Stress Softening Research Articles

Effect of epoxy macromolecules as interfacial mediators on the microstructure and physical properties of styrene butadiene rubber/talcum powder composites

Poly(isoprene-co-glycidyl methacrylate) epoxy macromolecules were synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization to act as interfacial mediators between talcum powder (Talc) and styrene-butadiene rubber (SBR) with the aim of improving the properties of SBR/Talc composites. The epoxy macromolecules were uniformly dispersed on the surface of Talc using the spray-drying method. Subsequently, the modified Talc was utilized in the preparation of SBR composites. During hot vulcanization, isoprene double bonds could directly graft onto the rubber skeleton. Simultaneously, the epoxy groups opened the ring and formed covalent bonds with silanol. The interfacial covalent bonds were found to significantly enhance the dispersion of Talc and the interfacial interactions between SBR and Talc, as evidenced by scanning electron microscopy, cross-linking density measurements, and rubber processing analyzer tests. Differential scanning calorimetry results indicated that the number of interfacial covalent bonds and the content of glassy layers in the composites increased with the rise in GMA content and modified Talc. At equivalent filler loadings, epoxy macromolecules with 20 wt% and 34 wt% GMA increased the tensile strength by 31 % and 49 %, respectively. Concerning viscoelastic properties, composites containing interfacial covalent bonds exhibited superior stress relaxation and stress softening properties.

Thermo-mechanical aging of carbon-black reinforced styrene-butadiene rubber under cyclic-loading

PurposeThe research aims to investigate the impact of thermo-mechanical aging on SBR under cyclic-loading. By conducting experimental analyses and developing a 3D finite element analysis (FEA) model, it seeks to understand chemical and physical changes during aging processes. This research provides insights into nonlinear mechanical behavior, stress softening and microstructural alterations in SBR compounds, improving material performance and guiding future strategies.Design/methodology/approachThis study combines experimental analyses, including cyclic tensile loading, attenuated total reflection (ATR), spectroscopy and energy-dispersive X-ray spectroscopy (EDS) line scans, to investigate the effects of thermo-mechanical aging (TMA) on carbon-black (CB) reinforced styrene-butadiene rubber (SBR). It employs a 3D FEA model using the Abaqus/Implicit code to comprehend the nonlinear behavior and stress softening response, offering a holistic understanding of aging processes and mechanical behavior under cyclic-loading.FindingsThis study reveals significant insights into SBR behavior during thermo-mechanical aging. Findings include surface roughness variations, chemical alterations and microstructural changes. Notably, a partial recovery of stiffness was observed as a function of CB volume fraction. The developed 3D FEA model accurately depicts nonlinear behavior, stress softening and strain fields around CB particles in unstressed states, predicting hysteresis and energy dissipation in aged SBRs.Originality/valueThis research offers novel insights by comprehensively investigating the impact of thermo-mechanical aging on CB-reinforced-SBR. The fusion of experimental techniques with FEA simulations reveals time-dependent mechanical behavior and microstructural changes in SBR materials. The model serves as a valuable tool for predicting material responses under various conditions, advancing the design and engineering of SBR-based products across industries.

Creep analysis and service life prediction of turbine blade with progressive damage

Creep failure is one of the dominate failure mode for high temperature turbine blade during service. Under the tensile stress caused by large centrifugal force of the blade and the thermal stress and thermal softening of the material, the displacement as well as the creep strain and damage increase gradually. The present paper firstly gives the temperature field of the blade under typical service condition with numerical modelling. Then Norton’s creep constitutive relation and Lemaitre-Chaboche damage model are introduced into the finite element model, and three different working conditions are considered here to investigate its effect on creep service life of the turbine blade. Numerical results show that, the proposed numerical approach can predict the evolution of the creep process and the damage. Meanwhile, the introduction of cyclic factor is capable of reflecting the fatigue effect of cyclic load.

