Large Number Of Loading Cycles Research Articles

Evaluation of large axial strain of granular sand in post-liquefaction stage using DEM simulation

Field investigations in recent studies have revealed that significant damage to foundations often occurs in the post-liquefaction stage, during which sand undergoes substantial deformation. As a result, numerous researchers have dedicated considerable effort to studying the evolution of the axial strain at this stage. However, the accurate measurement of the exact value of this strain is challenging mainly owing to the limitations of the triaxial apparatus. In this study, the numerical method of discrete element method (DEM) is used to simulate undrained cyclic triaxial loading tests according to a large number of loading cycles. The mechanical behaviour of granular sand under different cell pressures was reproduced using the DEM method, wherein the liquefaction resistance increased with the cell pressure. The post-liquefaction axial strain exhibited a similar pattern of variation among the calculated cases at different cell pressures. The value of the double amplitude of the axial strain stabilised at a maximum value after a certain loading cycle. The microscopic characteristics derived from the DEM calculations, including the contact number and force chain network, were analysed to provide reasonable explanations. The sand fabric was re-established after a large number of loading cycles and controlled by cyclic loading, which helped stabilise the accumulated axial strain.

A numerical framework for modelling settlements of railway ballast layers

Permanent deformation in ballast layers is a major contributing factor to the railway track geometry deterioration. In spite of a considerable amount of research on understanding and predicting performance of ballast layers, accurately capturing their settlements remains a challenge. In order to contribute to solving this important issue, a new numerical method for predicting ballast settlements is presented in this paper. This method is based on the finite element (FE) method combined with a constitutive model that captures permanent deformation accumulation in unbound materials under cyclic loading. This allows predicting permanent deformations of large structures and at large number of load cycles in a computationally efficient manner.The developed constitutive model is validated based on triaxial test measurements over wide range of loading conditions. Stress state in ballast layers has been examined with a 3D FE model, for several embankment structures and traffic load magnitudes. The determined stress distributions and loading frequencies were used as an input of the constitutive model to evaluate permanent strains and settlements of ballast layer. The influence of embankment structural designs and traffic loading magnitudes on the ballast layers settlements is examined and the results obtained are compared with the existing empirical performance models.

A simplified method for calculating the accumulation of irreversible ro-tations of wind turbine shallow foundations

Wind turbines represent a convenient source of renewable energy and their diffusion is a fundamental step for reducing carbon dioxide emissions, main responsible for global warming. Turbine towers are characterized by large heights, therefore the wind load induces considerable bending actions at the base of the structure. Although, especially offshore, deep foundations are usually adopted, shallow foundations are still an option in case of onshore installations [1]. These circular shallow foundations are massive concrete structures (Figure 1) that counteract the bending moment with their own weight. The optimization of the design and the extension of the service life are fundamental from both economic and environmental perspectives. These will increase the competitivity of energy production from renewable wind sources over fossil ones, thus boosting the transition toward sustainable energy.
 From a geotechnical perspective, the isolated foundations of wind turbines are a peculiar case since the accumulation of vertical settlements and horizontal displacements are not a main concern. On the contrary, the accumulation of excessive rotations due to the wind cyclic loads may reduce the efficiency of the turbine and, in particularly critical cases, define the end of service of the structure.
 The accumulation of irreversible rotation during the exercise cyclic loads may be induced by both the development of irreversible strain in the soil and the formation of cracks in the concrete foundation. This second aspect can however be neglected, since, in the current practice, very over-conservative approaches are used to design the reinforcements. Recent experimental small scale tests (Figure 1) proved that, even when stirrups are completely removed, exercise loads do not induce the formation of cracks [2]. Therefore, the accumulation of cyclic irreversible rotation is only due to the soil.
 Recently, numerous constitutive relationships accounting for the cyclic behaviour of the soil were proposed [3,4]. These in principle allow to perform finite element analyses capable of reproducing the soil-structure interaction. However, during the foundation design life a very large number of load cycles (up to 108) is expected, leading to unacceptable computational times.
 A way to circumvent this problem is the employment of models conceived in the framework of the macroelement approach [5]. This is based on the assumption of reproducing the response of a complex system by using a very small number of degrees of freedom and by introducing an upscaled constitutive law relating generalized stresses (forces and moments) and strains (displacements and rotations). The abrupt reduction in degrees of freedom significantly reduces the computational times. However, the definition of the upscaled constitutive laws and the calibration of its parameters are particularly critical since they will be affected not only by the soil behaviour, but also by the foundation geometry and mechanical properties.
 In this work, the authors intend to propose a new one-dimensional macroelement to reproduce the moment-rotation response of shallow foundations for wind turbines. This generalized constitutive law, inspired to the one proposed in [6] for reproducing the lateral response of piles, is conceived in the framework of the bounding surface plasticity theory. The main ingredients of this model are a bounding surface and a mixed isotropic-kinematic generalized strain hardening controlling the ratcheting.
 The model is capable of qualitatively reproduce (Fig. 2) the experimental results of [2] and seems to be a very promising approach for design purposes. In addition, the model can also simply be introduced in structural finite element codes allowing to solve soil-structure interaction problems also accounting the turbine tower. This can be used to adequately reproduce the whole system response and to also optimize the tower design to dynamic loads.

