Amplitude Loading Research Articles

The influences of normal load and displacement amplitude on fretting wear behavior of M50 bearing steel

This study aims to obtain key parameters such as the fretting wear coefficient and wear rate of M50 bearing steel through fretting wear experiments. By integrating the Umeshmotion subroutine, a validated 3D ball-plane energy dissipation fretting wear model was established. The research explores wear behavior and transition mechanisms under different normal loads and displacement amplitudes. Experimental and finite element analyses show that fretting wear rate is negatively correlated with normal load and positively correlated with displacement amplitude. These variables influence contact stress, shear stress, and slip distance, affecting wear morphology. Results indicate that increasing normal load transitions fretting wear from gross slip to partial slip, while increasing displacement amplitude shifts it from partial slip to gross slip.

Numerical analysis of plastic deformation mechanisms in polycrystalline copper under cyclic loading with different frequencies

The frequency of cyclic loading has a strong effect on the fatigue lifetime of materials. High loading frequencies allow reaching very high cycle fatigue regimes. The effects of cyclic loading with different frequencies are studied using the finite element method within the framework of crystal plasticity. The numerical study represents copper polycrystal that undergoes tension–compression loading with frequencies 80 Hz and 20 kHz respectively. The spatial distributions of stresses, strains, and plastic slip are used for estimation of volume fraction, morphology, and plasticity mechanism of persistent slip bands. The results show that at 80 Hz cyclic loading, plasticity in persistent slip band cells is dominated by the creation and annihilation of dislocations while at 20 kHz cyclic loading, plasticity is driven by the back-and-forth movement of dislocations inside the persistent slip band cells. The numerical study shows a correlation between amplitude and frequency of loading with spatial distribution and morphology of persistent slip bands that can be related to the fatigue lifetime.

Time‐Frequency Analysis of Experimental and Analytical Rotor Thrust during a Rotor Speed Change

A study was conducted examining a small-scale, two‐bladed rotor undergoing a change in rotor speed. The data acquired consists of time histories of nonstationary signals; therefore, a Stockwell transform was employed to analyze the data in lieu of traditional Fourier transform-based methods. The analysis included extraction of time‐varying frequency content of the rotor thrust and hub motion, instantaneous rotor speed, damping ratios, and instantaneous phase difference between thrust and hub motion. This work is divided into two parts. First, an analytical study was conducted to understand how rotor transient response, determined using a time‐marching solution, is affected by the inclusion of a simplified elastic support structure model, and is used to demonstrate the utility of the Stockwell transform. The second part of the study compared the results from an analytical model of the NASA Multirotor Test Bed (MTB) undergoing a rotor speed change to wind tunnel data. The current analytical model of the MTB, including an elastic support structure, properly predicted the measured trends in the frequency content of the thrust; however, it underpredicted the amplitude of these unsteady loads.

Efficient reliability-based concurrent topology optimization method under PID-driven sequential decoupling framework

The continuous improvement of advanced equipment performance has promoted the development of detailed structural design. The detailed design of the structure should meet many requirements such as high reliability, strong robustness, lightweight, and high efficiency. This paper proposes a proportional-integral-derivative-driven efficient reliability-based concurrent topology optimization strategy under the sequential framework. Considering the uncertainty of load position, load direction, load amplitude, and material properties, an efficient reliability-based concurrent topology optimization model is constructed based on the sequential strategy. Based on effectively quantifying the nonlinear characteristics brought by multi-source uncertainty, a constraint refinement movement strategy based on the proportional-integral-derivative controller is proposed, which to some extent overcomes the tedious calculation of uncertainty quantification. This paper provides sensitivity information on macroscopic and microscopic level set functions under displacement constraints. Four numerical examples demonstrate the effectiveness, efficiency, and generalization ability of the proposed method.

3D DEM simulations of cyclic loading-induced densification and critical state convergence in granular soils

Granular soils exhibit very complex responses when subjected to cyclic loading. Understanding the cyclic behavior of such materials is not only crucial for engineering applications but also the bottleneck of most of constitutive models. This study employs 3D Discrete Element Method (DEM) simulations to explore the accumulative plastic deformation and the internal fabric evolution within granular soils during cyclic loading. Two novel observations are identified: (1) A distinct and unique linear relationship between post-cyclic loading void ratio e and log (p*/p0) is found independent of the amplitude of cyclic load and the initial stress state prior to cyclic loading, where p* is the mean pressure incorporating cyclic loading stress and p0 is the mean pressure prior to cyclic loading; (2) When resuming drained triaxial loadings after cyclic loadings, we observe that both microstructural and macroscopic variables converge to the same values they would have reached for pure monotonic drained triaxial loadings. This intriguing behavior underscores and extends to more general loading paths the influential and attractive power of the critical state.

