Softening Behavior Research Articles

Synergistic effect of Polyvinyl Acetate (PVA) and Enzyme-Induced Carbonate Precipitation (EICP) on the mechanical properties of natural sands

Effective enhancement of the mechanical properties of cohesionless soils is crucial for diverse geotechnical applications, given their inherent vulnerability to load-induced failure due to the absence of inter-particle bonding. Soil failures pose significant risks to both human lives and infrastructure, necessitating the development of environmentally friendly soil improvement methods. Conventional techniques often entail invasive processes and substantial carbon emissions. In response, contemporary approaches seek to minimize environmental impact while preserving organic material characteristics. This study investigates the synergistic effect of polyvinyl acetate (PVA) and enzyme-induced carbonate precipitation (EICP) treatment for enhancing the mechanical properties of cohesionless natural sands. Beach and river sands were treated with varying proportions of PVA in conjunction with an optimized EICP solution for yielding the best results. Unconfined compressive strength (UCS) tests were conducted at 7, 14, and 28-day curing intervals to assess the performance of the soil-polymer-EICP composites (SPEC). The results demonstrated substantial improvements in compressive strength and elastic modulus with increasing PVA content. For beach sand, after 7 days of heat curing, the peak strength increased from 0.89 MPa to 11.07 MPa for composites with 1% and 11% PVA, respectively. Similarly, for river sand, the peak strength increased from 0.87 MPa to 8.96 MPa under the same conditions. The findings also highlighted the softening behavior induced by PVA with heat curing over the period. This softening phenomenon was attributed to the thermo-plastic characteristics of the polymer film induced by temperature conditions.

Cross-scale mechanical softening of Marcellus shale induced by CO2-water–rock interactions using nanoindentation and accurate grain-based modeling

Mechanical softening behaviors of shale in CO2-water–rock interaction are critical for shale gas exploitation and CO2 sequestration. This work investigated the cross-scale mechanical softening of shale triggered by CO2-water–rock interaction. Initially, the mechanical softening of shale following 30 d of exposure to CO2 and water was assessed at the rock-forming mineral scale using nanoindentation. The mechanical alterations of rock-forming minerals, including quartz, muscovite, chlorite, and kaolinite, were analyzed and compared. Subsequently, an accurate grain-based modeling (AGBM) was proposed to upscale the nanoindentation results. Numerical models were generated based on the real microstructure of shale derived from TESCAN integrated minerals analyzer (TIMA) digital images. Mechanical parameters of shale minerals determined by nanoindentation served as input material properties for AGBMs. Finally, numerical simulations of uniaxial compression tests were conducted to investigate the impact of mineral softening on the macroscopic Young’s modulus and uniaxial compressive strength (UCS) of shale. The results present direct evidence of shale mineral softening during CO2-water–rock interaction and explore its influence on the upscale mechanical properties of shale. This paper offers a microscopic perspective for comprehending CO2-water-shale interactions and contributes to the development of a cross-scale mechanical model for shale.

Effect of strain level on the cyclic response and microstructure characteristics of selective laser melted 304L

Considering the relationship between austenite stability and strain level, the cyclic response curves are obtained for SLM 304L under different strain amplitude at R = 0.3. The results indicate that since the microstructure characteristics shift from stacking faults (SFs) at low strain amplitude to martensite and twins at high strain amplitude, the cyclic softening behavior transitions to cyclic hardening behavior. Besides, it also indicates that high strain levels can overcome the influence of initial microstructure on fatigue performance, presenting a new sight to understand the relationship between cyclic hardening and martensite transformation.

Analysis-oriented stress-strain model for concrete in steel tubed geopolymer concrete (STGC) columns

To alleviate the brittleness of geopolymer concrete and further promote its engineering application for environmental benefits, a novel type of column, i.e., steel tubed geopolymer concrete (STGC) column, has been proposed recently. Note that an accurate axial stress-strain model is necessary for a comprehensive understanding of the compressive behavior of STGC columns. However, the existing analysis-oriented models are all developed for the conventional concrete-filled steel tube (CFST) columns, and the confinement mechanism of steel tubed concrete columns is significantly different from that of concrete-filled steel tube columns since the axial deformation of steel tube and core concrete is not synchronized for steel tubed concrete columns during the loading process due to the discontinuous steel tube. Furthermore, the dilation properties of STGC columns at the initial loading are significantly overestimated by the existing lateral-axial strain models. Besides, steel-confined geopolymer concrete (GPC) experiences a more remarkable softening behavior resulting from the more significant brittleness of GPC than that of ordinary concrete. Thus, the deformation models are proposed in this study and the active-confinement base model is also developed for GPC based on the mechanical characteristics of STGC columns under axial compression. Then a new analysis-oriented model is proposed for steel tubed geopolymer concrete. Comparisons between the theoretical calculations and the test results indicate that the proposed model can provide reasonable predictions for both steel stress evolution and the stress-strain relationship of STGC.

