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This study presents a procedure based on constant amplitude (CA) fatigue data to predict the statistical fatigue lifetime of glass/orthopolyester composites subjected to repeated ordered and random two, three, and six sequences of block loadings. A numerical routine was developed to detect cycle‐by‐cycle the statistical strength degradation progression until failure, assuming that the strength at the end of a block cycle equals the strength at the start of the successive one and that the individual samples' static strength, the amount of degraded strength, and fatigue life share the same rank in their respective cumulative distribution function. Predictions conform to the statistically undetectable loading sequence effects and lightly overestimate the lifetimes of random and ordered high‐to‐low (1/100 cycles) repeated two‐block loadings. The vanishing effect of the loading sequence when the block extents remain fixed, the block extent effects for a given three‐block sequence, and the lifetimes of three‐block loadings were fully predicted. The six‐block sequence's experimental lifetimes with different block loading orders and block extent fell within the predicted lifetimes' cumulative distribution function. A reliable damage rule based on residual strength was proposed and compared to the Miner's rule. [ABSTRACT FROM AUTHOR]

The purpose of this investigation is to assess the effect of fiber bridging on fatigue delamination propagation. Fiber bridging occurs when testing beam type laminates specimens consisting of unidirectional plies. Unidirectional double cantilever beam specimens composed of the carbon fiber reinforced polymer prepreg AS4/8552 were tested by means of fatigue cycling. A Paris relation was determined based on these tests. Fiber bridging in beam specimens composed of unidirectional plies causes the apparent fatigue delamination curves to exhibit slower growth predicting overly conservative results. In Part I of this study, the effect of fiber bridging was eliminated experimentally from the results. In Part II of this study, a cohesive zone model is developed and used to carry out finite element analyses to simulate the experiments, as well as to eliminate the influence of fiber bridging. Highlights: Fatigue delamination propagation tests were carried out on UD DCB laminate specimens.Fiber bridging was observed.Measurements were made of the fiber bridging (FB) zone.In Part II, a cohesive zone model is used to quantify the effect of FB and eliminate it. [ABSTRACT FROM AUTHOR]

This paper reviews quantitively the multiaxial fatigue assessment of steel and aluminum welded joints, focusing on Eurocodes (ECs) and the recommendations of the International Institute of Welding (IIW). Extensive fatigue data under constant and variable amplitude loading are reanalyzed using stress analysis approaches such as nominal stress, hot spot stress, and effective notch stress. Evaluation of the ECs and IIW criteria reveals an effective assessment of multiaxial fatigue, with a satisfactory level of conservatism. Further research is needed especially for variable amplitude (VA) loading to enhance the precision and reliability of assessments, contributing to improved design practices and structural integrity in welded joint applications. Highlights: The multiaxial fatigue criteria proposed by EC3 and the IIW are reviewedDesign criteria are applied in terms of nominal, hot spot, and effective notch stressBoth constant and variable amplitude load histories are consideredStandard approaches are characterized by a large level of conservatism [ABSTRACT FROM AUTHOR]

In carrying out fatigue delamination propagation tests to assess the propagation rate versus a function of the energy release rate, the question arises as to the necessary number of cycles required to properly characterize the behavior. Tests were performed elsewhere on two different carbon/epoxy, multidirectional woven composite laminates containing a delamination using constant amplitude cycling by means of displacement control for various cycle ratios. The aim was to carry out the tests for 3.0×106 cycles. Most specimens complied with this requirement. In this study, the fatigue data are analyzed including the first 0.5×106 cycles, the first 1.0×106 cycles, the first 1.5×106 cycles, and 3.0×106 cycles. It was seen that although the delamination length versus the cycle number could be quite similar between different cycle ranges, the Paris relation constants could be significantly different. It is suggested to carry out tests for as many cycles as possible. Highlights: Double cantilever beam (DCB) specimens fabricated from multidirectional woven material were considered.Two material systems were examined.Different cycle ranges were used: 0.5 × 106, 1.0 × 106, 1.5 × 106, and 3.0 × 106.It was found that more reliable results were obtained for longer cycle ranges. [ABSTRACT FROM AUTHOR]

