Reloading Curves Research Articles

Mechanical characterization of tablets using post compression in-die cyclic loading

The purpose of this work is to use post compression in-die cyclic loading as an analytical powder compression tool. Cyclic loading experiments (partial unloading followed by reloading) were performed on tablets formed from three relatively coarse powders (∼100μm) comprised of microcrystalline cellulose (MCC), ibuprofen (IBU) and lactose monohydrate (LAC). The reloading curve was always linear initially, irrespective of the shape of the unloading curve. Hence, nonlinearities in the unloading curve should be attributed to inelastic phenomena rather than to nonlinear elasticity. The slope of the reloading curve generally decreased with increasing degree of unloading, indicating a progressive damage of the contact network upon unloading. For MCC and IBU, consistent unloading curves following primary and secondary loading were obtained. For LAC, the secondary unloading curves were displaced towards smaller tablet heights, suggesting that that particle fragmentation occurs during unloading and reloading, also when the maximal tableting pressure is not exceeded.

A microstructural insight into the compression behaviour of scaly clays

Scaly clays are intensely fissured clays with lens-shaped elements of millimetre size and they show a complex compression behaviour that poses challenges to the design and construction of geostructures (excavations, retaining diaphragms and tunnels). Scaly clays show a normal compression line (NCL) where plastic deformation accumulates, as typically observed in non-scaly clays. Yet the response observed upon unloading and subsequent reloading is very peculiar, (a) the unloading–reloading cycle is typically a closed loop with relatively large hysteresis; (b) the compressibility recorded at high overconsolidation ratio of the unloading or reloading branches is close to the NCL compressibility. This paper presents a microstructural study on an Italian scaly clay where scanning electron microscope observations are integrated with mercury intrusion porosimetry analyses and X-ray computed tomography images. The mechanism associated with the closing of inter-scale porosity and the generation of new intra-scale porosity was identified as the process responsible for the plastic deformation. Experimental observation of reconstituted clay showed a ‘quasi-reversible’ behaviour upon loading and unloading and a pore size distribution characterised only by interparticle porosity. The observation that unloading and reloading curves are parallel in natural and reconstituted clays, led to the postulation that the interparticle porosity is controlling the elastic response.

Cyclic compressive behavior of high-performance hybrid fiber reinforced recycled aggregate concrete: Degradation law and acoustic emission features

To tackle the issues of inadequate mechanical properties of recycled aggregate concrete and its limited application in load-bearing structural components, a high-performance hybrid fiber reinforced recycled aggregate concrete (HP-HFRAC) was developed in this study. Sixteen groups of HP-HFRAC specimens fabricated with varying replacement rates of recycled coarse aggregate and different fiber parameters were subjected to uniaxial compression, as well as acoustic emission (AE) tests, to investigate the cyclic behavior and uncover the underlying mechanisms. The findings demonstrated a strong correlation between the AE signals and the macroscopic phenomenon throughout the whole compression process. The AE amplitude distribution was found to be capable of identifying damage mechanisms, including matrix cracking (40–50 dB), fiber sliding (50–80 dB), and fiber pull-out (more than 80 dB). Additionally, the inclusion of hybrid fibers contributed to mitigating the degradation of stiffness and the accumulation of plastic strain, resulting in the ductile failure of the specimens and significantly enhancing the energy dissipation capacity. Specifically, the peak stress of specimens with 1.5% steel fibers increased by 19% compared to that of specimens without steel fibers, compensating for the strength loss due to the presence of recycled coarse aggregate. Finally, constitutive equations governing the skeleton curves and the unloading and reloading curves of HP-HFRAC subjected to cyclic compression were formulated, which were validated using both the test results and the predicted results of the physics-based data-driven model previously published in our companion paper. The findings of this study might contribute to the development of sustainable high performance recycled aggregate concrete for reliable application in load-bearing components.

