Fatigue Testing System Research Articles

Glenoid component cyclical failure decreases with increasing baseplate contact: a biomechanical study

BackgroundGlenoid baseplate loosening remains a common mode of failure in reverse shoulder arthroplasty. One of the key factors to baseplate stability is theorized to be maximization of baseplate backside contact. The purpose of this biomechanical study is to investigate the role of varying degrees of backside bony glenoid support in component stability for reverse total shoulder arthroplasty. MethodsTwenty synthetic scapular models were divided into 3 test groups of 5 scapulae with glenoid baseplate contacts of 40%, 60%, and 75%, and one control group with glenoid baseplate contact of 100%. Standardized application of a commercially available glenoid baseplate and glenosphere was performed. The scapulae were mounted on a linear bearing with a humeral component and polyethylene liner which were affixed to a biaxial servohydraulic fatigue testing system. Each specimen was loaded for 10,000 cycles or to failure, about a 55° arc along the glenosphere at a rate of 1 Hz as a 750 N compression load was applied. Failure was defined as fracture of the scapula with implant fixation compromise. Before and after loading, stability of the baseplate was assessed by quantifying the total motion between the model and the baseplate with digital calipers as a ramp load between 0 and 150 N was applied. Two-sample unpaired t-tests were performed with significance set at P < .05. ResultsBaseplate contacts of 40% (1623 ± 227, P = .0001), 60% (3299 ± 1170, P = .0001), and 75% (5615 ± 1587, P = .0077) demonstrated statistically significant decrease in the average number of cycles to failure in all cohorts compared to our control (8641 ± 1070). Cycles taken for initial cracks to progress to failure showed no significant differences; 40% contact (862 ± 452, P = .4751), 60% contact (1651 ± 996, P = .4318), 75% contact (2882 ± 1347, P = .0620), and 100% control (1166 ± 657). Baseplate contacts of 40% (6150.4 ± 444.0, P = .0006), 60% (4647.1 ± 552.3, P = .0072), and 75% (2927.8 ± 918.5, P = .2573) demonstrated increasing micromotion (pre-post cyclical loading) in all cohorts compared to our control (2074.7 ± 1164.6) with statistical significance at 40% and 60%. ConclusionThese biomechanical tests demonstrate that decreasing glenoid baseplate backside contact leads to increased micromotion and fewer cycles to failure. This supports the surgical goal of achieving maximal glenoid baseplate backside contact, suggesting that decreased glenoid baseplate support could contribute to significant loosening.

Enhancing high cycle fatigue performance of plasma nitrided AISI 4140 steel by post-aging treatment and direct current magnetic field

Machine elements become unable to perform their duties as a result of fatigue damage. In addition, machine elements that are subjected to fatigue under cyclic loads are exposed to electric and magnetic fields when they are close to electrical and magnetic field sources such as electric motors. Moreover, plasma nitriding is often used to increase the fatigue strength of materials. Although the fatigue properties of surface-treated materials are frequently studied, the fatigue behavior of these materials under a magnetic field is not fully known. Therefore, this study focuses on examining the effects of magnetic field on the fatigue properties of surface-treated materials. For this purpose, AISI 4140 steel samples were plasma nitrided and subsequently post-aged, and then they were tested using a rotating bending fatigue testing system by exposing them to a magnetic field for 30 % and 100 % of their fatigue life. ε-Fe2–3N and γ’-Fe4N phases were seen in surface-treated samples, in addition to these phases, peaks belonging to the α”-Fe16N2 phase were observed in post-aged samples. Plasma nitriding raised the hardness of the material because of nitride phases and α”-Fe16N2 caused an extra increase. The highest diffusion depth was seen in the post-aged samples because post-aging facilitated the diffusion of nitrogen. Surface treatments increased the fatigue strength of the material. All samples tested under a magnetic field exhibited higher fatigue strength than samples tested without a magnetic field because fatigue crack initiation was prolonged by the magnetic field. Compared to non-magnetic and 30 % magnetic samples, the fatigue strengths of the samples in a 100 % magnetic field were lower. Furthermore, it was observed that applying a magnetic field had no effect on the samples' fractographic structure.