Molecular dynamics simulation of bonding role of cyclic borate ester in improving mechanical properties of the HTPB propellant

Excellent mechanical properties are the fundamental requirement for the practical application of solid propellants. However, solid oxidant fillers such as hexahydro-1,3,5-trinitros triazine (RDX) seriously weaken the mechanical strength of the propellant due to poor adhesion with the binder matrix. In this work, novel cyclic borate ester (CBE) bonding agents with long-chain alkyl moiety were designed by the molecular dynamics (MD) method to improve the unfavorable interfacial bonding effect. The interface models, which consist of RDX substrate and binder matrix where hydroxyl-terminated polybutadiene (HTPB) crosslinked with curing agents, were constructed to reveal the interface enhancement mechanism by CBE bonding agents. The results indicate that the designed CBE bonding agents with appropriate solubility parameters (SPs) can migrate from the binder matrix to the RDX surface. Besides, CBE bonding agents exhibit strong interaction with RDX compared to the binder matrix due to the formation of hydrogen bonds. Finally, the simulated tensile tests with two tensile modes showed that CBE bonding agents can enhance the interfacial strength and reduce stress softening rates by the calculation of debonding work. Moreover, this improvement can be controlled by adjusting the chain length of CBE bonding agents. The results obtained in this work deepen the understanding of the interfacial strengthening mechanism of bonding agents for solid propellants and provide a framework for designing high-performance bonding agents based on the MD method.

Strain softening characteristics and stress–strain relationship of Guiyang carbonate laterite

Strain softening characteristics and stress–strain relationship of Guiyang carbonate laterite

Experimental characterization and constitutive modeling of thermoplastic polyurethane under complex uniaxial loading

This paper presents the testing and constitutive modeling of a Thermoplastic Polyurethane (TPU) compound used in commercial applications. The tested specimens were extracted directly from a TPU sphere used in check valves through water-jet cutting. The tests included tensile and compression tests under complex uniaxial loading protocols to capture different nonlinear phenomena, such as stress softening, hysteresis, relaxation, creep, and rate dependence. The material is modeled assuming a nonlinear elastic equilibrium path that may exhibit stress softening (i.e., Mullins effect), and a hysteretic viscoplastic response that presents rate dependence at three different time scales. To achieve this constitutive behavior, a Parallel Rheological Framework model is used. The nonlinear elastic equilibrium path is modeled using the generalized Yeoh hyperelastic model. The stress softening of the equilibrium path is modeled using the Ogden-Roxburgh damage model on the deviatoric response. The hysteretic viscous response is further split into three viscoplastic chains to represent time dependence at three different time scales in a decoupled way. Each viscoplastic chain is modeled using the Bergstrom-Boyce model with its standard evolution law of the creep strain. The model parameters were found using a stochastic optimization scheme to simultaneously fit all the considered tests. The outstanding agreement between the model and the experimental data across a wide range of loading scenarios provides additional insight into the time-dependent behavior and deformation mechanism of TPUs. Moreover, it shows that the mechanical behavior of these materials can be represented by decoupling the nonlinear viscoplastic behavior in different time scales.

Effects of Trace Zn on the Deformation Mechanisms of Mg–Gd–Y–Zr Alloy Investigated by In Situ Synchrotron Diffraction

Addition of trace Zn can impose notable effect on the deformation behavior of Mg–Gd–Y–Zr alloy, while the underlying mechanisms have not been revealed. In the present work, Mg–8.5Gd–2.5Y–0.3Zr (wt%) (0Zn) and Mg–8.5Gd–2.5Y–0.5Zn–0.3Zr (wt%) (0.5Zn) alloys are fabricated by casting and extrusion, to obtain a bimodal microstructure containing fine dynamic recrystallized (DRXed) grains and coarse unDRXed grains. The as‐extruded 0Zn and 0.5Zn alloys are studied by in situ synchrotron diffraction under uniaxial tension and compression to clarify the effect of trace Zn on the deformation mechanisms. It is found that both alloys exhibit stress softening in the basal slip‐favored grains under both tension and compression, and adding trace Zn highly enhances the stress softening. Furthermore, the addition of Zn stimulates the occurrence of discontinuous yielding which is in connection with the stress softening, resulting from the interaction between basal dislocations and solute atmospheres. The tension–compression‐yielding symmetry of the alloy is improved by adding Zn, which is mainly attributed to the suppression effect of γ′ phases and Gd/Y–Zn dimers on tensile twinning. Finally, the addition of Zn can promote the tensile and compressive strength, owing to the strength enhancement of the relevant deformation modes and the increase of the fraction of unDRXed regions.

