Cyclic Loading Process Research Articles

Microstructural evolution of strain rate related tensile elastic prestrain on the high-cycle fatigue in medium-carbon steel

When engineered structures undergo regular cyclic loading processes, they would often be affected by extensional strain. To highlight the effect of tensile strain rate on subsequent fatigue damage in medium-carbon steel, predeformation was entirely controlled in the elastic regime with strain rates ranging from 10−5s−1 to 10−2s−1. Evolutionary response of sample temperature and peak cyclic strain, microstructures, internal fatigue initiation, fatigue propagation in samples fractured during tensile elastic prestrain (TEP)-HCF tests were studied. Our results revealed that compared with non-prestrained, the effect of TEP rate on fatigue life was non-monotonic and beneficial. Strain rate related TEP had fundamentally realized lattice structure reconstruction and transform in sliding mode, and overall slipping of lattice structure and free consumption of interface dislocations that resist fatigue crack propagation was key for the observed leap in fatigue strength.

Effect of crack angles on energy characteristics of sandstones under a complex stress path

In order to obtain influence laws of crack angles on energy characteristics of sandstones in complex stress environment, this study performed a cyclic loading and unloading test under stress gradients with a constant lower limit of stress on sandstone samples with cracks at different angles. By utilizing the integral method for area, total energy density, elastic energy density and dissipated energy density of the sandstone samples with cracks at different angles were derived. Moreover, this study explored the increase laws of the three energy densities with the number of cyclic loading and the upper limit of stress in each cyclic loading. The results demonstrate that during the whole cyclic loading process, the three energy densities increase with the increase of the number of cyclic loads, and the growth rate of elastic energy density is obviously larger than that of dissipated energy density. In addition, In the whole cyclic loading and unloading process, the energy densities of the sandstones with cracks at different angles show obvious growth relationships in the form of a quadratic function with upper limit of stress in single cyclic loading and unloading. The index that characterizes the storage energy capability and dissipated energy capability of the rock, namely the energy storage coefficient and the energy dissipation coefficient, is defined. By analyzing the relationships of energy storage coefficient and energy dissipation coefficient of rocks with crack angles in rocks, it is found that the larger the crack angle, the larger the energy storage coefficient of rocks while the smaller the energy dissipation coefficient. This explains the phenomenon that the larger the crack angle, the stronger the bearing capacity of rocks from the perspective of energy.

A numerical study of particle friction and initial state effects on the liquefaction of granular assemblies

Liquefaction of sandy soil due to cyclic loading can result in catastrophic damage to the built environment. Liquefaction has been previously studied through field testing, laboratory experiments, and numerical simulations. However, the particle-scale behavior of granular materials during the initiation of liquefaction has not been comprehensively quantified. In the current work, the discrete element method is employed to study the effect of global void ratio, initial confining stress, overconsolidation ratio, and particle friction on liquefaction resistance. Mechanical coordination number, local void ratio distribution (LVRD) entropy, fabric anisotropy and average rotational velocity are quantified in each assembly to provide insight into the particle-scale physics governing liquefaction resistance. Results show that lower global void ratio, increased confining stress, higher OCR values, and higher particle friction all increase liquefaction resistance. Immediately prior to the onset of liquefaction, the mechanical coordination number in each assembly sharply decreased to approximately 2.5, with the remaining contacts attributed primarily to particle collision after liquefaction initiation and fabric collapse. Anisotropy induced in the cyclic loading process was due to normal contact force anisotropy, which was more prominent in the specimens with higher initial confining pressures. Liquefaction resistance for overconsolidated specimens was found to be lower than that of normally consolidated specimens at the same void ratio. We observe liquefaction resistance to be sensitive to the coefficient of interparticle sliding friction, especially for lower friction coefficients. Average particle rotational velocities are shown to increase with increasing interparticle friction. The quantity of energy dissipated through frictional sliding was controlled by both the rate of dissipation and the number of loading cycles to liquefaction. In sum, the simulations elucidate significant connections between micromechanical properties and liquefaction response at different initial states and with different particle frictions.