Investigation of soil damping for offshore wind turbine monopile-soil system in stiff clay on elastoplastic-damage model

Damping plays a crucial role in the design of offshore wind turbine (OWT) monopile foundations. The soil damping of the monopile-soil system (MSS) represents the energy dissipation mechanism arising from the interaction between the pile and the soil. It is typically derived by back-calculating from the overall damping measured in the entire OWT structure. However, few studies have independently examined the soil damping in MSS, and the impact of key parameters such as pile diameter, pile embedded depth, cyclic load amplitude, and load eccentricity on the variation of soil damping in MSS remains unclear. This paper introduces an elastoplastic-damage constitutive model for the numerical simulation of the damping ratio variation in seabed soil and MSS. The model is implemented in ABAQUS software and validated against cyclic triaxial tests on stiff clay soil. On this basis, a three-dimensional finite element sensitivity study was conducted to elucidate the effect of these key parameters on the MSS damping ratio. The results of the study reveal that the MSS damping ratio exhibits a nonlinear and asymmetric trend as the loading cycles increase. The MSS damping ratio decreases with increasing pile diameter and embedded depth but increases with increasing lateral cyclic load amplitude and load eccentricity from the mudline.

Dynamic biaxial loading of vascular smooth muscle cell seeded tissue equivalents

An intricate reciprocal relationship exists between adherent synthetic cells and their extracellular matrix (ECM). These cells deposit, organize, and degrade the ECM, which in turn influences cell phenotype via responses that include sensitivity to changes in the mechanical state that arises from changes in external loading. Collagen-based tissue equivalents are commonly used as simple but revealing model systems to study cell–matrix interactions. Nevertheless, few quantitative studies report changes in the forces that the cells establish and maintain in such gels under dynamic loading. Moreover, most prior studies have been limited to uniaxial experiments despite many soft tissues, including arteries, experiencing multiaxial loading in vivo. To begin to close this gap, we use a custom biaxial bioreactor to subject collagen gels seeded with primary aortic smooth muscle cells to different biaxial loading conditions. These conditions include cyclic loading with different amplitudes as well as different mechanical constraints at the boundaries of a cruciform sample. Irrespective of loading amplitude and boundary condition, similar mean steady-state biaxial forces emerged across all tests. Additionally, stiffness-force relationships assessed via intermittent equibiaxial force–extension tests showed remarkable similarity for ranges of forces to which the cells adapted during periods of cyclic loading. Taken together, these findings are consistent with a load-mediated homeostatic response by vascular smooth muscle cells.

Experimental behavior, numerical modeling and parameters evaluation of three-dimensional seismic isolation device

In order to improve the seismic performance of lightweight flexible structures, a new type of air spring‐lead rubber bearing (AS-LRB) three-dimensional seismic isolation device with both horizontal and vertical seismic isolation was proposed. The construction of the AS-LRB was introduced, the horizontal and vertical mechanical properties of the AS-LRB were experimentally studied, the finite element (FE) model was developed based on the material properties of the AS-LRB, and the calculation method of the horizontal and vertical mechanical property parameters of the AS-LRB was proposed. The research results show that the air spring (AS) in the AS-LRB bears the vertical seismic isolation, and the lead rubber bearing (LRB) bears the horizontal seismic isolation. The energy dissipation capacity of horizontal seismic isolation is obvious, and its horizontal mechanical properties are significantly affected by the loading amplitude and vertical force. The load displacement behavior of vertical seismic isolation exhibits nonlinear characteristics, and its vertical mechanical properties are obviously affected by vertical force. In comparison with the test results, the FE model proposed can accurately simulate the AS-LRB, and the calculation method can accurately calculate the horizontal and vertical mechanical property parameters of the AS-LRB.

Nonlinear spring model for dynamic uplift behaviour of suction caisson under impact loading

Suction caissons are widely employed as support structures for various fixed or floating structures. The impact loading in extreme environment is a key condition for marine foundation design. In this paper, a nonlinear spring model is proposed to predict the dynamic behaviour of suction caisson under impact loading, and its reliability is verified by experimental tests and finite element simulations. A mass module is introduced to describe the foundation inertia action, and a novel component consisting of a reverse end bearing spring and a soil plug slider is developed to decouple the overall vertical stiffness of suction caisson. The friction module is updated with t-z springs positioned along the depth to reflect the stress distribution in the soil layer. Afterwards, the influence of impact loading amplitude and loading history are studied. For the impact loadings with different amplitude (Fu), the maximum vertical displacement of caisson is only 0.02D when the uplift loading reaches 0.4Fu, indicating a marked contribution of inertia force. It is recommended to properly consider foundation inertia action under high magnitude impact loading, which can effectively optimize the structure design. In light of this, a design chart for suction caisson applied in engineering practices is presented.

