Cyclic Shear Deformation Research Articles

Visco-Hyperelastic Constitutive Modeling for High-Damping Rubber Materials During Combined Quasi-Static Compression–Cyclic Shear Deformation Process

High-damping rubber materials utilized in high-damping rubber isolation bearings are frequently subjected to multiple deformations during the occurrence of earthquakes. Typically, large combined compression–shear deformations of the material could potentially cause compressive shear damage to rubber bearings. During this process, visco-hyperelastic properties of rubber materials will greatly change, which would significantly impact the seismic performance of rubber bearings. Thus, to give out a deep insight into their variations, it is necessary and urgent to develop a high-performance numerical method to investigate this process. This paper proposed a visco-hyperelastic constitutive modeling approach for high-damping rubber materials based on the experimental assessment of combined quasi-static compression–cyclic shear deformation process. Within the thermodynamic framework, the Clausius–Duhem inequality associated with the intrinsic dissipation of the material was firstly derived in accordance with the Lagrangian formulism. Then, stress–strain relations were obtained upon considering the occurrence of entropy production due to viscous dissipation. In the model, Stumpf–Marczak strain energy density function, which satisfies the Baker–Ericksen (B–E) inequality, was harnessed to describe the hyperelasticity of the material. By introducing higher orders of strain and strain rates and taking their couplings into account, a generalized viscous dissipation potential was proposed to capture nonlinear strain and strain rate-sensitivity effects of the material. To identify constitutive parameters, the deformation gradient was particularized for the combined quasi-static compression–cyclic shear deformation process. And, an inverse identification procedure was carried out at different levels of compression stress. The prediction results revealed that the proposed model exhibits remarkable prediction ability and adaptivity for different rubber materials during this process. Several new insights were highlighted on the variations of visco-hyperelastic characteristics of high-damping rubber materials with respect to the compression stress. The accuracy of the model was further validated by design parameters including initial shear modulus, secant shear modulus and equivalent viscous damping factor. This work could provide a fundamental guideline for the optimization and reliability analysis of high-damping rubber isolation bearings used in the field of seismic engineering.

Critical behavior of thick rubber bearings under compression and shear

Thick rubber bearings (TRBs) are used for seismic isolation as well as for subway-induced vertical vibration mitigation. Under earthquake ground shaking, TRBs typically undergo large horizontal displacements that lead to a reduction of their vertical bearing capacity, which should be carefully evaluated during design. This study investigates the performance of TRBs under compression and compression-shear loading. Eight full-scale TRB specimens were designed and tested. The test results show that increasing the axial load increases the compressive stiffness of TRBs. During compression-shear loading, TRBs under design level axial loads failed due to rubber rupture at shear strain γ > 350 %, while under higher axial loads, they failed because of instability at γ ＜ 300 %. In addition, in cyclic shear deformation under axial loads larger than twice the design level axial load, the TRBs exhibited negative stiffness at the unloading branch of the F-u loop. The effective damping ratio significantly increased with increased axial load. Then, the test data were used to validate existing mechanical models for the prediction of the compression-shear behavior of elastomeric bearings. Existing analytical models were modified by accounting for the compressive stiffness change due to increased axial loads, leading to more accurate prediction. Finally, models for the critical load of TRBs under zero and lateral displacement were examined and improved.

Energy-Based Assessment of Liquefaction Behavior of a Non-Plastic Silt Based on Cyclic Triaxial Tests

Earthquakes cause cyclic shear deformations in soil and build-up of excessive pore water pressure as a result of undrained loading, accompanied with rearrangement of soil particles and degradation in stiffness of the soil due to decrease in effective stresses. During loading, the onset of soil liquefaction is defined as a stress state in which the excess pore water pressure is equalized to the total stress. From this point of view, assessment of the pore water pressure development pattern under cyclic loading has been one of the most salient research topics in geotechnical and earthquake engineering. In this study, results of a series of cyclic triaxial tests on non-plastic silt specimens consolidated under 100 kPa effective isotropic consolidation pressure were used to question the modelling ability of pore pressure development models previously proposed for sands. Tests were performed on specimens of 6 different initial relative densities (Dr) ranging between 30-80% and 10 different cyclic stress ratios (CSR). The key parameters of pore water pressure development and shear deformation in the energy-based model used are relative density, cyclic stress ratio and number of cycles. The results revealed that, these energy-based models have a strong potential in evaluation of pore water pressure development pattern of non-plastic silts. Test results also show that the increase in relative density and decrease in CSR causes a ladderlike behavior among pore water pressure and cyclic shear strain, which is relevantly rendered by energy-based models.

