Stress-softening Behavior Research Articles

A viscoelastic damage model for nanoparticle/epoxy nanocomposites at finite strain: A multiscale approach

Experimental tests show that nonlinear viscoelasticity characterizes the mechanical behavior of boehmite nanoparticle (BNP)/epoxy nanocomposites. This paper presents the development and numerical implementation of a physically based constitutive model for BNP/epoxy nanocomposites undergoing finite strain. The proposed constitutive model allows capturing the main features of the stress-strain relationship of BNP/epoxy nanocomposites, including the nonlinear hyperelastic, time-dependent and softening behavior. The characterizing feature of this study is to propose a methodological framework based on molecular dynamics simulations and experimental tests to identify the material parameters for the model. Molecular simulations in conjunction with the Eyring viscosity theory are used to characterize the viscoelastic deformation of epoxy resins under loading. The concept of strain amplification is also adopted to account for the effect of nanoparticles on the stress–strain response of the nanocomposites. The stress softening behavior is captured by a monotonically increasing function of deformation, so-called damage variable. The results show that the model predictions of stress-strain relationships are in good agreement with experimental data at different BNP weight fractions. Finally, the constitutive model is implemented in the finite element analysis and examined by means of a benchmark example. Experimental–numerical validation confirms the predictive capability of the present modeling framework, which provides a suitable tool for analyzing BNP/epoxy nanocomposites.

Free radical polymerization simulation and molecular entanglement effect on large deformation behavior

In this paper, we proposed a novel molecular dynamics (MD) free radical polymerization algorithm that can dynamically simulate chain growth of the thermoplastic network and produce unit cells having experimentally observed molecular weight distributions. In the proposed algorithm, a coarse-grained force field was implemented by combining bonded terms from the PCFF and nonbonded terms from the TraPPE-UA to alleviate computational times. We controlled molecular weight distribution by the number of initiator radicals. Effects of the molecular weight on density, and glass transition temperature were investigated. A linear relationship of the conversion ratio with specific volume change was discovered. More importantly, the PMMA system by the proposed MD polymerization algorithm could explain physical causes of stress-softening behavior often observed in the large deformation tensile tests in terms of molecular weight and unfolding of chain entanglement. The proposed polymerization algorithm will facilitate studies on large deformation nonlinear constitutive behavior and modelings of thermoplastic polymers.

Cyclic uniaxial mechano optical studies on stress-softening behavior of natural rubber/clay nanocomposites

A real-time spectral birefringence technique was implemented to follow the coupled relationships between birefringence, true stress and true strain of natural rubber (NR)/organo-modified clay (OC) nanocomposites (NRCNs) during cyclic stretching and retraction. The dynamics of structural evolution was also followed by off-line Wide Angle X-ray Diffraction. The results show that the birefringence and true stress at the same level of strain increases with the OC content during stretching. During the strain retraction, the birefringence of NRCNs with low OC content initially decreases slower when plotted against true strain and then decreases faster as the strain is retracted further. In contrast, the NRCNs with higher OC content exhibit a lower birefringence than the value during stretching due to more rupture of rubber-filler bonding occurred during stretching. The birefringence-true stress retraction curves show that the birefringence of NRCNs with low OC concentrations increases slightly which is caused by the further formation of rubber crystallites at high strain when optimum amount of filler is present, then the birefringence declines slowly due to the relaxation of rubber chains. While the NRCNs with higher OC content have a rapid stress decrease with a small strain retraction (limited chain relaxation), thus they exhibit a birefringence plateau during the initial stress retraction and a sharp decline as the stress decreases further.

New insights on the relationship between flow stress softening and dynamic recrystallization behavior of magnesium alloy AZ31B

The dynamic recrystallization (DRX) behavior of magnesium alloy AZ31B with large initial grain size was investigated. Two methods were applied to establish the DRX kinetics model. One is based on the values of DRX volume fraction evaluated by true stress-strain curves (Model 1). The other is based on the values of DRX volume fraction evaluated using optical micrographs (Model 2). It is found that the predicted DRX volume fraction by Model 1 is significantly larger than that by Model 2. It indicates that the value of DRX volume fraction (Xdrx) cannot be calculated by the true stress-strain curves for the magnesium alloy AZ31B with large initial grain size. To understand the phenomenon, the reason was analyzed and discussed. We found that the main reason can be attributed to the strong fine-grain strengthening (FGS) effect of magnesium alloy AZ31B. For the studied material, the flow behavior will be mainly affected by two factors during DRX: 1) the decrease of average dislocation density which gives rise to the decrease of flow stress; 2) the decrease of average grain size which results in the increase of flow stress. The latter causes that the DRX volume fraction evaluated by the true stress-strain curves is obviously larger than the real one. The research results will be good references for the evaluation of DRX volume fraction of other FGS materials with large initial grain sizes.