Experimental study on cyclic axial tensile mechanical properties of SAP-PVA fiber concrete at different temperatures

This study conducted uniaxial cyclic axial tests on internally cured SAP-PVA fiber reinforced concrete specimens at different temperatures using an MTS universal hydraulic servo machine, obtaining the failure modes and uniaxial cyclic stress-strain curves of concrete with different mix proportions. Utilizing the experimental data, characteristic points of the cyclic stress-strain curves, including loading and unloading, were obtained for different SAP-PVA fiber reinforced concretes. Subsequently, the variations in mechanical parameters such as plastic strain and elastic modulus were analyzed, and the relationship between unloading strain, reloading strain, and plastic strain was investigated. Corresponding regression models for the relationship between plastic strain and loading and unloading strain were established, and the accuracy of the model was validated using various experimental data. The results indicated a continuous decrease in the secant elastic modulus and peak stress but increase in the peak strain of SAP-PVA concrete with increasing temperature, indicating a significant negative impact of high-temperature effects on the mechanical properties of concrete. As the cyclic load increased, plastic strain accumulated, and the cumulative relationship between unloading strain and plastic strain showed weak correlation with high-temperature effects. The unloading model parameters of SAP-PVA concrete were independent of temperature load and only influenced by the degree of damage. With an increase in material damage, the nonlinearity of the unloading curve increased. Compared to the unloading curve, temperature load significantly affected the nonlinearity of the reloading curve. This study revealed the cyclic tensile mechanical properties of SAP-PVA fiber concrete at different temperatures, providing experimental and theoretical references for the practical application and calculation of such concrete in engineering projects.

Distinctive mechanism and model for whole-life ratcheting of cement-stabilized aggregates in tensile fatigue tests

In light of the limited research on the fatigue damage and plastic strain evolution of cement-stabilized aggregates (CSA) despite their widespread application, this study aims at modeling the ratcheting of CSA, which provides better characterization of fatigue by counting plastic strain accumulation. Uniaxial and indirect tensile fatigue tests were conducted to obtain the plastic strain accumulation and stress-strain curves. A bar system was constructed to describe the ratcheting mechanism of CSA, which considers the non-homogeneity of CSA's components and composes parallel bars with a distribution of plastic-damage properties. The ratcheting rate variation was attributed to the strength distribution of the bars. Then, to prevent complex and hard-to-implement parameter fitting, a predigested ratcheting model was proposed, which focuses only on the secant modulus and simplifies the generation of ratcheting to the difference between reloading and unloading secant modulus. The test results revealed a three-stages characteristic in the ratcheting evolution of CSA. The non-coincidence of reloading and unloading curves was deemed the intuitive cause of the ratcheting. The numerical implementation of the proposed mechanism indicated that the strength and modulus discrepancies between weak and strong bars can lead to ratcheting. By comparing with the experimental results, the effectiveness of the proposed model was verified in describing the ratcheting evolution of CSA and to characterizing the non-linearity of the accumulation curves. Moreover, the parameter fitting process requires the results of the current fatigue test instead of parallel tests or other loading tests, successfully eliminating calibration difficulties resulted from significant property discrepancies among CSA specimens.

Study on stress–strain relationship and constitutive model of recycled aggregate concrete under axial cyclic compression

AbstractThe effects of dry or saturated state, water–cement ratio, coarse aggregate type and steel fiber on the stress–strain relationship of RAC under cyclic loading were studied. What is more, the characteristics of stress–strain curve, plastic strain, stress degradation and stiffness degradation of RAC under cyclic loading were analyzed. The microstructure of RAC was analyzed. Based on the principle of surface energy, the reason for the decrease in compressive strength of wet concrete was analyzed. In addition, the envelope equation of stress–strain curve under cyclic loading, unloading and reloading curve was established. The test results showed that the peak stress of the envelope line of RAC under cyclic loading was affected by dry or saturated state, water–cement ratio and coarse aggregate type, but the addition of steel fiber could reduce the degradation rate of stress and stiffness of RAC after peak strain. The plastic strain accumulation of RAC before and after the peak stress was quite different, but dry or saturated state, water–cement ratio, coarse aggregate type and steel fiber have no obvious influence on the plastic strain accumulation of RAC. The pores and cracks of RAC provide space and channels for the moisture absorption and water absorption. The Weibull–Lognormal statistical distribution envelope model, unloading curve model and reloading curve model established were in good agreement with the experimental curves. The research results provided a reference for the study of the full curve constitutive model of RAC under cyclic loading.