In this investigation, three subjects are considered. First, the effect of the human factor is examined. In carrying out analyses of fatigue delamination propagation tests on laminate composites, the delamination length must be measured. The human effect on measurement of the delamination length a by different investigators is discussed. A limited influence of the human factor on the measurement of the delamination length a, as well as on delamination propagation rate da/dN, is observed in this study. Secondly, the paper proceeds to discuss the influence of the R‐ratio on the fatigue delamination growth rate. It is found that a higher rate of crack/delamination propagation is associated with lower R‐ratios which appears to contradict conventional wisdom. This behavior is confirmed in tests. Thirdly, a comparison between the fatigue propagation rates of two material systems is considered. It is concluded that the energy release rate used to assess these materials should not be normalized. Highlights: Impact of human factor on fatigue delamination tests in laminate composites.Limited influence of the human factor on delamination length and propagation rate.The lower the R‐ratio, the higher the delamination propagation rate.The crack driving force for laminates should be taken as GImax. [ABSTRACT FROM AUTHOR]

This study focuses on the fatigue behaviour analysis of glass fibre-reinforced polymer (GFRP) composite specimens under high-cycle fatigue loading conditions. Therefore, property validation is recommended in the material development process upon further investigation of the fabricated GRFP. This study aims to evaluate the behaviour of the fabricated GFRP fatigue specimen when subjected to high-cycle fatigue loads and compare it to existing studies. A GFRP fatigue test sample was fabricated using the hand layup process into a flat rectangular panel, which was then cut into a small dimension of 28×2×0.2 cm fatigue specimen. Fatigue tests were performed on five flat specimens at different constant amplitude loads or stress levels between 40% and 80% of ultimate tensile strength to obtain the stress-life curve for the fabricated GFRP. Results showed that the high-stress levels of 80% contributed to the most reduced fatigue life cycle of GFRP. This result is consistent with previous studies and lies within the published life cycle range, validating the fabricated GRFP. A new parameter called the failure modulus, or Mf, may be used to quantify a particular set of fatigue tests. [ABSTRACT FROM AUTHOR]

Plain bend bars made from FV566 martensitic stainless steel were extracted from the root of ex‐service power plant turbine blades and several industry‐relevant notch geometries were introduced. Some of the samples were shot peened. The notched bend bars were loaded plastically in the low‐cycle fatigue regime and finite element (FE) modeling carried out to investigate the effects of changing notch geometry, combined with shot peening, on fatigue behaviors such as crack initiation, short crack growth, and coalescence. Shot peening damaged the notch surface, accelerating initiation behaviors, but had a lifetime‐extending effect by retarding short crack growth in all tested notch geometries. At a total strain range higher than 1.2%, the lifetime extension benefit from shot peening was diminished due to compressive residual stress relaxation in the notch stress field. Notch geometry (and the associated varying constraint levels and stress/strain gradients) was found to have no notable difference on fatigue life when tested at identical notch‐root strain ranges. Highlights: Initiation activity increased with increasing strain range regardless of notch geometry. Surface damage from the shot peening increased initiation activity and lowered a/c ratios. Shot peening reduced the early short crack growth rate at lower ΔK by a factor of 10. Shot peening increased lifetimes up to a strain range of 0.8%–1.2%. [ABSTRACT FROM AUTHOR]

