A viscoelastic–plastic constitutive model for uniaxial ratcheting behaviors of polycarbonate

In this paper, a modified viscoelastic–plastic constitutive model has been proposed on the framework of Anand's work to describe the uniaxial ratcheting behavior of polycarbonate (PC) under tension–tension cyclic loading. The experimental observation illustrates that the previously accumulated deformation has an assignable influence on the subsequent material response during the ratcheting process of PC. Thus, the deformation resistance in the viscoelastic micromechanism is assumed to be evolving with the local accumulated inelastic strain rather than keeping unchanged in the original Anand's model. The proposed model is validated firstly by the monotonic tension and creep experiment results of PC. Then, its capability to describe the uniaxial ratcheting behaviors is compared with Anand model. Finally, the modified model is adopted to study the effect of mean stress, stress amplitude, loading rate, and peak holding time on the ratcheting behaviors of PC. It is shown that the proposed model can predict reasonably the uniaxial tension–tension ratcheting behavior of polymer. POLYM. ENG. SCI., 55:2559–2565, 2015. © 2015 Society of Plastics Engineers     

Cyclic deformation behavior of an epoxy polymer. Part I: Experimental investigation

A series of uniaxial cyclic tests were carried out on solid cylindrical specimens of an epoxy resin, Epon 826/Epi‐Cure Curing Agent 9551. The focus of the study was to investigate time‐dependent viscoelastic behavior of this thermosetting polymer material under cyclic loading and to develop a constitutive model with the capabilities to simulate the observed deformation response. The tests include stress‐controlled or strain‐controlled cyclic loading with/without mean stress or mean strain at various amplitudes and loading rates. It was found that the cyclic stress‐strain response of this material is amplitude‐dependent and rate‐dependent, and the response to axial tension is different from that in compression. The stress‐strain loops exhibit more pronounced nonlinearity with high amplitudes or low loading rates. For stress‐controlled cyclic loading with mean stress, ratcheting strain is accumulated, which is of viscoelastic nature, and this is confirmed by its full recovery after load removal. For strain‐controlled cyclic loading with mean strain, the mean stress relaxation occurs, which contributes to the observed longer life in comparison to the stress‐controlled cyclic loading with mean stress. Polym. Eng. Sci. 44:2240–2246, 2004. © 2004 Society of Plastics Engineers.     

Separating stress and time dependent effects in the temperature dependent creep of polyethylene nanocomposites

The nonlinear time dependent creep of linear‐low density polyethylene (LLDPE) reinforced with montmorillonite layered silicate was investigated. A previous study related the time/stress dependence of creep compliance of the material at room temperature using the Burger and Kohlrausch‐Williams‐Watts models. Using both the creep and recovery compliance curves, we employ the Schapery formulation to study the relationship between deformation, time, stress, and temperature of LLDPE nanocomposites. Smooth mastercurves are constructed using time–temperature–stress superposition principles. The stress and temperature‐related creep constants and shift factors were determined for the material using the Schapery nonlinear viscoelastic equation. The prediction results confirm the enhanced creep resistance of nanofillers even at extended time scales and low temperatures. POLYM. ENG. SCI., 50:1646–1657, 2010. © 2010 Society of Plastics Engineers     

Predictions of two nonlinear viscoelastic constitutive relations for polymers under multiaxial loadings

Two viscoelastic constitutive relations in differential form are further developed here to include material nonlinearity and distinction between loading and unloading regimes, which is a characteristic of polymers. The effects of hydrostatic pressure and anisotropy in tension and compression on the deformation response of polymers are accounted for through the definition of a pressure‐dependent equivalent stress. In the uniaxial stress state, these constitutive relations reduce to the two well‐known mechanical analogue representations: “Kelvin–Voigt‐type” and “Maxwell‐type” rheological models. The predictive capabilities of these constitutive relations are then assessed against a wide range of experimental results, which include both uniaxial and biaxial stress states subjected to quasi‐static and cyclic‐loading conditions. The predictions of both models are found to be in good agreement with the test data. POLYM. ENG. SCI., 47:593–607, 2007. © 2007 Society of Plastics Engineers.     