Behavior and constitutive model of ultra-high-performance concrete under monotonic and cyclic tensile loading

Ultra-high-performance concrete (UHPC) holds great promise for constructing lightweight and high-performance concrete structures. Hence, the proportion of live load increases, in turn, leads to a higher live-to-dead load ratio. UHPC structures suffer from cyclic stress amplitude in higher possibility. Therefore, the behavior and constitutive model of UHPC under cyclic tensile loading is of significance for the understanding of bearing capacity and deformation property for structures subjected to cyclic loading, which, nevertheless, is seldomly reported. In this regard, the present study conducted direct tensile tests on 35 UHPC dog-bones with four steel fiber volume fractions (i.e., 0%, 1%, 2%, and 3%) and two fiber shapes (i.e., straight and hooked-end). A constitutive model for UHPC under tensile loading was proposed, implemented into OpenSees, and employed in numerical simulations of UHPC beams subjected to bending in cyclic loading. The numerical results were compared with test results on UHPC beams for model verification. The experimental and numerical results show that the UHPC with straight fiber volume fractions less than 1% demonstrated a brittle failure, whereas the UHPC with straight fiber volume fractions higher than 1% or with a hooked-end fiber volume fraction of 2% exhibited a ductile failure. The increase in fiber volume fraction resulted in great enhancements of the initial crack and peak stresses, and the peak and ultimate strains, and the energy absorption capacity. Besides, the use of hooded-end fibers also led to a slight improvement in tensile strain behavior of UHPC but negatively affected the initial crack stress and peak stress. It also provided sufficient bonding between fiber and matrix. The envelope curves and failure patterns for UHPC under monotonic and cyclic loading are close. The proposed constitutive model for UHPC under tensile loading is composed of an envelope curve that is assumed bi-linear for strain softening UHPC or tri-linear for strain hardening UHPC, an unloading curve and a reloading curve described by an exponential function, and a damage index defined as the reduction of unloading modulus. The proposed constitutive model for UHPC under tensile loading can provide acceptable results for the prediction of the bearing capacity and deformation property of UHPC beams without reinforcements subjected to bending in cyclic loading.

Mechanical properties of bolted steel laminated flattened-bamboo lumber connections under cyclic loading

In beam-column systems, bolted steel connections in laminated composite structures are being increasingly employed for their superior mechanical performance. Laminated flattened-bamboo lumber (LFBL) is a newly engineered bamboo product and a promising structural material since its production process could achieve the high-efficiency utilization of bamboo resources. This research investigated the load–displacement behavior of bolted steel connections of LFBL under cyclic compression. A total of 30 specimens in 6 groups were tested to determine the hysteresis curves, the effects of the bolt number, and failure modes under cyclic compression parallel and perpendicular to the grain. The test results illustrated that splitting and crushing failure were the main failure modes. With the increase in bolt quantity, the maximum load and initial stiffness of all specimens were significantly increased, while the ductility slightly decreased. The theoretical models of the skeleton curves and the reloading and unloading curves under cyclic loads were put forward, and the proposed equations were able to predict the entire cyclic load–displacement response. This study is aimed at offering guidelines for LFBL applications in future construction engineering.

Cyclic compressive stress-strain behaviours of normal weight concrete at Arctic low temperatures

To propose more accurate constitutive models for low-temperature concrete structures subjected to cyclic loading, this paper experimentally studied the cyclic compressive behaviours of normal weight concrete (NWC) at low temperatures. Firstly, cyclic compression tests on 36 NWC prisms of C25, C45, and C55 grades were performed at four low-temperature levels, i.e., 20, −30, −60, and − 80 °C. By comparing with monotonic results, it was confirmed that the low-temperature cyclic envelope curves of NWC can be predicted by the corresponding monotonic constitutive models. Furthermore, the effects of low temperatures and grades of NWC on key indexes in constitutive models of NWC under cyclic compression were discussed and analyzed in detail, e.g., plastic strain, stress deterioration ratio, endpoint strain, and damage variable. Through the regression analysis of test data, the cyclic constitutive models composed of the envelope, unloading, and reloading curves were established to describe cyclic stress-strain behaviours of NWC at 20 ∼ −80 °C. Finally, the validations proved that the developed models provided reasonable predictions on low-temperature cyclic response of NWC.

