Cyclic Loading Histories Research Articles

Post-Cyclic Drained Shear Behaviour of Fujian Sand under Various Loading Conditions

In offshore engineering, the sand beneath an embankment may be subjected to traffic loads, resulting in a series of engineering issues. The behaviour of the sand beneath the embankment may change under a long-term traffic load. A series of drained cyclic and post-cyclic monotonic triaxial tests were performed on Fujian sand with different relative densities. The drained strength and stress–dilatancy behaviours were studied. The results indicated that the normalised peak strength ratio after cyclic loading was greater than that without cyclic loading, depending on the cyclic stress amplitude, while the critical state strength seemed to be only slightly affected by the cyclic loading history. The dilative response of sand could also be influenced by cyclic loading-induced fabric. Under constant relative density conditions, the higher the cyclic stress amplitude applied to the sand sample, the larger the volume strain produced in the critical state. Furthermore, cyclic-induced fabric could be destroyed after 6% axial strain.

Towards the estimation of ultimate compression tolerance as a function of cyclic compression loading history: implications for lifting-related low back injury risk assessment

This study aimed to mathematically characterize the ultimate compression tolerance (UCT) as a function of spinal joint posture, loading variation, and loading duration. One hundred and fourteen porcine cervical spinal units were tested. Spinal units were randomly assigned to subthreshold cyclic loading groups that differed by joint posture (neutral, flexed), peak loading variation (10%, 20%, 40%), and loading duration (1000, 3000, 5000 cycles). After the assigned conditioning test, UCT testing was ­performed. Force and actuator position were sampled at 100 Hz. A three-­dimensional relationship between UCT, loading variation, and loading duration was most accurately characterized by a second order polynomial surface (R2 = 0.644, RMSE = 1.246 kN). However, distinct UCT responses were observed for flexed and neutral postures. A single second-order polynomial most accurately characterized the UCT – loading duration relationship (R2 = 0.905, RMSE = 0.718 kN) for flexed postures. For neutral joint postures, separate second-order polynomial equations were developed to characterize the UCT – loading duration relationship for each variation group (R2 = 0.618–0.906, RMSE = 0.617 kN–0.746 kN). These findings suggest that UCT responses are influenced by joint posture and these data may be used to inform ergonomic tools for the assessment of low back injury risk during occupational lifting.

Response of lightly overconsolidated clay under irregular cyclic loading and comparison with predictions from the strain accumulation procedure

Offshore wind turbine foundations are designed to withstand environmental loads from the wind and waves, both of which are cyclic in nature. The current design methods consider site-specific cyclic load histories and typically require these to be translated from a time–load history with irregular characteristics to an idealised history of parcels of cycles with uniform amplitude and constant average load. The Rainflow counting method is typically used for this translation. The idealised history is then applied in a design method, for example the strain accumulation method. These methods assume that the idealised load history will give approximately the same effect on the soil as the irregular time history. This paper investigates this assumption by a laboratory test programme where the soil response under realistic irregular loading is compared with the response under idealised loading. The laboratory programme consists of cyclic direct simple shear tests on lightly overconsolidated North Sea clay. For most problems, the test results suggest that the assumption is reasonable and represents a convenient simplification for practical design. However, for load histories with large average load, prediction of permanent strain based on idealised histories may underestimate the strain observed in tests with irregular time histories.

Ratcheting evaluation of pressurized straight pipe using Ahmadzadeh–Varvani hardening rule

This study evaluates the Ahmadzadeh–Varvani (A-V) hardening rule for the ratcheting behavior of pressurized straight pipe made of austenitic stainless steel Z2CND18.12N under bending loading and vertical displacement control, respectively. Based on the quasi-three point bending apparatus, the straight pipe specimen is placed in a nearly horizontal position, and the applied displacement to the specimen achieves cyclic bending. The displacement is called as vertical displacement in this study. Firstly, the A-V model is implemented into ABAQUS with the radial return scheme with sub-increments; and the consistent tangent modulus is derived for A-V model, and gives quadratic convergence for the solution. And then the numerical calculation is developed to simulate ratcheting behavior of pressurized straight pipe. The influences of internal pressure, cyclic bending loading or cyclic vertical displacement, loading history and control modes on ratcheting strain of straight pipe are studied, respectively. By comparison with the experimental data, it is found that the predicted results of A-V model are in good agreement with the experimental data of pressurized straight pipe.