Investigation on deformation behaviors and dynamic recrystallization mechanism of spray formed Al–Zn–Mg–Cu alloy under hot compression

The thermal deformation behavior of spray formed Al–Zn–Mg–Cu alloy was investigated by the isothermal hot compression tests at the strain rates of 0.001–10 s−1 with the temperature range of 350–450 °C. An Arrhenius constitutive equation was established by the corrected strain-stress curves, and then the processing map was constructed based on the 3D instability map and 3D power dissipation map. The influence of strain rate and temperature on both flow stress and dynamic softening has been unveiled. The results show that dynamic recovery (DRV) is the primary softening mechanism and dynamic recrystallization (DRX) is substantively retarded due to the fine dispersed particles uniformly distributed in the spray formed alloy. Continuous dynamic recrystallization (CDRX) is the primary DRX mechanism at a low temperature or high strain rate. DRX grain was observed at the grain boundaries, especially at the triple junctions. The appropriate thermal deformation condition is recommended at the temperature range from 430 °C to 450 °C and strain rates from 0.003 s−1 to 0.1 s−1.

Robust anti-impact, energy absorption and thermal properties of polyurethane nanocomposites modified by phenol-amine chemistry

It is still a considerable challenge for polyurethane elastomers (PUE) to possess outstanding mechanical and thermal performance simultaneously against harsh dynamic impact environment due to their heat accumulation, thermal stress softening and mechanical failure. Thus, this article innovatively prepared binary nanofibers composed of carbon nanofiber (CNFs) and aramid nanofibers (ANFs) to reinforce PUE, where catechol (CC) and polyethyleneimine (PEI) were served as interfacial modifier between nanofibers and polymer matrix. PUE with 1.5 wt% binary nanofibers achieve 31.62 % increase in crosslinking density, 146.8 °C improvement in thermal decomposition temperature compared to Neat PUE. Besides, the absorption energy and dynamic compression strength of composites were increased by 40.36 % and 38.26 %, respectively. Because reinforced nanofibers with crosslinking network structures improve the interface interaction between fillers and matrix, facilitate stress transfer and increase the energy threshold of thermal decomposition. The paper supplements the impact resistance analysis of PUE-based protective materials under impact loads, providing a systematic and scientific reference for the design and manufacture of impact resistant materials.

Analysis of the Mullins effect in buckling instability of double-network hydrogel beams under swelling equilibrium

Due to their outstanding physical and mechanical properties, double-network (DN) hydrogels have gained a most attention among various synthetic tough hydrogels. The Mullins effect and buckling instability are two frequent phenomena that may occur simultaneously in slender DN hydrogel structures as high load-bearing candidates. The swelling/deswelling degree of the DN hydrogel affects the coupling phenomena. It is essential to understanding the interplay between these behaviors. In this work, a physically based damage constitutive model for a DN polymer under water-diffusion equilibrium and cyclic loadings is developed. This theory of coupled swelling and load-induced deformations show good capability in capturing the Mullins effect of swollen DN hydrogels and the corresponding swelling ratio. The model parameters are determined by fitting experimental data of a freely swollen DN hydrogel under cyclic compression. Based on the constitutive model and determined parameters, the buckling instability of DN hydrogel beams is studied via the analytical formula of incremental modulus. The stability diagrams of the DN hydrogel beams under virgin loading and reloading are presented. The influences of stress softening, strain stiffening and chemical potential on buckling conditions for compressive stress and slenderness ratio are thoroughly analyzed. It demonstrates that the stress softening is dramatically against the stability of the beam, but the strain-stiffening effect would conversely help widen the stable range. Besides, it is found that a DN gel beam immersed in a sufficient low chemical potential environment has better buckling stability. These theoretical results are valuable in the preparation and structural design of DN hydrogels for repeated use purpose.