• A novel impact fatigue device based on the split Hopkinson pressure bar. • A novel method to achieve repeated impact loading with constant amplitude. • The method has the advantages of controlling loading waveform and monitoring load. • The loading rate has a significant effect on the fatigue life of Ti-6Al-4 V. The lack of reliable testing methods and standards hinders systematic research on the impact fatigue performance of materials. The aim of developing an impact fatigue test method is to generate repeated impact loads with a constant amplitude, which is difficult to achieve using various existing impact test devices. This study investigated the principles of cyclic loading-resetting and constant-amplitude loading based on the split Hopkinson pressure bar (SHPB) system, established a novel impact fatigue test device, and verified the developed method by testing the impact fatigue life of a Ti-6Al-4V alloy. Electromagnetic valves, laser sensors, and a vacuum pump were used in the developed device to launch and reset the striker bar; a servo motor and laser sensors were used to reset the loading bars and specimen, and the entire system was controlled by a programmable controller to achieve continuously repeated loading. To achieve constant-amplitude loading, the conditions required to ensure that the specimen moves away from the incident bar before the returning stress wave reloads the specimen was derived. It was found that a constant-amplitude repeated impact on the specimen could only be achieved through the precise design of the geometric configuration and material of the loading bars. This method is considerably simpler than various existing methods based on energy absorption and is more applicable to impact fatigue tests. The verification tests showed that the highest loading frequency of the device was 0.5 Hz, the loading rate exceeded 105 kN/s, and the amplitude error of the repeated impact loads did not exceed 2.45 %. Under loads with the same amplitude, the impact fatigue life of a Ti-6Al-4V alloy was considerably shorter than the non-impact (low strain rate) fatigue life, which indicates the necessity of investigating the strain rate effect on the fatigue performance of materials. [ABSTRACT FROM AUTHOR]

There is mutual coupling between amplitude control and frequency tracking control in the closed-loop control of micromechanical resonant sensors, which restricts sensor performance. This paper introduces the principle of an in-plane vibration micromechanical resonant accelerometer with electrostatic stiffness. The characteristic parameters of the microaccelerometer were obtained through computer-aided dimension measurement and an open-loop frequency sweep test of the fabricated microstructure. An accurate numerical model was established based on the accelerometer's dynamic principle and characteristic parameters. We established the double closed-loop driving analysis model of amplitude automatic gain control and resonant frequency phase-locked tracking. We used the averaging method to analyze the steady-state equilibrium point and the stable condition. We concluded that the integral coefficient can improve the startup overshoot when the amplitude automatic gain control loop satisfies the stability condition. Under the constraint of frequency tracking, the sizeable coefficient of the integrator can improve the system instability of the amplitude control loop. The theoretical analysis and simulation were helpful in the design and debugging of the system circuit. [ABSTRACT FROM AUTHOR]

There is mutual coupling between amplitude control and frequency tracking control in the closed-loop control of micromechanical resonant sensors, which restricts sensor performance. This paper introduces the principle of an in-plane vibration micromechanical resonant accelerometer with electrostatic stiffness. The characteristic parameters of the microaccelerometer were obtained through computer-aided dimension measurement and an open-loop frequency sweep test of the fabricated microstructure. An accurate numerical model was established based on the accelerometer’s dynamic principle and characteristic parameters. We established the double closed-loop driving analysis model of amplitude automatic gain control and resonant frequency phase-locked tracking. We used the averaging method to analyze the steady-state equilibrium point and the stable condition. We concluded that the integral coefficient can improve the startup overshoot when the amplitude automatic gain control loop satisfies the stability condition. Under the constraint of frequency tracking, the sizeable coefficient of the integrator can improve the system instability of the amplitude control loop. The theoretical analysis and simulation were helpful in the design and debugging of the system circuit.

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Fatigue analysis probes how cyclic random service loads can often lead to catastrophic structural failure of the component. In this research work the crank bar design of a Bike is validated for Fatigue analysis using SOLIDWORKS Simulation which enables designers to simulate Fatigue failure of the component using Stress Life (SN) method that is based upon standard material test to failure. Aluminum 6061 – T6 material is used in the design and Fatigue SN curve table data is taken from the SOLIDWORKS material library which is derived from material elastic modulus based on ASME Austenitic Steel curves. The crank arm length is 10 in and width is 1.5 in with overall constant thickness 0.8 in and crank mid-section thickness equals to 0.2 in. First the design is analyzed for Static strength by applying the bearing load of 350 lbs. The maximum VonMises stress calculated was 106.61 MPa which is below the allowable yield strength of the material 275 MPa. A fully reversible alternating stresses equivalent to static VonMises stress is loaded for 100,000 cycles which is the required life of the component. The total life calculated was 69,158 cycles which is less than 100,000 cycles and factor of safety is 0.93. The conclusion was the component has to be redesigned for Fatigue strength.