Cumulative buckling deformation of stiffened panel under cyclic loading

In this study, the cumulative buckling deformation process is evaluated for a stiffened panel subjected to two different uniaxial cyclic loading conditions, namely compressive loading only and alternating tensile-compressive loading. The impact of the cyclic load on the ultimate strength of the panel is then estimated. It should be noted that the occurrence of permanent deformations could be simulated by finite element analysis using a suitable model capable of correctly capturing the deformation components. The results show that the structure accumulates a deformation that appears to grow almost linearly therefore, consequently, it is realistic to expect that if a large number of load cycles of this magnitude are imposed, the accumulated plastic deformation can be quite severe. Furthermore, it is found that these residual deformations, caused by an entity of the cyclic load lower than the design limit, affect the tensile strength of the stiffened panel. Finally, the effects on the numerical evaluation of the ultimate strength of the structure are shown.

Very High Cycle Fatigue Behavior of Austenitic Stainless Steel in Annealed and Predeformed Condition

Abstract Engineering components in service nowadays are designed for a large number of loading cycles (∼109), which makes fatigue behavior in this cycle range (designated as very high cycle fatigue [VHCF]) a topic of significant interest. The present study aims to investigate the high cycle fatigue (HCF) and VHCF behavior in type 304 stainless steel in two different conditions (annealed and with a martensite volume fraction of ∼45 %) through low cycle fatigue predeformation at a subzero temperature. A fatigue diagram in the form of an S–N curve extending up to the VHCF range is generated, which shows different HCF and VHCF behaviors for the annealed and predeformed conditions. Further tests are carried out at different R ratios to generate constant-life Haigh diagrams for both conditions. Although no failure is observed in the VHCF range under the annealed condition, an internal crack initiation mode is observed under the predeformed condition (Type II behavior), which is attributed to the enhanced notch sensitivity under VHCF cycling induced by a significant extent of strain-induced martensite formed during predeformation. To address the influence of varying load history under service, specimens were prefatigued in HCF, followed by VHCF cycling. The HCF–VHCF boundary is found to be significantly impacted by the prior HCF damage, with lowering of the fatigue limit under VHCF.