Pullout behaviour of strip plate anchors in clay overlying sand

Plate anchors are being increasingly employed to establish mooring systems for offshore floating facilities owing to their notable efficiency and cost-effectiveness. The majority of prior studies have concentrated on plate anchors, examining the vertical to horizontal orientations, particularly when embedded in single layer clay or sand. However, it is common to encounter multiple layers of soil with varying characteristics in practical engineering, leading to inaccurate estimation of pullout capacity when based solely on the properties of a single soil layer. This paper reports pullout behaviours of strip plate anchors in clay overlying sand by adopting two dimensional finite element analysis. To simulate the hardening and subsequent softening behaviour of medium to dense sand, a modified Mohr-Coulomb model is considered. The current Finite Element (FE) results are in good agreement when compared with both previous FE simulations and physical model test data. Then, the soil flow mechanisms (e.g. the accumulated plastic shear strain, the friction angle) surrounding the anchor during pullout out are revealed. Based on a series of FE results, a calculation framework considering the effect of thickness of clay layer is designed to predict the pullout behaviour of plate anchors in clay overlying sand.

Temperature-dependent debonding behavior of adhesively bonded CFRP-UHPC interface

The adhesively bonded structure, comprising carbon fiber-reinforced polymer (CFRP) and ultra-high-performance concrete (UHPC), enhances structural strength while reducing brittleness and strain softening behavior. However, the adhesively bonded structure is inevitably influenced by temperature variations throughout its service life. When the adhesive layer's temperature surpasses the glass transition temperature (Tg), significant damage occurs to the bond layer joint. To investigate the debonding behavior of the CFRP-UHPC interface at various temperatures, a series of three-point-bending tests were conducted at room temperature, 120 %Tg, 150 %Tg, and 160 %Tg. This study introduced a temperature degradation factor, employing a proposed maximum load capacity prediction formula to adjust both the test results and data from other researchers. By adjusting the cohesion parameters with the temperature degradation factor, a temperature-dependent mixed-mode cohesive zone model (CZM) was developed. The model's validity was confirmed through finite element (FE) analysis, considering two distinct experimental scenarios. The paper concludes that the proposed model effectively simulates interface debonding behavior across varying temperatures.

Microstructural evolution of highly aligned discontinuous fiber composites during longitudinal extension in forming

The longitudinal extensional viscosity of a highly aligned discontinuous fiber (ADF) thermoplastic matrix composite is investigated to develop a model and validate microstructural evolutionary mechanisms. Samples stretched at constant temperature and strain rate are shown to exhibit a strain softening behavior. X-ray CT analysis and optical micrographs show that the composite microstructure deconsolidates before forming and evolves with deformation. The conventional unit cell micromechanical model includes the effects of matrix viscosity, fiber aspect ratio and fiber volume fraction. This model is modified to include the stiffening effect of fiber spacing variability, and the softening effects of porosity and decreasing fiber overlap length with elongation. Calibration of the model reveals that matrix shear strain rate is an order of magnitude higher than previously predicted due to local fiber spacing. This effect is captured by a fiber spacing variability parameter which scales average spacing down by an order of magnitude. The observed strain softening behavior is described and a combinations of fiber overlap length reduction and local fiber spacing increase.

Insight into annealing-induced hardening and softening behaviors in a laser powder-bed fusion printed in-situ composite eutectic high-entropy alloy