Double cantilever beam (DCB) specimens composed of carbon fiber reinforced polymer laminate composites were tested. Two material systems were investigated. One consisted of plies from a woven prepreg alternating with tows in the 0 ∘ / 90 ∘ -directions and the + 45 ∘ / - 45 ∘ -directions. The second was fabricated by means of a wet-layup process with the same multi-directions as the prepreg. In addition, for the second material system, a unidirectional (UD) fabric ply was added. The delamination for this laminate was between the UD fabric and the woven ply with tows in the + 45 ∘ / - 45 ∘ -directions. Both fracture resistance R-curve and fatigue delamination propagation tests were carried out. It is found that the initiation value of the interface energy release rate is substantially lower for the wet-layup; whereas, their steady state values are quite similar. The fatigue delamination propagation tests were performed at various cyclic R-ratios. The delamination propagation rate da/dN was calculated from the experimental data and plotted using a modified Paris equation with different functions of the mode I energy release rate. As expected, the da/dN curves depend upon the R-ratio. By using another parameter based on the Hartman–Schijve equation for metals, it is possible to obtain a master-curve for all R-ratios. It is seen that the propagation rate for the prepreg is faster than that of the wet-layup. [ABSTRACT FROM AUTHOR]

Five double cantilever beam specimens were tested quasi-statically to obtain a GIR resistance curve. In addition, nine double cantilever beam specimens were tested in fatigue to obtain a Paris-type relation to describe the delamination propagation rate da/dN where a is delamination length and N is the cycle number. Displacement ratios of Rd = 0.10 and 0.48 were used for five and four specimens, respectively. The specimens were fabricated by means of a wet-layup process from carbon fiber reinforced polymer plies. The interface containing the delamination was between a unidirectional fabric and a woven ply. The fracture toughness and fatigue delamination propagation protocols are outlined. The mechanical and thermal residual stress intensity factors were obtained by means of finite element analyses and the conservative M-integral along the delamination front. They were superposed to determine the total stress intensity factors. It was found that the total mode I stress intensity factor dominates the other two stress intensity factors. Thus, nearly mode I deformation was achieved. Interpolation expressions for the mechanical and thermal residual stress intensity factors were determined using three and two-dimensional fittings, respectively. Results are presented with an expression for GIR determined. Moreover, the fatigue data is described including threshold values and master-curves. These results shed light on the behavior of delamination propagation in multidirectional laminate composites. [ABSTRACT FROM AUTHOR]

While it is well known that fatigue crack growth in metals that display confined slip, such as high strength aluminium alloys, develop crack paths that are responsive to the loading direction and the local microstructural orientation, it is less well known that such paths are also responsive to the loading history. In these materials, certain loading sequences can produce highly directional slip bands ahead of the crack tip and by adjusting the sequence of loads, distinct fracture surface features or progression marks, even at very small crack depths can result. Investigating the path a crack selects in fatigue testing when particular combinations of constant and variable amplitude load sequences are applied is providing insight into crack growth. Further, it is possible to design load sequences that allow very small amounts of crack growth to be measured, at very small crack sizes, well below the conventional crack growth threshold in the aluminium alloy discussed here. This paper reports on observations of the crack path phenomenon and a novel test loading method for measuring crack growth rates for very small crack depths in aluminium alloy 7050-T7451 (an important aircraft primary structural material). The aim of this work was to firstly generate short- crack constant amplitude growth data and secondly, through the careful manipulation of the applied loading, to achieve a greater understanding of the mechanisms of fatigue crack growth in the material being investigated. A particular focus of this work is the identification of the possible sources of crack growth retardation and closure in these small cracks. Interpreting these results suggests a possible mechanism for why small fatigue crack growth through this material under variable amplitude loading is faster than predicted from models based on constant amplitude data alone.

