Numerical simulation of fatigue crack propagation in heterogeneous geomaterials under varied loads using displacement discontinuity method

Heterogeneous brittle geomaterials are highly susceptible to cyclic loads.They contain inherent flaws and cracks that grow under fatigue loads and lead to failure.This study presents a numerical model for analyzing fatigue in these materials based on the two-dimensional(2D)boundary element method and linear elastic fracture mechanics.The process is formulated by coupling the displacement discontinuity method with the incorporation technique of dissimilar regions and the governing equations of fatigue.The heterogeneous media are assumed to consist of materials with different properties,and the interfaces are assumed to be completely bonded.In addition,the domains include multiple cracks exposed to constant and variable amplitude cyclic loads.The stress intensity factor is a crucial parameter in fatigue analysis,which is determined using the displacement field around crack tips.An incremental crack growth scheme is applied to calculating the fatigue life.The growth rate values are employed to estimate the length of crack extension when there are multiple cracks.The interaction between cracks is considered,which also includes the coalescence phenomenon.Finally,various structures under different cyclic loads are examined to evaluate the accuracy of this method.The results demonstrate the efficiency of the proposed approach in modeling fatigue crack growth and life estimation.The behavior of life curves for the heterogeneous domain was as expected.These curves illustrate the breakpoints caused by utilizing discrete incremental life equations.At these points,the trend of the curves changed with the material properties and fatigue characteristics of the new material around the crack tips.

Effect of Fatigue Loading on the Mechanical Properties and Resistance of High-strength Straight-hole Recycled Pervious Concrete to Rainstorm-based Waterlogging

A novel high-strength straight-hole recycled pervious concrete(HSRPC)for the secondary highway pavement was prepared in this paper.This study aimed to investigate the effect of porosity(0.126%,0.502%,and 1.13%),vehicle loading stress level(0.5 and 0.8)and service life on the resistance to rainstormbased waterlogging of HSRPC under fatigue loading.The mechanical properties of HSRPC in terms of flexural strength and dynamic elastic modulus were studied.The waterlogging resistance of HSRPC was described by surface water depth and drainage time.The microstructure of HSRPC were observed with scanning electron microscopy(SEM).Results showed that although the dynamic elastic modulus and flexural strength of HSRPC decreased with the increasing number of fatigue loading,the flexural strength of HSRPC was still greater than5 MPa after design service life of 20 years.After 2.5×10^(5)times of fatigue loading,the permeability coefficient of HSRPC with a porosity of 0.502%and 1.13%increased by 18.4%and 22.9%,respectively;while the permeability coefficient of HSRPC with 0.126%porosity dropped to 0.35 mm/s.The maximum surface water depth of HSRPC with a porosity of 0.126%,0.502%,and 1.13%were 8,5 and 4 mm,respectively.SEM results showed that fatigue loading expanded the number and width of cracks around the tiny pores in HSRPC.

Fatigue test loading methodfor wagon body basedon measured load

Purpose–In this paper,the C80 special coal gondola car was taken as the subject,and the load test data of the car body at the center plate,side bearing and coupler measured on the dedicated line were broken down to generate the random load component spectrums of the car body under five working conditions,namely expansion,bouncing,rolling,torsion and pitching according to the typical motion attitude of the car body.Design/methodology/approach–On the basis of processing the measured load data,the random load component spectrums were equivalently converted into sinusoidal load component spectrums for bench test based on the principle of pseudo-damage equivalence of load.Relying on the fatigue and vibration test bench of the whole railway wagon,by taking each sinusoidal load component spectrum as the simulation target,the time waveform replication(TWR)iteration technology was adopted to create the drive signal of each loading actuator required for the fatigue test of car body on the bench,and the drive signal was corrected based on the equivalence principle of measured stress fatigue damage to obtain the fatigue test loads of car body under various typical working conditions.Findings–The fatigue test results on the test bench were substantially close to the measured test results on the line.According to the results,the relative error between the fatigue damage of the car body on the test bench and the measured damage on the line was within the range of
16.03%–27.14%.Originality/value–The bench test results basically reproduced the fatigue damage of the key parts of the car body on the line.