Experimental investigation of fracture mechanism in organically modified silica-based coating applied on austenitic stainless steel AISI 904L under monotonic and very high cycle fatigue loading

Surface morphology significantly influences the fatigue life of the metallic materials. Therefore, improving surface performance is important for economic and safety applications. Silica-based coatings are anticipated to protect the metallic materials under synergistic operating conditions, such as fatigue and corrosion. However, pure inorganic silica-based coatings are brittle and fail to protect metallic materials. The properties of the sol–gel coatings can be determined by optimizing synthesis factors, such as synthesis steps, precursors, solvents, and catalysts. Organically modified silica-based sol–gel coatings were synthesized using 3-glycidoxypropyl trimethoxysilane and 3-aminopropyltriethoxysilane as precursors, with ethanol as the solvent. The resulting coating was named EtOH. This coating was applied on the surface of stable austenitic stainless steel AISI 904L with the dip coating method. The fracture behavior of the coating during monotonic loading has been studied by interrupted tensile tests at different load steps and examined closely with scanning electron microscopy. On the other hand, very high cycle fatigue experiments were conducted using an ultrasonic fatigue testing system at load frequency of 20 kHz on coated specimens to investigate the fracture behavior of the coating during cyclic loading. Three different kinds of fracture due to stress relaxation in the coating and at its interface with substrate were observed in monotonic loading. The same kinds of stress relaxation were observed in cyclic loading with the difference being that the range of experienced elongation in cyclic tests was significantly smaller. Therefore, the fracture in cyclic loading were concentrated in the vicinity of macro crack. The application of organically modified coatings could suppress the persistent slip bands and result in increased fatigue life for coated specimens.

Experimental study on the influence of welding structure details of TC4 titanium alloy under thermo-vibration coupling environment on vibration fatigue life

The widespread application of titanium alloy materials in aerospace structural design makes them susceptible to thermo-vibration coupling fatigue failure in harsh vibration and thermal environments. Vibration fatigue issues significantly affect the safety and operational reliability of aircraft. In order to obtain optimal design details for titanium alloy welding structures under thermo-vibration coupling conditions, experimental specimens with different structural details of TC4 titanium alloy welding structures were designed to simulate actual structural designs. The structural details included skin with U-shaped supports at different angles, skin with L-shaped supports, and skin with T-shaped supports. A thermo-vibration coupling vibration fatigue test system was established, and vibration fatigue tests were conducted at a temperature of 150°C. All structural fatigue crack failures occurred at the welds. The experimental results were statistically analysed, and using the Chauvinet criterion, abnormal data points were removed. The influence of structural details on vibration fatigue life was determined through F-tests. It was found that for the skin with a U-shaped support structure, a support angle of 90° resulted in a longer vibration fatigue life. When comparing skin with T-shaped support and skin with L-shaped support structures, the T-shaped support structure exhibited a longer vibration fatigue life. Among the three structural types, the skin with a T-shaped support structure has the longest vibration fatigue life. These experimental conclusions serve as important references for the design of thin-walled structures in aircraft structural design.

Very high cycle fatigue assessment of thermoplastic-based hybrid fiber metal laminate by using a high-frequency resonant testing system

The prolonged fatigue lifetime of fiber metal laminates (FML) compared to monolithic metals is a key aspect for safety-relevant components, where detailed knowledge about the fatigue properties up to the very high cycle fatigue (VHCF) regime is necessary. For thermoplastic-based FMLs, offering formability, recyclability, and mass production due to short consolidation cycle times, this knowledge needs to be established.In this study, FML containing AA6082 sheets and unidirectional glass and carbon fiber-reinforced polyamide 6 was investigated. Fatigue tests up to max. 109 cycles were conducted on a servo-hydraulic and a high-frequency resonant fatigue testing system with frequencies of 10 Hz and 1,000 Hz. Frequency-induced self-heating was evaluated and limited using air-cooling to maintain the matrix properties. Fatigue progress was monitored through high-speed optical deformation analysis.Compared to HCF loads, VHCF loads lead to reduced crack and delamination occurrence. Changes in microstructure are dominated by singular crack initiation and propagation within the aluminum. The FML’s S-N curve shows a significant flattening from the HCF to the VHCF regime, simplifying the predictability of the fatigue life. By using post-stretching, the VHCF strength can be increased by over 60 %, making this thermoplastic-based FML a considerable competitor in the field of FML.