An efficient implementation of a phase field model for fatigue crack growth

Recently, phase field modeling of fatigue fracture has gained a lot of attention from many researches and studies, since the fatigue damage of structures is a crucial issue in mechanical design. Differing from traditional phase field fracture models, our approach considers not only the elastic strain energy and crack surface energy, additionally, we introduce a fatigue energy contribution into the regularized energy density function caused by cyclic load. Comparing to other type of fracture phenomenon, fatigue damage occurs only after a large number of load cycles. It requires a large computing effort in a computer simulation. Furthermore, the choice of the cycle number increment is usually determined by a compromise between simulation time and accuracy. In this work, we propose an efficient phase field method for cyclic fatigue propagation that only requires moderate computational cost without sacrificing accuracy. We divide the entire fatigue fracture simulation into three stages and apply different cycle number increments in each damage stage. The basic concept of the algorithm is to associate the cycle number increment with the damage increment of each simulation iteration. Numerical examples show that our method can effectively predict the phenomenon of fatigue crack growth and reproduce fracture patterns.

Influence of Deposition Plane Angle and Saline Corrosion on Fatigue Crack Growth in Maraging Steel Components Produced by Laser Powder Bed Fusion

Maraging steels are used in several industries, namely in the molds industry. The determination of fatigue crack propagation resistance in 18Ni300 maraging steel at the Paris regime is a vital issue for safety-relevant components, which are designed to work for a large number of loading cycles before periodic inspections. The main goal of this work is to analyze the influence of the deposition plane angle and saline corrosion on fatigue crack growth in maraging steel samples produced by Laser Powder Bed Fusion (LPBF). The crack closure parameter was used in order to analyze the different fatigue crack growth behaviors, as well as the metallographic, hardness, fractography and corrosion/oxidation analysis. From this work, the main achievement was that the deposition plane angle did not reveal a notable influence in the fatigue crack growth behavior for the fatigue tests unsubmitted to saline corrosion. On the other hand, the fatigue crack growth behavior for the tests under saline corrosion showed an increase in the crack closure parameter due to the appearance of the crack closure induced by oxides, which reduced the fatigue crack growth speed. This phenomenon depends on the deposition plane angle, which controls the martensite amount and consequently controls the level of corrosion/oxidation.

A high-cycle accumulation model for clay and its application to monopile foundations

A high-cycle accumulation (HCA) model predicting the accumulation of permanent strain or excess pore water pressure in clay under a large number of load cycles is presented. Data from an extensive laboratory testing program on kaolin under undrained cyclic loading has been analysed for that purpose. The influence of strain amplitude, void ratio, stress ratio, overconsolidation ratio and loading frequency on the accumulation rates is considered in the constitutive equations of the HCA model. The proposed model is validated first by the simulation of element tests. Subsequently, its application to offshore wind turbine foundations under long-term lateral cyclic loading is presented by the back-analysis of a centrifuge test on a monopile in soft clay. The results are in good accordance with the measurements in terms of pile displacement and bending moment versus number of applied cycles. It is concluded that the proposed model is feasible to describe the long-term behaviour of clay subjected to high-cyclic loading.

Effect of heat treatment on fatigue crack growth performance of AlSi10Mg aluminum alloy submitted to LPBF

Aluminum alloys are used in several industries, namely in the aeronautic and aerospace industries due to its good corrosion resistance and good mechanical strength/weight ratio. The optimization of fatigue crack growth resistance in AlSi10Mg aluminum alloy is a vital issue for safety-relevant components, which are designed to work for a large number of loading cycles before periodic inspections. An unclear subject is the benefit effect of heat treatments in the fatigue crack growth of AlSi10Mg aluminum alloy submitted to LPBF. Therefore, the current work purposes to analyze the effect of a heat treatment at low temperature on fatigue crack growth of AlSi10Mg aluminum alloy submitted to LPBF. Fatigue crack growth tests in Mode I are performed in compact tension (CT) specimens at two different conditions: as-build and heat treated at low temperature. The possible befits effect is analyzed, as well as the effect of the average stress on the fatigue crack growth. The crack closure parameter is studied in order to analyze the different fatigue crack growth behaviors, as well as the microstructure, hardness, and fractography. From this work, the main achievement is the microstructural transformations associated with the standard heat treatments (T6 and stress relived at 300 °C) are unfavorable to fatigue strength in the AlSi10Mg aluminum alloy submitted to LPBF, while the non-standard stress relief heat treatment, performed at a lower temperature, cause a benefic effect in the fatigue crack growth resistance.