Experimental and DEM analysis for the shear characteristics of interface between sand and irregular concrete under dynamic normal loading

To explore the dynamic shear property of sand–irregular concrete interface, a series of direct shear tests were conducted under dynamic normal loading. These tests were designed with various joint roughness coefficients (JRC), amplitudes and frequencies of dynamic normal loading. DEM models were established to analyze the microscopic mechanical behavior. The research results indicate that a larger amplitude and frequency of the dynamic normal loading would lead to a decrease in the interface shear stress and dilation. As the JRC increased, the interface shear strength first increased and then decreased, and the dilation increased. A rougher surface would reduce the phase shift between peak shear and normal stress. The phase shift between normal stress and friction coefficient was always half a normal loading cycle. A greater JRC would activate a more violent particle motion and a thicker shear band. The increase in effective roughness would lead to an increase in the deviation angle of the anisotropic direction. The evolution of force chains was observed in three-dimensional space. Weak force chains were screened out during the shearing process. As the shearing developed, the number of force chains decreased, the average length and strength of force chains continued to increase.

Experimental and numerical study on the effect of load direction on the bolt loosening failure

The loosening is one of the main failure modes of bolted joints. Currently, researchers only focused on bolt loosening behavior under simple axial or transverse loads. Understanding the loosening failure mechanism of bolted joints under complex load is important for improving reliability. A multi-directional loading test device was designed, and bolt loosening experiments were conducted. The effect of load direction and amplitude on bolt loosening behavior were investigated. The results indicate that bolt loosening can be divided into two stages. Load direction and load amplitude are critical factors determining the loosening trend in the later stage. In addition, a refined finite element model of bolted joints was established to verify and explain the experimental results. The FEA results show that the relative sliding between internal and external threads and the stress redistribution on the threads are the main reasons for the bolt loosening. The smaller the angle between the load direction and the tangential direction of the contact surface, the relative sliding more likely to occur.

Experimental study on the dynamic behavior of a new medium–low-speed maglev subgrade structure

Constructing medium–low-speed magnetic levitation (MLS maglev) subgrade by borrowing the construction standards of high-speed railway (HSR) subgrade can result in enormous engineering waste because the amplitude, distribution width, and dynamic coefficient of the dynamic load of MLS maglev trains are much smaller than those of HSR trains. To address this problem, an innovative subgrade structure was proposed to match the dynamic loads of MLS maglev trains. Two experimental models are constructed to study the proposed MLS maglev subgrade at train speeds of 100 km/h, 120 km/h, 160 km/h, and 200 km/h. The two models are labeled as Models I and II, and the only difference between these two models is the type of surface layer material of the subgrade bed, whereas the other structural features are the same. Specifically, the Model Ⅰ employs graded gravel, whereas the Model Ⅱ uses A group filling. The experimental results indicate that for both models, the dynamic earth pressure amplitudes are all less than 20 % of the subgrade’s self-weight at the bottom surface of the subgrade bed. In addition, the cumulative settlement of the two models is below the cumulative settlement limit. Although both models with the proposed MLS maglev subgrade exhibit excellent long-term performance, the Model Ⅰ has superior attenuation characteristics of dynamic earth pressure, and smaller acceleration and dynamic deformation than that the Model Ⅰ. This is attributed to the graded gravel used in the Model Ⅰ, which possesses a greater dynamic modulus and damping ratio than the A group filling used in the Model Ⅱ. The results presented in this study could contribute to the comprehension of the dynamic behavior of the subgrade under the dynamic loads of MLS maglev trains. More importantly, compared to the existing MLS maglev subgrades, the proposed MLS maglev subgrade has lower construction standards and is thus suitable for practical engineering applications.

Modeling the nonlinear dynamic behavior of filled elastomers: Application to the vibration of structures with large preloads

This study offers a global mechanical approach from filled rubber characterization and modeling to how this behavior affects vibratory structural simulations. This work focuses on the characterization and the modeling of the dynamic behavior of a filled rubber. Particularly the effects of frequency, static preload and amplitude of cyclic loading (i-e Payne effect) are studied. A new hyper-viscoelastic constitutive model is proposed and its linearization for a specific loading case in order to obtain a straight-forward stress–strain relationship in the frequency domain. After validation of the implementation, this model is used in vibratory cantilever beam simulations of CFRP (Carbon Fiber Reinforced Polymer) laminates containing constrained rubber layers. Damping capability is then linked to the non-linear behavior of the rubber material.