Experimental Study and Seismic Response Evaluation of Chlorobutyl Rubber-Based Viscoelastic Dampers

Conventional viscoelastic devices often use high-damping elastomeric pads, typically made of patented formulations, that are bonded to steel plates. The response properties of these pads under cyclic shear deformations directly influence the load-deformation hysteretic response of the device. Chlorobutyl (CIIR) is a high-damping rubber commonly used in industrial applications. However, this study found that the damping properties of a typical CIIR rubber compound are insufficient for effective structural seismic mitigation at ambient temperatures above 0°C. The goal of this study was to develop a new composite of CIIR, referred to as modified CIIR, with improved damping properties and to compare its performance with that of the reference CIIR rubber. In the first phase of the experimental studies, the viscoelastic characteristics of the reference and modified CIIR rubber materials were evaluated using dynamic mechanical thermal analysis (DMTA) in tension mode. Prototype viscoelastic damper devices were then fabricated from both the reference and modified CIIR rubber materials and subjected to cyclic shear tests at room temperature and various loading frequencies. The results showed that the modified CIIR rubber exhibited significantly improved effective damping compared to the reference CIIR. The final component of this study involved investigating the seismic response of a 2D frame structure equipped with prototype dampers made from both reference and modified CIIR materials, using nonlinear time-history analyses. The analysis results indicated that the modified CIIR rubber can be effectively utilized in the seismic response mitigation of structures.

Fatigue failure of amorphous alloys under cyclic shear deformation

The accumulation of plastic deformation and flow localization in amorphous alloys under periodic shear are investigated using molecular dynamics simulations. We study a well-annealed binary mixture of one million atoms subjected to oscillatory shear deformation with strain amplitudes slightly above a critical value. We find that upon approaching a critical strain amplitude from above, the number of shear cycles until the yielding transition is well described by a power-law function. Remarkably, the potential energy at the end of each cycle as a function of the normalized number of cycles is nearly independent of the strain amplitude, which allows for estimation of the fatigue lifetime at a given strain amplitude. The analysis of nonaffine displacements of atoms elucidates the process of strain localization, including irreversible rearrangements of small clusters until the formation of a system-spanning shear band.

Analytical investigation of the finite viscoelastic model proposed by Simo: critical review and a suggested modification

Rubber components such as engine or suspension bearings are loaded during operation with large deformations and high-frequency loads. In industrial applications, finite element analysis software is therefore needed to simulate and predict the behaviour of these components under different scenarios of loading conditions. The usage of such software requires the user to be aware of certain limitations and shortcomings in the implemented material models. In this paper, the stresses as well as the storage and loss modulus are calculated analytically for an example of cyclic simple shear deformations. The analysed material model was firstly proposed by Simo and is available in Abaqus version 2018 for viscoelastic materials under finite strains. The analytical solution is used to highlight the non-physical response of the model under certain loading conditions. A modification of the modelling approach is then proposed to avoid such limitations. The modified model is implemented in the Abaqus software using a user material subroutine (UMAT). The behaviour of the modified model and the original Abaqus model are compared using an example of tie rod under different loading conditions. It is shown that with the suggested modification, reasonable results are obtained and the non-physical responses are eliminated.

Relaxation dynamics in amorphous alloys under asymmetric cyclic shear deformation

The influence of cyclic loading and glass stability on structural relaxation and yielding transition in amorphous alloys was investigated using molecular dynamics simulations. We considered a binary mixture cooled deep into the glass phase and subjected to cyclic shear deformation where strain varies periodically but remains positive. We found that rapidly cooled glasses under asymmetric cyclic shear gradually evolve towards states with lower potential energy and finite stress at zero strain. At the strain amplitude just below a critical value, the rescaled distributions of nonaffine displacements converge to a power-law decay with an exponent of about -2 upon increasing number of cycles. By contrast, more stable glasses yield at lower strain amplitudes, and the yielding transition can be delayed for hundreds of cycles when the strain amplitude is near a critical value. These results can be useful for the design of novel thermo-mechanical processing methods to improve mechanical and physical properties of metallic glasses.

Monotonic and cyclic properties of silty sand and sandy silt for foundation design of offshore windfarms

This paper presents results of a series of monotonic and cyclic direct simple shear laboratory tests performed on reconstituted samples of two silty sands and one sandy silt. The laboratory program aimed to determine the cyclic shear strength and deformation characteristics of soils to be used in the offshore wind turbine foundation design. Various cyclic contour diagrams including cyclic shear strength and average and cyclic shear strains for different number of cycles were provided. The effect of strain rate for drained monotonic tests and overconsolidation ratio effect on both monotonic and cyclic properties were discussed. This study indicated that the fines content plays an important role in static and cyclic shear strength of silty soils, in addition to mineralogy and coefficient of uniformity.