Insights on the J‐integral expression of pure shear carbon black filled natural rubber specimen and predicting the crack growth rate using finite element method

AbstractThe J‐integral approach manifests itself in an efficient way to determine the crack growth and failure mechanism of tread and sidewall compounds used in tyres. Therefore, for a pure shear (PS) specimen of carbon black filled natural rubber, the J‐integral formula was vivisected, and the material parameters were defined using the concepts of solid mechanics considering the planar stress conditions. Theoretical calculations, experimental observations, and finite element analysis were executed to calculate the J value for different strain percentages. Different hyperelastic material models were used to understand the hyperelastic behavior of the test compound, but Yeoh model was found to be the best fit with the least error against the experimental test data. The frequency sweep dynamic mechanical analyzer test was done to observe the viscoelastic response of the material. It was observed that the J value decreased with decreasing contour radius and had exhibited stark difference with the global tearing energy values, indicating the effects of stress softening and the dependence of J value on the elastic characteristics of the material. Further, the J value attained from finite element methods for a random strain 22% was used to predict the crack growth rate of the pre‐notched PS specimen.Highlights J‐integral formula for pure shear specimen using solid mechanics approach. J value comparison of theoretical, experimental, and finite element methods. Dependence of J value on the elastic characteristics of the material. Different hyperelastic models compared and Yeoh model chosen for analysis. Prediction of crack growth rate at a random strain percentage.

An electroplastic constitutive model of fcc metals and their alloys under high current density

The mechanical behavior of fcc (face center cubic) metals and their alloys such as copper-based and aluminum-based materials changes obviously under high current density, but there is a lack of suitable constitutive model to describe the electroplastic behavior of these materials, which limits the accuracy of the mechanical response prediction in applications, such as electromagnetic launch. In this paper, a novel nonlinear constitutive model for electroplastic behavior under the high current density of fcc metals and their alloys is proposed. The model proposed is based on the theory of dislocation evolution, energy transfer theory and electron transport theory and takes into account the effects of high current density on dislocation density, strain rate and resistivity. Considering the evolution of forward and reverse dislocations caused by pulsed current, the relationship between the evolution rate of reverse dislocation and strain is established. Due to the sensitivity of the electroplastic effect to strain rate, the strain rate under electric current is obtained by combining the theory of dislocation thermal activation and energy transfer. According to the concept of thermal resistance and dislocation resistance, the relationship between resistance and current density is derived. The quantitative results demonstrate that this model can well capture the flow stress softening under high current density (>3000 A/mm2) and the transient hardening after current removal because of the consideration of a more suitable strain rate and dislocation evolution. The critical current density that has a significant effect on the strain rate and the current density corresponding to the subsection point of the resistivity are quantitatively obtained. Especially, it is shown that the evolution rate of the reverse dislocation decreases nonlinearly with the increase of strain after the current is removed. These results will be helpful to study the mechanical behavior of the rail during electromagnetic launch and further optimize the design of electromagnetic launch device.

Stress softening of nanoparticle-crosslinked hydrogels described using a physics-based damage model

Despite the promising applications of hydrogels, their poor mechanical properties still greatly limit their further applications. To improve the mechanical properties of hydrogels, various strategies have been proposed. Hydrogels with nanoparticle-crosslinked polymer networks show excellent toughness, self-recovery, and other advantages, and thus have great prospects for use in tissue engineering, artificial muscles, flexible electronics, and other fields. There have been experimental and theoretical studies of its damage. However, the underlying microscale physical mechanisms have not been fully elucidated. Herein, we established a physics-based constitutive model to describe the mechanical behavior of nanoparticle-crosslinked hydrogels under cyclic loading. The deformation-induced damage and the rate-dependent damage were explained by the network alteration and kinetics of chain dissociation/association, respectively. The kinetics dissociation/association theory was modified considering the polymer chains that wind around nanoparticles. The Mullins stress softening and recovery during cyclic loading were described. Cyclic loading tests on nanoparticle-crosslinked hydrogels were carried out to verify the proposed constitutive model. It is demonstrated that the model can well describe the mechanical behavior of nanoparticle-crosslinked hydrogels during cyclic loading.