Experimental characterization and continuum modeling of inelasticity in filled rubber-like materials

Filled rubber-like materials are important engineering materials, and they are widely used in aerospace, automotive, and other industries. However, their nonlinear, inelastic, and rate-dependent constitutive behavior is not fully understood and modeled with varying degrees of success. Much of the previous literature has focused on either capturing quasi-static stress-softening behavior or rate-dependent viscous effects, but generally not both concurrently. In this work, we develop a thermodynamically consistent constitutive model which accounts for both of those phenomena concurrently. A set of comprehensive mechanical tensile tests were conducted on the filled rubber Viton. The constitutive model was then calibrated to the experimental data, and numerically implemented into the finite element package Abaqus by writing a user material subroutine UMAT. The constitutive model was validated by comparing a numerical simulation prediction with an inhomogeneous deformation experiment.

Development of a finite element model to study the effect of temperature on erosion resistance of polyurethane elastomers

In this study, a numerical model based on the finite element technique was developed to study the effect of temperature on the erosion mechanism of material removal during solid particle impact on polyurethane elastomers. The hyperelastic, isotropic hardening, and Mullins damage criteria were chosen as the material model formulations to account for elastic, plastic, and stress softening behavior of the elastomer, respectively. The model inputs were determined experimentally by tensile testing and cyclic loading. In the finite element modeling approach that was developed the impact of ten erodant particles at a single location on the substrate elastomer at controlled temperatures of 22°C, 60°C, and 100°C was simulated. Erosion testing experiments were conducted to provide data for model verification. The results obtained from the finite element model showed that the final elongation at break and associated ultimate stress have the most significant influence on the erosion rate in cases where the stresses produced exceeded the failure stress during impact. This was the case for PU at 100°C in which the material had the lowest failure stress. The model also successfully simulated the mechanism of material removal by accumulating residual strains such that detachment of larger pieces of material occurred at the surface. The plastic deformation and Mullins stress softening were found as parameters affecting this type of wear. The Mullins damage caused by the impact of particles facilitated the localized detachment of small fragments from the surface upon impact of subsequent particles. Overall, although the model allowed for the study of the wear mechanisms and was capable of predicting the morphology of the eroded surfaces of the PU, the model failed to predict accurately the erosion rates, most probably due to the assumptions that were made to simplify the model.

Smoothed polygonal finite element method for generalized elastic solids subjected to torsion

Orthopaedic implants made of titanium alloy such as Ti-30Nb-10Ta-5Zr (TNTZ-30) are biocompatible and exhibit nonlinear elastic behavior in the ‘small’ strain regime (Hao et al., 2005). Conventional material modeling approach based on Cauchy or Green elasticity, upon linearization of the strain, inexorably leads to Hooke’s law which is incapable of describing the said nonlinear response. Recently, Rajagopal introduced a generalization of the theory of elastic materials (Rajagopal, 2003, 2014), wherein the linearized strain can be expressed as a nonlinear function of stress. Consequently, Devendiran et al. (2016) developed a thermodynamically consistent constitutive equation for the generalized elastic solid, in order to capture the response of materials showing nonlinear behavior in the small strain regime. In this paper, we study the response of a long cylinder made of TNTZ-30 with non-circular cross section subjected to end torsion. An explicit form of the constitutive equation derived in Devendiran et al. (2016) is used to study the response of the cylinder. The cross-section is discretized with quadratic serendipity polygonal elements. A novel one point integration rule is presented to compute the corrected derivatives, which are then used to compute the terms in the stiffness matrix. Unlike the conventional Hooke’s law, the results computed using the new constitutive equation show stress softening behavior even in the small strain regime.