An elastoplastic damage model of concrete under cyclic loading and its numerical implementation

A novel elastoplastic damage model describing the complex mechanical behaviors such as stiffness degradation and irreversible deformation of concrete under cyclic loading is constructed and the complete procedure for numerical implementation is presented. To solve the key problems including multi-axial stress states, asymmetry in tension and compression and conversion between tension and compression under cyclic loading, a series of approaches are put forward. A scalar equivalent strain based on the Hsieh-Ting-Chen strength criterion in the framework of strain space is used to convert the complex multiaxial stress state to the simple uniaxial one. Correspondingly, the equivalent strain obtained by the characteristic strength curve addresses the asymmetry in tension and compression, so that the stress–strain relationship in both uniaxial tension and uniaxial compression can be represented by the same curve, and a single damage scalar is available to characterize both tensile damage and compressive damage. To overcome the difficulty of conversion between tension and compression owing to the non-negative equivalent strain, a net equivalent strain is defined to keep the curve proceeding in the first quadrant under reverse loading. Meanwhile, a nominal damage variable is proposed to ensure that the reloading curve can return to the original stress–strain envelope. A new framework of the model with a concise mathematical form has been numerically implemented and is independent of the selection of fundamental governing equations. Typical experimental tests involving three-point bending test, mixed-mode bending test, cyclic uniaxial test, and reciprocating loading test are used for verification. The results calculated by the proposed model are all in good agreement with the tests. As a result, the correctness and reliability of the novel model are demonstrated.

Development of Cyclic Stress-Strain Curves for Modified Rat-Trap Bond Concrete Brick Masonry from Experimental Investigations

Abstract: Present study is based upon the experimental results obtained by reloading and unloading of concrete brick masonry samples constructed in modified rat-trap bond under uniaxial compression perpendicular to their bed joints. Considering the advantage of air gap between perpends for thermal comfort, Flemish bond was modified as rat-trap bond using half scale modular bricks (95mm × 95mm × 45mm) and called Modified Rat-Trap bond concrete brick masonry. The air gap created within the wall was filled up with insulating material thermocol (Expanded polystyrene). General polynomial expression has been developed for both reloading and unloading curves separately which were found suitable to predict the behavior of said masonry at any given residual strain. With the help of this parent polynomial, the particular reloading and unloading curves are then developed by transferring the parent equation to stress-strain coordinate. It was observed that the nature of reloading and unloading curves is primarily influenced by plastic strain. A fair consistency was observed between the experimental and computed curves. Keywords: Uniaxial, Perpend, Wallet, Monotonic, Common Point, Stability Point,

Hysteresis modeling of timber-based structural systems using a combined data and model-driven approach

This paper presents a novel computational approach to empirical hysteresis modelling applied to timber-based structures based on a combined data model-driven strategy. While the backbone curve is simulated using the experimental cyclic response based on a step-by-step optimization problem (data-driven approach), analytical functions describe the re-loading curves (model-driven approach). Empirical hysteresis models developed so far for timber structures are model-driven. However, the backbone curves can exhibit a highly irregular non-smooth trend, difficult to mirror using analytical formulations. The challenge in mirroring the experimental backbone using closed-form formulations has led to an extended set of parameters to be calibrated in existing literature models This paper presents a novel approach to the empirical hysteresis model, where the experimental data are directly involved, as a whole, in the model formulation. This model aims to be a possible trade-off between model complexity and accuracy. A reduced number of parameters needed to describe the re-loading paths is counterbalanced using an entire subset of the experimental data. The paper delivers the developed Matlab and Python codes for further implementation as a user-defined element within a Finite Element software.

The effect of corrosion on the hysteresis properties of welded steel

ABSTRACT To study the effect of corrosion on the mechanical properties of welded steel hysteresis, a cyclic load test was performed on corroded welded steel. Accordingly, a generalised hysteretic mechanical model of welded steel with the corrosion degree as a variable was established. Taking a D36 steel plate fabricated via manual arc welding as the research object, specimens were prepared using the accelerated electrochemical corrosion method. Mechanical performance experiments under tension, compression, and multiple cyclic loading systems were conducted on specimens, the hysteretic mechanical properties of welded steel were mostly concerned. On that base, a generalised hysteretic material model for welded-corroded steel which consists of a skeleton curve, an unloading curve and a reloading curve is proposed. All the parameters used to describe these curves are related to the degree of corrosion, determined by the regression on the test data. The accuracy and effectiveness of the model were verified experimentally.

