Low-amplitude Loading Research Articles

Static and dynamic diffuse wave inspection of delaminations in carbon fiber reinforced composites

This paper aims to realize a self-reference delamination inspection in CFRPs with diffuse ultrasonic waves. The static experiments are first conducted on samples with a machined defect of 0.5 mm in height which simulates an opening state delamination. The diffusivity decreases with delamination diameter (pristine, 6 mm, 12 mm) at a constant depth and increases with delamination depth (0.25 mm, 0.75 mm) at a given diameter. However, no clear pattern can be found for the dissipation coefficient because of the intrinsic absorption and manufacturing uncertainties. Both coefficients are insensitive to the delamination height under loading. In contrast, the corresponding maximum cross-correlation coefficient from coda wave interferometry shows a variation of 2.4–7 % in different samples. A sharp transition can be found due to the clapping effect when the delamination is fully closed. After then, the static loading is replaced by acoustic stressing pulse from PZT in a closed delamination sample. The low frequency pulse induced reverberation field is sampled by a high frequency diffuse wave semi-synchronously, which mimics a cyclic and low amplitude loading during service. All the dynamic cross-correlation coefficient curves present an ascending trend during voltage ramp-up due to the viscoelastic effect, no matter in the intact zone or delamination zone. When the voltage threshold of 250 V is reached, the clapping effect can be triggered. A descending trend has been found not only when the excitation is right above but also near the delamination. This can be applied as an indicator of the delamination existence regionally without scanning. Such nonlinear measurement system can be expanded to passive imaging and other deficiency inspection in CFRPs with less demanding facilities.

Very High Cycle Fatigue Damage of TC21 Titanium Alloy under High/Low Two-Step Stress Loading

Very high cycle fatigue (VHCF) tests were carried out under variable amplitude loading for TC21 titanium alloy. The first level of high amplitude loading was set as 950 MPa close to yield strength, and the second level of low amplitude loading was determined between 435 MPa and 500 MPa where fatigue cracks initiated at the specimen subsurface under constant amplitude. The results indicate that the high/low stress block significantly reduced the cumulative fatigue life of low stress amplitude, and the fatigue crack initiation site changed from the specimen subsurface under constant loading to the specimen surface under stress block. Based on continuum damage mechanics, the fatigue damage model of two-step stress block was established to estimate the fatigue damage process. The prediction of cumulative fatigue life generally agreed with the experimental data. The cumulative fatigue damage of the stress block was related to the stress amplitude and the cycle ratio, which determined the stress fatigue damage and its interaction damage. The surface crack initiation in the stress block accelerated fatigue damage of low stress amplitude, reducing the cumulative life.

Analytical Models of Concrete Fatigue: A State-of-the-Art Review

Fatigue failure phenomena of the concrete structures under long-term low amplitude loading have attracted more attention. Some structures, such as wind power towers, offshore platforms, and high-speed railways, may resist millions of cycles loading during their intended lives. Over the past century, analytical methods for concrete fatigue are emerging. It is concluded that models for the concrete fatigue calculation can fall into four categories: the empirical model relying on fatigue tests, fatigue crack growth model in fracture mechanics, fatigue damage evolution model based on damage mechanics and advanced machine learning model. In this paper, a detailed review of fatigue computing methodology for concrete is presented, and the characteristics of different types of fatigue models have been stated and discussed.

The in‐service fatigue fracture mechanisms for the I‐stage low‐pressure compressor disk of the aircraft engine D30KU‐154

AbstractThis paper contains the in‐service fatigue fracture analysis for the first stage low‐pressure compressor disk of the aircraft engines D30KU‐154. Based on the results of the fractographic investigation on collapsed compressor disks the fatigue crack initiation and propagation principles were established. It is shown that the crack initiation in the rim part of the compressor disk is due to a high frequency loading that leads to very high cycle fatigue fracture. The total fatigue lifetime of the compressor disk is determined by simultaneous action of low amplitude loading due to blades vibration, and high amplitude loading due to flight cycle (centrifugal forces). Study of in‐service fracture of the compressor disk was based on the evaluation of numerical simulations of the stress state in the damaged zone under corresponding loading conditions. The estimation of fatigue lifetime and crack path predictions were performed based on the multiregime fatigue fracture model developed by the authors.