Coupled sliding–decohesion–compression model for a consistent description of monotonic and fatigue behavior of material interfaces

A thermodynamically consistent model proposed in this work introduces a generative symbolic framework for computational components, which can capture the inelastic behavior of interfaces with 3D kinematics in response to monotonic, cyclic, and fatigue loading histories. It contributes to a long list of existing cohesive zone models by introducing novel forms of potentials for free energy, threshold function, and dissipation to deliver the following model properties: (i) the evolution equations derived from the potentials are linked in such a way that damage develops along with the cumulative measure of plastic sliding, (ii) the convex, continuous, and smooth shape of the threshold function introduced in the effective stress domain enables a general and efficient time integration that automatically handles unloading and reloading, and (iii) the non-associative flow potential includes a scalable degree of coupling between normal and tangential damage evolution. The studies performed in the paper demonstrate that these model ingredients lead to a consistent coverage of arbitrary non-proportional loading scenarios in tangential and normal directions. For monotonic loading, the presented examples illustrate the ability of the model to reproduce the shear dilatancy, pressure sensitivity including the vertex effect, stiffness recovery in compression, and abrasion due to sliding. For cyclic fatigue loading, the studies show that the model reflects the link between the hysteretic behavior and the fatigue damage evolution. This link constitutes the basis for a physically sound description of fatigue degradation along material interfaces. It manifests itself in the presented energy breakdown with distinguished fractions of energy release due to damage and plasticity ascribed to normal and tangential directions. Two calibration and validation examples using pull-out tests exposed to monotonic and cyclic loading are provided to show the applicability of the model for the characterization of the bond between steel bars and concrete. A publicly available implementation using a computer algebra system (CAS) is provided in the form of an interactive Jupyter notebook to document the reproducibility of the results.

Ratcheting and low cycle fatigue of nickel-based alloy GH3536 formed by selective laser melting at 800 °C

ABSTRACT The cyclic uniaxial stress-controlled ratcheting behaviour of GH3536 formed by selective laser melting (SLM) was tested at 800 °C. The effects of different stress rates and building orientations of 0°, 45° and 90° were investigated. Results present that the ratcheting behaviour of SLM GH3536 at 800 °C exhibits significant stress rate dependence. Moreover, the accumulated ratcheting strain increasing with increasing the stress amplitude and stress rate. It is noted that the building orientation angle of the specimen has an important influence on the mechanical performance. The 45° specimen in the experimental conditions has the greatest low cycle fatigue life. The ratcheting evolution over the whole cyclic load history can be divided into three stages. The relationship between steady ratcheting strain range and low cycle fatigue life was established.

Constitutive model for cyclic behavior of mild steel under various strain amplitudes

To enable accurate simulation of steel material under various loadings, cyclic behaviors of mild steel Q235 were extensively investigated through experimental analysis and constitutive modeling in this work. The studied steel was tested under cyclic loading protocols with constant strain amplitudes and variable strain amplitudes. The evolutions of stress amplitude, effective stress and back stress components, and elastic stiffness during the whole cyclic loading history are quantitatively scrutinized. The results demonstrate that mild steel exhibits cyclic capacity depended strongly on strain amplitude. Besides, the strain history effect depends on both the historical maximum strain amplitude and the target unloading strain amplitude, indicating the existence of a critical state for the incomplete evanescence of strain memory surface to be activated. An abrupt drop of effective stress at onset of plastic straining is observed in experimental tests and contributes to the early re-yielding of the reversed curve. Furthermore, elastic stiffness in the cyclic loading phase differs much from that in initial tension. Based on those observations, a new constitutive model with robust ability to predict hysteretic behavior of structural steel under complex loading paths is proposed. This model considers the strain range dependence and the strain history dependence effects. In addition, a new method to identify the yield points of hysteretic loops is proposed in this paper to enable simulations of back stress with the Armstrong-Frederick hardening model without considering the strain range dependence effect. The validity of this model is demonstrated through comprehensive comparison between simulated results and experimental data.

