУЧОГО ГВИНТА ВЕРТОЛЬОТА ЗА ДОПОМОГОЮ СИСТЕМИ ANSYS

The helicopter main rotor blade is the basic product that determines the reliability and service life of the helicopter as a whole. The problem of predicting and ensuring the specified blade life is an urgent problem considered at the stage of its design. To determine the fatigue life of the blade it is necessary to know the characteristics of the stress-strain state. A method has been developed for determining the characteristics of the stress-strain state of the spar of the regular part of the rotor blade of a helicopter using the ANSYS system. Application of numerical methods of stress-strain state characteristics calculation allows to reduce considerably time and cost of blade design. The calculation results of regular part of the Mi-8 main rotor blade at the hover mode when it is loaded by aerodynamic and inertial load from the rotation, as well as the force of its own weight are presented in the work. Using the ANSYS system, a finite-element model of the regular part of the blade, consisting of a set of beam elements of variable cross-section, was developed, the calculation was carried out taking into account the geometric nonlinearity of the structure behavior and the analysis of the obtained results. To describe the response of materials to external influences, an elastically deformable isotropic body model is used with assignment of the appropriate elastic constants of the material. Analysis of calculation results includes determination of reactions at attachment points, values of maximum displacements of structural elements and stresses in weak sections. Diagrams of internal force factors (axial and shear forces and bending moment) along the blade span are plotted. With the help of these diagrams weak sections are determined and values of axial force and bending moment in these sections are calculated. Axial force reaches its maximum value Nx = 333689 N in the section along the axis of rib № 1. In this section, the bending moment reaches a maximum value of Mymax = 3078.3 N×m. At cross section r = 0.73 between axes of ribs No. 13 and No. 14, where shear force equals to zero, value of bending moment My = -1147,5 N×m. Thus, regular part of the blade is in combined stressed state - bending with tension. Static strength of the blade has been estimated using safety factor. To estimate a static strength equivalent von Mises stresses were considered as the maximum stresses. Safety factor of static strength of regular part of the blade in the weak section was 1,7. To estimate fatigue strength, distribution of the first principal stresses in the load-carrying elements was analyzed in terms of typical stress concentrators. The maximum level of the principal stresses in the considered sections was s1 = 138 MPa, which indicates that the blade material operates in the range of high cycle fatigue.

Optical stress concentration and stress gradient monitoring during elasto-plastic fatigue tests with Digital Image Correlation

Predictions of fatigue failure at stress concentrations rely on prediction by empirical formulae or experimental test data. However, there remains a level of uncertainty in the life estimation, which can be reduced when monitoring the behavior around the stress concentration. In this contribution, the stress field, calculated for an isotropic material from optical strain measurement, is monitored over specimen fatigue life. Changes in the maximum relative stress gradient χmax, describing the decay of a stress concentration, and the distance of the maximum gradient from the hole are evaluated. Experimental data on three specimens with different load levels in the high-cycle fatigue range show that both parameters change significantly shortly before fatigue failure. These encouraging results indicate that failure can be predicted by monitoring either, the value of χmax, or the distance of χmax from the hole edge.

On the determination of the bending fatigue strength in and above the very high cycle fatigue regime of shot-peened gears

Demands on modern gearboxes are constantly increasing, for example to comply with lightweight design goals or new CO2 thresholds. Normally, to increase performance requires making gearboxes and powertrains more robust. However, this increases the weight of a standard gearbox. The two trends therefore seem contradictory. To satisfy both of these goals, gears in gearboxes can be shot-peened to introduce high compressive residual stresses and improve their bending fatigue strength. To determine a gear’s tooth root bending fatigue strength, experiments are conducted up to a defined number of load cycles in the high cycle fatigue range. However, investigations of shot-peened gears have revealed tooth root fracture damage initiated at non-metallic inclusions in and above the very high cycle fatigue range. This means that a further reduction in bending load carrying capacity has to be expected at higher load cycles, something which is not covered under current standard testing conditions. The question is whether there is a significant decrease in the bending load carrying capacity and, also, if pulsating tests conducted at higher load cycles—or even tests on the FZG back-to-back test rig—are necessary to determine a proper endurance fatigue limit for shot-peened gears. This paper examines these questions.