Deep learning-based modeling of the strain rate-dependent thermomechanical processing response for a novel HIPed P/M nickel-based superalloy

Understanding and modeling the thermomechanical processing (TMP) response of a novel HIPed powder metallurgy (P/M) superalloy is crucial for its industrial application. This research characterizes the TMP-responding behavior of a novel HIPed FGH4113A P/M superalloy at 1000–1150 ℃ with strain rates of 0.01–5 s−1. The results depict that the adiabatic temperature rise during high-strain-rate TMP will accelerate the stress softening. A two-stage deep learning (DL)-based constitutive model framework, coupled with the deformation-induced temperature rise and its influence on flow stress, was first proposed and compared with the traditional Arrhenius-type model. Two types of DL approaches including the backpropagation (BP) and long short-term memory (LSTM) neural networks were trained and compared separately. It is noted that the LSTM neural network, considering previous deformation history in its unique gate structure, depicts the best prediction accuracy and generalization ability under large strains than other models. Then the strain rate-dependent hot workability and flow softening mechanisms were modeled and discussed. High-strain-rate deformation (5 s−1) in certain temperatures (1110–1150 ℃) can avoid unstable defects and transform the generated deformation heat into the driving force for the activation of multiple dynamic recrystallization mechanisms. Therefore, the near fully recrystallized microstructure can be achieved similarly to that at 0.01 s−1, indicating the feasibility and superiority of the high-strain-rate TMP of P/M superalloys in a certain temperature range.

Modeling the hot deformation behavior of micro-alloyed steel in the single and two-phase fields

Continuous casting is a well-established process to produce steel slabs. However, the surfaces of the slabs may crack during processing. The occurrence of cracks is related to different phenomena, i.e., ferrite formation, presence of precipitates, and microstructural modifications during manufacturing processing. In the present work, we developed a physically based mesoscale model to describe the plastic deformation of micro-alloyed steel in the single and two-phase fields, as well as the microstructure evolution. We implemented a dislocation density-based constitutive model to calculate the strain hardening and the stress softening produced by dynamic recovery using the Kocks-Mecking (KM) formalism for the austenite and ferrite. We coupled the KM model with the Johnson-Mehl-Avrami-Kolmogorov model to consider the dynamic recrystallization of the austenitic phase. The nucleation and growth of the recrystallized grains, driven by the stored energy, compete with the annihilation of dislocations due to dynamic recovery. In the two-phase domain, the iso-work condition for the load partition is implemented. We calculated the ferrite volume fraction by fitting the data obtained using JmatPro software. Moreover, an Arrhenius-type equation correlates the yield stress to the Zener-Hollomon parameter. We validated the model with isothermal uniaxial compression tests of microalloyed steel over the temperature range of 650 °C-1100 °C and strain rates of 10−2 s−1 and 10−3 s−1 using a Gleeble® 3800 thermomechanical simulator.

Multistep deformation of helical fiber electrospun scaffold toward cardiac patches development

The scaffolds used for cardiac patches must mimic the viscoelastic behavior of the native tissue, which expands up to high deformation levels of its sedentary size during the systole segment of pumping blood. In our study, we exposed fabricated electrospun samples to repeated multistep tension by applying and removing deformation to mimic the mechanical behavior of helical fibered cardiac scaffolds. Since the fiber-based specimens exhibit viscoelastic behavior, the transient responses to constant deformation caused stress relaxation and stress recovery. However, these transient viscoelastic operations performed at high strain enable unpredictable phenomena, usually hidden behind stress softening and folding (plasticity) phenomena; the material significantly reduces the required stress, and remaining deformation occurs. Thus, by regulating the fabrication (electrospinning parameters) process and preconditioning before setting, the actual viscoelastic behavior of the electrospun scaffolds will be evident, as well as their limitations towards their application to cardiac patches development.

An analytical method for predicting the soil-structure interaction of axially loaded piles in sands incorporating the two-surface plasticity model

The paper proposed a novel and practical analytical method for predicting the soil-structure interaction in sands. To well capture the stress softening and soil dilatancy behaviors during loading, a developed two-surface plasticity model for interface shearing is adopted to determine the 2-D stress–strain state of the soil-structure interface and the shear band, while the 3-D elastoplastic behavior of soil around the shear band is determined by another developed two-surface plasticity model for triaxial compression. Following a standardized solving procedure, the rigorous derivation for the stress–strain relationship in plastic zone is formulated as a system of first-order differential equations, which are solved as an initial value problem. Combined with the finite difference method (FDM), the load–displacement response of the axially loaded pile and the stress–strain state around the pile are presented. To verify the proposed analytical approach, a FEM simulation is performed using a user-defined subroutine. The soil with different initial void ratios ranging from very dense to loose is also modeled to demonstrate the effect of the initial void ratio on soil-structure response. The proposed analytical approach is also validated against centrifuge tests and field tests, manifesting the validity and capability of the proposed method.