Fatigue Analysis for Void Repair of Cement Concrete Pavement with Under Slab by Polymer Grouting

After the appearing of voids beneath cement concrete slabs, the pavement loses a continuous and uniform lower support structure, and the stress state of the road panel is extremely unfavorable. The polymer grouting repair is timesaving, efficient and pollution-free. In order to verify the performance improvement and fatigue damage evolution of cement concrete pavement before and after grouting repair, a material damage constitutive model was established. The UMAT subprogram was introduced into the finite element software ABAQUS to analyze the structure under the action of moving cyclic loading, stress response and fatigue damage evolution process before and after regional grouting repair. The results show that the Mises stress and vertical displacement of the grouting repairing slab are very close to the normal state, which indicates that the grouting repair has a prominent influence on the bottom void of the slab. With the rise of loading time, the fatigue damage of the pavement structure is increasing, but the trend is gradually reduced, and the number of load times and the degree of fatigue damage are nonlinear. From the long-term cyclic loading and comprehensive analysis of the construction period, the polymer grouting repair is better than cementitious grout.

Study on the gear fatigue behavior considering the effect of residual stress based on the continuum damage approach

The fatigue failures of gears have great influence on lifetime and reliabilities of mechanical transmissions. Initial residual stress (IRS) induced in the manufacturing process, together with the applied loading stress, contributes to gear fatigue behavior. Gear fatigue behavior represents a continuous damaging process during a high-cycle period. In the present work, a damage-coupled numerical model considering the effect of IRS is developed to investigate the gear fatigue performance. The deterioration of gear material, the detailed evolution of damage and the stress response during the cyclic loading process are calculated and recorded based on the continuum damage mechanics (CDM) using a user material subroutine (UMAT) in ABAQUS. Both the tooth surface contact fatigue and tooth root bending fatigue of the gear are evaluated, and the influence of IRS on stress response and damage evolution is analyzed. Results show that the risk of surface contact fatigue failure of this gear is much greater than that of the tooth bending fatigue. The initial compressive residual stress has positive effect on contact fatigue performance while the initial tensile residual stress with amplitude of 380 MPa would reduce the gear contact fatigue life by 20%.

Experimental investigation of pretensioned bolts under cyclic loading: Damage assessment using acoustic emission

Understanding the acoustic emission effects on bolts under cyclic loading is of great significance for the support of roadways. The presented research focuses on the acoustic emission characteristics of bolts under cyclic loading. The following main conclusions were drawn: (1) With a higher loading frequency, the acoustic emission counts rate increases, while the total energy released in a given cyclic loading path decreases. (2) A fitting formula is established according to the relationship between the tension amplitude and cumulative acoustic emission counts, which can analyze the tension magnitude level of the cyclic load. (3) A damage factor for a cyclic load is proposed based on the acoustic emission counts generated during the cyclic and monotonic loading process that can analyze the degree of damage to the anchorage system caused by the cyclic load. (4) Based on the spatial distribution of the acoustic emission orientation points and the acoustic emission energy generated during the pull-out process, the acoustic emission damage evolution process of the anchorage specimens is deduced, and the mechanism of the high stability of the pretension anchorage system after cyclic loading is analyzed. The above conclusions may provide some experimental references for the application of acoustic emission technology in bolts supporting roadways.

Experimental study on four-point cyclic bending behaviours of concrete with high density polyethylene granules

In recent years, plastic pollution has become more serious. The incorporation of waste plastic into concrete as part of the aggregate not only greatly reduces the environmental pressure, but also lowers the cost of concrete. In order to investigate the effect of plastic content on the mechanical properties of concrete, the MTS322 device was used to perform four-point bending monotonic and cyclic loading tests on concrete specimens with six contents of high density polyethylene (HDPE) granules. The test results show that with the increase of HDPE granule contents, both the tensile strength and the initial elastic modulus of concrete with HDPE granules declined gradually, while the peak strain increased. The plastic strain during the loading process was not affected by the HDPE granule content, but increased with the increase of unloading strain. According to the degradation of secant modulus during the cyclic loading process, the damage was defined, based on which the cyclic stress-strain model of concrete with HDPE granules was obtained. According to equations provided, the predicted model was in good agreement with the test results.

Volumetric Compression Behavior of Fine Grained Soil After Cyclic Loading Process

近年の多くの地震ではこれまで液状化しにくいとされてきた細粒分を多く含む土の液状化被害が多くみられる．本研究では非塑性シルトと低塑性粘土，高塑性粘土を用いて繰返しせん断が作用した時の各試料の軟化挙動と体積変化挙動を観察した．飽和試料を中空ねじり試験機を用いて繰返し載荷実験を行い，その時の応力ひずみ履歴と過剰間隙水圧，有効応力経路の挙動を把握した．さらに，繰返し載荷後に得られる排水量から体積圧縮量を算出した．一連の試験の結果，塑性指数Ipの違いにより軟化挙動と体積変化挙動に違いがみられることがわかった．