Stress softening behaviour of HDNR bearings: modelling and influence on the seismic response of isolated structures

SummaryHigh‐damping natural rubber (HDNR) bearings are extensively employed for seismic isolation of structures because of their low horizontal stiffness and high damping capacity. Filler is used in HDNR formulations to increase the dissipative capacity, and it induces also a stress softening behaviour, known as the Mullins effect. In this paper, a wide experimental campaign is carried out on a large number of virgin HDNR samples to better investigate some aspects of the stress softening behaviour, such as the direction dependence and recovery properties, and to characterize the stable and softening response under different strain histories. Test results are also used to define a model for simulating the response of HDNR bearings in shear that advances the state of the art in the description of the stress softening, which can be significant during the earthquake time history. The proposed model is used to analyse the seismic response of a simplified isolated structure modelled as an SDOF system under ground motions with different characteristics and by considering two different conditions for the bearings: one assuming the virgin (or fully recovered) rubber properties and the other assuming the stable (or fully scragged) rubber properties. The results show that, in the case of far‐field records, the differences between the responses are limited although not negligible, whereas for near‐fault records, modelling the bearings as being in their virgin state significantly reduces the effect of this kind of motion on isolated structures. Copyright © 2017 John Wiley & Sons, Ltd.

Biocomposites from Natural Rubber: Synergistic Effects of Functionalized Cellulose Nanocrystals as Both Reinforcing and Cross-Linking Agents via Free-Radical Thiol-ene Chemistry.

Natural rubber/cellulose nanocrystals (NR/CNCs) form true biocomposites from renewable resources and are demonstrated to show significantly improved thermo-mechanical properties and reduced stress-softening. The nanocomposites were prepared from chemically functionalized CNCs bearing thiols. CNCs served as both reinforcing and cross-linking agents in the NR matrix, and the study was designed to prove the cross-linking function of modified CNCs. CNCs were prepared from cotton, and the cross-linkable mercapto-groups were introduced onto the surface of CNCs by esterification. Nanocomposite films were prepared by dispersing the modified CNCs (m-CNCs) in NR matrix by solution casting. The cross-links at the filler-matrix (m-CNCs-NR) interface were generated by photochemically initiated thiol-ene reactions as monitored by real-time FTIR analysis. The synergistic effects of reinforcement and chemical cross-linking at the m-CNCs-NR interface on structure, thermo-mechanical, and stress-softening behavior were investigated. Methods included field emission scanning electron microscopy (FE-SEM), swelling tests, dynamic mechanical analysis, and tensile tests. Compared to biocomposites from NR with unmodified CNCs, the NR/m-CNCs nanocomposites showed 2.4-fold increase in tensile strength, 1.6-fold increase in strain-to-failure, and 2.9-fold increase in work-of-fracture at 10 wt % of m-CNCs in NR.

Tu1155 Stress Softening Behavior in the Mucosa-Submucosa and Muscle Layers in Normal and Diabetic Rat Esophagus

Tu1155 Stress Softening Behavior in the Mucosa-Submucosa and Muscle Layers in Normal and Diabetic Rat Esophagus

Constitutive equations of flow stress of magnesium AZ31 under dynamically recrystallizing conditions

Constitutive equations for the relationship between flow stress, strain, strain rate and temperature for magnesium AZ31 alloy under hot working conditions where dynamic recrystallization is prevalent have been developed. Equation development data were obtained using isothermal plane strain compression (PSC) tests carried out at 300–500°C with strain rates ranging from 0.5 to 50s−1, to an equivalent strain of 0.7. The predicted flow stress curves show good comparison with the experimental isothermal flow curves in terms of peak, steady state stress and flow softening behaviour but at higher Zener–Hollomon (Z) values (>1011s−1) the predicted peak stress deviates from the isothermal value in the range of 14–25MPa suggesting a breakdown in the hyperbolic sine equation at those Z values. The developed constitutive equations for the valid thermomechanical conditions were adopted in a finite element model to simulate the PSC conditions. The distributions of strain, strain rate and temperature qualitatively suggest higher strain rate at the centre of the sample which agrees well with that of the quantitative analysis of the dynamically recrystallized grain size.

Evaluation of variation in unbound layers’ moduli and its effect on pavement design

This study evaluates the uniformity of the pavement unbound layers’ moduli along a section of a test road in Edmonton, Alberta using falling weight deflectometer (FWD) test data. The FWD tests were performed on the finished subgrade and base surfaces during construction along the outer wheel path (OWP) and centerline (CL). The subgrade modulus along the OWP and CL showed a coefficient of variance (COV) of 0·31 and 0·59, correspondingly. Similar variation was observed in the subgrade modulus after placement of the base layer. Subgrade modulus displayed stress-softening behavior under the different bulk stresses during the FWD tests.Tests conducted on top of the base indicated that variation also exists in the base modulus, with COVs of 0·23 and 0·26, respectively, along the OWP and CL. Variation in the unbound layers’ moduli was found to be influential on the mechanistic empirical pavement design guide (MEPDG)-predicted rutting.