In this work, a quadrature type active phase shifter based on field effect transistors (FET) is designed and implemented at the frequency of 2.44 GHz. The phase shift is obtained by the addition of two orthogonal vectors, varying adequately control voltages at constant amplitude. The results of the design simulations are shown by the Microwave Office software and the phase shift achieved by this design using the ARLON 25N substrate is 89.45°, a value very close to that theoretically expected (90°) and a gain of approximately 7.7 dB. Unfortunately, its practical implementation on a printed circuit board of FR4, caused a decrease of the phase shift to 79°, and insertion losses, because the FR4 substrate introduces losses close to 7 dB. However, its operation is checked. This phase shifter can be used in phased arrays of uniform amplitude because a function is obtained in Matlab which describes the behavior of the control voltages to maintain the amplitude at the constant output. [ABSTRACT FROM AUTHOR]

The aim of this work was to study the effect of stitch pattern and stitch tension on tension-tension fatigue performance of quasi-unidirectional non-crimp fabric reinforced glass-fibre/epoxy laminates. Internal structure variations of the laminates were characterised using cross-sectional microscopy imaging for the evaluation of fatigue test results. Reinforcements for the study were manufactured with three different stitch patterns and two different stitch tensions. Based on the results, the stitch pattern contributes to in-plane and out-of-plane waviness of fibres, as well as on the size and shape of the axial fibre bundles. The fatigue life and slope parameter of the fitted S-N curve were significantly dependent on the stitch pattern, while they were not dependent on the applied stitch tension. [ABSTRACT FROM AUTHOR]

Residual strength models are widely used for the fatigue analysis of composites subjected to both constant and variable amplitude fatigue. However, they often require large experimental efforts to determine the model parameters. The aim of this research is to develop a simplified mathematical model which uses a single set of parameter values to predict the strength degradation of the elements subjected to different load levels, and thus, to reduce the required experimental effort for the determination of model parameters for each load level separately. The new two-parameter model is developed here on the basis of normalization of the difference between the residual strength and maximal applied load in the constant amplitude cyclic loading, herein referred to as the strength reserve, with respect to initial conditions. The model is validated using different experimental data sets from the literature. High correlation with the experimental data is observed. Moreover, the curves obtained by using the single set values of parameters matched the curves of some of the most accurate residual strength models from the literature. [ABSTRACT FROM AUTHOR]

A criterion is developed which predicts matrix fatigue crack initiation for Uni-Directional (UD) composite plies subjected to multiaxial fatigue load at all stress-ratio's: Tension-Tension, Compression-Compression and Tension-Compression. This research is based on physical observations of matrix damage types and their respective driving forces. Existing fatigue prediction formulations, that partly succeed in predicting fatigue life to initiation, are investigated for their key attributes which are subsequently combined in a coherent way. The framework requires 7 material parameters: 4 for Tension-Tension load, 2 for Compression-Compression load and 1 to take into account the accelerated occurrence of damage under Tension-Compression load. The material parameters can be calibrated from only 7 crack initiation S-N curves. 5 experimental datasets, a variety of the two most common reinforcing fibres and matrix (Carbon and Glass fibres combined with an epoxy or PEEK resin), are selected for a thorough verification and validation of the criterion. The agreement of the prediction with experiment is, remarkably, excellent for Glass/Epoxy, good for Carbon/Epoxy and reasonable for Carbon/PEEK. This new framework establishes a solid base for further developments to predict matrix crack initiation and the inclusion of other failure types such as fibre kinking. [ABSTRACT FROM AUTHOR]

In this paper, a method is proposed for evaluating the delamination growth rate da / dN for any given R -ratio (load or displacement ratio) using data from a relatively small number of tests. To this end, double cantilever beam (DCB) specimens fabricated from a plain woven prepreg (G0814/913) arranged in a multi-directional (MD) layup were tested. First, quasi-static tests were carried out to obtain the resistance G IR -curve. Then, constant amplitude fatigue tests were preformed to determine the delamination growth rate da / dN . In both tests, displacement control was imposed. Four different cyclic displacement ratios R d , namely 0.1, 0.33, 0.5 and 0.75, were used for the fatigue tests. When the delamination growth rate da / dN , calculated from the experimental data, was plotted with respect to G Imax and Δ G Ieff = ( G Imax - G Imin ) 2 , different behavior of the da / dN curves was observed. In addition, modification of the Hartman-Schijve representation was made. When the da / dN data was plotted with respect to the new modified representation which was denoted here as Δ K ‾ I , all of the data obtained for different displacement ratios collapsed into one master curve. From this master curve, da / dN values may be calculated for any given R -ratio. [ABSTRACT FROM AUTHOR]

