Influence Of Loading Frequency Research Articles

A phase field framework for corrosion fatigue of carbon steel

Corrosion fatigue damage occurs when metallic materials are subjected to cyclic loading in a corrosive medium. In this study, a phase field framework is proposed to predict the corrosion fatigue of carbon steels. The coupling effect of fatigue and corrosion is explicitly implemented in the proposed phase field framework by coupling the displacement field, electrochemical field and phase field. A degradation function of the interface free energy density with the consideration of elastic and plastic strain energies is introduced to account for the fatigue damage accumulated during the corrosion fatigue process. The applicability of this framework is validated by accurately capturing the pure fatigue and corrosion fatigue behaviors of compact tension specimens, particularly the acceleration effect of corrosion on the fatigue crack growth. The propagation morphology and rate of the corrosion fatigue crack in single pit and multiple pit models are studied. The distribution of stress state and strain energy density induces the directionality of crack propagation. The influence of loading frequency on the corrosion fatigue process is discussed in detail. Due to the corrosion-fatigue coupling effect, the corrosion rate increases with increasing of the loading frequency, resulting in an accelerated corrosion fatigue process. Moreover, the significance of the plasticity in the prediction of corrosion fatigue is emphasized.

Strengthening behavior and microstructure of 2195 Al-Cu-Li alloy under cycling loading

Cyclic strengthening process, as a newly developed aluminum alloy strengthening technique, has garnered significant attention due to its advantages of rapidity, efficiency, and superior mechanical properties. This study investigated the effects of strain amplitude and loading frequency on cyclic strengthening, including mechanical properties and microstructural evolution. At room temperature, the cyclic strengthening effect of the 2195 alloy increases with increasing strain amplitude, while the influence of loading frequency is pronounced within the elastic range but nearly negligible within the plastic range. Microstructural analysis reveals that cyclic strengthening behavior within the elastic range is attributed to the precipitation of clusters, whereas within the plastic range, it is attributed to the precipitation of clusters and dislocation multiplication. Unlike other plastic deformations, cyclic plastic loading generates dislocations primarily in the form of dislocation loops. The dynamic precipitation of clusters and the diffuse distribution of dislocation loops significantly enhance the alloy's strength with minimal sacrifice of elongation. Experimental investigations on the influence of loading frequency on these precipitation behaviors demonstrate a positive correlation with dislocation generation and a negative correlation with cluster precipitation. Comparison of specimens with different strain amplitudes reveals that larger strain amplitudes provide more energy for cluster precipitation, thereby promoting precipitation. However, excessively large strain amplitudes lead to the annihilation of vacancies due to the introduction of more dislocations, thus inhibiting cluster precipitation. This indicates that the precipitation of clusters during cyclic deformation is profoundly influenced by dislocation behavior. This study deepens the understanding of cyclic strengthening mechanisms and provides support for subsequent development of cyclic strengthening processes in other materials design.

Dynamic characteristics of compacted landfill waste material from cyclic triaxial tests

This study conducted a series of cyclic and monotonic triaxial tests on reconstituted landfill waste material from a closed landfill site in Sydney, Australia, to assess its dynamic behaviour under various testing conditions. Specifically, the effects of cyclic deviatoric stress, loading frequency, and effective confining stress on the cumulative plastic axial strain, resilient modulus, and damping ratio under undrained cyclic loading conditions were investigated. Results indicated that the plastic deformation, resilient modulus, and material damping are significantly influenced by dynamic stress and confining stress, with a lesser impact from loading frequency. Notably, as the number of loading cycles increased, the cumulative plastic axial strain and resilient modulus exhibited an increase, whereas the damping ratio decreased. Furthermore, increasing cyclic deviatoric stress led to an increase in both cumulative plastic axial strain and damping ratio, while an increase in confining stress resulted in a decrease in these parameters. Conversely, the resilient modulus showed an increase with rising cyclic deviatoric stress and confining stress. The influence of loading frequency on cumulative plastic axial strain and resilient modulus was minor, and its effect on the damping ratio was rather negligible. The study observed that initial loading cycles caused rearrangement and reorientation of waste components and the mobilisation of fibres with tensile forces as loading progressed, suggesting that these landfill waste samples behaved comparably to fibrous soil with randomly distributed fibres. Through nonlinear regression analysis, an empirical relationship for cumulative plastic axial strain incorporating cyclic deviatoric stress, confining stress, number of cycles, and frequency was derived. This research contributes valuable insights into the behaviour of compacted landfills as railway subgrades, providing a foundation for informed decision-making in the design of transport infrastructure over closed landfill sites.