Atomic mechanism of near threshold fatigue crack growth in vacuum

Structural failures resulting from prolonged low-amplitude loading are particularly problematic. Over the past century a succession of mechanisms have been hypothesized, as experimental validation has remained out of reach. Here we show by atomistic modeling that sustained fatigue crack growth in vacuum requires emitted dislocations to change slip planes prior to their reabsorption into the crack on the opposite side of the loading cycle. By harnessing a new implementation of a concurrent multiscale method we (1) assess the validity of long-hypothesized material separation mechanisms thought to control near-threshold fatigue crack growth in vacuum, and (2) reconcile reports of crack growth in atomistic simulations at loading amplitudes below experimental crack growth thresholds. Our results provide a mechanistic foundation to relate fatigue crack growth tendency to fundamental material properties, e.g. stacking fault energies and elastic moduli, opening the door for improved prognosis and the design of novel fatigue resistance alloys.

Repetitive in vivo manual loading of the spine elicits cellular responses in porcine annuli fibrosi.

Back pain and intervertebral disc degeneration are prevalent, costly, and widely treated by manual therapies, yet the underlying causes of these diseases are indeterminate as are the scientific bases for such treatments. The present studies characterize the effects of repetitive in vivo manual loads on porcine intervertebral disc cell metabolism using RNA deep sequencing. A single session of repetitive manual loading applied to the lumbar spine induced both up- and down-regulation of a variety of genes transcribed by cells in the ventral annuli fibrosi. The effect of manual therapy at the level of loading was greater than at a level distant to the applied load. Gene ontology and molecular pathway analyses categorized biological, molecular, and cellular functions influenced by repetitive manual loading, with over-representation of membrane, transmembrane, and pericellular activities. Weighted Gene Co-expression Network Analysis discerned enrichment in genes in pathways of inflammation and skeletogenesis. The present studies support previous findings of intervertebral disc cell mechanotransduction, and are the first to report comprehensively on the repertoire of gene targets influenced by mechanical loads associated with manual therapy interventions. The present study defines the cellular response of repeated, low-amplitude loads on normal healthy annuli fibrosi and lays the foundation for future work defining how healthy and diseased intervertebral discs respond to single or low-frequency manual loads typical of those applied clinically.

Experimental and Simulation Study on the Ignition Criterion of JHL‐3 under Non‐Shock Loading

AbstractThe non‐shock ignition of explosives can bring huge accidental disasters, so it is meaningful to study the conditions under which explosives ignite. The safety performance of JHL‐3, a polymer‐bonded explosive (PBX), under low amplitude and long pulse load has been analyzed based on experiment and simulation from a macro perspective, and the load criterion for ignition of JHL‐3 is given. First, JHL‐3 was loaded under confining pressure by the modified separated Hopkinson pressure bar. By observing whether the explosives ignite at different pulses whose width and amplitude can be changed by changing the length and initial speed of the striker, we find that the greater the loading pressure, the shorter the loading time required for the ignition of JHL‐3. According to the experimental results, the relationship between the amplitude and width of the loading pulse at which the JHL‐3 is ignited is fitted. Then, load JHL‐3 of different densities under the same conditions to analyze the influence of density on the ignition sensitivity of JHL‐3. The experimental results show that the sensitivity is highest when the density is between 1.7–1.75 g/cm3. Finally, based on the Uintah Computational Framework (UCF), the experiment is simulated by the coupling algorithm (MPMICE) of material point method (MPM) and implicit continuous‐fluid Eulerian (ICE). JHL‐3 is modeled by the Visco‐Scram model, and the WSB model is used as a reaction model to simulate the combustion behavior of the explosive after ignition. The simulation results closely match the experimental results, further verifying the accuracy of the ignition criterion. The ignition criterion can predict the ignition of explosives under non‐shock loading conditions, which has a guiding effect on the storage, transportation, and packaging of explosives.