In the present study, the non-metal acoustic wave monitor, TH204, has been used to determine P-wave velocity of compacted expansive soil under the condition of drying-wetting cycles with constant amplitude to explore the change in P-wave velocity of compacted expansive soil with the cyclic number, cyclic amplitude and control moisture content. The results show that the P-wave velocity of the compacted expansive soil follows a non-linear decrease rate with increasing the cyclic number, while it tends to be stable. Also, under the conditions of equivalent control moisture rate and cyclic number, the cyclic amplitude has great effect on the P-wave velocity of expansive soil. Thus, with increase in the cyclic amplitude, the P-wave velocity decrease. Secondly, under the same cyclic number, the P-wave velocity changes with the control moisture rate monotonously. Further, the study shows that the peak values of P-wave velocity appear near the optimum moisture rate, and the peak value position remains unaltered with change of cyclic amplitude. [ABSTRACT FROM AUTHOR]

It is accepted that fatigue crack paths in metals that display confined slip, such as high strength aluminium alloys, are responsive to loading direction and local microstructural orientation. It is less well recognised that crack paths in these alloys are also responsive to the loading history since certain loading sequences can produce highly directional slip bands ahead of the crack tip. By adjusting the sequence of loads, distinct fracture surface features or progression marks can result, even at very small crack depths. An investigation into the path a fatigue crack selects as it progresses through a material when it is cyclically loaded with particular combinations of constant and variable amplitude sequences has provided insight into the way these cracks grow. This makes it possible to design load sequences that allow very small advances of crack growth to be measured post-test by Quantitative Fractography, at growth rates well below the conventionally recognised threshold of the aluminium alloy examined here. This paper reports on observations of the dependence of the crack path on the loading history applied to aluminium alloy 7050-T7451 (an important aircraft primary structural material) coupons, which was made possible through the use of novel test loading sequences that produce distinct markings on the crack surface. These markings allow the measurement of crack growth rates at very small crack depths and very low rates of growth in this alloy. The aims of this work were firstly to generate small-crack constant amplitude growth rate data and secondly, to achieve a greater understanding of the mechanisms of fatigue crack growth in this material. A particular focus of this work was the identification of possible sources of crack growth retardation and acceleration in small cracks. The results suggest that for small cracks in this material, the rate of crack growth under variable amplitude loading will tend to be faster than predictions made based on the crack growth rate under constant amplitude loading, due to crack path considerations. [ABSTRACT FROM AUTHOR]

While it is well known that fatigue crack growth in metals that display confined slip, such as high strength aluminium alloys, develop crack paths that are responsive to the loading direction and the local microstructural orientation, it is less well known that such paths are also responsive to the loading history. In these materials, certain loading sequences can produce highly directional slip bands ahead of the crack tip and by adjusting the sequence of loads, distinct fracture surface features or progression marks, even at very small crack depths can result. Investigating the path a crack selects in fatigue testing when particular combinations of constant and variable amplitude load sequences are applied is providing insight into crack growth. Further, it is possible to design load sequences that allow very small amounts of crack growth to be measured, at very small crack sizes, well below the conventional crack growth threshold in the aluminium alloy discussed here. This paper reports on observations of the crack path phenomenon and a novel test loading method for measuring crack growth rates for very small crack depths in aluminium alloy 7050-T7451 (an important aircraft primary structural material). The aim of this work was to firstly generate short- crack constant amplitude growth data and secondly, through the careful manipulation of the applied loading, to achieve a greater understanding of the mechanisms of fatigue crack growth in the material being investigated. A particular focus of this work is the identification of the possible sources of crack growth retardation and closure in these small cracks. Interpreting these results suggests a possible mechanism for why small fatigue crack growth through this material under variable amplitude loading is faster than predicted from models based on constant amplitude data alone. [ABSTRACT FROM AUTHOR]