Laser powder-bed fusion (LPBF) printed AlCoCrFeNi2.1 eutectic high-entropy alloy (EHEA) typically exhibits an in-situ composite structure with an out-of-equilibrium character. Its distinctive hierarchical microstructure implies the potential challenges and opportunities in engineering advanced materials with high performances. Here, an informative overview of the microstructure evolution across various scales and its effect on tensile properties in LPBFed AlCoCrFeNi2.1 subjected to annealing treatments over a wide temperature range is discussed. Microstructural observations indicate that spinodal decomposition within the B2 lamellae becomes evident after annealing at 500 °C, marked by a pronounced compositional fluctuation of Cr. Annealing the sample at 600 °C leads to the precipitation of BCC nanoparticles through structural disordering of Cr-rich regions within the modulated nanostructure. Tensile tests and strengthening models reveal that the annealing-induced hardening responses are largely associated with precipitation strengthening resulting from the ordering strengthening of L12 nanoprecipitates and the coherency and modulus strengthening of BCC nanoprecipitates, as well as the spinodal hardening from modulated nanostructure. Notably, BCC precipitation strengthening plays a crucial role in enhancing the strength of the annealed alloys. A strong precipitation strengthening effect is realized due to the coarsening of the BCC and L12 nanoprecipitates at 600 °C, and the strengthening effect from BCC precipitates gradually weakens as their dissolution at 650 °C, resulting in abnormal hardening behavior. Upon annealing at higher temperatures (700–1000 °C), phase decomposition, precipitation dissolution, even recrystallization occur sequentially, resulting in varying degrees of softening behaviors.

Influence of Severe Plastic Deformation and Aging on Low Cycle Fatigue Behavior of Al-Mg-Si Alloys.

Strain-controlled low cycle fatigue (LCF) tests were conducted on conventionally grained (CG) and ultrafine-grained (UFG) Al-Mg-Si alloys treated under various aging conditions. In the cyclic stress response (CSR) curves, CG peak-aged (PA) alloys showed initial cyclic hardening and subsequent saturation, whereas CG over-aged (OA) alloys displayed cyclic softening behavior close to saturation. The UFG materials exhibited continuous cyclic softening except for UFG 3; it originates from the microstructural stability of the UFG materials processed by severe plastic deformation (SPD). Using a strain-based criterion, the LCF behavior and life of the CG and UFG materials were analyzed and evaluated; the results are discussed in terms of strengthening mechanisms and microstructural evolution. In the CG materials, the LCF life changed markedly owing to differences in deformation inhomogeneity depending on the precipitate state. However, the UFG materials displayed a decreasing LCF life as cyclic softening induced by dynamic recovery became more severe; additionally, a relationship between the microstructural stability of the UFG materials and the cyclic strain hardening exponent n' was suggested.

Optimization of hot-rolling parameters for a powder metallurgy Ti–47Al–2Cr–2Nb-0.2W alloy based on processing map and microstructure evolution

In this work, a two-stage rolling method with varied temperature and strain rate was proposed for powder metallurgy (PM) Ti–47Al–2Cr–2Nb-0.2W alloy sheets based on the guidance of processing map and microstructure evolution. Compared with conventional rolling at a high temperature and a low strain rate, the TiAl alloy exhibited enhanced plastic deformability through the implementation of the two-stage rolling method, resulting in a higher cumulative true strain. Microstructure analysis revealed significant grain refinement in the rolled sheet. During the first stage of hot rolling with high temperatures and low strain rates, the softening behavior caused by dynamic recovery (DRV) and dynamic recrystallization (DRX) is conducive to the plastic deformation in the second stage rolling (low temperatures and high strain rates). In addition, the formation of mechanical twins further promotes DRX behavior. The softening mechanism of α2 phase is DRV, and that of γ phase is continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX).

Quantification of static softening process and its effects on work hardening characteristics of a typical high strength steel during multi-pass deformation

Heavy components of 300 M steel are usually manufactured by multi-pass forging. It is necessary to study the flow characteristics of 300 M steel during multi-pass deformation, which helps to regulate the flow behaviors during the actual forging process. In the study, multi-pass compression experiments are conducted on the Gleeble-3500 device to mimic the forging process of 300 M steel. Results show that the deformation parameters and inter-pass holding parameters can affect the work hardening rate significantly. It can be ascribed to coupling effects of dynamic softening and static softening behaviors. A unified static softening kinetics model is established to evaluate the coupling effects of static recovery, static recrystallization, and metadynamic recrystallization on the static softening behaviors. The established static softening kinetics model shows high prediction accuracy with a reliability of 0.99605. Furthermore, a new constitutive model is established to describe the effects of dynamic softening and static softening on the flow stress during multi-pass deformation. The prediction accuracy of the new constitutive model is 0.98897 with a mean absolute error of 4.075%, which demonstrates that the established constitutive model is reliable.