Post-cyclic behavior of Haikou marine clay and their predictions using back-propagation neural network model

The evaluation of post-cyclic behavior of soft clay is critical for the lifetime safety and performance assessment of various infrastructures built on/in it. In this study, by employing the marine clays collected from Haikou, China, a series of both conventional shear tests and post-cyclic shear tests under undrained condition were performed using triaxial setup to investigate the post-cyclic behavior of the clay, with the investigation foci placed on the post-cyclic shear stress and secant modulus. Some important factors, namely confining pressure, loading frequency, cyclic shear strain amplitude and post-cyclic shear strain, were taken into consideration. From both the results from the tests and the parameter sensitivity analysis using random forest method, the confining pressure and cyclic shear strain amplitude were found to be evidently influential on the post-cyclic behavior of the clay, while the influence of loading frequency was relatively insignificant. In addition, an intelligent model was established based on the back-propagation neural network method to predict the post-cyclic behavior of Haikou marine clay, which was proven to be more favorable as compared to other two prediction methods developed based on multi-variate regression analysis and random forest algorithm.

Permanent deformation prediction model for freeze–thaw coarse–fine mixture of geomaterials with varying fine content: Influence of loading frequency

The impact of cyclic loading frequency (fcyc) on the permanent deformation (εp) of freeze–thaw coarse–fine mixture of geomaterials (FTCF) has been extensively investigated. In this work, long-term cyclic triaxial tests were conducted on FTCF specimens with varying fcyc and deviatoric stress (qcyc) with different numbers of freeze–thaw cycles (NFT), in order to investigate εp under freeze–thaw cycling. This study systematically analysed and discussed the effects of fcyc and qcyc on εp of FTCF samples with different fine particle contents (FC). A rate-dependent multistage load-prediction model for εp was proposed and evaluated. The results showed that the freeze–thaw cyclic had a less significant impact on εp when compared to the dynamic triaxial loading. The speed and piston effects of the FTCF under dynamic loads were mutually restricting, with their combined impact closely related to the loading frequency. A higher deformation resistance for a coarse-grained skeleton is attained with the effective filling of fine particle clusters in the pores of skeleton. A function was proposed to describe the relationship between the hyperbolic model parameters and fcyc, qcyc, as well as FC. This function could be used to estimate the hyperbolic model parameters under different dynamic stresses and material states. An equivalent stress-state parameter was introduced to consider the effect of the loading frequency, enabling the exploration of dynamic loading's influence on the equivalent vibration number (Neq). A comparison between the predicted results and the test data showed that the proposed model could accurately reproduce the cumulative behaviour of the εp of FTCF under different fcyc and qcyc.

Influence of loading frequency on ULCF life of structural steel under variable surface roughness

AbstractThis paper investigates the effects of a wide range of loading frequencies ranging from 0.005 to 5 Hz and blasting induced surface roughness ranging from 20 to 100 μm on the ultra‐low cycle fatigue (ULCF) life of structural steel. The combined effect of these parameters on ULCF life has not been investigated so far. To this aim, comprehensive ULCF tests were performed on steel specimens under a constant displacement‐controlled environment until the failure occurred. The experimental results manifest that the surface roughness and loading frequency are the governing parameters affecting the ULCF life. The test material exhibits cyclic softening behavior under all loading conditions. An increase in loading frequency from 0.005 to 5 Hz causes a significant increase of 33% and 27% in ULCF life for 20 and 100 μm rough specimens, respectively. However, the effect of frequency on ULCF life becomes less significant at higher values of surface roughness. Moreover, an increase in surface roughness from 20 to 100 μm causes a significant reduction of about 45% and 47% in ULCF life at the loading frequencies of 0.005 and 5Hz, respectively. Furthermore, a correlation between fatigue life and loading frequency as a function of surface roughness is derived by the power law relationship.

Loading rate influence on high-cyclic loading of clays

Experimental observations reported in the literature, based on cyclic triaxial and cyclic simple shear tests, show that the loading frequency influences the excess pore pressure and strain accumulation for fine-grained soils under undrained conditions. A high-cycle accumulation (HCA) model for clay was introduced by Wichtmann (2016) and Staubach et al. (2022) to quantify the strain/pore pressure accumulation as a function of the number of applied cycles, amplitude, void ratio, stress ratio, OCR and loading frequency. This article explores the convenience of including the loading frequency factor in the HCA clay model based on the interpretation of a series of cyclic undrained triaxial tests performed on three different clay materials, namely Dorfner kaolin, Lower Rhine clay and Onsøy clay. Analysis of results shows that for those specific three clay materials, the normalization of the pore pressure accumulation rate u̇acc with the amplitude function fampl purifies the data from the influence of loading frequency and thus no explicit frequency function ff is required.