Strength-induced Peridynamic model for the dynamic failure of porous materials

Predicting the dynamic failure process of porous materials is a challenging task due to their complex structure. To minimize the use of time-consuming peridynamic (PD) models and to avoid surface effect issues in the dynamic failure of complex porous materials, this paper proposes a strength-induced PD model. The paper first presents the dynamic formula and relevant finite element discrete equation of the coupled PD and classical continuum mechanics (PD-CCM) model based on the Morphing method. The Morphing function is implemented to control the material parameters and enable the free transformation of PD and CCM models. Based on the coupled PD-CCM model, the strength-induced PD model is established to adaptively expand the PD subdomain in porous materials by controlling the Morphing function value through the strength state of the structure. This model enables the PD subdomain to appear automatically when the porous materials reach the critical stress state. The proposed model accurately predicts the location of crack initiation and path while minimizing computational costs and improving efficiency. Three two-dimensional numerical examples are used to verify the effectiveness, efficiency, and accuracy of the model. The results of the simulation suggest that the location where the crack initiates in the porous materials is strongly influenced by the amplitude of the dynamic load. Cracking is dependent on the pores and typically occurs through them.

Fatigue Analysis of Composite Bolted Joints under Random and Constant Amplitude Fatigue Loadings.

This paper attempts to analyze the random fatigue life and failure modes of joints using two calculation methods. Three kinds of tests were carried out, which were the static test, constant amplitude fatigue test and the random fatigue test, and four kinds of joints were designed. After the static test, the joint was subjected to a constant amplitude fatigue test by selecting different percentages of load according to the static strength. In order to predict the random fatigue life more precisely, two calculation methods were carried out, which were the linear cumulative damage method and the equivalent loading finite element method. Based on the linear cumulative damage hypothesis, the fatigue life of the joint was established as a function of the load amplitude, and then, the random life prediction was calculated by the amplitude distribution of the random loading. Another method was the equivalent loading method, which was to obtain the equivalent constant amplitude fatigue loading of the random loading spectrum. The finite element model was established based on the stiffness and strength degradation rule. The equivalent random life and fatigue failure modes of the joint were modeled. The two life prediction methods show good agreement with the fatigue experimental result, and all prediction results were included in a scatter band of the factor of 2.

Micromechanical analysis of contact erosion under cyclic loads using the coupled CFD‒DEM method

Different layers of soil often have distinct particle sizes. When exposed to the natural environment, soil is easily affected by natural rainfall, rising groundwater levels, and human activities, leading to particle contact erosion, which reduces the safety and service performance of the soil structure. In this paper, a coupled computational fluid dynamics–discrete element method (CFD–DEM) model was employed to investigate the particle migration phenomena, mechanical response of contact interfaces, variations in flow fields, and macroscopic deformation during the contact erosion process under cyclic loads at different frequencies and amplitudes. The conclusions are presented as follows: (1) Within one cycle of cyclic loading, both compression during loading and stress relaxation during unloading are the main factors triggering the migration of fine particles. (2) The migration and loss of fine particles mainly occur in the early stages of cyclic loading, where strong contact force chains are formed within the fine particle layer, leading to significant plastic deformation of the soil at the macroscopic level. (3) Under cyclic loading, changes in the soil pore structure cause an upwards hydraulic gradient in the initial quiescent water flow field. This hydraulic gradient can rupture weak contact force chains and cause particle pumping. (4) Increasing the frequency and amplitude of cyclic loading intensifies the erosion of fine particles, causing greater axial deformation of the soil. Compared to cyclic loading frequency, the amplitude of cyclic loading has a greater impact on contact erosion.

Mechanical Behavior of Geogrid Flexible Reinforced Soil Wall Subjected to Dynamic Load