Effects of Constant Amplitude Cyclic Loading on the Nonuniform Deformation of Sandstone Specimens

In order to explore the mechanical response mechanism of rock materials under cyclic loading, uniaxial constant amplitude cyclic loading tests for sandstone specimens were carried out. The images of specimen deformation during the tests were captured by charge‐coupled device (CCD) cameras. Based on the digital image correlation method (DICM), the evolution laws of nonuniform deformation and displacements around localization bands during cyclic loading were investigated. The experimental results show that, during the cyclic loading process, the nonuniform deformation continually escalates with the number of cycles increasing and fluctuates with the cyclic loading stress condition; the nonuniform deformation lags behind the variation of loading stress; and the whole nonuniform deformation experiences a slow evolution stage and a fast evolution stage. At the loading stage or unloading stage, the nonuniform deformation of rock deteriorates with the number of cycles increasing under the same stress condition. In each loading cycle, the nonuniform deformation at the unloading stage is more than that at the loading stage under the same stress condition. The time of dislocation displacements and tension displacements meets hysteresis, compared with the time of stress change. In addition, the dislocation displacements and tension displacements around localization bands in general increase with the number of cycles increasing. The displacement evolution around localization bands has the same hysteresis and accumulation laws as that of nonuniform deformation.

Molecular dynamics simulation of void nucleation, growth and closure of nano-Cu/Al films under cyclic loading

In this paper, molecular dynamics method is used to simulate the evolution mechanism of void nucleation, growth and closure of diffusion-welded copper/aluminum bilayer film under cyclic loading condition with a strain-to-width ratio of <i>R</i> = –1. It is found that under cyclic loading condition, the voids mainly nucleate inside the aluminum side of the copper/aluminum bilayer film, and two kinds of evolution modes of voids I and II are found. The void I nucleates at the position of the gap defect produced by the Kirkendall effect when the copper-aluminum diffuses to form the bilayer film. Under this nucleation mode, after the gap defects have become void, the void moves into the area where copper atoms are relatively dense inside the OTHER structure on the aluminum side. When gaps accumulate to form voids, the voids grow at a fixed position. The void II on the aluminum side nucleates at the position of the gap defect formed by overcoming the stair-rod dislocation and then remains motionless in the process of nucleation, growth and closure. Comparing with the void I, the stress corresponding to the nucleation of void II is large, the growth speed of the void II is fast and the size of the void II is slightly large in the process of strain loading. The void II closure speed is also faster in the strain unloading stage. The two kinds of voids have two common characteristics in the process of nucleation, growth and closure. 1) Both kinds of voids nucleate at the position of the gap defect inside OTHER structure on the aluminum side. 2) In the process of voids growth and closure, both kinds of voids have the same shape changes. In the void growth stage, both kinds of voids first grow along the strain loading direction, then expand in the direction perpendicular to the strain loading direction, and finally, the shapes of two kinds of voids tend to become spherical. In the stage of void closure, the two kinds of voids are first compressed into ellipsoidal shape along the strain loading direction, and then disappear from both ends of the void to the center of the void in the direction perpendicular to the strain loading direction. In the subsequent cyclic loading process, none of new voids appears again at the position where the voids disappearred, but the nucleation of voids at other position of gap defect forms inside the other structure located on the aluminum side.

Simulation of Rock Mechanical Behavior Under Cyclic Loading Using Clump Parallel-Bond Models

In order to investigate rock mechanical behavior under cyclic loading and unloading conditions, the clump parallel-bond model (CPBM) combined with the newly-proposed loading procedure was used in numerical simulations and the simulated results were compared with those of the experiment. Then the intact rock under different confining pressures and pre-cracked rock with different flaw inclination angles are also investigated in detail. The related numerical results have demonstrated that: (1) the CPBM, combined with the use of the newly-proposed loading procedure, can be used to modelling the intact rock and pre-cracked rock mechanical behavior under cycle loading and unloading conditions. The simulated results are in good agreement with the experimental results; (2) the number of microscopic cracks increases with the cycle increases during the loading process, while few microscopic cracks are generated during the unloading process. The higher the confining pressure, the less damage the rock has accumulated during the cyclic loading process; (3) the inclination of the pre-existing flaw has a significant effect on the macroscopic fracture pattern.

Structure of carbon steel under plastic deformation

Results of studies on the structure of carbon steel 1045 under severe plastic deformation are presented. The atomic force microscopy method was used to estimate the metallographic structure of steel damage after cyclic impact. It was found that the plastic flow localization process occurs in narrow micro-volumes. During the process of cyclic loading, fatigue strength increases, while plastic deformation decreases, and vice versa.