Research on the influence of loading frequency, material elasticity, and geometric parameters on mechanical characteristics of the new mesh-type high damping rail pad for fastening system

The dynamic stiffness (DS) curve of the rail pad (RP) is related to its damping performance. In a vibration period under the action of a sinusoidal load, the energy consumed by the damping force of the RP is equal to the energy generated by the applied load. The theoretical derivation found that the DS curve area of the RP is proportional to its damping ratio (DR) and loading frequency, and the accuracy of the theoretical derivation is verified by establishing a finite element model of the fastening system. The finite element calculation (FEC) found that the larger the loading frequency, the larger the DS curve area of the RP. The larger Young’s modulus of the RPs, the smaller the area of its DS curve. The prismatic rail pad (PRP) and mesh-type high damping rail pad (MTHDRP) are respectively assembled in the fastening system, and the static/dynamic stiffness (S/DS) curves of the two RPs are compared through the FEC, it is concluded that the MTHDRP has lower S/DS, and its linearity of the SS curve is better, indicating that the MTHDRP has better stability and stiffness retention. Meanwhile, the area of the DS curve of the MTHDRP is significantly larger than that of the GRP, indicating that it has better damping performance. The S/DS tests of the two RPs verified the accuracy of the FEC. Finally, taking the elasticity of the damping block (DB), the height of the DB, and the meshes numbers as the research variables, the law of their influence on the S/DS and DR of the MTHDRP is studied. It is concluded that by increasing the elasticity of the DB, the S/DS of the MTHDRP will increase, and the DR will decrease. The S/DS and DR of the MTHDRP will increase with the increase of the height of the DB. As the meshes numbers increase, both the S/DS and DR of the MTHDRP will decrease.

Influence of load frequency and corrosive environments on fatigue behavior of as-extruded Mg–Zn–Zr–Nd alloy

Fatigue resistance is a key criterion for new material that would be applied as an implant. As a “smart” implant material with good biodegradability and high strength, Mg–2Zn–0.5Zr–0.5Nd alloy has been recognized as a promising candidate for bone implant. A series of tests on fatigue properties of extruded Mg–2Zn–0.5Zr–0.5Nd alloy are carried out in this study. Alternating cyclic dynamic loads at frequencies of 5 Hz and 10 Hz both in air and in 0.9 wt% NaCl solution were loaded on extruded Mg–2Zn–0.5Zr–0.5Nd alloy respectively. In air condition, the fatigue life variational trends of Mg–2Zn–0.5Zr–0.5Nd alloy at different frequencies are similar according to the stress-life (S–N) curves. However, under high fatigue cycles, the lower loading frequency prolongs the loading time of repetitive stresses and reduces the fatigue life of the samples. In 0.9 wt% NaCl solution, the S–N curves under different frequencies show different changing trends due to the synergistic effect of corrosion environment and loading frequency. It is also found that the fatigue resistance of the alloy in 0.9 wt% NaCl solution is poorer than that in air due to the significant promotion of the formation and growth of corrosion pits by the NaCl environment. In addition, according to the fatigue fracture morphology analysis, it can be found that the failed samples show different fracture patterns in air and 0.9 wt% NaCl solution.

Effect of dynamic cyclic shear on frictional strength weakening of a plane joint

Understanding and predicting the frictional behavior of rock joints subject to dynamic cyclic loading is essential for the seismic safety of many rock engineering problems. In this paper, cyclic shear experiments were conducted based on a shaking table apparatus. A series of cyclic friction tests covering various earthquake-relevant frequencies was conducted on dry planar joints of granitic rock. The friction behavior especially the dynamic evolution of the frictional strength under cyclic loading was investigated, with the influence of loading frequency on the frictional strength weakening and energy dissipation quantified. Based on the experimental results, we propose a phenomenological model characterizing the dynamic frictional behavior of planar granite joints under cyclic loading. This empirical formulation relates the evolution of joint frictional strength to the number of cycles of dynamic loading. As the frequency increases, the frictional strength and dissipated energy density both show a pronounced reduction, while the strength weakening ratio and the critical number of cycles (at which the residual strength is reached) increase in a logarithmic fashion. The frictional strength evolution is described by the product of the peak frictional strength and a damage function, which is further related to the number of cycles and the frequency. In addition, a close inspection of fracture surface morphology after the cyclic loading was conducted to understand the role of surface wear and gouge formation in the frequency-enhanced dynamic friction weakening of rock joints.