A study on stress-softening of nitrile butadiene rubber reinforced by in situ zinc dimethacrylate

The stress-softening behavior of nitrile butadiene rubber reinforced by in situ zinc dimethacrylate was studied. The degree of stress-softening effect in the fourth stretch-strain cycle of the nitrile butadiene rubber with 10 phr zinc dimethacrylate was only 1.03 (strain = 100%), while it reached to 50.39 at 40 phr zinc dimethacrylate (strain = 200%). The stress-softening effects of carbon black and silica filled nitrile butadiene rubber were also studied, which was used to compare the different stress-softening mechanisms of zinc dimethacrylate. Mooney–Rivlin semi-empirical equation was introduced here to analyze the stress–strain behavior of the nitrile butadiene rubber/zinc dimethacrylate, and the results showed that the nitrile butadiene rubber/zinc dimethacrylate system has an apparent Payne effect and it is easy to achieve the inextensibility limit of rubber chains. Crosslink density analysis indicated a high ionic crosslink density in the nitrile butadiene rubber filled with high content zinc dimethacrylate, which contributed to the low elastic-recovery of the stress-softening.

Semiflexible filament networks viewed as fluctuating beam-frames

We present a new method combining structural and statistical mechanics to study the entropic elasticity of semiflexible filament networks. We view a filament network as a frame structure and use structural mechanics to determine its static equilibrium configuration under applied loads in the first step. To account for thermal motion around this static equilibrium state, we then approximate the potential energy of the deformed frame structure up to the second order in kinematic variables and obtain a deformation-dependent stiffness matrix characterizing the flexibility of the network. Using statistical mechanics, we then evaluate the partition function, free energy and thermo-mechanical properties of the network in terms of the stiffness matrix. We show that penalty methods commonly used in finite elements to account for constraints, are applicable even when statistical and structural mechanics are combined in our method. We apply our framework to understand the expansion, shear, uniaxial tension and compression behavior of some simple filament networks. We are able to capture the stress-stiffening behavior due to filament reorientation and stretching out of thermal fluctuations, as well as the reversible stress-softening behavior due to filament buckling. Finally, we apply our method to square networks and show how their mechanical behavior is different from triangular networks with similar filament density and persistence length.

Specific nonlinear viscoelasticity behaviors of natural rubber and zinc dimethacrylate composites due to multi‐crosslinking bond interaction by using rubber process analyzer 2000

AbstractIn this paper, the dynamic mechanical properties of the natural rubber (NR) which was filled with in situ zinc dimethacrylate (ZDMA) were investigated using a Rubber Process Analyzer (RPA2000). A weak rigid filler–filler network was formed in the uncured NR/ZDMA compounds. Pronounced Payne effect and stress‐softening behavior were observed in the vulcanizates, which indicated that a strong and special filler structure was formed after vulcanization. However, an ionic network might be formed with a high ZDMA loading, which was not favorable to rebuild the poly‐ZDMA network. Finally, two tentative regions of networks deformation during the dynamic strain sweep were discussed: filler–filler and ionic bonds dominating region and rubber network dominating region. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers

실내시험에 의한 새로운 격자지보재의 하중지지력 평가

최근 건설되는 터널의 심도가 깊어져 난공사 구간이 증가되며, 초장대 터널의 증가로 터널 기술 개발이 필요해지고 있다. 터널의 기술개발의 하나로 터널 강지보재로 사용되는 높이 95mm 격자지보재에 사용되는 스파이더를 최적화하여 U자형과 보강재스파이더를 개발하였다. 개발된 격자지보재의 하중지지력을 평가하기 위하여 국내에서 사용되는 4절점 휨강도 실험을 실시하였으며 실내 실험을 위해 기존 격자지보재와 개발된 격자지보재의 시편을 직선으로 제작하여 실시하였다. 실험 결과 새로운 격자지보재는 기존의 격자지보재에 비하여 하중지지력이 높게 나타났다. 지지력 평가에 의한 시편의 응력-변형 거동을 분석한 결과 기존 격자지보재는 탄소성 거동이 나타났고, 새 격자지보재는 응력연화의 거동이 나타났다. 새 격자지보재는 하중이 가해지는 지점의 위치에 따라 지지력 거동이 달라짐을 알 수 있었다. Recently, the depth of tunnel constructed is getting deeper, which increases difficulty in construction works. Deliberate tunneling techniques are needed as the span and length of tunnels are increased. As one of the technical developments for tunnel, U-shaped and reinforced spider lattice girders are developed by optimizing the spider used in 95mm lattice girder as tunnel steel ribs. In order to evaluate the load bearing capacity of the lattice girder, the 4-point flexural tests are carried out. For the laboratory tests, straight specimens are made for the existing lattice girder and the new lattice girder. The results of the flexural tests showed that the maximum load bearing capacity of the new lattice girders was higher than the traditional one. The load-displacement behavior of the test specimens showed the elasto-plastic behavior in the existing lattice girder and the stress softening behavior in the new lattice girder. It was found that the load bearing capacities are changed depending on the location of the loading points.