Peridynamic modeling of rail wear during sliding contact considering thermal effects

Numerical simulations of rail wear during sliding contact pose significant challenges owing to the complex coupling between thermomechanical contact loads, material properties, and profile changes. This study proposes a modeling approach for rail wear during sliding contact, using nonlocal peridynamic (PD) thermomechanics and a bond damage criterion based on ratchet failure. To facilitate test verification, a two-dimensional PD model for twin-disc testing with elastoplastic materials was developed, and numerical simulations and corresponding twin-disc testing were performed during wheel idling under different loads, idling speeds, and idling times. The PD model accurately predicted rail wear under all operating conditions, exhibiting excellent agreement with the test results, and thus validating the proposed method and supporting the ratchet failure mechanism. Subsequently, thermomechanical modeling of sliding contacts with different creepages was performed. The PD model predicted continuous wear along the contact surface, with an increase in wear depth corresponding to higher creepage values. As the contact temperature increased with creepage, thermal stress and thermal softening caused slight and sharp increases in rail plastic strain, respectively. Therefore, thermal softening is the main factor responsible for the significant increase in wear rate with temperature. Finally, wear results of the PD model and classical Archard’s wear model were compared. The PD models can capture variations in wear rates that are difficult to address using the Archard model.

Effect of dry-wet cycles on the strength and deformation of the red-bed rockfill material in western Yunnan

Introduction: The shear strength deterioration of red-bed rockfill under the dry-wet cycle is the key factor affecting the slope stability of accumulation body. Studying the strength deterioration law and deterioration mechanism of red-bed rockfill can provide theoretical support for slope stability control.Methods: Through the disintegration resistance test of argillaceous siltstone rockfill in Lanping lead-zinc Mine, the disintegration characteristics of red-bed soft rock were studied. The effects of the number of dry-wet cycles on the cohesion, internal friction angle, shear dilation rate and shear modulus of the red-bed rockfill were investigated by using a dry-wet cycle shear tester to conduct shear tests on the reduced scale graded soil material, and the strength deterioration mechanism of the soils was revealed from the perspective of meso-structure.Results: The results showed that argillaceous siltstone was rich in clay minerals and produces strong disintegration when exposed to water. The disintegration process could be divided into three stages: massive disintegration stage, transitional stage and stabilization stage. With the accumulation of dry-wet cycles, the shear dilation rate and shear modulus of the argillaceous siltstone rockfill gradually decrease, and the shear failure developed gradually from strain hardening to shear plastic flow, and the characteristic of weak stress softening occurred. After eight dry-wet cycles, the cohesion and internal friction angle of argillaceous siltstone rockfill materials decreased by 89.87% and 18.94%, respectively, indicating a higher effect on the cohesion than on the internal friction angle.Discussion: The thickening of the bound water between the fine particles on the shear surface, the weakening of the coarse particle attachment, and the increase in the number of directionally arranged fine particles were the main reasons for the continuous deterioration of the soil strength.

Constitutive laws of softened UHPC in biaxial tension–compression: Experimental study using a planar bi-directional element tester

Ultrahigh-performance concrete (UHPC) has been gradually applied in bridge and building engineering to replace traditional reinforced concrete (RC). More realistic simulations are required for the design of structures. However, a two-dimensional constitutive model for UHPC is lacking. Tsinghua University developed a planar bidirectional element tester (PBET) that can perform tests on various structural types of element specimens. In this study, one nonreinforced UHPC element specimen under uniaxial compression and ten nonreinforced UHPC element specimens under biaxial tension and compressive coupling condition were tested using PBET. The compressive stress–strain relationship was established based on the uniaxial compressive test. By analyzing the test results, the softening effect of the principal tensile strain on the peak compressive stress and strain of UHPC was evaluated. Stress and strain softening coefficients were proposed, and the constitutive law of softened UHPC under compressive stress was modified and verified using the test results, which contributes to the improvement and development for the two-dimensional constitutive law for UHPC.