GIGACYCLE FATIGUE BEHAVIOR OF CAST ALUMINUM IN TENSION AND TORSION LOADING

An improved understanding of fatigue behavior of a cast aluminum alloy（2-AS5U3G-Y35）in very high cycle regime is developed through the ultrasonic fatigue test in axial and torsion loading.The new developed torsion fatigue system is presented.The effects of loading condition and frequency on the very high cycle fatigue（VHCF）are investigated.The cyclic loading in axial and torsion at 35 Hz and 20 kHz with stress ratio R=-1 is used respectively to demonstrate the effect of loading condition.S-N curves show that the fatigue failure occurs in the range of 105—1010 cycles in axial or torsion loading and the asymptote of S-N curve is inclined,but no fatigue limit exists under the torsion and axial loading condition.The fatigue fracture surface shows that the fatigue crack initiates from the specimen surface subjected to the cyclic torsion loading.It is different from the fatigue fracture characteristic in axial loading in which fatigue crack initiates from subsurface defect in very high cycle regime.The fatigue initiation is on the maximum shear plane,the overall crack orientation is on a typical spiral 45° to the fracture plane and it is the maximum principle stress plane.The clear shear strip in the torsion fatigue fracture surface shows that the torsion fracture is the shear fracture.

Experimental study on mechanical properties of dowel bar embedded in concrete under fatigue loads

To investigate the mechanical properties of a dowel action under fatigue loads, nine reinforced concrete specimens were fabricated, and the monotonic and fatigue loadings were performed on these specimens, respectively. All of these specimens were divided into two series. Six specimens in SeriesⅠwith different bar diameters of 12, 20 and 25 mm were subjected to monotonic loads and were used to confirm the ultimate bearing capacity. The remaining three specimens in Series Ⅱ were subjected to fatigue loads and were designed to investigate the attenuation character of dowel action and the fatigue failure modes. The test results show that the accumulated fatigue damage due to fatigue loads can reduce the ultimate bearing capacity of specimens. With the increase in fatigue loads, the failure mode can transform to fatigue rupture of the dowel bar under the serviceability loading state,i. e. 55% of the monotonic capacity. The fatigue life is determined by the fatigue properties of steel and concrete.Based on the test data, the failure process of dowel action can be divided into two stages： the accumulation of fatigue damage and the fatigue rupture of dowel bar.

Fatigue Life Prediction under Service Load Considering Strengthening Effect of Loads below Fatigue Limit

Lightweight design requires an accurate life prediction for structures and components under service loading histories. However, predicted life with the existing methods seems too conservative in some cases, leading to a heavy structure. Because these methods are established on the basis that load cycles would only cause fatigue damage, ignore the strengthening effect of loads. Based on Palmgren-Miner Rule （PMR）, this paper introduces a new method for fatigue life prediction under service loadings by taking into account the strengthening effect of loads below the fatigue limit. In this method, the service loadings are classified into three categories： damaging load, strengthening load and none-effect load, and the process for fatigue life prediction is divided into two stages： stage I and stage II, according to the best strengthening number of cycles. During stage I, fatigue damage is calculated considering both the strengthening and damaging effect of load cycles. While during stage II, only the damaging effect is considered. To validate this method, fatigue lives of automobile half shaft and torsion beam rear axle are calculated based on the new method and traditional methods, such as PMR and Modified Miner Rule （MMR）, and fatigue tests of the two components are conducted under service loading histories. The tests results show that the percentage errors of the predicted life with the new method to mean life of tests for the two components are –3.78% and –1.76% separately, much lesser than that with PMR and MMR. By considering the strengthening effect of loads below the fatigue limit, the new method can significantly improve the accuracy for fatigue life prediction. Thus lightweight design can be fully realized in the design stage.

The Transport Properties of Concrete under the Simultaneous Coupling of Fatigue Load and Environment Factors

A set of coupling experimental instrument was designed to study the transport properties of chloride ion in concrete under simultaneous coupling action of fatigue load and environmental factors. Firstly the water-saturated performance of modem concrete was investigated, then diffusion performance of chloride ion under different stress levels and different temperature were studied respectively; meanwhile, the time- dependent behavior of the chloride ion diffusion in concrete was also researched. The results showed that the saturation degree of concrete can reach as high as 99%. Besides, diffusion coefficient of chloride ion increased with increasing of the stress level and temperature, and when the stress level and temperature are at 0.6 and 60 ℃ respectively, the diffusion coefficient is 6.3 ×10 -14 m2/s, moreover the diffusion coefficient of chloride ion in concrete decreased with time under the simultaneous coupling action of fatigue load and environment factors.