Based on the piston force analysis of the hydraulic free piston diesel engine, a nonlinear vibration model is established. Then the solution of the nonlinear vibration model is given by the generalized harmonic KBM method. The reasons that affect the constant amplitude of the nonlinear vibration model are analyzed according to the expression of the constant amplitude. The constant amplitude is limited by many factors and the system will be unstable if the correlated variables are out of range. The influential factors, such as the fuel injection position and quality, are investigated. In addition, the fluctuation of pump chamber caused by the variation of response characteristics of check value also influences the constant amplitude. All these reasons may lead to the unstability of the oscillatory system. Because the combustion condition is influenced by the air intake and fuel injection, the selection of unstable region is decided by the scavenging and combustion. Therefore the scavenging influenced by the port opening is researched and the results are validated by experiment. In order to get the optimal design of HFPE, the stability range of the piston constant amplitude and judging in equation are proposed, and the parameters in the stable region are obtained. All these efforts establish the theoretical foundation for control strategy of stability improvement. [ABSTRACT FROM AUTHOR]

This study provides two theorems defining two classes of conservative nonlinear oscillators that have some characteristics of the linear harmonic oscillators, one of which is an amplitude-independent period. These theorems also define their response in terms of initial conditions. The first class of these nonlinear oscillators is also characterized by a constant amplitude, while the amplitude of the second one decreases in time. A few illustrative examples are also presented. [ABSTRACT FROM AUTHOR]

Highlights: [•] Fatigue crack tends to propagate along the L-direction. [•] No remarkable crack branching was observed under CA loading condition. [•] Significant crack branching appeared in VA loading condition. [•] The underloads following the peak load result in further retardation. [ABSTRACT FROM AUTHOR]

Abstract: Different approaches – the nominal stress, structural hot spot stress and notch stress approach – to analyse the fatigue strength of welded structures made from wrought aluminium alloys were studied. Experimental and numerical investigation was carried out for this purpose on detail specimens and components. The results shown here were generated during the research project “Extrusion profile and sheet metal structures of wrought aluminium alloys in vehicle construction”. The studies show that due to the existing guidelines, welds on structures made from aluminium alloys are sometimes designed very conservatively. It is possible to optimise and reliably design welded joints of thin sheet structures by applying the notch stress approach using the reference radius r ref =0.05mm and the reference SN curves derived here. [Copyright &y& Elsevier]

Abstract: It is well known that variable amplitude fatigue loading produces progression marks on fatigue crack surfaces that are related to the loading sequence. These marks are generally a local change in the crack path. The same pattern of loading can produce a pattern of progression marks that have differences from material-to-material or from heat treatment-to-heat treatment, yet the crack path changes that produce these markings are not considered in the prediction of the crack growth behaviour. These path changes can be used to: investigate how the crack grows, aid crack growth measurement and shed light on the mechanism that forms striations. Consequently, an understanding of these path changes and their fundamental cause in structurally significant alloys is important to the explanation of how fatigue cracks grow and how their life can be predicted. In this paper, a number of simple loading sequences were used to investigate the influence that underloads have on the crack path, to develop a better understanding of the formation of fatigue striations and the coarser crack path changes associated with loading changes. The material chosen was aluminium alloy (AA)2024-T3. The results from the tests reported here were compared to previously investigated AA7050-T7451 specimens that were loaded in a similar manner. It is shown that the fatigue crack surfaces that were produced here were the direct consequence of the applied loading interacting with the crystal structure of the material. By changing the loading, via the addition of underloads it was possible to produce fatigue crack surfaces that where composed of not only striations but ridges, depressions and fissures. These features give an indication of the crack growth mechanism. Although, AA2024-T3 and AA7050-T7451 have different chemical compositions, mechanical properties and micro-structures, it was shown that both materials share essentially similar fracture features corresponding to crack propagation at the cycle-by-cycle level. It also appears that despite the above noted differences, similar failure mechanisms may take place. [Copyright &y& Elsevier]