A stiffness-based phenomenological model to predict the fatigue life of unidirectional CFRP laminates under tensile fatigue loadings

Fibre-reinforced composite materials can withstand large number of loading cycles compared to traditional materials. However, predicting the damage progress and strength loss in a composite structure due to fatigue is difficult because of the complex interaction of different failure mechanisms. This work investigates the decrease in the stiffness and strength in a high-performance undirectional CFRP laminate subjected to on-axis fatigue loads. A stiffness-based phenomenological model is proposed in order to evalute the damage growth due to fatigue through the longitudinal stiffness degradation. Assuming that the laminate ultimate strain is independent of the distributed damage caused by fatigue, the residual strength model can be deduced, or its integral form, the S-N curve. Thanks to this assumption, the residual stiffness model is related to the residual strength model, and thus it has reduced the experimental characterization of phenomenlogical-based approaches. The accuracy of the model is verified by comparing the experimental data against the derived S-N curves.

Abnormal grain growth in ultrafine grained Ni under high-cycle loading

Abnormal grain growth can occur in polycrystalline materials with only a fraction of grains growing drastically to consume other grains. Here we report abnormal grain growth in ultrafine grained metal in a rarely explored high-cycle loading regime at ambient temperature. Abnormal grain growth is observed in electroplated Ni microbeams with average initial grain sizes less than 640 nm under a large number of loading cycles (up to 109) with low strain amplitudes (< 0.3%). Such abnormal grain growth occurs predominantly in the family of grains whose <100> orientation is along the tensile/compressive loading direction. Micromechanics analysis suggests that the elastic anisotropy of grains dictates the thermodynamic driving force of abnormal grain growth, such that the lowest strain energy density of the <100> oriented grain family dominates grain growth. This work unveils a unique type of abnormal grain growth that may be harnessed to tailor grain microstructures in materials.

Determination of fatigue crack propagation thresholds for steel in presence of environmental effects

The experimental determination of the resistance to fatigue crack propagation in steel, particularly in the so-called near-threshold regime, is a crucial issue for safety-relevant components which are designed to operate for a large number of loading cycles before undergoing periodic inspections. This work summarizes the most relevant results of extensive experimental campaigns conducted at BAM and IPM over the last years, which have been devoted to the determination of fatigue crack propagation characteristics on medium and high strength steels. The influence of environment, oxide-induced crack closure and test methodologies in the near-threshold regime are discussed.

Discrete element modelling of rockfill railway embankments

There is a need of reducing the uncertainty in traffic loading-induced settlements within railway embankments. A previously developed model for unbound stone-based materials has been implemented for modelling rockfill embankments. Particles were represented by simple breakable tetrahedral clumps of spheres with four asperities each. Both corner breakage and particle splitting were allowed. Embankments with heights between 2 and 10 m were generated by successive dumping and compaction of layers of clumps on top of each other, mimicking the construction of real embankments. Cyclic loading of the embankments representing railway traffic, for both breakable and unbreakable assemblies, was carried out. Results show that the mechanical response is marked by a substantial degree of uncertainty exacerbated by particle degradation, especially for intermediate to high embankments. An analysis of particle rotation showed that particle rearrangement mostly accumulates in the top layers, resulting in a lack of influence of embankment height on settlements. Breakage, even being of (very) limited magnitude, had a statistically significant effect. Good agreement with common geostatic theories predicting horizontal pressures was also observed. Regarding resilient response, linear stiffening with embankment height is observed with a minor influence of breakage. All in all, it is shown that the specific scale, boundary and stress conditions of embankments results in a behaviour deviating from that observed under triaxial conditions. Therefore, the key contribution is showing that it is possible to realistically model high rockfill embankments under a large number of loading cycles and furthermore including degradation, something not attempted to date.Graphic abstract