Annealing glasses by cyclic shear deformation.

A major challenge in simulating glassy systems is the ability to generate configurations that may be found in equilibrium at sufficiently low temperatures, in order to probe static and dynamic behavior close to the glass transition. A variety of approaches have recently explored ways of surmounting this obstacle. Here, we explore the possibility of employing mechanical agitation, in the form of cyclic shear deformation, to generate low energy configurations in a model glass former. We perform shear deformation simulations over a range of temperatures, shear rates, and strain amplitudes. We find that shear deformation induces faster relaxation toward low energy configurations, or overaging, in simulations at sufficiently low temperatures, consistently with previous results for athermal shear. However, for temperatures at which simulations can be run until a steady state is reached with or without shear deformation, we find that the inclusion of shear deformation does not result in any speed up of the relaxation toward low energy configurations. Although we find the configurations from shear simulations to have properties indistinguishable from an equilibrium ensemble, the cyclic shear procedure does not guarantee that we generate an equilibrium ensemble at a desired temperature. In order to ensure equilibrium sampling, we develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial generation step and has acceptance probabilities that depend not only on the change in internal energy but also on the heat dissipated (equivalently, work done). We show that such an algorithm, indeed, generates an equilibrium ensemble.

Effect of deformation twinning on microstructure refinement of Fe-38Mn alloy during friction stir processing

The effect of deformation twinning on microstructure refinement was investigated for Fe-38Mn alloy during friction stir processing. It was proved that the friction stir processing microstructure of Fe-38Mn alloy was gradient distribution. The stir zone contained both recrystallized grains and fine deformed grains with average grain size of about 15 µm, and the proportion of twin boundaries in the deformed grain zone was up to 35%. Moreover, the cyclic multidirectional shear induced micro-shear bands and sub-grains with high density dislocations, as well as plentiful deformation twins. The microstructure refinement of Fe-38Mn alloy during friction stir processing resulted from the dynamic recrystallization mechanism and twinning mechanism. In addition, the cyclic multidirectional shear deformation enhanced the deformation twinning effect, so that the microstructure refinement process was completed quickly and effectively. The above works indicate a dynamic mechanism of microstructure refinement in term of the deformation twinning during friction stir processing.

Molecular dynamics study of fatigue behavior of nickel single-crystal under cyclic shear deformation and hyper-gravity condition

Dynamic mechanical properties play an essential role in governing the intrinsic fatigue behavior of superalloys. In this work, [001](010), [110](−110), and [101](010) pre-existing center cracks model of nickel single crystals under increasing cyclic shear deformations were studied by molecular dynamics simulations. More importantly, we introduced three hyper-gravity forces, i.e. 3 × 1012 g, 4 × 1012 g, and 5 × 1012 g, during the fatigue deformation to simulate the high-speed rotation of the blade. The stress intensity factor for the first dislocation nucleation indicates that the critical stress is strongly dependent on the hyper-gravity intensities and temperatures. The fatigue life decreased rapidly with the elevated hyper-gravity strength. Moreover, the [001](010) crack propagation shows a brittle-to-ductile transition at temperatures below 300 K and is suppressed at high temperatures. The crack length in the relation to hyper-gravity intensities is discussed and shows anisotropy along the direction of hyper-gravity. No crack propagation is observed in [110](−110) and [101](010) central crack models.

Mechanical annealing and yielding transition in cyclically sheared binary glasses

The effect of cyclic shear deformation on structural relaxation and yielding in binary glasses was examined using molecular dynamics simulations. We studied a binary mixture slowly cooled from the liquid phase to about half the glass transition temperature and then periodically deformed at small strain amplitudes during thousands of cycles. We found that the potential energy decays logarithmically upon increasing number of cycles. The analysis of nonaffine displacements revealed that the process of mechanical annealing proceeds via intermittent plastic rearrangements whose spatial extent decreases upon reaching lower energy states. We also probed the yielding behavior for glasses with different degrees of annealing by adjusting strain amplitude near the critical value. Interestingly, in contrast to zero-temperature amorphous solids, the critical strain amplitude remains unchanged for glasses with initially different energy levels. The formation of a shear band at the yielding transition correlates well with the sharp increase of the number of atoms with large nonaffine displacements.