Undrained cyclic behavior of underconsolidated marine clay in multidirectional simple shear tests

In the field of marine reclamation engineering, underconsolidated marine clay often presents challenges owing to its susceptibility to multidirectional cyclic stresses and potential for excessive deformation. This research examined the undrained cyclic behavior of underconsolidated marine clay through multidirectional cyclic simple shear tests. It explored shear strain evolution, the cyclic shear stress–strain relationship, and stiffness degradation by analyzing the impacts of clay consolidation levels and phase differences in the cyclic stress. The findings indicated that as the degree of consolidation increased, the rate of cyclic shear strain development in marine clay gradually diminished. Conversely, an enhanced phase difference led to a quicker evolution of shear strain. Additionally, as loading continued, the tested clay exhibited notable softening behavior, leading to stiffness degradation. A larger phase difference resulted in more pronounced stiffness degradation, although a higher degree of consolidation effectively delayed this degradation. These findings provide new insights on the cyclic behavior of underconsolidated marine clay under multidirectional loading, offering crucial information for marine reclamation engineering.

Wood sandwich softening behavior via coupling of moisture and heat

The controllability of the position and thickness of the compressed layer in the sandwich compression wood is primarily based on the yield stress distribution during a hydrothermal treatment. In this study, the variation law of the yield stress of poplar wood was analyzed in the moisture content (MC) range of absolute dryness to saturation and the temperature range of 30–210℃. A prediction model of wood yield stress response to MC and temperature was developed and the formation of sandwich compression was analyzed. The yield stress of the wood was influenced by the thermal effect and plasticizing effect. In the process of increasing temperature and MC, the yield stress decreased gradually. And the yield stress change rate was 0.29–0.46 MPa in the MC range of 5–10%. The prediction model of wood yield stress was developed by a multiple linear regression analysis. This example demonstrated that coupling distributions of MC and temperature were formed upon heating at 180℃, which led to a gradient distribution of the glass transition temperature and yield stress inside the wood. This phenomenon resulted in the sandwich softening behavior under the coupling of moisture and heat, which was the key formation mechanism of sandwich compressed wood.

Approximate analytical solutions of the 1:3 internal resonance response of piezoelectric energy harvester considering two types of coupled frequency components

The 1:3 internal resonance effect in the L-shaped piezoelectric vibration energy harvester leads to an expanded frequency band for energy harvesting and better matching of external excitation frequency in the environment. The electromechanical-coupled governing equations for this vibration energy harvester have been validated in our previous work (Nie et al., 2019). The effect of load resistance on the energy harvester’s natural frequency and damping ratio is addressed. The quadratic and cubic nonlinearities in this system leads to two types of coupled frequency components appear, they ultimately affect the approximate solution of the voltage response. The method of multiple scales is used to derive the two types of coupled frequency components of the system along with their contribution to the output responses. The revised approximate analytical solutions of the output responses are then presented. The system’s stability is assessed through the Jacobi matrix of modulation equations. The nonlinear softening phenomenon that favors the broadening of the bandwidth of the energy harvester is analyzed. The vibration patterns in regions with nonlinear softening and non-softening behavior are investigated through frequency spectra, phase trajectories, and Poincaré cross-sections. The findings reveal that the load resistance significantly affects the damping ratio of the harvester. Inclusion of quadratic and cubic nonlinearities results in three frequency components in the output responses spectrum, with an approximate ratio of 1:2:3. Two types of coupled frequency components appeared in the spectrum of the system’s output responses. The contribution of coupled frequency components to the output response proves crucial, and the revised approximate solutions are in good agreement with that of numerical solutions. The output responses are significantly affected by the initial conditions in the nonlinear softening region, the large and small initial conditions yield solutions in the upper and lower branches, respectively.

An experimental investigation on undrained cyclic behaviour of a saturated intact loess

There are growing evidence indicating that earthquakes occur more frequently in the Chinese Loess Plateau, which can possibly cause saturated intact loess liquefaction, leading to geological disasters. However, the cyclic behaviour of saturated intact loess is still much less investigated. In the presented work, typical intact loess was collected to carry out a comprehensive experimental investigation, including both undrained monotonic and cyclic triaxial shear tests with different confining stresses and cyclic stress. The results indicate that the intact loess shows an overall clay-like cyclic behaviour. It shows a strain softening behaviour under undrained monotonic shearing, while under undrained cyclic shearing, a well-defined failure pattern of plastic strain accumulation is observed, and an axial strain of 3 % is determined as the failure criterion. Although different excessive pore water pressure generation patterns and failure criteria are found under monotonic and cyclic conditions, a quantitative relationship is established between the monotonic and cyclic stress-strain behaviour based on the unique relationship found between axial strain and the defined allowable stress. Additional micro-structure observations and analyses further reveal the differences in loess structure destruction caused by different loading conditions. This study helps to further understand the cyclic behaviour and failure mechanism of intact loess, and to provide a useful reference for the evaluation and prevention of possible soil liquefaction failure in loess areas.

Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue.

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

Microstructural effects and constitutive modelling of cyclic softening behaviour in Ti–6Al–4V titanium alloys

Cyclic softening in Ti–6Al–4V titanium alloy significantly influences the reliability and performance of critical engineering components. This study addresses the lack of a comprehensive understanding of cyclic softening in different microstructures of Ti–6Al–4V titanium alloys. Microstructures with bimodal and lamellar morphologies were prepared by heat treatment of Ti–6Al–4V titanium alloy at various temperatures. Interrupted low-cycle fatigue tests revealed a larger cyclic softening for the bimodal microstructures than the lamellar microstructures. Finite element analysis (FEA) captured the cyclic softening by incorporating the Voce isotropic hardening model with the Chaboche kinematic hardening model. Two nonlinear kinematic hardening terms, along with the Voce isotropic hardening model whose parameters were calculated using the variation in cyclic yield strength and cyclic stress amplitude resulted in good prediction for bimodal and lamellar microstructures, respectively. The accuracy of the model is further improved when a linear kinematic term is added to it. Transmission electron microscope, electron backscatter diffraction, and energy dispersive spectroscopy analysis revealed that the extensive softening in the bimodal microstructure is associated with the dislocation localization in the primary alpha (αp) leading to a considerable plastic strain accumulation and subsequent crystal re-orientation. The alloying element partitioning, lamella width, and the ease of slip transmission at the secondary alpha (αs) and beta (β) interface also play essential roles in the cyclic softening.

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

Investigating the Constitutive Model of Frozen Supersulfate Saline Soil: Insights from Fractional Calculus

The study of the mechanical properties of frozen saline soil is one of the key issues in addressing the design of infrastructure in cold regions. This research focuses on the supersulfated saline soil of the Ningxia Yellow River Irrigation Area in China, conducting triaxial tests under negative temperatures (−5, −10, −15 °C, and − 20 °C) with varying water contents (12%, 16%, 20%). Based on fractional calculus theory and incorporating an exponential decay factor, this study proposes a novel fractional-order constitutive model for a unified description of the softening and hardening behaviors in frozen saline soil. The model treats frozen saline soil as a composite blend of ideal solids and ideal fluids in varying proportions, taking into account the material's inherent time-dependency and non-linear stress-strain relationships. Finally, the validity of the model is verified by the calculated values of the model and the triaxial tests. The results indicate that, based on preliminary judgment, due to the presence of salt solutes, a large amount of liquid water remains in the supersulfated saline soil at temperatures ranging from 0 to −10 °C, forming an unstable state called “warm frozen saline soil”. The mechanical properties of frozen saline soil depend on the relative content of unfrozen water, ice crystals, and salt crystals and the formation of ice and salt crystals significantly enhances the strength of frozen saline soil. The computational results of the improved fractional constitutive model align well with experimental results, effectively describing the stress-strain relationship of frozen supersulfate saline soil. In the model, the parameter κ functions analogously to an elastic modulus and exhibits a linear relationship with temperature, and the parameter α characterizes the strain hardening of saline soil, while β describes its softening behavior. The proposed fractional constitutive model, with only three parameters having clear physical significance, is convenient for practical engineering applications.

Experimental characterization of a nonlinear mechanical oscillator with softening behaviour for large displacements

This paper presents an experimental insight into the performance of a mechanical oscillator consisting of an X-shaped-spring configuration. This configuration achieves an overall softening characteristic with quasi-zero stiffness behaviour far away from the static equilibrium point. Such a geometrical nonlinear configuration has attracted significant research attention in the last few years, particularly for its application as a vibration isolator with the possibility to extend the quasi-zero-stiffness region beyond that of the classical three-spring nonlinear isolator. However, previous experimental evidence has been limited to small amplitude vibration excitation only. Furthermore, it has been focused mainly on the isolation region, rather than on the large amplitude response, thus circumventing an insight on the damping effects and its modelling. To address this gap, in this paper, both frequency sweeps and random excitations are applied to a prototype device for experimental characterization. A nonlinear stiffness model is developed based on the geometry of the system and a nonlinear damping model is assumed based on experimental observation. The proposed model accurately describes the dynamic behaviour of the system as shown by comparison of theoretical and experimental data.