The geogrid flexible reinforced soil wall is widely used in engineering practice. However, a more comprehensive understanding of the dynamic behavior of reinforced soil wall is still required for a more reasonable application. In order to explore the mechanical behavior of a geogrid flexible reinforced soil wall, the model test was carried out to investigate the dynamic deformation of geogrid reinforced soil wall subjected to a repeated load. The numerical simulation was also conducted for comparison and extension with regards to the earth pressure and the reinforcement strain. The change rules for the deformation of the wall face, the vertical earth pressure and the reinforcement strain subjected to dynamic load with four frequencies (4, 6, 8 and 10 Hz) and four amplitudes (30–60, 40–80, 50–100 and 60–120 kPa) were obtained. The factors that affect the mechanical behavior of geogrid flexible reinforced soil wall were analyzed. The results show that the dynamic deformation characteristics of reinforced soil wall are affected by the number of vibrations, the amplitude of dynamic load and the frequency of vibration. The maximum lateral displacement of the reinforced soil wall occurs on the third to the fifth layer. With an increase in dynamic load amplitude, the development of dynamic deformation gradually increases, and after a cumulative vibration of 200 × 104 times, the cumulative lateral deformation ratio and the cumulative vertical deformation ratio of the wall face is less than 1%. The vertical earth pressure of geogrid flexible reinforced soil wall increases partially along the length of the reinforcement, and the vertical earth pressure of the third layer is basically unchanged when subjected to a dynamic load. With an increase in vibration number, the change in the reinforcement strain of the third layer is more complex, and the change rules of the reinforcement strain of each layer are different. The reinforcement strain is small, with a maximum value of 0.1%.

Challenges in Rotor Aerodynamic Modeling for Non-Uniform Inflow Conditions

Within an international collaboration framework, the accuracy of rotor aerodynamic models used for design load calculations of wind turbines is being assessed. Where the use of high-fidelity computation fluid dynamics (CFD) and mid-fidelity free-vortex wake (FVW) models has become commonplace within the wind energy community, these still fail to meet the requirements in terms of execution time and computational cost needed for design load calculations. The fast but engineering fidelity blade-element/momentum (BEM) method can therefore still be considered the industry workhorse for design load simulations.At the same time, upscaling of wind turbine rotors makes inflow non-uniformities (e.g. shear, veer, turbulence) more important. The objective of this work is to assess model accuracy in non-uniform inflow conditions, which violate several BEM assumptions. Thereto a comparison in turbulent inflow has been executed including a wide variety of codes, focusing on the DanAero field measurements, where a 2.3-MW turbine was equipped with, among other sensors, a pressure measurement apparatus. The results indicate that, although average load patterns are in good agreement, this does not hold for the unsteady loads that drive fatigue damage and aero-elastic stability. A simplified comparison round in vertical shear was initiated to investigate the observed differences in a more controlled manner. A consistent offset in load amplitude was observed between CFD and free-vortex codes on the one hand and BEM-type codes on the other hand. To shed more light on the observations, dedicated efforts are ongoing to pinpoint the cause for these differences, in the end leading to guidelines for an improved BEM implementation.

Analysis of the effect of vibrational stress relief process parameters on 2024Aluminium alloy

In principle, after all manufacturing processes are performed, a set of residual stresses occur in the product that have their particular distribution given the manufacturing process performed. The residual stresses must be removed to achieve the desired dimensional accuracy and quality. Among stress-relieving processes performed for a piece following the manufacturing process, we can refer to thermal and vibratory stress relief (VSR). Both methods perform the same function as they enter a part or all of a piece into the plastic phase, causing a fracture of residual stresses to be released with local plastic deformations. The process is as follows: The stress induced by thermal or vibratory loads is added to the residual stresses and exceeds the yield stress. This research, which is focused on VSR, aims to evaluate the effect of the main parameters of the VSR method, including load amplitude or amount, load application frequency, and cycle numbers. The general trend of the problem is that the VSR process is performed for a piece with residual stress, and the effect of the abovementioned parameters on reducing its residual stresses is evaluated.

Dynamic response characteristics and water-gas-heat synergistic transport mechanism of proton exchange membrane fuel cell during transient loading

During the current transient loading process, the proton exchange membrane fuel cell (PEMFC) is prone to voltage undershoot phenomenon, which result in internal complex chemical reactions, water vapor changes, and even reaction gas starvation. In this paper, the dynamic response characteristics of hydrogen-oxygen PEMFC and the mechanism of water-gas-heat synergistic transport during current transient loading are investigated by combining experimental and simulation methods. The experimental results show that an increase in the current loading amplitude exacerbates gas starvation and membrane dehydration leading to the deterioration of the dynamic response characteristics of PEMFC during transient current loading. To compensate for the lack of experimental methods to study the PEMFC water-gas-heat synergistic transport mechanism, this paper establishes a three-dimensional PEMFC transient model. The minimum values of reactant gas concentration in the anode and cathode catalyst layers are 0.0205 kmol/m3 and 0.0220 kmol/m3 at 65 °C, 0 backpressure and variable load conditions between 800 mA/cm2 and 1400 mA/cm2, respectively, which leads to more gas starvation at the anode. While comparing the energy wastage during current loading, it can be found that smaller current loading amplitude, higher stoichiometric ratio, and higher temperature and backpressure all contribute to the reduction of energy wastage.