Three-dimensional finite element analyses of tyre derived aggregates in ballasted and ballastless tracks

Scrap tyres are a significant source of pollution and pose a grave threat to the environment and human health. The present study aims to examine the application of Tyre Derived Aggregate (TDA) in a concrete slab track and ballasted track and compare its performance in both track forms. In this study, long-term performance of slab track and ballasted track subjected to train induced loading is demonstrated based on the three-dimensional finite element modelling. The most suitable constitutive hyperelastic model for TDA has been identified. Subsequently, the most suitable position for the location of TDA is determined for both track types. A comparative analysis between slab track and ballasted track, with and without TDA, is presented in terms of stress transfer, vibration reduction and displacement (elastic and plastic). It is shown that TDA helps in reducing up to 50% vibration levels of both track types. The influence of train speed and axle load on the vertical and horizontal displacement and stress response of both track forms is shown for a large number of load cycles. Overall, it is observed that the long-term performance of TDA is better in slab track compared to ballasted track.

Large triaxial test study on dynamic characteristics of round gravel

A series of large-scale drained dynamic triaxial tests were conducted on Nanning saturated gravel soil to investigate dynamic characteristics. The effects of relative density, dynamic stress amplitude, and the number of load cycles on the pore pressure, accumulation strain, and stress–strain hysteresis loops of saturated round gravel soil were analyzed. Experimental results indicated that the curves of accumulated axial strain with the number of load cycles present stable type. When the dynamic stress amplitudes were small, the increasing rule conforms to hyperbolic function. A linear relation between the parameter α in the hyperbolic function with the dimensionless DCR had been found. A double-lined model was set up to simulate the stress–strain hysteresis of saturated round gravel under a large number of load cycles. Then, results of the double-line model were validated against triaxial test results. The model was verified to be capable of predicting with accuracy the relationship between the stress–strain and area change behavior of saturated gravel soils. A particular feature of the model was that it only has three parameters than other models and applicable.

A p-y Analysis of Laterally Loaded Offshore-Well Conductors and Piles Installed in Normally Consolidated to Lightly Overconsolidated Clays

This paper presents a cyclic equivalent spring (p-y) model describing lateral soil resistance on offshore well conductors and piles in normally to lightly overconsolidated clays subjected to fatigue cyclic motions. Improved understanding and characterization of cyclic lateral soil response is critical in fatigue assessment of well conductors and piles subjected to dynamic fatigue loads. Key features of the model include nonlinear load-displacement behavior with stiffness degradation during cyclic loading. The model provides a full description of soil resistance during lateral loading, including an initial short-excursion monotonic loading stage, a transient stage of progressive degradation in stiffness from the first excursion, and a steady-state stage involving minimal changes in soil stiffness after a large number of load cycles. The model input parameters obtained from back-analysis of data derived from centrifuge tests on model conductors subjected to harmonic lateral loads are presented in this paper. This model has capabilities of simulating random load sequences. Fatigue damage in well conductors and piles arises from changes in axial and bending stresses, with the latter being more dependent on lateral soil response. Accordingly, the proposed model is evaluated primarily in terms of its ability to accurately predict bending moments when the spring model is used in conjunction with a laterally loaded soil-structure interaction model. The model successfully predicts the maximum change in cyclic bending moment (change in moment during a load reversal) and the location of the maximum cyclic moment along the conductor depth approximately within a 20% range. This performance evaluation was derived by comparing the model computations/predictions to the test data from the centrifuge program and validated within the tests displacement range of 0.1D. The current form of the model does not consider consolidation effects, which may significantly affect long-term loading predictions used in fatigue life assessments.