Fatigue Characteristic of Designed T-Type Specimen under Two-Step Repeating Variable Amplitude Load with Low-Amplitude Load below the Fatigue Limit

In order to investigate the non-linear fatigue cumulative damage of joints in ocean structural parts, one type of low carbon steel Q345D was employed to prepare designed T-type specimens, and a series of fatigue experiments were carried out on the specimens under two-step repeating variable amplitude loading condition. The chosen high cyclic loads were larger than the constant amplitude fatigue limit (CAFL) and the chosen low cyclic loads were below the CAFL. Firstly, the S-N curve of designed T-type specimen was obtained via different constant amplitude fatigue tests. Then, a series of two-step repeating variable load were carried out on designed T-type specimens with the aim of calculating the cumulative damage of specimen under the variable fatigue load. The discussions about non-linear fatigue cumulative damage of designed T-type specimens and the interaction effect between the high and low amplitude loadings on the fatigue life were carried out, and some meaningful conclusions were obtained according to the series of fatigue tests. The results show that fatigue cumulative damage of designed T-type specimens calculated based on Miner’s rule ranges from 0.513 to 1.756. Under the same cycle ratio, the cumulative damage increases with the increase of high cyclic stress, and at the same stress ratio, the cumulative damage increases linearly with the increase of cycle ratio. Based on the non-linear damage evaluation method, it is found that the load interaction effect between high and low stress loads exhibits different damage or strengthening effects with the change of stress ratio and cycle ratio.

Influence of bolts on seismic performance of earthquake-resilient prefabricated sinusoidal corrugated web steel beam-column joints

Earthquake-resilient structures have been widely recognized and applied in the seismic field of prefabricated steel structures due to their excellent performance. The prefabricated sinusoidal corrugated web steel beam-column joint (PSCWJ) with the earthquake-resilient design concept has been previously proposed. To study the impact caused by the bolt parameters on the seismic behavior of the new PSCWJ, five specimens were designed, with varying the number of flange connecting bolts, type of bolt holes, and interval between the middle bolts. A low cycle reciprocating load test and the finite element (FE) simulations were conducted on the specimens to determine the failure mode, energy dissipation capacity, ductility, hysteretic curves, sliding curves, strain curves, skeleton curves, and other main indexes on seismic performance. And the study indicates that the PSCWJ has excellent bearing capacity and seismic performance, the new prefabricated joint can realize the dual energy dissipation by buckling and sliding of the flange cover plate (FCP), and the number of flange connecting bolts directly determines the sliding load of FCPs. A rational interval between middle bolts can control the buckling load of FCPs and provide the joint with a satisfactory bearing capacity. The setting of slotted hole can increase the rotation and energy dissipation capacity of the joint. Further, the energy dissipation performance of the repaired specimens is stable under the low frequency constant amplitude loading, thereby ensuring that the PSCWJ can be used as a damper.

The Reaction Threshold and Damage Characteristic of Typical Explosive under Low Amplitude Loading

To study the reaction threshold and damage characteristic under low amplitude loading, two HMX based explosives were chosen for the study. Low amplitude loading experiment was conducted based on card gap test. By adjusting the thickness of card, the applied pressure on the explosive sample was changed. The reaction situation of the explosive was judged by the witness board and the steel tube. The results show that the explosives, especially the casting molding explosive having the reaction threshold and detonation threshold. The detonation threshold of the casting molding explosive is 4.72~5.28GPa and the reaction threshold is 2.34~2.46GPa. The detonation threshold of the pressed fitting explosive is 2.46~2.72GPa and the reaction threshold is 2.12~2.23GPa.The damage characteristics of samples before and after shock loading were studied by use of CT system. The results of CT show that no macro-damage appear in explosive by pressed fittingaftershock damage, while cavity appear in explosive by casting molding in the position above 7~8mm of the witness board, the cavity’s length is 7~8mm, diameter is 1~2mm.