MULTIAXIAL CREEP-FATIGUE LIFE EVALUATION UNDER PROPORTIONAL LOADING

A new method was proposed for the multiaxial creep-fatigue life evaluation under proportional loadings. Because this method was derived from the strain range partitioning method with a multiaxiality factor, it was possible to consider the influence of both creep-fatigue interaction and multiaxial stress state on fatigue life. In order to predict the combined axial-torsional fatigue life the damage under combined loading was defined as linear summation of the damages under axial loading and torsional loading. Axial-torsional creep-fatigue tests were carried out using tubular specimens of 316LC austenitic stainless steel and the ferritic rotor steel. This rotor steel was developed for the permanent magnet type eddy current retarder in heavy trucks. Experimentally obtained lives of both steels were well corresponded with the lives predicted by the proposed method. It was found that the proposed method was effective in multiaxial fatigue life evaluation under proportional creep-fatigue loadings.

PREDICTION OF FATIGUE LIVES OF RC BEAMS STRENGTHENED WITH CFL UNDER RANDOM LOADING

The investigation on fatigue lives of reinforced concrete （RC） structures strength- ened with fiber laminate under random loading is important for the repairing or the strengthening of bridges and the safety of the traffic. In this paper, two methods are developed for predicting the fatigue lives of RC structures strengthened with carbon fiber [aminate （CFL） under random loading based on a residual life and a residual strength model. To discuss the efficiency of the model, 12 RC beams strengthened with CFL are tested under random loading by the MTS810 testing system. The predicted residual strength approximately agrees with test results.

Rain-Flow and Reverse Rain-Flow Counting Method for the Compilation of Fatigue Load Spectrum

The rain-flow counting method is widely used to compile the fatigue load spectrum, The second stage counting of the rain-flow method is a troublesome process. In order to overcome this drawback, the rain-flow and reverse rain-flow counting method is proposed in this paper. In this counting method, the rule for counting of the rain-flow method is modified, so that the sequence of load-time need not be adjusted. This is a valid and useful method to count cycles and compile the load spectrum and it can be widely used in ocean engineering.

Experimental investigations on mechanical performance of rocks under fatigue loads and biaxial confinements

In this research,a series of biaxial compression and biaxial fatigue tests were conducted to investigate the mechanical behaviors of marble and sandstone under biaxial confinements.Experimental results demonstrate that the biaxial compressive strength of rocks under biaxial compression increases firstly,and subsequently decreases with increase of the intermediate principal stress.The fatigue failure characteristics of the rocks in biaxial fatigue tests are functions of the peak value of fatigue loads,the intermediate principal stress and the rock lithology.With the increase of the peak values of fatigue loads,the fatigue lives of rocks decrease.The intermediate principal stress strengthens the resistance ability of rocks to fatigue loads except considering the strength increasing under biaxial confinements.The fatigue lives of rocks increase with the increase of the intermediate principal stress under the same ratio of the fatigue load and their biaxial compressive strength.The acoustic emission(AE)and fragments studies showed that the sandstone has higher ability to resist the fatigue loads compared to the marble,and the marble generated a greater number of smaller fragments after fatigue failure compared to the sandstone.So,it can be inferred that the rock breaking efficiency and rock burst is higher or severer induced by fatigue loading than that induced by monotonous quasi-static loading,especially for hard rocks.

Residual Tensile Strength of Plain Concrete Under Tensile Fatigue Loading

The functional relation between the residual tensile strength of plain concrete and number of cycles was determined. 99 tappered prism specimens of plain concrete were tested under uniaxial tensile fatigue loading. Based on the probability distribution of the residual tensile strength, the empirical expressions of the residual tensile strength corresponding to the number of cycles were obtained. The residual tensile strength attenuating curves can be used to predict the residual fatigue life of the specimen under variable-amplitude fatigue loading. There is a good correlation between residual tensile strength and residual secant elastic modulus. The relationship between the residual secant elastic modulus and number of cycles was also established.