Nonlinear dynamics and stages of damage of Ti6Al4V and Ti45Nb titanium alloys in very high cycle fatigue

The paper presents an experimental methodology aimed at evaluating a very-high cycle resource for aviation titanium alloys Vt-6 (Ti6Al4V) and Ti45Nb for medical applications with different microstructures (large-crystal and submicrocrystalline ones). The submicrocrystalline (SMC) state was obtained by an intensive plastic deformation realized in two ways: the three-dimensional forging for Ti45Nb and radial-shear rolling for Ti6Al4V. The experimental program tests high-cycle and very-high-cycle loading (number of cycles 107-109) realized using the in situ determination method of the accumulation of the irreversible fatigue damage by analyzing nonlinear forms of feedback in a closed system ultrasonic fatigue setup. This makes it possible to establish the connection of the microscopic fatigue mechanisms with the model views and consider the stages of the damage development based on the nonlinear kinetics of the defect accumulation under cyclic loading in high- and gigacycle fatigue modes. We established various relations between changes in the amplitude of the second harmonic of vibrations of the free end of the samples with different internal structures, which are associated with the mechanisms of stress relaxation and damage accumulation. The grain size reduction in Ti45Nb alloy by the three-dimensional forging improved the fatigue properties by 1.3-1.5 times, whereas for VT-6 alloy, the radial-shear rolling method could not increase the fatigue properties in the very high cycle fatigue range, which may be caused by the presence of large residual internal stresses. Based on the scale parameters obtained earlier from the fracture surface morphology and the relations established in this work, the kinetic equations for the origin and growth of fatigue cracks in the gigacycle loading range will be constructed. This equation, based on the empirical power parameters related to the structure of the material, will allow us to determine the number of cycles for the origin of an internal crack and its growth to the surface.

Revealing the local fatigue behavior of bimodal copper laminates by micropillar fatigue tests

Cyclic micropillar compression is a powerful technique for characterizing the local fatigue properties of microstructurally complex materials. Here, it was applied to a bimodal copper sample made of alternating ultrafine and coarse grained layers. Micropillars were fabricated from both domains, as well as from the interface between them. The three different areas were investigated from the quasi-static to the high cycle fatigue range (up to 1 million cycles). In line with expectations, the CG micropillars exhibit the smallest fatigue strength and the UFG specimens the highest one. More surprisingly, the micropillars containing a bimodal UFG/CG interface exhibit a slightly shorter fatigue lifetime than plain UFG specimens. The likely reason is their more complex stress state, which alternates between tension and compression and results in the formation of surface extrusions, which lead to eventual failure.

Utilization of CFRP in High-Speed Stamping Presses and its Gigacycle Fatigue Testing at Resonance Frequency

Carbon fiber reinforced polymer (CFRP) utilization meets the requirements of stiffness, damping, and light weight for enhanced performance of machine tools. Stamping presses are expected to function for billions of cycles, resulting in the fatigue of the employed materials and parts. High-speed stamping presses, such as the Bruderer BSTA-200, should fulfil the increasing customer requirement of enhancing both quality and quantity of the delivered parts. Among the quickest presses currently available in the market, these BSTA presses can reach speeds up to 2000 strokes per minute (spm) with a stroke of 8 mm and still continue operating for many decades. For this project, new requirements were defined: a 25% increase of the stamping speed reaching up to 2500 spm, while maintaining the same stroke of 8 mm. The ram was redesigned by making use of CFRP, and because of its high stiffness and strength, it enabled a weight reduction of 65%. Owing to the stamping force of 200 kN and the impact of the stamping process, the material of the ram is highly strained. A major concern in utilizing CFRP in machine tools is the fatigue and change in material properties with increasing stress cycles. Therefore, the fatigue behavior of CFRP had to be validated in the very high cycle fatigue (VHCF) range. This was performed using a newly developed fatigue test bench. To complete 109cycles within a few weeks, the testing occurred at the specimen’s resonance frequency with a constant and controlled strain of 0.1%. Aspects such as resonance frequency testing, heating of the specimen, and an accurate measuring system were considered. The specimens had to be designed and optimized for this type of testing, thus resulting in a cylindrical tube shape with a unidimensional (UD) arrangement of the fibers in longitudinal and transverse direction.

Effects of the heterogeneous microstructure of a 7050-T7451 aluminium alloy FSW joint on fatigue behaviour under different stress ratios

Using ultrasonic fatigue tests with stress ratios of −1.0, −0.3 and 0.3, the effects of the stress ratio on the fatigue behaviour of a friction stir welding (FSW) 7050-T7451 aluminium alloy joint in the high cycle fatigue (HCF) range and very high cycle fatigue (VHCF) range were investigated. For all stress ratios, two types of crack initiation mechanisms (surface crack initiation and interior crack initiation) were observed. Surface crack initiation occurred on the entire life region; however, interior crack initiation was only observed in the VHCF range. It is concluded that the surface crack initiation was dominant in the HCF range, while in the VHCF range both types of crack initiation mechanisms existed. Because of the different microstructures and differences in the mechanical properties of the subzones of the FSW joint, the position of fatigue failure was selective. The Walker model was employed to correlate the fatigue life of the FSW joint under different stress ratios and well fitted results were obtained in the VHCF region.