An approach to construct the stress (or load) vs. cycles curve for composite structures under constant amplitude loading is presented. The approach is based on the assumption that the cycles to failure are a function of the probability of failure during any given cycle. In this first investigation, this probability of failure during any cycle is assumed to be constant and equal to the probability of failure obtained from static test results and the associated statistically quantified scatter. Expressions for the cycles to failure as a function of R ratio are derived. These expressions do not require any curve fitting and do not involve any experimentally determined parameters. The fatigue predictions do not require any fatigue tests for calibration. Comparisons to several test cases found in the literature show this first simple model to be very promising. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a simple damage model for fatigue life predictions of welded joints under nonproportional, constant, and variable amplitude loading histories. This model, an extension of Sonsino’s effective equivalent stress amplitude method, consists of four material parameters accounting for the severity of nonproportional loading paths, the material’s susceptibility to nonproportional hardening, the material’s fatigue life under shear versus normal stresses, and the mean stress effect. These four parameters can be obtained by fatigue testing for S–N curves under bending only, torsion only, and 90° out-of-phase loading. This paper investigates the validity of the fatigue damage model by comparing the analytical and the published experimental results for various welded joint configurations subjected to multiaxial constant amplitude loads. This paper also describes a procedure to predict fatigue lives of welded joints under nonproportional variable amplitude loading histories based on the linear cumulative damage rule, the proposed equivalent stress amplitude and the Wang–Brown reversal counting technique. [Copyright &y& Elsevier]

Fatigue analysis is a complex and uncertain process. Various models have been proposed; however, no universal or all-encompassing model exists.A state-of-the-art literature review of available fatigue crack propagation models, both for constant and variable amplitude loadings, was conducted to identify their advantages and limitations. Emphasis was placed on models that were simple to evaluate and required few (if any) empirical curve-fitting parameters.An experimental fatigue program was conducted, consisting of constant and semi-random (variable) amplitude cyclic loadings on 350WT steel 40J at −40°C. The fatigue models examined in the literature review were then compared to results obtained from the experiments.Findings for the constant amplitude loading (CAL) fatigue baseline data obtained experimentally for 350WT steel are reported and evaluated against the predictions by various models. Results of an experimental investigation into fatigue crack propagation (FCP) response of the steel under variable amplitude loading (VAL), consisting of CAL with random overloads (OL) is also presented. This includes a summary of theoretical models applicable to VAL fatigue crack propagation, and comparison of the experimental results to the models. [Copyright &y& Elsevier]

The attractive properties of the digital constant amplitude modulation scheme CPM (continuous phase modulation) have been demonstrated in a previous paper in this journal.1 This concerned both the power and spectral efficiency of the large family of CPM schemes over the Gaussian channel. In this paper the considered channel can be both bandlimited or band- and amplitude-limited at the same time. Analytical results as well as simulations are presented for a number of selected CPM schemes. In today's increasing demand for bandwidth, CPM is an attractive candidate for future satellite applications because of its spectral efficiency. In addition to this comes the fact that the transmitted signal has a constant amplitude and good detection performance when optimal coherent detection is performed. [ABSTRACT FROM AUTHOR]

There is an increasing demand for digitial radio transmission. The cost of a channel is proportional to the bandwidth. For many applications power is limited. For satellite applications constant amplitude modulation is advantageous because of non-linear amplification. In this paper a class of power and bandwidth efficient constant amplitude continuous phase modulation (CPM) schemes is presented. The signals are analysed in great detail and the tools for both error probability analysis and power spectral calculations are presented. Numerical data for raised cosine (RC) pulse shaping is presented. This paper is basically an overview with new results on the trellis description of CPM. The transmission is assumed to be ideally coherent over the Gaussian channel. In a following paper we will deal with transmission imperfections such as bandlimitation and hard limiting and their effect on CPM1. [ABSTRACT FROM AUTHOR]