Fatigue damage analysis of epoxy asphalt pavement for steel bridges considering coupled effects of heavy load and temperature variations

To investigate the fatigue damage of epoxy asphalt pavement(EAP)under a heavy load and a d temperature load,the load-figure of the heavy load on the steel bridge deck pavement(SBDP)was simulated first,and the temperature distribution of SBDP during the temperature-fall period in winter was also calculated.Secondly,t e moving heavy load coupled W t the most unfavorable temperatre load was applied to the SBDP,and the tensile stress on the top of SBDP was calculated.Finally,the fatigue damage of EAP was evaluated considering the extreme situation of heavily overloaded and severe environments.The results show that botte heavy load and the temperature load during t e temperature-fall period c n increase the tensile stress on the top of SBDP significantly.In the exteme situation of heavily overloaded and severe environments,a fatigue crack is easily generated,and thus the SBDP should avoid t e coupling effects of the heavy loadand the temperature load in winter.

Chloride Ion Transport in Fly Ash Mortar under Action of Fatigue Loading

In order to study the chloride ion transport performance in fly ash addition mortar, a new method, in which the fatigue loading and chloride diffusion are undertaken simultaneously, was developed. This method realizes coupling the fatigue damage process and the process of chloride transporting of fly ash mortar. The transport performance of chloride in fly ash mortar specimens was studied under different stress levels. Moreover, the effect of fly ash content on transport performance of chloride ion in mortar was investigated. AE （Acoustic Emission） and SEM were used to acquire the damage distribution of mortar specimens under action of fatigue load. The results show that the diffusion coefficient of chloride in mortar specimens increases with stress level of fatigue loading. The addition of fly ash can mitigate the penetration of chloride ion. The results of microcmck 3D location acquired by AE, accompanied with crack characterizing from SEM, indicate that the damage degree of mortar specimen increases with stress level of fatigue loading. Furthermore, higher damage degree of mortar leads to more the chloride ion content in the sample.

Effect of fatigue loading-confining stress unloading rate on marble mechanical behaviors: An insight into fracture evolution analyses

Rocks in underground works usually experience rather complex stress disturbance.For this,their fracture mechanism is significantly different from rocks subjected to conventional triaxial compression conditions.The effects of stress disturbances on rock geomechanical behaviors under fatigue loading conditions and triaxial unloading conditions have been reported in previous studies.However,little is known about the dependence of the unloading rate on fatigue loading and confining stress unloading(FL-CSU)conditions that influence rock failure.In this paper,we aimed at investigating the fracture behaviors of marble under FL-CSU conditions using the post-test X-ray computed tomography(CT)scanning technique and the GCTS RTR 2000 rock mechanics system.Results show that damage accumulation at the fatigue stage can influence the final fracture behaviors of marble.The stored elastic energy for rock samples under FL-CSU tests is relatively larger compared to those under conventional triaxial tests,and the dissipated energy used to drive damage evolution and crack propagation is larger for FL-CSU tests.In FL-CSU tests,as the unloading rate increases,the dissipated energy grows and elastic energy reduces.CT scanning after the test reveals the impacts of the unloading rate on the crack pattern and a fracture degree index is therein defined in this context to represent the crack dimension.It shows that the crack pattern after FL-CSU tests depends on the unloading rate,and the fracture degree is in agreement with the analysis of both the energy dissipation and the amount of energy released.The effect of unloading rate on fracture evolution characteristics of marble is revealed by a series of FL-CSU tests.

Numerical investigation on the fatigue failure characteristics of waterbearing sandstone under cyclic loading

The strength of sandstone decreases significantly with higher water content attributing to softening effects.This scenario can pose a severe threat to the stability of reservoirs of pumped storage power stations developed from abandoned mines,especially when subjected to the cyclic loading condition caused by the repeated drainage and storage of water(fatigue damage).Based on this,it is essential to focus on the fatigue failure characteristics.In this study,the mineral composition of the used sandstone of Ruineng coal mine in Shanxi Province,China,was first tested to elucidate the rock softening mechanism after absorbing water.Next,a numerical model for replicating the mechanical behavior of water-bearing sandstone was established using twodimensional particle flow code(PFC2D)with a novel contact model.Then,16 uniaxial cyclic loading simulations with distinct loading parameters related to reservoir conditions(loading frequency,amplitude level,and maximum stress level)and different water contents were conducted.The numerical results show that all these three loading parameters affect the failure characteristics of sandstone,including irreversible strain,damage evolution,strain behavior,and fatigue life.The influence degree of these three parameters on failure behavior increases in the order of maximum stress level,loading frequency,and amplitude level.However,for the samples with different water contents,their failure characteristics are similar under the same loading conditions.Furthermore,the failure mode is almost unaffected by the loading parameters,while the water content plays a significant role and causing the transformation from the tensile splitting with low water content to the shear failure with higher water content.