Multiple-mechanism and microstructure-based crystal plasticity modeling for cyclic shear deformation of TRIP steel

The transformation-induced plasticity (TRIP) steel has an excellent synergy between strength and ductility and is widely used in industry. Cyclic loading is often seen in its industrial application. Therefore, it is of great significance to study cyclic plastic behavior of the TRIP steel. The TRIP steel's cyclic shear behavior and microstructure evolutions were investigated by mechanical testing, electron backscatter diffraction (EBSD) characterization, and in-situ electron channeling contrast imaging (in-situ ECCI) observation. Then, a multiple-mechanism crystal plasticity constitutive model was developed, considering both dislocation slip and martensitic transformation mechanisms. Furthermore, an isotropic hardening law and a modified kinematic hardening rule were taken into account. The crystal plasticity model was implemented into DAMASK with the spectral method. A polycrystalline RVE with realistic grain morphology was constructed from the EBSD data. The simulations of the TRIP steel under cyclic shear loading showed that the samples under higher strain amplitude exhibit stronger cyclic shear hardening. The activation of the martensitic transformation mechanism promotes cyclic hardening. In grain level, the grains with Taylor factor (related to orientation) between 3.3 and 3.9 can activate more slip systems and have a better cyclic hardening ability. So, the Taylor factor is defined as an indicator describing the cyclic response of individual grains in polycrystalline materials. Considering the capability of the established modeling framework, it is of great significance to guide the TRIP steel to serve safely and help the microstructural design in grain scale.

Micromechanism of Plastic Accumulation and Damage Initiation in Bearing Steels under Cyclic Shear Deformation: A Molecular Dynamics Study

Fatigue failure usually occurs on the subsurface in rolling bearings due to multiaxial and non-proportional fatigue loadings between rolling elements. One of the main stress components is the alternating shear stress. This paper focuses on the micromechanism of plastic accumulation and damage initiation in bearing steels under cyclic shear deformation. The distribution of subsurface shear stress in bearings was firstly investigated by finite element simulation. An atomic model containing bcc-Fe and cementite phases was built by molecular dynamics (MD). Shear stress–strain characteristics were discussed to explore the mechanical properties of the atomic model. Ten alternating shear cycles were designed to explore the mechanism of cyclic plastic accumulation and damage initiation. Shear stress responses and evolutions of dislocaitons, defect meshes and high-strain atoms were discussed. The results show that cyclic softening occurs when the model is in the plastic stage. Severe cyclic shear deformation can accelerate plastic accumulation and result in an earlier shear slip of the cementite phase than that under monotonic shear deformation, which might be the initiation of microscopic damage in bearing steels.

A new explanation of Rolling Contact Fatigue in bearing steels based on multiscale models

Abstract Rolling Contact Fatigue (RCF) is harmful and inevitable to bearings and usually results in the initiation of subsurface damage. The root cause for this damage is the cumulative plastic deformation accentuated by carbides. This paper gives a new explanation of RCF based on multiscale models. The distribution and change law of subsurface shear stress in bearing steels was previously investigated by a finite element model. A two-phase atomic model of bcc-Fe and cementite was built. Ten alternating shear load cycles were designed to explore the mechanisms of the cyclic plastic accumulation when the atomic model was initially in the elastic, elastic- plastic and plastic stages, respectively. The results show that cyclic softening diversely occurs in all three types of stress responses. Severe cyclic shear deformation eventually leads to earlier cyclic softening and stress yield, which might be the micromechanism of plastic accumulation and RCF in bearing steels.

Correlation between plastic rearrangements and local structure in a cyclically driven glass.

The correlation between the local structure and the propensity for structural rearrangements has been widely investigated in glass forming liquids and glasses. In this paper, we use the excess two-body entropy S2 and tetrahedrality ntet as the per-particle local structural order parameters to explore such correlations in a three-dimensional model glass subjected to cyclic shear deformation. We first show that for both liquid configurations and the corresponding inherent structures, local ordering increases upon lowering temperature, signaled by a decrease in the two-body entropy and an increase in tetrahedrality. When the inherent structures, or glasses, are periodically sheared athermally, they eventually reach absorbing states for small shear amplitudes, which do not change from one cycle to the next. Large strain amplitudes result in the formation of shear bands, within which particle motion is diffusive. We show that in the steady state, there is a clear difference in the local structural environment of particles that will be part of plastic rearrangements during the next shear cycle and that of particles that are immobile. In particular, particles with higher S2 and lower ntet are more likely to go through rearrangements irrespective of the average energies of the configurations and strain amplitude. For high shear, we find very distinctive local order outside the mobile shear band region, where almost 30% of the particles are involved in icosahedral clusters, contrasting strongly with the fraction of <5% found inside the shear band.