Study on Corrosion Fatigue Behavior of 304L Austenite Stainless Steel in 325 °C High-Temperature Water Environment

The fatigue crack growth behavior of 304L austenitic stainless steel (SS) in a 325 °C high-temperature and high-pressure water environment were investigated by a corrosion fatigue test system, by electron back scatter diffraction (EBSD), and by a transmission electron microscope (TEM). The experimental results indicated that the crack growth rate (CGR) of 304L SS increases with increasing the stress intensity factor, stress level, and fatigue frequency (f). Compared to dissolved hydrogen (DH) in a high-temperature water environment, dissolved oxygen (DO) significantly enhances the CGR by about an order of magnitude higher. The crack tip of 304L SS after the corrosion fatigue test under higher stress levels is sharper, with more secondary cracks on the fracture surface, while the crack tip under lower stress levels is blunter with relatively fewer secondary cracks. The oxidation behavior at the crack tip was analyzed under different loading and water chemistry conditions, and a related effect on the crack tip and CGR was clarified.

Acoustic and Vibration Response and Fatigue Life Analysis of Thin-Walled Connection Structures under Heat Flow Conditions

Thin-walled connection structures are commonly used in the hot-end components of aerospace vehicles. Large deflection nonlinear responses and fatigue failure occur due to their discontinuous mass distribution and prominent cross-sectional changes under the action of complex thermal, aerodynamic, and noise loads. A thermoacoustic fatigue test was carried out to obtain the acoustic and vibration responses and fatigue life changes of the connection structure under heat flow conditions in engineering applications. The high-temperature acoustic fatigue test system of aviation thin-walled structures was used, taking the high-temperature alloy thin-walled plate-load-bearing frame bolted connection structure as the research object. As a result, the vibration response and fatigue life under different thermoacoustic loads were obtained. The contact finite element method was used to simulate the connection pre-tightening force, and the coupled finite element/boundary element method was used to calculate the acoustic and vibration response of the heat flow conditions. The changing rules of the frequency response peak value at the critical point of the thin-walled connection structure under the effects of different temperature fields, fluid fields, and sound fields were obtained through the processing and analysis of the calculation results. Considering the structural vibration fatigue damage mechanism, this study employed an improved rainflow counting method to compute the rainflow circulation matrix (RFM) and rainflow damage matrix (RFD) of the vibration stress time history at critical points within the structure framework. Said method was combined with Miner’s linear cumulative damage theory to estimate the fatigue life under various thermal-fluid-acoustic coupled loads. A comprehensive analysis validates the accuracy of the established numerical simulation calculation model in identifying critical connection points within structures subjected to pre-tightening forces. This model effectively characterizes thermal, aerodynamic, and acoustic loads on high-temperature alloy thin-walled-load-bearing frame bolted connection structures. It delineates the relationship between vibration response and fatigue life while assessing the impact of three distinct load parameters.

Notch Fatigue Property of 7050-T7451 Aluminum Alloy under Bending Resonance Environment

Based on the electromagnetic shaker table, the resonant fatigue testing system and the corresponding conventional fatigue testing system were designed respectively. The fatigue life (S-N) curves of smooth and notched 7050-T7451 aluminum alloy specimens were measured in the range of 105-107 cycles, and the notch fatigue property of 7050-T7451 aluminum alloy under bending resonance environment was studied. The results indicate that the fracture mechanism under bending resonant fatigue environment is roughly the same as that under bending conventional fatigue loading. All the S-N curves obtained through resonant and conventional fatigue tests show a continuously downward trend, and there are no obvious fatigue limits. Notch fatigue property under bending resonance environment presents “stage characteristics”, which increases first and then decreases with the increase of cycles. There is a critical cycle number Nc at 8×105 cycles, corresponding to the maximum fatigue notch factor Kf-max (or the maximum notch sensitivity factor qmax). There are two critical cycles N1 and N2. When N1&lt;N&lt;N2, the notch fatigue property of the material and the corresponding structures under resonance environment requires more consideration than conventional fatigue loading.

Microstructural damage assessment in alloy 617M near high cycle fatigue threshold at elevated temperature

AbstractHigh cycle fatigue (HCF) behavior of Ni superalloy 617M is investigated at 973 K and R‐ratio −1 on a resonance‐based fatigue testing system at 85 Hz frequency. The alloy experiences an abrupt drop in fatigue life within a narrow domain of 2.5–5 MPa near its fatigue strength at 320 MPa. Electron microscopy and diffraction techniques were employed to thoroughly analyze the nominal fatigue damage. The characterization revealed the significance of precipitation of secondary phases M23C6, Ti (C, N), and γ′ phase in dictating the HCF strength of the alloy. Cyclic loading at high temperature causes γ‐matrix hardening and secondary phase precipitation synergistically strengthening the material beyond its yield strength. Conjunctively, dynamic strain aging was also seen to play a major role in the evolution of fatigue damage. The work highlights the collective contribution of γ′‐phase precipitation, carbides, and dynamic strain aging and their influence on the HCF behavior of alloy 617M.