Bearing characteristics and fatigue damage mechanism of multi-pillar system subjected to different cyclic loads

Aiming to investigate the fatigue damage mechanism and bearing characteristics of multi-pillar system under cyclic loading,a series of axial cyclic loading tests with different cyclic amplitudes were carried out on triple-pillar marble specimens.The acoustic emission(AE)and digital image correlation(DIC)were jointly applied to monitoring and recording damage evolution and failure behavior of each pillar,which reproduced the cataclysmic instability process of underground pillar groups.Experimental results indicated that the cyclic amplitude exceeding the threshold of damage initiation weakened the resistance to deformation,resulting in obvious release of dissipated energy and the reduction of bearing capacity.Conversely,after low-amplitude cyclic loading,both the pre-peak bearing capacity and the post-peak ductility of the pillar system increased due to the compaction of initial defects,indicating that the peak bearing capacity was closely related to the extent of pre-peak fatigue damage.The axial strain of each pillar was measured by DIC virtual extensometer to present the damage extent during cyclic loading phase.Meanwhile,fracture evolution of typical load drop points was also characterized by transverse strain fields(εxx),and observations showed that the damage extent of key pillar undergoing high-amplitude cyclic loads was more serious and violent,accompanied by the ejection of rock debris and loud noises.

COMPUTER CONTROLLED METHOD FOR MEASUREMENT OFSURFACE CRACK LENGTH ON PLATE SUBJECTEDTO FATIGUE LOADING

The calibration curves obtained using strain gages are used to predict surface crack length on plate specimen subjected to 4-point bending fatigue loading. The results shows that the proposed procedure is of high precision with the maximum error percentage being less than 6%, and it can be easily used to estimate or monitor the surface crack length under fatigue loading both in laboratory and in engineering. It is also quite meanful for nondamage detecting.

DELAMINATION FORMATION AND DELAMINATION PROPAGATION OF COMPOSITE LAMINATES UNDER COMPRESSIVE FATIGUE LOADING

Fatigue tests of the smooth composite laminates and the notched composite laminates under compressive cyclic loading have been carried out. The damage mechanism is discussed and analyzed. Damage evolution is monitored using stiffness decay. From these tests, it is found that the initial delamination occurs at the free boundary of smooth specimens, or the notch boundary of notched specimens, subjected to the compression-compression cyclic load. A point of view in relation to two-phases of compression fatigue delamination of composites is proposed, namely, compression-compression delamination consists of the delamination formation phase and the delamination propagation, and there is a 'damage transition point' to separate this two-phases. Furthermore, an empirical modulus degradation formula and its parameters fitting method are presented. According to the test data handling results, it is shown that this formula is univocal and can fit the test data conveniently. In addition, two kinds of new anti-buckling devices are designed for these tests. At last, the E-N curves, the D-N curves and the S-N curve of the smooth carbon fiber reinforced composite laminates of T300/648C are determined to predict the fatigue life of the notched composite laminate. And the E-N curve of the notched specimens at the given load ratio R = 10 and minimum load Pmin = -0.45 kN is also measured to verify the estimated result of fatigue life.

Fatigue characteristics and microcosmic mechanism of Al-Si-Mg alloys under multiaxial proportional loadings

With the increasing use of Al-Si-Mg alloys in the automotive industry,the fatigue performance of Al-Si-Mg alloy has become a major concern with regard to their reliability.The fatigue characteristics and microcosmic mechanism of an Al-Si-Mg alloy under multiaxial proportional loadings were investigated in this research.As low cycle fatigue life and material strengthening behavior are closely related,the effect of equivalent strain amplitude on the multiaxial fatigue properties was analyzed.Fatigue tests were conducted to determine the influence of equivalent strain amplitude on the multiaxial proportional fatigue properties.The fatigue life exhibits a stable behavior under multiaxial proportional loadings.The dislocation structures of the Al-Si-Mg alloy were observed by transmission electron microscopy（TEM）.The dislocation structure evolution of the Al-Si-Mg alloy under multiaxial proportional loadings during low cycle fatigue develops step by step by increasing fatigue cycles.Simultaneously,the dislocation structure changes with the change in equivalent strain amplitude under multiaxial proportional loadings.The experimental evidence indicates that the multiaxial fatigue behavior and life are strongly dependent on the microstructure of the material,which is caused by multiaxial proportional loadings.