Discrete Element Simulation of the Macro-Meso Mechanical Behaviors of Gas-Hydrate-Bearing Sediments under Dynamic Loading

Under the action of dynamic loadings such as earthquakes and volcanic activities, the mechanical properties of gas-hydrate-bearing sediments will deteriorate, leading to a decrease in the stability of hydrate reservoirs and even inducing geological disasters such as submarine landslides. In order to study the effect of dynamic loading on the mechanical properties of hydrate sediments, triaxial compression tests of numerical specimens were carried out by using particle flow code (PFC2D), and the macro-meso mechanical behaviors of specimens were investigated. The results show that the loading frequency has a small effect on the stiffness of the hydrate sediment, while it has a large effect on the peak strength. The peak strength increases and then decreases with the increase in loading frequency. Under the same loading frequency, the peak strength of the hydrate sediment increases with the increase in loading amplitude, and the stiffness of the specimen decreases with the increase in loading amplitude. The maximum shear expansion of the specimen changes with the movement of the phase change point and the rearrangement of the particles. The maximum shear expansion of the specimen changes with the movement of the phase change point and the change of the bearing capacity of the particles after the rearrangement, and the more forward the phase change point is, the stronger the bearing capacity of the specimen in the plastic stage. The shear dilatancy angle and the shear dilatancy amount both increase linearly with the increase in loading amplitude. The influence of loading frequency and amplitude on the contact force chain, displacement, crack expansion, and the number of cementation damage inside the sediment is mainly related to the average axial stress to which the specimen is subjected, and the number of cracks and cementation damage of the sediment specimen increases with the increase in the average axial stress to which the sediment specimen is subjected. As the rate of cementation damage increases, the distribution of shear zones becomes more obvious.

Research on the Influence of Loading Frequency on the Dynamic Response of Concrete Sleepers

The load generated during train operation is transmitted to sleepers through rails, and then from sleepers to trackbeds. As one of the important components of the track structure, sleepers are very important to the service-life and safety of railways. The running speed of the train will produce different load frequencies on the rails. To explore the response of sleepers under cyclical train loads, this research used the discrete element method to simulate rails and sleepers, and realizes the loading of sleepers by applying cyclic loads to the rails. The discrete element method was used to simulate the compression-failure test of the concrete sample to verify the reliability of parameters of the discrete element model. On this basis, the sleeper was simulated by the discrete element, and the change law of the mechanical parameters such as particle displacement, contact force, and stress of the sleeper under different loading frequencies were analyzed. The research results show that the sleeper particles under the rail had a large vertical displacement, and the maximum displacement and the maximum contact force of the particles in the sleeper increased with increasing loading frequency. The stress change trend of the sleeper under the left and right rails was the same, and both showed periodic changes with cyclic loading. The loading frequency had little effect on the stress of the sleeper. The vertical displacement, velocity, and acceleration amplitude of the rail all increased with increasing cyclic loading frequency, thereby increasing the force between the rail and the sleeper, and increasing the dynamic response of the sleeper.

Influence and Modeling of Loading Frequency on Dynamic Mechanical Properties of Thermally-Aging HTPB Coating

For the sake of studying the influence of loading frequency on the hydroxyl-terminated polybutadiene (HTPB) coating’s dynamic mechanical properties during aging, the one month’s thermal accelerated aging test was carried out at 70°C. The dynamic mechanical properties of the aged HTPB coatings were tested through dynamic mechanical analysis (DMA) Q800 with the loading frequency range of 0~100Hz, the dynamic strain amplitude of 0.1% and the test temperature of 25°C. The change models of the dynamic modulus with the loading frequency were established. The results showed that with the extension of the aging time, the storage modulus and the loss modulus both rose, which were related with the change of the crosslinking network structure. The storage modulus increased exponentially with the loading frequency, and the correlation coefficients fitted by the exponential models were all greater than 0.96. The loss modulus changed in sections. When the loading frequency was less than 70 Hz, the loss modulus showed a cubic function growth relationship with the loading frequency, and the correlation coefficients were larger than 0.98; when the loading frequency was between 70 Hz and 100 Hz, the loss modulus showed a quadratic function relationship with the loading frequency that first decreased and then increased, and the correlation coefficients were all larger than 0.97.