Test Data Evaluation of Very High Cycle Fatigue Based on Maximum Likelihood Method

The very high cycle fatigue tests of TC4 alloy were accomplished through ultrasonic fatigue experiment which were conducted on the ultrasonic fatigue testing system at frequency range of 20000 ±1000 Hz. In contrast to the commonly used Basquin model, a Maximum Likelihood Method to fit the three-parameter nonlinear model was used to verify the adaptability in very high cycle fatigue regime. These two methods were used to estimate S-N curves of three types of materials which were TC4 alloy, GH4169 alloy and TC17 alloy in the very high cycle fatigue regime and the results were compared with test data. The evaluation result of the MLM model based on the three-parameter nonlinear model shows a good agreement with test data. The mean and variance of relative error of the MLM model are less than those of the Basquin model, providing a suitable evaluation method for predicting very high cycle fatigue limit which often has higher scatter.

Damage assessment during ultrasonic fatigue testing of a CF-PEKK composite using self-heating phenomenon

The knowledge and experience with the very high cycle fatigue (VHCF) behavior are limited compared to the low cycle and high cycle fatigue behavior of fiber-reinforced composite materials. Accelerated cyclic loading using an ultrasonic fatigue testing system is one potential solution to evaluate the longevity of composite materials within a reasonable time. Insufficient sampling rates and the inherent inaccuracies of non-contact measurement devices pose critical challenges in the adaptation of accelerated fatigue experiments. This study aims to overcome these challenges by combining the temperature response of the composite specimen and the input parameters for the dynamic response of the in-house developed ultrasonic fatigue testing system to detect damage before failure. Increasing- and constant-amplitude fatigue experiments were conducted on a carbon fiber satin fabric-reinforced poly-ether-ketone-ketone (CF-PEKK) composite material. These experiments were carried out under three-point bending loading conditions at a cyclic frequency of about 20 kHz. Various parameters, such as the surface temperature, the cyclic displacement, and the input resonance parameters of the ultrasonic generator, were recorded during these experiments. The VHCF behavior of the CF-PEKK material system was characterized based on these results and through digital light optical microscopy.

Design and research of a heavy load fatigue test system based on hydraulic control for full-size marine low-speed diesel engine bearings

As the power density design indicators of marine low-speed diesel engines gradually increased, resulting the loads of marine low-speed diesel engine bearings become increasingly complex. It's easy to cause crankshaft fatigue damage, leading to a very significant economic loss. Due to the maximum thrust loads of full-size-bearing is larger than 2000kN, the bearings performance tests are very expensive on a complete diesel engine. So, newly developed bearings must be verified on a specialized test rig. The research goal is to design a novel fatigue life test system (Bearing diameter: 300mm–520mm, Speed: 5r/min-200r/min, Thrust: 0kN–2800kN) that can simulate the working conditions of full-size low-speed marine diesel engine bearings. Adopting the advanced hydraulic-based control passive pressurization technology. Multi-platform joint simulation technology is used to make sure that the maximum thrust of the test rig is proportional to the eccentricity of the eccentric shaft. The final eccentricity of the shaft is determined by 3mm for test rig. The results based on 475mm×150mm bearing is published for the first time. The test load can be well enveloped in the load of the target diesel engine, with maximum load fluctuation less than 0.2%. The test rig can meet the performance testing requirements of full-size bearings.

Bond Wire Fatigue of Au, Cu, and PCC in Power LED Packages.

Bond wire failure, primarily wire neck breakage, in power LED devices due to thermomechanical fatigue is one of the main reliability issues in power LED devices. Currently, the standard testing methods to evaluate the device's lifetime involve time-consuming thermal cycling or thermal shock tests. While numerical or simulation methods are used as convenient and quick alternatives, obtaining data from material lifetime models with accurate reliability and without experimental fatigue has proven challenging. To address this issue, a mechanical fatigue testing system was developed with the purpose of inducing mechanical stresses in the critical region of the bond wire connection above the ball bond. The aim was to accelerate fatigue cracks at this bottleneck, inducing a similar failure mode as observed during thermal tests. Experimental investigations were conducted on Au, Cu, and Pd-coated Cu bonding wires, each with a diameter of 25 µm, using both low- and high-frequency excitation. The lifetime of the wire bond obtained from these tests ranged from 100 to 1,000,000 cycles. This proposed testing method offers material lifetime data in a significantly shorter timeframe and requires minimal sample preparation. Additionally, finite element simulations were performed to quantify the stresses at the wire neck, facilitating comparisons to conventional testing methods, fatigue test results under various operating conditions, material models, and design evaluations of the fine wire bond reliability in LED and microelectronic packages.