Effects of prior non-liquefying undrained cyclic loading on sand liquefaction resistance via discrete element analysis

Earthquake cases demonstrate that prior earthquakes have critical impacts on the liquefaction resistance of sandy soils during subsequent earthquakes. Most previous studies focused on the influence of previous liquefaction events on soil reliquefaction resistance, while few have investigated the effects of prior non-liquefying undrained cyclic loading history on the liquefaction resistance. In this study, discrete element method (DEM) was employed to simulate the liquefaction behaviors of triaxial specimens reconsolidated from non-liquefying states during prior undrained cyclic tests with various cyclic stress ratios (CSRs). Results showed that prior non-liquefying loading could increase or decrease the sand liquefaction resistance, which significantly depended on the CSR of the prior loading and the excess pore pressure ratio (ru) caused during the prior loading. Specimens that were previously loaded under larger CSRs had stronger anisotropy and fewer interparticle contacts after reconsolidation and thereby exhibited lower liquefaction resistance, while specimens that were reconsolidated from prior tests with smaller CSRs had weaker anisotropy and more interparticle contacts and thus exhibited obviously higher liquefaction resistance. Sand liquefaction resistance after a prior non-liquefying loading was well correlated with initial anisotropic degree and mechanical average coordination number.

Kinematic Hardening Model Comparison of Square Hollow Section Under Cyclic Bending

This study compares the different linearity of the kinematic hardening model of the Square Hollow Section (SHS) under cyclic bending loading. Four specimens of a simple support beam cyclically tested in previous research are listed as hot-rolled, hot-finished, and two cold-formed. Using the bilinear, multilinear, and Chaboche models, each specimen is modeled in kinematic hardening. The variables or node sets for each linearity model are estimated using tensile test data, and Chaboche variables are obtained using the least-square fitting method. Each linearity model for each specimen is built-in FEA using a shell model. The numerical model applied the same cyclic loading history as the previous test. The numerical analysis comparison concluded that Chaboche and the multilinear kinematic model generate the expected result fitted to test hysteresis of cold-formed one and cold-formed 2 SHS, but the bilinear models are not fitted. Moreover, all kinematic models are not fit for the hot-rolled and hot-finished SHS compared to the test hysteresis. So, for hot-rolled and hot-finished SHS, the combined hardening is suggested; there is a possibility it is because of the lower yield ratio that both sections have. Overall, during a cyclic bending analysis of cold-formed SHS, multilinear or Chaboche models are preferable if the data is limited.

Experimental Study on Progressive Damage Evolution in Rocks Subjected to Post-peak Cyclic Loading History

Abstract Because of the release of in situ rock stress, rocks surrounding deep underground excavations are mostly driven into a post-peak damage state. Thus, investigations on cyclic loading-induced damage of rocks are of paramount significance in terms of the long-term stability of rock structures. In this study, using a damage-controlled testing method, the effect of post-peak cyclic loading on the failure behavior of different rock types was comprehensively evaluated. This investigation revealed that post-peak cyclic loading imposes no significant influence on the overall failure behavior of rocks. The evolution of damage variables also indicated that the large portion of axial strain damage (Da) occurs during the first cycle at the peak strength, whereas lateral strain damage (Dl) evolved more rapidly than Da did in the post-peak regime under further loading and unloading cycles. The cumulative permanent axial strain (∑εap) evolved nonlinearly with the axial stress ratio (σi/σa−peak) in the post-peak regime, which was manifested as sparse-dense-sparse hysteretic loops. A rapid reduction in the crack damage stress ratio was observed for rocks in the initial sparse hysteretic loops, which was followed by a lower decrease rate in the subsequent dense hysteretic loops, and an almost constant value was finally reached in the last sparse hysteretic loops. Furthermore, tangent Young’s modulus (Etan) and Poisson’s ratio (υ) evolved in three main stages: One, Etan first increased and then decreased in the initial sparse hysteretic loops, while υ continuously increased, representing significant deformation in the lateral direction. Two, Etan decreased in the dense hysteretic loops, while υ increased at a higher rate for stronger rocks because of the decrease in Da accumulation. Three, the increase rate of υ declined in the second set of sparse hysteretic loops, and Etan decreased until complete failure occurred.

Influence of Loading Conditions on the Mechanical Performance of Multifilament Coreless UHMWPE Sutures Used in Orthopaedic Surgery.