Study on the properties of ethylene‐vinyl acetate rubber vulcanizate filled with superfluous magnesium hydroxide/methacrylic acid

AbstractEthylene‐vinyl acetate rubber (EVM) vulcanizates cured by dicumyl peroxide (DCP) with excellent mechanical properties were obtained by adding superfluous magnesium hydroxides (MH)/methacrylic acid (MAA). Different factors such as the DCP content and MH content were investigated to reveal their effects on the properties of the MH/MAA‐filled EVM vulcanizates. The formulation of DCP of 2 phr, MH of 60 phr, and MAA of 5 phr is recommended for the EVM vulcanizates with excellent mechanical properties. The stress relaxation and stress softening behavior of MH/MAA‐filled EVM vulcanizates were studied. The stress relaxation and stress softening became faster and more obvious with increasing MH content. The hot air aging resistance of EVM vulcanizates filled with different fillers such as silica and high abrasion furnace were compared, and the MH/MAA‐filled EVM vulcanizates had the best aging resistance at 40‐phr filler content. The MH/MAA‐filled EVM vulcanizates had excellent flame retardancy due to the high MH content. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

A non-monotonous damage function to characterize stress-softening effects with permanent set during inflation and deflation of rubber balloons

A non-monotonous stress-softening phenomenological model is applied to study the Mullins effect with residual strains to characterize the inflation and deflation of rubber balloons. It is shown that analytical predictions based on our proposed non-monotonous softening function and the modified stress-softening non-Gaussian average-stretch full-network constitutive equation that accounts for residual strains are consistent with experimental data. Also, we use the constitutive equation for equibiaxial extension to predict stress-softening behavior in a kinematically equivalent simple compression deformation state.

Lipid domains and mechanical plasticity of Escherichia coli lipid monolayers

Lipid monolayers can be laterally dilated under the action of the barriers in a Langmuir trough thus allowing for measurements of their mechanical response. We study the stress response of Escherichia coli polar lipid extract and POPC against oscillatory deformations stressed up to a 20% of the initial area. For E. coli monolayers a nonlinear regime described by a series of Fourier harmonics of the excitation mode is found beyond a critical strain (u(C) approximately 1%). In contrast, the mechanical response of POPC monolayers is found linear upon much larger deformations. For E. coli monolayers the stress-strain plot reflects stress softening (plastic-like) behaviour whilst POPC behaves as a linear elastic body. No viscous delay with respect to the applied strain is detected in both systems, as expected for high fluid materials. The presence of phase coexistence domains as lipid reservoirs to facilitate lateral diffusion is claimed as a plausible mechanism underlying the observed mechanical plasticity.

Mullins effect characterization of elastomers by multi-axial cyclic tests and optical experimental methods

Besides the typical hyperelastic behaviour, large elastic deformations with non-linear stress–strain behaviour, rubber-like materials may also exhibit some inelastic effects, like hysteresis and permanent set. One of them is a particular damage phenomenon called Mullins effect. This is visible when cyclic tension tests are performed with increasing values of deformation. Material is deformed up to a fixed strain value and then unloaded. When a second load is applied it is possible to observe a stress softening effect. In the present work uniaxial and equibiaxial tension tests have been carried out by a standard tensile machine and by an hydraulic bulge test experimental rig, respectively. In both tests optical methods have been used for strain measurement. Experimental data have been successively introduced in a numerical procedure that permitted to extract the best material parameters for two of the most known pseudo-elastic models [Ogden, R.W., Roxburgh, D.G., 1999. A pseudo-elastic model for the Mullins effect in filled rubber. Proceedings of the Royal Society London A 455, 2861–2877; Dorfmann, A., Ogden, R.W., 2004. A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber. International Journal of Solids and Structures 41, 1855–1878] accounting for both stress-softening behaviour and residual strain.