Monotonic and cyclic stress-strain models for confined concrete-masonry shear wall boundary elements

Simulation of the seismic response of fully grouted reinforced masonry shear walls (RMSWs) built with reinforced masonry boundary elements (RMBEs) necessitates reliable nonlinear models of their RMBEs. The axial monotonic and cyclic full stress-strain curves of RMBEs are essential for predicting the lateral cyclic response of RMSWs with boundary elements. Therefore, a reliable stress-strain constitutive model for the axial monotonic and cyclic behavior of RMBEs is required. The authors recently investigated the axial monotonic compressive behavior of unconfined and confined RMBEs built with different section configurations, vertical reinforcement arrangements, transverse confinement ratios, and different construction procedures. In the current study, the authors investigated the cyclic behavior of some RMBEs whose counterparts were previously tested under axial monotonic compression. In addition, more specimens with different confinement configurations and different grout strengths were tested. Comparisons of the test results showed that increasing the vertical reinforcement ratio increased the axial load carrying capacity of the tested RMBEs but decreased their strain ductility. In addition, using a low compressive strength grout significantly reduced the strain ductility of the RMBEs. Moreover, monotonic and cyclic stress-strain models for confined and unconfined concrete-masonry boundary elements subjected to axial compression loading were developed. The proposed models showed good-to-excellent agreement with the experimental results, predicting the stress-strain rising curve, stress drop, and postpeak behavior. Furthermore, unloading and reloading curves, strength degradations, and softening of reversal and reloading branches due to cyclic degradations were well captured by the proposed model.

Experimental study of hysteretic behavior of corroded steel with multi-angle welding joints

To rationally characterize the macroscopic behavior of in-service offshore structures affected by the coupled welding-corrosion action in steel components, the hysteretic behavior of corroded D36 marine structural steel with multi-angle welding joints is experimentally studied. To simulate possible corrosion-welding scenarios, the tested specimens are prepared with the gas arc welding (MAG) method for three welding angles and processed with the accelerated electrochemical corrosion for five corrosion degrees. The elasticity modulus, tensile strength, and elongation of welded-corroded steel is observed in the monotonic tensile test conducted before the cyclic test where the hysteretic performance and energy dissipation ability is mostly concerned. On the basis of these test results, a generalized hysteretic material model for welded-corroded steel which consists of a skeleton curve, an unloading curve and a reloading curve is proposed. All the parameters used to describe these curves are related to the degree of corrosion and welding angle, determined by the regression on the test data. The effectiveness of the proposed model is verified with the tested data, including those from the specimens additionally and specifically tested.

The correlation between the mixed-mode oligo-cyclic loading induced mechanical and microstructure changes in HDPE

Two grades of HDPE (one is for PE-100 pipeline application and one is for blow molding) were processed to vary their crystallinity and molecular topology in order to investigate and understand the microstructural origin of the seismic performance of HDPE materials. For a given grade, the quenched sample exhibits a lower crystallinity, thinner crystallites, and a higher density of entanglement/tie molecules compared to the isothermal one. The HDPE samples are submitted to mixed-mode, oligo (plastic)-cyclic tensile deformation (that simulates the seism) with the applied maximum strain below or at the onset of necking propagation. The changes of numerous macroscopic mechanical metrics with increasing cycles were monitored (e.g. stress at maximum strain, residual strain at zero stress, secant modulus, and hysteresis loop area). These mechanical changes not only depend on the maximum imposed cyclic strain, but also the microstructure of HDPE. A physical scenario is proposed to describe the microstructural changes during the cyclic deformation and explicate the macro-micro correlations. Moreover, the post-cyclic tensile (reloading) curve can return to the original one rapidly for each sample, this phenomenon indicates the neglecting effect of the following cycles on the further loading path. It is also found that the material designed for the PE-100 pipeline shows limited variation between the initial and post-cyclic tensile toughness, indicating that the pre-loaded materials require nearly the same energy to rupture as the pristine ones. This is evidence that the material for PE-100 pipeline has a good resistance against the damage induced by seismic events.