The high-throughput bridge to the rapid evaluation of fatigue reliability of structural engineering materials

A high-throughput strategy using miniature specimens to evaluate the ASTM-defined fatigue endurance limits of some engineering materials through a high-throughput symmetry bending cantilever beam fatigue testing system is proposed. Employing such a high-throughput testing method for examining some typical engineering materials, we reveal that the fatigue limits obtained by the traditional testing standard can be directly determined by the high-throughput method-obtained fatigue limit multiplied by a suitable conversion factor. Such a high-throughput method was validated theoretically by the proposed crack initiation model and experimentally by the F316 stainless steel specimens subjected to different aging treatments and Gamma-ray irradiation.

Very High Cycle Fatigue Properties and Damage Evolution in Al-Si Cast Alloys

Abstract The steady progress in electro mobility increases the demand for lightweight space frame and engine solutions. Advanced aluminum-silicon cast alloys with additions of magnesium, copper, or both for precipitation hardening are promising candidates for lightweight structures because of their high strength-to-weight ratio. For a reliable design, the fatigue performance in the very high cycle fatigue (VHCF) regime must be understood. Therefore, this study deals with the influence of frequency on VHCF properties as well as fatigue damage evolution in AlSi7Mg and AlSi10Mg sand-cast alloys. The VHCF tests were performed using a resonant (70 Hz), a high-frequency resonant (1 kHz), and an ultrasonic (20 kHz) fatigue testing system. Thereby, a significant frequency effect could be determined that resulted in an increased fatigue lifetime by 1 decade at 1 kHz and by 2 decades at 20 kHz, whereas no significant change in fatigue limit could be determined. Moreover, the fatigue crack initiation mechanisms change from surface crack initiation at 70 Hz and 1 kHz to volume crack initiation at 20 kHz. Using the defect-based Murakami approach, including a lightweight extension of Noguchi, a defect-induced (size, location) frequency effect could be excluded. Based on damage monitoring, the effect could be related to the crack propagation phase, which is accelerated at low frequencies (&amp;lt;100 Hz) because of a humidity reaction with the fatigue crack surface and the formation of atomic hydrogen resulting in a saturated hydrogen embrittlement per cycle. At high frequencies of 1 kHz and 20 kHz, no saturated hydrogen embrittlement per cycle can be reached.

Effects of Long Term Fatigue Cycling on In Situ Fenestrations of Polyethylene Terephthalate and Expanded Polytetrafluorethylene Thoracic Aortic Stent grafts: An Experimental Study

In this study, the long term durability of fenestrations after in situ fenestration (ISF) of five commercial thoracic aortic stent grafts was evaluated in an invitro experiment after a simulated 10 year period. Five different thoracic aortic stent grafts (Relay, Valiant, Hercules, TAG, and Ankura, with a diameter of 34 mm) received both needle and laser ISF invitro. A Viabahn (11× 50 mm) was released in each fenestration as a bridging stent graft. Long term fatigue tests (simulating 10 years) of each of the fenestrated stent grafts were then conducted in a flow fatigue test system. The area, shape, margin, and the long and short axis of all the fenestrations were evaluated with light microscopy before and after the fatigue test. The leakage from the fenestration junction before and after the long term fatigue was also measured. The experimental results showed no obvious difference between needle and laser fenestrations. The long axes of all the fenestrations remained unchanged, while the short axes increased after the fatigue test, which was significant in Relay, Valiant, and Hercules polyethylene terephthalate stent grafts. The shape scores of fenestrations improved after the fatigue test in Valiant and Hercules, remained unchanged in Relay and Ankura, and worsened in the TAG. After the fatigue cycling, the average leakage from the fenestration junction decreased in all the stent grafts, and the Ankura had the maximum decline rate. The ISF technique was durable over a simulated 10 year period. The fenestrations were positively remodelled to be more circular, and the leakage from the junction decreased after long term fatigue testing.

The medial forearm fascia and lateral forearm fascia contribute to overhead elbow extension in displaced olecranon fractures: a biomechanical study.