This work studies the influence of loading velocity and previous cyclic loading history on the stiffness and strength of a multifilament coreless ultra-high-molecular-weight polyethylene (UHMWPE) surgical suture. Thread samples (n = 8) were subjected to a load-to-failure test at 0.1, 0.5, 1, 5, and 10 mm/s without previous loading history and after 10 cycles of loading at 1–10 N, 1–30 N, and 1–50 N. The experimental data were fitted to mathematical models to compute the stress–strain relation and the strength of the suture. The bilinear model involving two stress–strain ratios for low- and high-strain intervals was the best fit. The ratio in the low-strain range rose with loading speed, showing mean increases of 5.9%, 6.5%, 7.9%, and 7.3% between successive loading speeds. Without a previous loading history, this ratio was less than half than that at high strain. However, 10 cycles of 1–30 N or 1–50 N significantly increased the stress–strain ratio at a low strain level by 135% and 228%, respectively. The effect persisted after 2 min but vanished after 24 h. No influence was found on the suture strength. In conclusion, the stiffness of the studied suture was influenced by the strain level, loading velocity, and recent cyclic loading history. Conversely, the suture strength was not affected.

Experimental study on uniaxial ratchetting of VHB 4910 dielectric elastomer

In this work, a series of uniaxial cyclic tests of VHB 4910 dielectric elastomer were carried out to investigate the uniaxial ratchetting and its dependence on the stress level, stress rate, peak/valley stress hold and loading history. The results show that in the uniaxial stress-controlled cyclic tests, VHB 4910 produces obvious ratchetting, and the higher the applied stress level and the lower the stress rate, the more remarkable the ratchetting is. Compared with the experimental results of pure-shear cyclic deformation, the apparent modulus of VHB 4910 during uniaxial cyclic deformation is lower and the dissipation is smaller. In addition, the uniaxial ratchetting of VHB 4910 is also affected by the peak/valley stress hold and loading history. The peak stress hold will promote the generation of ratchetting, but the valley stress hold will hinder the increase of ratchetting strain. The cyclic loading history with a higher mean stress will inhibit the development of ratchetting in the subsequent cyclic loading case with lower mean stress.

Emerging anchored FRP systems bonded to steel subjected to monotonic and cyclic loading: A numerical study

Recently, the study of the bond behaviour of hybrid joints has increased due to their application in different industries. Their main purpose is to obtain lightweight but strong, durable structures. In addition, in some industries such as the automotive industry, those requirements may facilitate the construction of vehicles that have lower carbon dioxide emissions. Although the knowledge on the bond behaviour of hybrid bonded joints under monotonic loading is sufficient, the knowledge on the cyclic bond behaviour needs to be improved. The present work aims to mitigate that gap by proposing a numerical model in which the cyclic bond performance between a Carbon Fiber Reinforced Polymer (CFRP) bonded to a steel substrate can be analysed. The results provided by the Externally Bonded Reinforcement (EBR) are used as reference data. These other simulated bonding techniques cover cases where the CFRP is anchored to the substrate in different ways, which are becoming more popular, namely by: (i) linearly increasing the width of the CFRP; (ii) using the mixed adhesive concept (two solutions were considered); (iii) using a steel plate on top of the CFRP strip; and (iv) assuming no interfacial slips at the CFRP unpulled end, which is intended to simulate a perfect anchorage. Compared to the simulations carried out under monotonic loading, the simulations with the adopted cyclic loading history (loading/unloading cycles), allowed us to observe a degradation of the bond strength of the joints with the number of cycles. However, if the overlapped bonded joint is long enough, the strength of the CFRP-to-steel joints is not affected. Excluding the numerical specimens with the perfectly anchored CFRP, i.e. with an “ideal” anchorage, the length of the other adopted anchorages affected either the strength or the ductility of the joint, whether subjected to a monotonic or to the adopted cyclic loading protocol.