Fatigue Characteristics of Limestone under Triaxial Compression with Cyclic Loading

This paper presents an experimental investigation of the fatigue properties of limestone subjected to triaxial compression with axial cyclic loading. Tests were conducted on intact limestone samples with a loading frequency of 0.5 Hz and a confining pressure of 10 MPa. The test results show the following five points. (1) Under triaxial conditions, the axial and circumferential deformations at the failure point induced by cyclic loading are slightly larger than the corresponding deformations at the peak stress achieved by conventional compression tests. (2) The first level cyclic loading process has a strong influence on rock deformation in the primary phase during subsequent level cyclic loading. A smaller difference in stress amplitude between the two loading stress levels leads to less deformation during the latter. (3) Circumferential and volumetric changes are more sensitive to fatigue failure in terms of deformation and strain rate than axial changes. (4) The three phases of dissipated energy evolution are consistent with a sample’s deformation such that the energy dissipation characteristics reflect the fatigue damage evolution process. (5) A new damage formula is proposed that can concisely describe a rock’s zero-cycle damage and damage evolution.

Theb-value analysis of bedded shale under cyclic loading tests

Research on the damage evolution of bedded shale which can be described by different scales of cracks from micro- to macro-damage is significant. The b-value representing the relative proportion of micro-cracking to macro-cracking could be a good index for estimating the damage process of granite, sandstone, and marble as most of the previous studies have reported. The variation of the b-value of shale specimens with different bedding plane orientations subjected to cyclic load was investigated here. To ensure the reliability of the determination of the b-values, both the least squares method and maximum likelihood estimate were applied. And the sample range of acoustic emission events in data processing was redefined so that the previously generated cracks as well as the current formed cracks in this time window could all be used to calculate the b-value which reflects the accumulation of damage in one loading cycle. Cyclic load tests on stress levels with the first peak load of 30%–50% and above 80% of the estimated uniaxial failure strength, respectively, were conducted for shale specimens with bedding planes parallel and perpendicular to the loading direction. A change trend of the b-value in each test is observed as decreasing for one load cycle around the failure strength as well as the cyclic loading process prior to the final failure. Thus, this phenomenon of shale, only appearing as the stress exceeds 80% of the failure strength, has neither a relationship with the bedding plane nor the loading paths.

Damage evolution analysis of coal samples under cyclic loading based on single-link cluster method

In this paper, the acoustic emission (AE) response of coal samples under cyclic loading is measured. The results show that there is good positive relation between AE parameters and stress. The AE signal of coal samples under cyclic loading exhibits an obvious Kaiser Effect. The single-link cluster (SLC) method is applied to analyze the spatial evolution characteristics of AE events and the damage evolution process of coal samples. It is found that a subset scale of the SLC structure becomes smaller and smaller when the number of cyclic loading increases, and there is a negative linear relationship between the subset scale and the degree of damage. The spatial correlation length ξ of an SLC structure is calculated. The results show that ξ fluctuates around a certain value from the second cyclic loading process to the fifth cyclic loading process, but spatial correlation length ξ clearly increases in the sixth loading process. Based on the criterion of microcrack density, the coal sample failure process is the transformation from small-scale damage to large-scale damage, which is the reason for changes in the spatial correlation length. Through a systematic analysis, the SLC method is an effective method to research the damage evolution process of coal samples under cyclic loading, and will provide important reference values for studying coal bursts.

Mechanical Behavior and Damage Evolution for Granite Subjected to Cyclic Loading

This paper focuses on the mechanical behavior and damage evolution of Huashan granite subjected to cyclic loading. Four levels of confining pressure (0, 15, 25, and 35 MPa) were applied during cyclic axial loading by using a Rock Test System (MTS815) along with an acoustic emission (AE) monitoring device. Experimental results indicate that the number of AE activities is higher under cyclic triaxial loading compared to that under cyclic uniaxial loading. The measured stress‐strain curves of both uniaxial and triaxial tests under cyclic loading are concave‐up, but the degree of concavity is mild for the latter. As the cycle number rises, elastic modulus of the granite sample under different confining pressures increases. The slope of the peak strength versus confining pressure plot for the cyclic loading is larger than that for the monotonic loading. Besides, it is found that the dissipated energy increases with the increase of cyclic stress, but it hardly increases in proportion with the confining pressure. The damage parameters defined in terms of the plastic strain can be extended for the whole cyclic loading process, and they agree well with the energy‐based damage parameters.