Investigation of the influence of low amplitude loads on the fatigue life of CFRP specimens with impact damage under irregular loading

The research was made to study the effect of low amplitude loads on the fatigue life of CFRP samples with impact damage in a cyclogram of irregular loading. The evaluation of the applicability of the linear summation hypothesis of damage (Palmgren’s Miner’s rule) at this level of loading was also carried out. The results have shown that in some cases correction factors need to be introduced.

Fatigue damage of designed T-type specimen under different proportion repeating Two-Step variable amplitude loads

In order to investigate the fatigue damage evolution of typical joints of River-Sea-Going Ship (RSGS) under a repeating two-step variable amplitude (VA) loading condition, and to estimate the influence of the damage of low amplitude load below the fatigue limit and the interaction effect between the high and low amplitude loads on the fatigue life of the structure, a series of fatigue experiments of designed T-type specimen (DTS) under different repeating two-step VA loading conditions were carried out in this work, which are designed according to hull structure characteristics and actual service conditions of RSGS. The experimental results show that the interaction damage value (Dnl) firstly increases and then decreases with increasing the cycle ratio of low to high amplitude load from 1 to 5. The value of Dnl is negative when the cycle ratio is relatively large, not less than 4.5 in the current study, which indicates that the effect of loading interaction not only doesn’t cause damage but has a beneficial effect on the fatigue life of the DTS. The X-ray Diffraction (XRD) analysis was carried out subsequently at the fatigue crack initiation region with the aim of confirming the material characteristic at the microcrack tip changing from work-hardening state to work-softening state with the cycle ratio increasing.

Strength changes of 40 Cr steel subjected to cyclic torsion below the fatigue limit

Abstract This paper investigates the fatigue and static strength variation of 40 Cr steel which has been subjected to cyclic torsion below the fatigue limit. The experimental results show that an improvement in fatigue strength can be exhibited if low-amplitude cyclic torsion and loading cycles are properly selected. The static strength can also be strengthened through the improvement of fatigue strength. It should be added that there is no significant static strength change in the first 50 % of the fatigue damaging process.

Design principle of active load spectrum for shafting components in wheel hub reducer of electric vehicle

Design principle of active load spectrum is proposed for the lightweight design of shafting components. The characteristics of fatigue and the strengthening effect of low-amplitude load are conducted according to the material properties of the shafting components. The stress–life curve and three-dimensional surface of low-amplitude strengthening load are established for the life calculation of shafting components. Fast calculation method of working stress for variable size of shafting components is obtained considering the road cycle in Shanghai, the load spectrum is extrapolated, the torque working condition which is equivalent to load spectrum of 3000 km is achieved, and the fatigue damage and strengthening proportion of working stress spectrum of shafting components are adjusted, finally the minimum size of shafting components is designed to meet the requirement of service life. The design principle of active load spectrum can provide a new idea for the lightweight design of automotive components.

Effect of Low-Amplitude Load Oscillations on Stiffness and Hardness for Al and W in Loaded Nanocontacts

The effect low-amplitude oscillations have on the mechanical properties of Al and W in nanocontacts is studied by means of continuous stiffness measurements (CSM). It is established that the additional superpositioning of oscillations until a critical amplitude is reached has no effect on the mechanisms, kinetics, or plastic deformation of a material. The threshold amplitudes and frequencies of such oscillations are determined for Al (2.5 nm) and W (3.5 nm).

Lightweight design of gears in the wheel-side reducer based on Shanghai road driving cycle

The development of wheel-side reducer with proper durability is important for electric vehicles equipped with a wheel-side reducer system. Based on the Shanghai road driving cycle, a novel conversion method is proposed from vehicle speed to load, which provides a theoretical foundation for lightweight design and a durability analysis of the key components of the wheel-side reducer system. With the gears of the wheel-side reducer as an example, an electric drive system durability test specification is also developed on the basis of the Miner linear cumulative damage theory considering the material strengthening under low-amplitude loads. The durability test shows that the second round of the prototype design no longer has an infinite life compared with the first round of the prototype design. The method based on active load spectrum is more effective than the traditional design method.