Mathematical Modeling of Failure Process of AlMg2.5 Alloy in High and Very High Cycle Fatigue

Prediction of the endurance limit in the high and very high cycle loading range (102−1010) is an important problem in aircraft engine construction and high-speed rail transport. It involves the development of models and their experimental verification taking into account damage evolution stages and fatigue crack growth in a damaged medium. A damage evolution model that takes into account the kinetics of defects and microplasticity effects was proposed. The model was used to study the process of fatigue failure of an AlMg2.5 structural alloy. The model parameters were identified and verified using experimental data on static, dynamic, and fatigue loading, as well as tests at various temperatures. The numerical results were used to construct the Wohler curve, which was found to agree well with experimental data in the range of high cycle fatigue. The duality effect of the S-N curve was described. A computational experiment was performed to study the effect of dynamic loading on the fatigue strength. It was found that the fatigue limit depends weakly on the preliminary dynamic strain, which was confirmed by experimental data. Various mathematical packages and numerical methods for solving the constructed system of differential equations were compared. The Adams method and its modifications were shown to be optimal for the numerical integration of the problem under consideration. Wolfram Mathematica was found to be a preferred software package for numerical solution. The convergence of the numerical solution was investigated.

Acoustic Measurement of the Texture Characteristics of 15YuTA Construction Steel under Fatigue Failure

This paper presents results from studies on the change in the texture and Poisson coefficients of 15YuTA construction steel upon fatigue failure in the range of high-cycle fatigue by the ultrasonic pulse-echo technique. The coefficients of the orientation distribution functions ($$W_{4}^{{00}}$$ and $$W_{4}^{{20}}$$) used for construction of the pole figures were obtained using bulk elastic waves and the precise measurement of its propagation time. As a parameter characterizing the texture sharpness, the intensity ratio in the center of the pole figure and at a point remote from the center by 45° along the rolling direction was used. It was shown that change in the texture sharpness is attributed to the development of microplastic strain and accumulation of microdefects. A nonmonotonic dependence of the change in the sharpness of the texture on the number of loading cycles is observed. At the initial (first) stage of loading, there is some increase in the sharpness, which can be attributed to the development of microstrains on the most favorably oriented sliding planes. At the second stage, the decrease in the sharpness is associated with the scattering of the texture upon the increase in the density of microdefects during the destruction of the alloy. The parameter characterizing the sharpness of the texture can be used as a pre-destruction indicator by the ultrasonic monitoring of a construction material.

Correlation of the low and high frequency fatigue responses of pure polycrystalline copper with mechanisms of slip band formation

Ultrasonic fatigue testing at 20 kHz was developed to accelerate fatigue tests and explore the very high cycle fatigue range. However, the use of ultrasonic fatigue systems raises the open question of the impact of frequency on the material fatigue response. In this paper, the impact of the loading frequency on the fatigue response of face-centered cubic polycrystalline copper is investigated. Firstly, experiments with conventional fatigue devices inducing loading frequencies lower than 100 Hz were carried out and compared with previously published results obtained with an ultrasonic fatigue machine at 20 kHz. At a stress amplitude of 100 MPa, the number of cycles required for failure was found to be more than 200 times greater for tests at 20 kHz than for tests at frequencies below 100 Hz. Secondly, for both types of fatigue tests, the conditions in stress amplitude and number of cycles needed for the emergence of the early slip markings were investigated. The early slip marking S–N curve was found to have the same sensitivity as the failure S–N curve to the frequency effect. Thirdly, the different possible reasons responsible for this frequency effect are discussed. It is concluded that the physical mechanisms of slip marking formation is preserved while their kinetics is sensitive to the loading frequency. Finally, two simplified models were considered and for the first time, the frequency effect on the fatigue response of copper is quantitatively correlated with the occurrence of time-dependent dislocations cross slip and vacancies production/diffusion involved in the persistent slip band formation for face-centered cubic structure. The obtained results could be extended to a full class of materials where slip band formation plays a key role in the crack initiation process while suggesting no frequency effect for materials with a lower degree of plasticity development at crack initiation (High Strength Steels for example).