Yielding transition of a two dimensional glass former under athermal cyclic shear deformation.

We study numerically the yielding transition of a two dimensional model glass subjected to athermal quasi-static cyclic shear deformation, with the aim of investigating the effect on the yielding behavior of the degree of annealing, which in turn depends on the preparation protocol. We find two distinct regimes of annealing separated by a threshold energy. Poorly annealed glasses progressively evolve toward the threshold energy as the strain amplitude is increased toward the yielding value. Well annealed glasses with initial energies below the threshold energy exhibit stable behavior, with a negligible change in energy with increasing strain amplitude, until they yield. Discontinuities in energy and stress at yielding increase with the degree of annealing, consistent with recent results found in three dimensions. We observe a significant structural change with strain amplitude that closely mirrors the changes in energy and stresses. We investigate groups of particles that are involved in plastic rearrangements. We analyze the distributions of avalanche sizes, of clusters of connected rearranging particles, and related quantities, employing finite size scaling analysis. We verify previously investigated relations between exponents characterizing these distributions.

Seismic performance of reinforced concrete beams under freeze-thaw cycles

Previous studies have shown that freeze-thaw cycle (FTC) action in severe cold environments is a durability issue that seriously threatens the seismic performance of concrete members. However, research on the seismic resistance of reinforced concrete (RC) beams under FTC action is still scarce. This paper presents an experimental study of six undamaged and frost-damaged RC beams subjected to a low-cycle reciprocating load. The paper aims to investigate the influences of FTC number and concrete strength on the seismic resistance of damaged beams. The paper reports on frost damage at different levels, cyclic damage process, hysteresis response, strength, ductility, shear deformation, and energy dissipation. The test results demonstrate that as the FTCs rose, the width and number of frost-heave cracks on the surface of the beam gradually increased. Moreover, frost action had a significant negative effect on strength, deformation, and energy dissipation, especially when the beams were highly frost-damaged. Further, the shear deformation and shear component to whole deformation gradually increased. Based on the experimental results, a time-dependent evaluation model is proposed to estimate the residual capacity of key elements of RC frame structures in severe cold climates, taking into account the effects of FTCs, concrete strength, and uneven distribution of freeze-thaw damage.

Metastability as a Mechanism for Yielding in Amorphous Solids under Cyclic Shear.

We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first passage time into the absorbing state and suffices to capture the essential qualitative features recently observed in atomistic simulations of amorphous solids. Our results provide insight into the mechanism underlying yielding and its robustness. When the possibility of activated escape from absorbing states is added, it leads to a unique determination of a threshold energy and yield strain, suggesting thereby an appealing approach to understanding fatigue failure.

Mechanism of microstructure and texture evolution during shear loading of AA6063 alloys

The cyclic shear test of 6063 aluminum alloys under T4 and T6 conditions was carried out at room temperature. The microstructure and texture evolution were investigated using electron backscattered diffraction (EBSD) at several instances during cyclic shear deformation. Hardly any change in grain size was observed during the cyclic shear test of T4 and T6 samples. The local residual strain distribution measured in the form of average kernel misorientations (KAM) values increases continuously with an increase in shear strain for both samples. The increase in KAM value was higher for the T6 sample compared to the T4 sample during forward (F) shearing. On reversing the loading path, the increase in KAM value was higher for forward + reverse (FR) and forward + reverse + forward (FRF) straining of the T4 sample compared to the T6 sample. The cube texture was found to be unstable during shear deformation. A significant rotation of texture was observed in both T4 and T6 samples. However, the extent of rotation was slightly greater for the T6 sample as compared to the T4 sample. It was observed that the latent hardening of (1-11)<101>was more than (111)<1-01>in the T4 sample. Similarly, the latent hardening of (1-1-1)<011>was more than the (111)<1-01>in the T6 sample. The origin of latent hardening was attributed to the formation of sessile jogs during dislocation-dislocation interactions on different planes of T4 samples and the difference in volume fraction of precipitates on different planes of T6 samples. The mechanical properties show that the 0.2% YS increases with subsequent reverse and forward shearing for the T4 sample. However, the 0.2% YS during subsequent reverse shearing is lower than the initial forward shearing for the T6 sample. This decrease in yield stress upon loading reversal is attributed to the presence of deformation-induced intragranular back stresses within the T6 material. It is observed that the rate of cross slip of dislocations depends on the athermal dislocation content, presence of dislocation debris in the unfavorable grains, and the difference in the latent hardening values of different slip systems for the T4 and T6 materials.