Local buckling behaviour of high-strength steel tubular columns subjected to one-sided cyclic loading and implications in seismic design of steel MRFs

After yielding, steel structures progressively exhibit an asymmetrical hysteretic behaviour under earthquakes biased in one direction (ratcheting effect). This response may be favourable to structural components because of the absence of symmetrical cyclic loading reversals. To evaluate the inelastic behaviour of components to asymmetrical cyclic loading, this study develops a set of one-sided cyclic loading histories for columns on the basis of a parametric study on the asymmetrical hysteretic behaviour of steel moment-resisting-frames (MRFs). Experimental and computational results indicate that steel tubular columns subjected to one-sided cyclic loading may exhibit 15%–71% higher ductility compared with that under symmetrical cyclic loading showing adequate resistance to local buckling initiation and sufficient ductility afterwards. These reduced ductility demands may permit the use of high-strength steels in energy dissipative zones, such as high yield-to-tensile strength ratio (Y/T) steels, resulting in reduced material consumption and more economical seismic design of buildings. The above findings are utilized in the seismic design of a MRF employing high Y/T steel, which enjoys almost the same lateral strength as a corresponding conventional steel MRF but nearly 25% smaller cross-sectional area in columns. Nonlinear time-history analyses revealed that the high Y/T MRF behaved elastically under frequent events, whilst the ground floor columns of the conventional MRF yielded. Under rare seismic events, the average story drift ductility demand for the high Y/T MRF was only 1.77, while for the conventional MRF was 2.57. The former MRF successfully resisted the earthquake loads without experiencing local buckling in columns.

NUMERICAL ANALYSIS ON THE BOND PERFORMANCE OF DIFFERENT ANCHORED JOINTS UNDER MONOTONIC AND CYCLIC PULL-PUSH LOADING

The research on the bond behaviour of hybrid joints has increased in recent years as a result of their widespread use in many industry sectors that have the goal of building lightweight structures with good long-term performance. Although the bond behaviour of hybrid bonded joints under monotonic load is now well understood, their bond behaviour under cyclic loading still has to be improved. The goal of this study is to mitigate that gap by presenting a series of numerical simulations of Carbon Fiber Reinforced Polymer (CFRP) bonded onto a steel substrate through the use of the Distinct Element Method (DEM). Different bonding methods are considered and the results provided by the Externally Bonded Reinforcement (EBR) are used as reference. The other simulated bonding techniques included the linear increase of the width of the CFRP composite, the assumption of a mixed adhesive in which two solutions were investigated, and using an additional steel plate bonded on the top of the CFRP. The simulations that followed the selected cyclic loading history (loading/unloading) allowed us to notice a decrease in the joint bond strength with the number of cycles when compared to the monotonic loading simulations. However, the strength of the CFRP-to-steel joints was not affected if the overlapping bonded joint had a long length. On the other hand, the simulations of the CFRP-to-steel joints with a short bonded length revealed that the strength and ductility of these specimens are severely affected whether subjected to a monotonic or the adopted cyclic loading history.

Fractional-order bounding surface model for unsaturated soils under cyclic loading

Modelling of unsaturated soil stress–strain relationships under cyclic loading with constant matric suction is a topic that is poorly addressed by the current literature. Using the theoretical framework of the bounding surface plasticity and Barcelona basic model (BBM) combined with the concept of fractional accumulated strain rate, a bounding surface model for accurately describing the unsaturated soil stress–strain relationship with constant matric suction is established here. The fractional accumulated strain rate is introduced to consider the influence of cyclic loading history. The movable mapping centre rule is used to describe the hysteresis characteristics of the dynamic stress–strain curve during the unloading process. The shape of the dynamic stress–strain curve can be described reasonably by considering the cyclic loading process as the three processes of initial loading, unloading, and reloading. The cyclic loading test data of unsaturated silt, sand, and lean clay with constant matric suction is used for parameter calibration and model validations. Results show that the proposed model can accurately capture the dynamic stress–strain relationship of unsaturated soil with constant matric suction.

A deviatoric tensile-based critical plane model to predict peak/mean normal stress effects in multiaxial fatigue

This work aims to improve the modeling of peak/mean normal stress effects on multiaxial fatigue lives, applying a deviatoric strain-life model based on the critical plane approach to predict the initiation of tensile-driven cracks. Based on Kujawski’s deviatoric multiaxial fatigue damage parameter, this model assumes the peak deviatoric stress normal to the crack plane controls these effects. Tensile damage models based on deviatoric parameters can solve the main issue with Smith-Watson-Topper’s pioneer model, which is the prediction of no damage in cyclic compression-compression load histories. A calibration procedure based on Coffin-Manson parameters is presented, without the need for additional data-fitting constants to predict peak/mean stress effects. The calibrated multiaxial model is then compared with other tensile-based models for five structural metallic alloys, involving an extensive dataset with 312 uniaxial, torsion, and tension–torsion tests. It is found that the deviatoric formulation is able to explain the fatigue crack initiation behavior under highly compressive mean stresses, including the challenging case of compression-compression loadings. Under zero or positive mean stresses, this formulation provides similar predictions as the Smith-Watson-Topper model, reproducing the observed peak stress effects. Uniaxial versions of this deviatoric model are also presented and calibrated, showing that the minimum instead of the peak stress controls the damage parameter in uniaxial fatigue tests under highly compressive mean loads.