Investigations into non-metallic inclusion crack area characteristics relevant for tooth root fracture damages of case carburised and shot-peened high strength gears of different sizes made of high-quality steels

Case carburised and shot-peened high-strength gears can fail by tooth root bending failures in the very high cycle fatigue range of the S‑N-curve due to crack initiation at a non-metallic inclusion. It is essential to understand crack characteristics and mechanisms of such sub-surface initiated cracks, which are different to surface initiated cracks, in order to further increase the gear performance. This paper discusses the results of detailed analyses of such fractured surfaces.

Investigations on the fatigue strength of beam-welded butt joints taking the weld quality into account

For the fatigue design of welded structures under constant amplitude loading, often the nominal stress approach based on design S-N curves is used. The design S-N curves, which can be found in commonly used guidelines, cover arc welds as well as beam welds. However, the experimental data basis for the guideline consists mainly of arc-welded joints. Beam-welded components on the other hand show different weld geometries (e.g., weld width, weld enforcement, weld radii) compared with arc-welded components. The local geometry of weldments as well as imperfections can affect the fatigue strength, theoretically in dependence of the ultimate strength. Therefore, the fatigue strength of beam-welded samples in the high cycle fatigue range made from S355J2+N and S960Q was tested in this study. Additionally, the weld geometry of all samples was measured and classified according to the weld quality groups in ISO 13919-1. Furthermore, numerical notch stress calculations were conducted to cover imperfections and weld geometries that were not covered by the experimental investigations. Finally, recommendations for the fatigue resistance of beam-welded butt joints are given. Correlations between the fatigue strength and certain quality groups of selected geometrical features and imperfections are shown.

Fatigue of glued-in rods in engineered hardwood products — part I: experimental results

ABSTRACTGlued-in Rods (GiR) are among the high-performance joining technologies used in timber engineering. Engineering design procedures for GiR almost exclusively regulate softwood and softwood engineered wood products (EWP) under quasi-static loads. Since the use of hardwood is expected to significantly increase due to climate change, and potentially establish itself as predominant in Europe`s forests, GiR in combination with hardwood and corresponding EWP need to be investigated. Timber constructions subjected to cyclic loads are increasingly being used, as for example in timber bridges, high rise buildings, and wind turbine towers. No normative regulation is yet available for fatigue of GiR, which is for most part due to incomplete or completely missing experimental data. This paper is the first of a two part series; it presents fatigue investigations on GiR in combination with hardwood EWP with different types of rods, wood species and adhesives. Further, the embedment length and stress ratio were varried. In total, more than 70 cyclic tests were performed resulting in a high number of SN-curves showing the fatigue characteristics of GiR. The results show that two different damage mechanisms exist: in low cycle fatigue range (LCF), timber and adhesive fracture become dominant, while rod failure is the limiting factor in high cycle fatigue range (HCF). Based upon the documented experimental findings, existing standards for cyclic load on softwood connection technologies were discussed. The compagnion paper will present a design methodology based on a wood damage accumulation, giving a complete picture combined with existing metal fatigue models.

Acoustic study of the texture characteristics of 15YuTA construction steel in fatigue failure conditions

Ultrasonic echo-pulse method is used to study the texture changes and Poisson’s coefficients of 15YuTA construction steel upon fatigue failure in the range of high-cycle fatigue. To describe the texture change, pole figures were constructed using the values of the orientation distribution functions (W400 and W420) obtained from the results of precise measurements of the propagation time of elastic bulk waves in sheet materials. The intensity ratio in the center of the pole figure and the point remote from the center of the pole figure by 45° along the rolling direction was used as a parameter characterizing the texture sharpness. It is shown that change in the texture sharpness is attributed to the development of microplastic strain and accumulation of the microdamages. A nonmonotonic dependence of the change in the texture sharpness on the number of loading cycles is observed. At the initial stage of loading, there is some increase in the sharpness of the texture, which can be attributed to the development of micro-strains on the most favorably oriented sliding planes. At the second stage, a decrease in the texture sharpness is associated with the scattering of the texture as the density of microdefects increases during the destruction of the alloy. The parameter characterizing the texture sharpness can be used as a pre-destruction indicator when monitoring the material of the structure by the ultrasonic method.

Very High Cycle Fatigue - Testing Methods

This paper presents several approaches for investigating the Very High Cycle Fatigue (VHCF) range of composite materials. Starting from the special challenges associated with high frequency testing of composite specimens, the paper shows some solutions as well as results for such investigations. The test set-up used in the research of the authors is a four point bending rig, which allows for relatively high load frequencies and widely avoids overheating. These bending tests provide fatigue limits for the development of microcracking, while showing no specific fatigue damage phenomena in the very high cycle fatigue range. The approaches found both, in literature and at the actual method utilised here, are discussed. The paper relates to glass fibre reinforced plastics (GFRP), and does not include either simulation approaches or results.