In nonoperative management of displaced olecranon fractures, patients are able to maintain overhead extension despite a persistent nonunion. It has been hypothesized that this is feasible because of an intact lateral cubital retinaculum. The purpose of this biomechanical study was to determine the contribution of the medial and lateral cubital retinacula to overhead extension in the setting of a displaced olecranon fracture. Eight fresh-frozen cadaveric upper-extremity specimens were used in this study. The triceps muscle was loaded through a pulley system operated by an Instron 8874 Biaxial Servohydraulic Fatigue Testing System at a rate of 10 mm/second to simulate overhead elbow extension. Each specimen was tested in 4 states: (1) native state with an intact olecranon; (2) transverse olecranon fracture; (3) transection of 1 cubital retinaculum (medial or lateral); and (4) transection of both medial and lateral cubital retinacula. The primary outcome was the ability to perform overhead extension. The secondary outcome was the force needed to generate extension. Elbow extension was noted in each specimen for trials 1, 2, and 3. Only when both the lateral fascia and medial fascia were transected was elbow extension not achieved. There was no significant difference in the force required to generate extension in the first 3 trials (P=.99). There was no significant difference in the change in the maximum force required to achieve extension between the specimens with only the medial side transected and the specimens with only the lateral side transected (P=.07). In the setting of an olecranon fracture, this biomechanical study suggests that if either the lateral or medial cubital retinaculum remains in continuity with the distal ulna, active overhead extension can be maintained. This finding may explain the positive clinical outcomes of nonoperative management of displaced olecranon fractures in the elderly patient population. Determining the integrity of the fascial structures preoperatively may help select candidates for nonoperative treatment of displaced olecranon fractures.

In-situ SEM study on fatigue crack behavior of a nickel-based single crystal alloy at 950 °C and 1050 °C

As the blade material of engine, nickel-base single crystal superalloy has been subjected to complex service environment such as high temperature and alternating load for a long time. In this work, the mechanism of fatigue microcrack initiation and propagation in a nickel-based single crystal at 950 °C and 1050 °C was studied by using the in-situ scanning electron microscope high temperature fatigue test system. At 950 °C, the alloy deformation was controlled by slip and the crack shear γ/γ’ phase cracking, showing Stage I mode. At 1050 °C, the alloy crack tearing occurred at the γ phase parallel to the loading direction and γ/γ' interface perpendicular to the loading direction and presents a Stage II mode perpendicular to the loading axis, then changes into Stage I in the accelerating stage. The deformation mechanism of fatigue cracking at two temperatures was compared. Besides, the influence of the microstructure defects on the fatigue crack behavior was discussed. The results show that the propagation of the microcrack below 100 μm shows evident fluctuations, which is closely related to the microstructure and the development stage of the fatigue crack.

Investigation of CFRP-Countersunk Bolted Assembly Fatigue Damage under Three-Point Bending via Experimental and Numerical Analysis

In this research, the fatigue damage behavior under three-point bending of a composite joint incorporating a single countersunk fastener is investigated. Firstly, a self-developed fatigue test system was set up to test the fatigue characteristics of CFRP-countersunk bolted assembly under the displacement amplitude cycles of 103 to 106 to study the formation and expansion rule of damage and cracks. It found two typical damage processes, both of which involve some formal interface damage between fiber and matrix. Based on the experiment, a finite element fatigue damage analysis on this assembly was carried out according to the Hashin failure criterion. The simulation result shows an identical fatigue damage location and fatigue life with the experimental phenomenon. Moreover, it predicted the final fatigue life of the specimen under 10 hz cyclic loading with 1 mm displacement and 10 Nm bolt preloading. This research provides guidance for the engineering fatigue issues of single-bolted joint composite connection structures and provides a reference for the corresponding technical specifications formulation.

Natural Frequency and Modes of the Longitudinal and Torsional Vibrations in the Bars with Variable Cross Section

The paper is focused on the problem of natural frequencies and modes determination based on perturbation theory for longitudinal and torsional vibrations in bars with variable cross section. The mechanical properties and cross section geometry of the bar are changing small from the average value with regard to longitudinal coordinate. Based on the theory of small perturbations the analytical solution is obtained for natural frequencies and modes of the stationary harmonic vibrations in bars. The efficiency of the proposed method is supported by comparison and good agreement of the obtain results with a sharp solution for a given cross section profiles. It was established that the approximate solution is working good up to the ratio 2.5–3 between maximum and minimum diameter of cross section. The results of numerical simulations are aimed to estimate the geometry and elastic behavior of the metallic specimens for very high cycle fatigue experimental investigation under axial tension-compression and torsion loadings. The piezoelectric fatigue testing system and procedure is based on stationary vibration excitation in the metallic specimen at the first mode natural frequency.