Influence of Loading Frequency on Fatigue Resistance of D16T Alloy

Influence of Loading Frequency on Fatigue Resistance of D16T Alloy

Research on the Influence of Loading Frequency, Material Elasticity, and Geometric Parameters on Mechanical Characteristics of the Mthdrp for Rail Transit Fastening System

Research on the Influence of Loading Frequency, Material Elasticity, and Geometric Parameters on Mechanical Characteristics of the Mthdrp for Rail Transit Fastening System

Influence of Load Frequency and Corrosive Environments on Fatigue Behavior of As-Extruded Mg-Zn-Zr-Nd Alloy

Influence of Load Frequency and Corrosive Environments on Fatigue Behavior of As-Extruded Mg-Zn-Zr-Nd Alloy

Influence of loading frequency on mechanical properties of unbound granular materials via repeated load tests

Unbound granular material (UGM) is widely used in flexible pavement to carry vehicular dynamic loading with different loading frequencies. In this study, the influence of loading frequency on the mechanical properties of UGM was investigated via repeated load tests using the precision unbound material analyzer (PUMA). The confining stress, plastic strain, plastic strain rate, resilient strain, resilient modulus, and Poisson’s ratio of two granular materials were analyzed at four loading frequencies and two stress levels. The results showed that confining stress, plastic strain, plastic strain rate and Poisson’s ratio decreased as the increase of loading frequency. Resilient strain and resilient modulus did not show obvious trend with loading frequency. Compared with 1 Hz, confining stress of 19 mm gravel at 240 kPa decreased 28.1% at 5 Hz and 33.7% at 8 Hz. The maximum difference of confining stress at 5 Hz, 8 Hz and 10 Hz was only 0.78 kPa. Other indicators showed similar tendency at different loading frequencies. The results reveal that loading frequency has significant influence on mechanical properties of UGM, while the influence becomes small when the frequency exceeds certain value. Moreover, the loading stress and gradation of material had interaction effect with loading frequency. The coefficients of variation of measurement indicators decreased as the increased loading frequency, which suggested that appropriate frequency can help reduce the error of the testing results.

Dynamic behavior of natural sand soils and fiber reinforced soils in heavy-haul railway embankment under multistage cyclic loading

In this study, dynamic triaxial tests of natural sand soils and fiber reinforced soils were conducted. The influence of loading frequency, water content, and compaction degree on the dynamic shear modulus and damping ratio of natural soils were identified. Different fiber length, confining pressure, and fiber content were studied to gain the dynamic characteristics of fiber reinforced soils. The results show that the water content and compaction degree has a significant effect on the dynamic behavior of natural soils, and confining pressure and fiber content has a visible reinforcement effect on the dynamic characteristic of fiber reinforced soils. The empirical formulas of maximum dynamic shear modulus (Gd max), ultimate shear stress (τdult), and damping ratio (λ) were generate, which can provide references for fiber reinforced soil design.

Quantitative thermoelastic stress analysis by means of low-cost setups

A low-cost Thermoelastic Stress Analysis (TSA) experimental setup is proposed which uses an ordinary micro-bolometer and in-house developed signal processing scripts. The setup is evaluated by analysing the thermoelastic signal from a tensile and a SENT specimen made of stainless steel AISI 304L, and the bolometer performances are compared with those of a state of the art photon detector. Signal processing is based on off-line cross-correlation, using a self-reference signal which is retrieved from the acquired thermal data. Procedures are in particular developed to recognise, quantify and correct errors due to spectral leakage and loss of streamed frames. The thermoelastic signal amplitude/phase, the thermoelastic constant and the Mode I Stress Intensity Factor (SIF) from the bolometer and photonic cameras are evaluated considering the influence of loading frequency, sampling frequency, detector array sub-windowing and acquisition interval duration. A camera-specific linear calibration procedure is applied to correct the thermoelastic signal obtained with the bolometer. The procedure is extended to correct also SIF values, finding a good match with the SIFs obtained by the photon detector. An automatic iterative algorithm, based on the least square fitting of Williams’ series functions, is proposed to identify the crack tip position. An estimation of processing times of the developed signal processing scripts has been carried out, finding that a full crack characterisation (TSA maps, crack tip position, SIF) can be performed with a data acquisition time of 10-20 s, a post-processing time of less than 2 s and an overall hardware cost under 10 k€.

Comparison of Glass-Transition Temperatures for Epoxy Polymers Obtained by Methods of Thermal Analysis

In this review, the characteristic temperatures for epoxy polymers and epoxy matrices of fiber-reinforced composites in the glass-transition ( α-transition) range determined using different methods of thermal analysis (DSC, DMA, and TMA) are compared. The influence of loading frequency in the DMA method and of uniformity of heating and postcuring of specimens in all the methods is revealed. The agreement between the glass-transition temperatures given by different methods is achieved using the same characteristic points in experimental curves and the same time parameters (the frequency of external actions, heating rate, and the uniformity of temperature distribution in specimens in testing chambers).