Experimental study on cyclic tensile behaviour of concrete under various strain rates

Owing to difficulties relating to the direct tension test on concrete, few test data are available. To study the effect of strain rate and unloading stress on the mechanical properties of concrete, three strain rates of 10−6s−1, 10−5s−1 and 10−4s−1 and four unloading stresses are considered in this cyclic tensile–compressive test and the theoretical analysis is performed. In the paper, the non-classical strain is used to describe the tensile–compressive behaviour of plain concrete. Experimental results indicate that the residual strain and the non-classical compressive strain amplitude increase gradually with the increase of the unloading non-classical strain, which is a form of damage evolution. Meanwhile, the non-classical tangent modulus degrades with the reduction of the unloading stress. This means that the accumulation of non-classical deformation accompanies the stiffness degradation of the material during the process of continuous cyclic loading. This paper proposes a model to describe the stress–strain relation of concrete under cyclic tensile–compressive loading at various strain rates. Finally, the Weibull distribution model is introduced to make a statistical analysis of the damage evolution of concrete under post-peak monotonic and cyclic loading. The Weibull distribution model is shown to be a reasonable method to describe the post-peak damage evolution of concrete.

Mechanical properties in cyclic tension-compression loading process on sheet metal

In the process of reciprocating bending, any particle of the workpiece is subjected to cyclic tensile compression deformation. The workpiece undergoes a reciprocating bending deformation process, and each particle undergoes a cyclic tension-compression loading cycle. In this paper, cyclic tensile loading tests under different prestrains and strain amplitudes are carried out. The macroscopic behavior of 304 stainless steel and ST12 cold rolled plate under cyclic tension-compression loading and the effect of prestrain on the stable hysteresis loop of the two materials are studied. Thus, the evolution of macroscopic mechanical properties in the process of reciprocating bending deformation is deeply understood. The experimental results show that 304 stainless steel and ST12 cold rolled plate are characterized by cyclic softening; the prestrain has little effect on the stable hysteresis loop, the cyclic tension-compression loading eliminates the initial difference of the mechanical properties caused by the prestrain and makes the mechanical properties of materials tend to be uniform. It is also proved indirectly that the reciprocating bending has not only the effect of uniform curvature, but also makes the mechanical properties of the same layer of fibers be homogenized.

Application of compound Poisson process for modelling of ore flow in a belt conveyor system with cyclic loading

This paper deals with the analysis of the random process of cyclic loading of a mining belt conveyor with portions of ore discharged by loaders or trucks. Such transfer of transported ore from a cyclic to a continuous transport is typical for the specific mining operations implemented in the underground copper ore mines with room and pillar mining. The conveyors in such systems are usually significantly oversized in order to match the peak loads of cumulated discharges of ore hauled from mining fields by loaders. Therefore, the actual loadings that occur in the mining transportation systems need to be analysed to provide the data for more accurate design and control of belt conveyors. The large data-set of actual loadings of the belt conveyors has been used for the stochastic modelling of the analysed process. The compound Poisson process has been proposed as mathematical tool to analyse/describe properties of ore flow. The discussion of the chosen distribution functions and results of the fitted model simulations compared with the examined measurement data are presented. In this paper, the case of a belt conveyor loaded only by a single feeding point where loaders are randomly discharged have been analysed. More complex cases (several loading points, mixed ore supply from cyclic and continuous ore mass flow from preceding conveyors or ore bunkers) are under investigation and will be presented in the future.

Research on the fatigue equation of asphalt mixtures based on actual stress ratio using semi-circular bending test

The semi-circular bending (SCB) strength test and fatigue test were used in this paper to evaluate the strength property and fatigue performance of asphalt mixtures. The SCB strength test was carried out at 8 loading rates and 3 temperatures, followed by the SCB fatigue test at 5 load levels on one common stone matrix asphalt (SMA) mixture. The time–temperature characteristics of strength from SCB test were studied. The fatigue performance was evaluated based on displacement development and energy consumption during the cyclic loading process. And according to the established strength-loading rate model, the fatigue equation based on actual stress ratio was obtained as well. The results showed that asphalt mixture strength was affected by loading rate and temperature significantly, the relation between strength and loading rate could be approximately expressed as a power function; the relation between fatigue life and stress level (or nominal stress ratio) could also be expressed as a power function. The lower the stress level, the longer the fatigue life was, and the fatigue life and the cumulative energy consumption showed a good linear relationship in the double logarithmic coordinates; the fatigue equation based on actual stress ratio revealed the connection between fatigue failure and strength failure.