FEATURES OF DURABILITY CALCULATION FOR MACHINE PARTS AND STRUCTURAL ELEMENTS UNDER HIGH ASYMMETRIC LOW-AMPLITUDE LOAD CONDITIONS

The study has been conducted by means of physical, mathematical and computer modeling integrated method use. To prove the adequacy of the results obtained the experimental procedure on the existing equipment and laboratory facilities has been applied. The method of carrying out asymmetric stress cycles with mean stress of stretching to symmetric using the proposed piecewise – linear equations for evaluating the material sensitivity to asymmetry of the cycle has also been improved. It has enabled pipe column element durability under the condition of typical asymmetric low-amplitude loading calculation.

Research on Load-Spectrum Construction of Automobile Key Parts Based on Monte Carlo Sampling

Abstract Load spectrum is a decisive factor that is used to analyze fatigue, reliability, and durability of components. In this article, the typical load spectrum of proving ground is collected through load measurement equipment. Load-spectrum preprocessing, including spikes filter, signal denoising, and low-amplitude load elimination, are completed. According to parts correlation of automotive transmission systems, the load transmission route is established. The Monte Carlo sampling is applied to analyze interference of random factors in the process of load transfer route. Load spectrum of key parts of the automobile is determined and thus rain flow counting analysis is scheduled. A non-parametric method is used to complete load-spectrum extrapolation. Eventually, one-dimensional and two-dimensional programming load spectrums are built. The technical basis for fatigue life prediction and references for other similar researches are provided in this article.

Probabilistic modeling of unified S-N curves for mechanical parts

This article aims at modeling unified S-N curves based on multifailure modes and stress ratios. Heterogeneous mixture distributions are used to describe life distribution of multifailure modes. Bayes clustering is applied to cluster failure data to avoid convergence to global optima. Derived from regression analysis, failure data are compensated by nonrandom error. The relationship between distribution parameters and stress is established, and the ultimately unified probabilistic S-N curve is modeled. Two assumptions are presented to modify an original S-N curve model with varied stress ratios. The first one is to take into account the effects of low-amplitude load “exercising,” which we call results in the “pseudo-fatigue damage.” The other one is to set up probability density function of fatigue limit considering uncertainty. Combined with material parameters modification, thus a new modified and unified S-N curves model is available for not only researchers, but engineers as well.

Fatigue life prediction method for AISI 316 stainless steel under variable-amplitude loading considering low-amplitude loading below the endurance limit in the ultrahigh cycle regime

To investigate the effect of cycle ratio of combined high- and low-amplitude loading corresponding to loading above and below the fatigue limit on fatigue life (cumulative fatigue damage), fatigue tests were conducted under repeated two-step amplitude loading condition with varying cycle ratios (the number of high amplitude cycles was kept at 10 cycles, the number of low amplitude loading cycle was set at four different values 103, 104, 5×104, and 10/105 cycles in one block) using AISI 316, a type of commercial austenitic stainless steel. The test results indicate that low-amplitude loading following high-amplitude loading contributed to the fatigue damage and affected fatigue life. Furthermore, both the EN (European) and KHK (The high pressure gas safety institute of Japan) standards, which describe predictive approaches for variable-amplitude loading conditions that consider stress levels below the fatigue limit in an S–N curve based on the oblique hyperbola model, gave inaccurate evaluation of fatigue life because of the effect of cycles of low-amplitude loading below the fatigue limit in one block. Fatigue damage at saturation in one block contributed by low-amplitude was proved. A reasonable predictive approach that considering the number of cycles of low-amplitude loading in one block using linear cumulative fatigue damage rule has been established based on repeated two-step amplitude loading test results, and its precision was confirmed through random-amplitude loading tests.