Contact resistivity due to oxide layers between two REBCO tapes

In a no-insulation (NI) REBCO magnet, the turn-to-turn contact resistivity (ρc) determines its quench self-protection capability, charging delay time and the energy loss during field ramps. Therefore it is critically important to be able to control a range of ρc values suitable for various NI magnet coils. In this work, we investigate two possibilities to control ρc: by controlling the oxide layer of the copper surface of REBCO tapes; and by controlling the oxide layer in stainless steel co-wind tapes. We used a commercial oxidizing agent Ebonol® C to treat the copper surface of REBCO tapes. The copper oxide layer was characterized by cross-sectional transmission electron microscopy (TEM) and x-ray photoelectron spectroscopy (XPS). The oxide layer formed in Ebonol® C at 98 °C for 1 min is Cu2O of 0.5–1 μm. The ρc between two oxidized REBCO is in the order of 35 mΩ cm2 at 4.2 K which decreases to 10 mΩ cm2 after 30 000 contact pressure cycles. The ρc increases but only by 5% at 77 K. We also investigated the effect of oxidation of stainless steel co-wind tape on ρc. The native oxides on 316 stainless steel tape as well as those heated in air at 200 °C–600 °C were examined by TEM and XPS. The native oxides layer is about 3 nm thick. After heating at 300 °C for 8 min and 600 °C for 1 min, its thickness increases to about 10 and 30 nm respectively. For the stainless steel tapes with about 10 nm surface oxides, pressure cycling for 30 000 cycles decreases ρc by almost 4 orders of magnitude. Whereas at 77 K, it only decreases by a factor of 3. For a surface with 30 nm oxide, the ρc decreases moderately with load cycles. The results suggest that for an oxidized stainless steel to achieve stable ρc over large number of load cycles a relatively thick oxide film is needed.

An explicit high-efficiency algorithm for simulating high-cycle fatigue behavior of metals

This article presents a direct and efficient algorithm for simulating high-cycle fatigue failure effects within the framework of a recently proposed elastoplastic model, in which fatigue failure effects of metals are incorporated as inherent constitutive features. Toward bypassing very time-consuming procedures in conducting numerical integrations of the elastoplastic rate equations for extremely large number of loading cycles, from the new model it is possible to derive an explicit expression for the fatigue life directly in terms of the stress amplitude. Numerical examples show that the new algorithm thus established is much more efficient than usual direct numerical procedures and that is particularly the case in simulating fatigue failure effects with very high cycle number.

Assessment of the rehabilitation benefits by finite element method

Cruciform fillet welded joints are found in many industrial applications. Welded structures are often subjected to load cycles due to loads that can vary in position and value. As a result of these loads, the phenomenon of fatigue occurs. Fatigue consists in the occurrence of failures, after applying a large number of load cycles, of loads below the yield limit of the material from which the structure is made. Fatigue mattempts have to be carried out over very long periods of time and are very expensive because of the expensive machines. A method by which the fatigue behavior of fillet welded joints can be predicted is the finite element method. The paper proposes to investigate by the finite element method, the fatigue life of some cruciform-fillet-welded specimens, making a comparison of two applied rehabilitation techniques.

Analysis of mechanical properties of transition segment of road and bridge based on high-strength foam concrete

The settlement difference in the transition section of road and bridge may lead to traffic accidents, which has many negative effects. Back filling of foam concrete behind abutment is a good method of treatment. In this study, a kind of high-strength foam concrete was designed for back filling of transition section of road and bridge, and the mechanical properties of the transition section of road and bridge were analyzed. It was found that only a large number of micro cracks grew in high-strength concrete under a large number of load cycles, and structural damage did not happen, indicating the high-strength foam concrete had high strength and long service life; the static base pressure was about 40 KPa, indicating a small burden on the structure. Under the vehicle load, the vertical displacement of the transition section of road and bridge with back filling of high-strength foam concrete behind abutment was about 0.7 m and the maximum vertical stress was about -40 KPa, which was significantly lower than that of the ordinary concrete, and the stability was favourable, indicating that the high-strength foam concrete had good vibration absorption effect. The analysis results verifies the value of the high-strength foam concrete as the backfill material of the transition section of road and bridge, providing some theoretical basis for its application and popularization.