Nonlinear anelastic behavior and unloading-reloading constitutive models of severe plastic compressive deformation

The nonlinear anelastic behavior in unloading and unloading‒reloading processes of severe plastic compressive deformation (SPCD) has a decisive impact on the springback of deformed parts. The strain hardening, strain softening and anisotropy affect the anelastic behavior of the deforming material. In this study, the quasi-static single-pass and multi-pass SPCD tests were carried out on the samples along different directions of hot-rolled copper plates. The nonlinear unloading behavior and the variation law of anelastic strain after single-pass and multi-pass compressions and between passes were analyzed, and the effect of the anisotropy on the anelastic strain was clarified. At the micro level, the anelastic strain model in the strain hardening and softening stages was established based on the relationship between anelastic strain and dislocation density, the Hall-Petch and Talor strength models, strain hardening EM model and modified softening constitutive model. Thereby, the nonlinear unloading‒reloading models in an anelastic exponent form and in a modified anelastic hyperbolic sine form were constructed, respectively. At the macro level, the anelastic strain function related to strain were established on the basis of the chord modulus model in a power exponent form and strain hardening and softening constitutive models. Thereby, 1-D ET nonlinear unloading‒reloading constitutive model in a power exponent form was constructed. The nonlinear symmetric relationship between unloading and reloading curves was analyzed. It was found that the 1-D ET model in power exponent form and expression in polynomial form can accurately describe the instantaneous slope of symmetric axis. Finally, the anelastic strain and the unloading‒reloading curves of the single-pass and multi-pass SPCDs and inter passes were predicted using the anelastic strain model and the nonlinear unloading‒reloading model, and compared with the experimental results. The comparison indicated that the established anelastic strain model can accurately predict the anelastic strain in the strain hardening and softening stages of SPCD, and the established unloading‒reloading model can accurately predict the nonlinear relationship between stress and strain in the unloading‒reloading of SPCD.

A Network Evolution Model for Recovery of the Mullins Effect in Filled Rubbers

The stress-softening phenomenon, named as the Mullins effect, can widely occur in filled rubbers after cyclic loading and unloading conditions. The reloading curve is typically below the initial loading curve unless the applied strain exceeds the previously applied maximum strain. Experimental observations have also shown that the Mullins effect can be recovered by annealing the pre-deformed filled rubbers at a high temperature while the recovery level strongly depends on the annealing time and temperature. In this work, we develop a theoretical model to describe the recovery of the Mullins effect by incorporating the dynamic scission and recovery of polymer chains into the eight-chain model. Experiments have also been performed on two types of filled rubbers to validate the theory. The results show that the model is able to capture the main features of the experimental observations including the Mullins effect of virgin specimens and the recovery of the Mullins effect of pre-deformed specimens subjected to different annealed conditions.

Dynamic performance of RAC-filled double-skin tubular columns subjected to cyclic axial compression

To meet the requirements of sustainable development, recycled aggregate concrete (RAC) was suggested to be used in double-skin tubular columns (DSTCs). These new RAC-filled DSTCs were loaded by a cyclic axial compression to investigate their dynamic performance. An experimental program including 15 RAC-filled DSTCs with different loading schemes and recycled coarse aggregate (RCA) substitution rates was conducted. All RAC-filled DSTCs failed due to the rupture of the basalt fibre-reinforced polymer (BFRP) outer tube. According to the experimental results, it can be concluded that: (1) the RCA substitution rate and loading scheme exhibited an important influence on the mechanical behaviour of the RAC-filled DSTCs and stress–strain relationship of the confined RAC core; (2) the confinement effect enhanced the ultimate load and improved greatly the deformation ability of the RAC-filled DSTCs; (3) the plastic and unloading strains exhibited a very good linear relationship; (4) the dynamic load caused the plastic strain and the strength deterioration of the RAC core. Additionally, existing theoretical models were modified to predict the unloading and reloading curves of RAC-filled double-skin tubular columns and an acceptable accuracy was achieved.

Cyclic indentation of polymers: Instantaneous elastic modulus from reloading, energy analysis, and cyclic creep

Abstract