Structural response of steel lined pipes under cyclic bending

Motivated by reeling installation of mechanically-lined offshore steel pipes, the present paper investigates the structural performance of a bi-material lined pipe under cyclic bending, using advanced finite element tools. A three-dimensional finite element model is developed, simulating the manufacturing process of the lined pipe in the first stage of the analysis, followed by the cyclic bending response of the lined pipe in the second stage. Five bending cycles are considered, representing the two installation cycles and three additional cycles of a failure-repair scenario. The loading cycles impose a bending curvature range corresponding to the strains developed during a typical reeling installation process. Different loading patterns are considered and their effect on liner performance are investigated. The results show that the application of reverse (negative) curvature during the loading cycles, representing the straightener, has a significant influence on the wrinkle size of the liner developed at the two critical generators, and its rate of increase, compared with cyclic bending patterns with non-negative curvature. Numerical results on imperfection sensitivity are obtained, considering two types of imperfection of the liner pipe. In addition, the structural performance of liners with different thickness is examined, and the results show that there exists a minimum value of wall thickness, above which the liner does not exhibit local buckling at the end of the cyclic loading history. The beneficial effect of internal pressure on liner cyclic response is also verified, especially for thin-walled liners, preventing the development of wrinkles. Finally, the effect of manufacturing process is examined, showing the superior structural performance of partially-heated lined pipes, with respect to fully-heated lined pipes, and to lined pipes manufactured by purely-mechanical process.

Damage fatigue simulation in quasi-brittle material using a version of discrete element method

The simulation of the damage process is a challenge for researchers nowadays. In ductile materials, the continuum damage mechanics is based on the plasticity framework, but quasi-fragile materials have some characteristic phenomena such as localization and size effects, among others, that cannot be taken into account with this approach. The discrete element method has demonstrated considerable success in simulating the damage process in this kind of material. One of the advantages of this approach consists of capturing the transition between continuum and cracked regions in a natural way. In the first part of this work, extensive validation of the proposed numerical method is done, where fissures are introduced in a lattice structure. The variations of the mechanical properties are evaluated and compared to the analytical responses based on continuum damage theory. In the second part, an application considering the damaging process due to cyclic load history simulates a fatigue process with special attention on the transition between the continuum to macro-cracks nucleation. Finally, in the framework of quasi-brittle materials, a discussion about the performance of this approach in quantifying damage is presented.

A stress-weighted ductile fracture model for steel subjected to Ultra Low Cycle Fatigue

A new criterion is proposed to simulate the initiation of ductile fracture due to Ultra-Low Cycle Fatigue (ULCF). Building on previous research, the new fracture criterion broadens the scope of ULCF models to account for a broader range of multi-axial stress and strain states that may be encountered in steel structures. The model formulation, supported by observations from finite element plasticity simulations of void growth and fractographic analyses of fracture surfaces, describes damage accumulation as a function of plastic strain, stress triaxiality, and the Lode stress parameter. The damage rate model is integrated over arbitrary cyclic loading histories of local strains and stresses to predict ULCF fracture. The proposed criterion (termed the Stress Weighted Ductile Fracture Model – SWDFM) is supported by a series of 66 coupon scale experiments on two grades of low-carbon structural steel (A572 and A36). These tests interrogate a range of positive and negative stress triaxiality with absolute values between 0.1 and 1.6, Lode stress parameters between 0 and 1, and monotonic and cyclic loading histories. The SWDFM criterion, which requires the calibration of only two material parameters for the materials investigated in this study, is evaluated against the experimental test data using an average-error assessment as well as a cross-validation analysis. Three other ULCF rupture criteria are similarly assessed and compared. The SWDFM is shown to accurately predict ULCF initiation over a wide range of stress states and loading histories, suggesting that the model represents well the micro-mechanical mechanisms of ULCF.