A rate‐type nonlinear viscoelastic–viscoplastic cyclic constitutive model for polymers: Theory and application

A thermodynamically consistent rate‐type viscoelastic–viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time‐dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one‐dimensional rheological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub‐components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time‐dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time‐dependent stress–strain responses of the PC can be reasonably predicted by the proposed model. POLYM. ENG. SCI., 56:1375–1381, 2016. © 2016 Society of Plastics Engineers     

Cyclic deformation behavior of an epoxy polymer. Part II: Predictions of viscoelastic constitutive models

The experimental results presented in Part I of this study were used to evaluate the predictive capabilities of two viscoelastic constitutive models. One of the models, developed by Xia and Ellyin, is in a differential form. The other, which is a modified Schapery model by Lai and Bakker, is in an integral form. The results of the comparison indicate that the Xia‐Ellyin constitutive model simulated the experimental observations well. This was attributed to the existence of a general rule that delineates the loading and unloading parts of the cyclic response. The modified Schapery model was able to predict the general trends of the deformation behavior; however, it was unable to correctly simulate the unloading behavior. This difference became more pronounced when the applied cyclic stress/strain was high. At high applied loads, the material response became more nonlinear. POLYM. ENG. SCI. 45:103–113, 2005. © 2004 Society of Plastics Engineers     

A simple constitutive model for cyclic compressive ratchetting deformation of polyteterafluoroethylene (PTFE) with stress rate effects

Pure polyteterafluoroethylene (PTFE) were prepared by using the process of cold pressure and sintering. A series of unaxial cyclic compression tests were carried out on solid cylindrical specimens of pure PTFE. The focus of study was to investigate time‐dependent ratchetting behavior of PTFE under cyclic loading. It is shown that the stress–strain hysteresis loops exhibit pronounced nonlinearity with high stress range. The cyclic hardening is rate and stress range dependent. However, mean stresses have less effect on cyclic hardening than stress ranges. It is shown that viscoelasticity is obvious in the beginning cycles. The same stress range produces almost the same viscoelastic delay at the beginning of the compression cycles. A modified universal ratchetting model (URM), which is rate dependent is employed to predict the ratchetting strain under compressive cyclic loading condition at room temperature. POLYM. ENG. SCI., 48:29–36, 2008. © 2007 Society of Plastics Engineers     

Long‐term mechanical behavior of aramid fibers in seawater

Aramid fibers are today proposed in ropes and cables for marine applications. As these highly crystalline materials are loaded in tension for a longer period in seawater, their long‐term mechanical behavior has to be understood. However, the response is time‐dependent and exhibits a nonlinear effect with stress. In this study, two types of aramid fibers are studied: Twaron and Technora. Mechanical properties are measured using static tensile tests and creep‐recovery tests. A nonlinear viscoelastic–viscoplastic model, based on the Schapery formulation, allows discriminating between the instantaneous and the time‐dependent response as well as the reversible and nonreversible phenomena (plasticity). First, this procedure allows the overall mechanical behavior of the fibers to be compared, considering creep rate, plasticity, and instantaneous moduli. Then, using these parameters, the effect of the testing condition, air or seawater is studied. Finally, the effect of aging in seawater is quantified for both fibers. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

Tensile creep of a long‐fibre glass mat thermoplastic (GMT) composite. II. Viscoelastic‐viscoplastic constitutive modeling

In Part I of this article, the short‐term tensile creep of a 3‐mm‐thick continuous long‐fibre glass mat thermoplastic composite was characterized and found to be linear viscoelastic up to 20 MPa. Subsequently, a nonlinear viscoelastic model has been developed for stresses up to 60 MPa for relatively short creep durations. The creep response was also compared with the same composite material having twice the thickness for a lower stress range. Here in Part II, the work has been extended to characterize and model longer term creep and recovery in the 3‐mm composite for stresses up to near failure. Long‐term creep tests consisting of 1‐day loading followed by recovery were carried out in the nonlinear viscoelastic stress range of the material, i.e., 20–80 MPa in increments of 10 MPa. The material exhibited tertiary creep at 80 MPa and hence data up‐to 70 MPa has been used for model development. It was found that viscoplastic strains of about 10% of the instantaneous strains were developed under load. Hence, a non‐linear viscoelastic–viscoplastic constitutive model has been developed to represent the considerable plastic strains for the long‐term tests. Findley's model which is the reduced form of the Schapery non‐linear viscoelastic model was found to be sufficient to model the viscoelastic behavior. The viscoplastic strains were modeled using the Zapas and Crissman viscoplastic model. A parameter estimation method which isolates the viscoelastic component from the viscoplastic part of the nonlinear model has been developed. The model predictions were found to be in good agreement with the average experimental curves. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Time‐dependent response of polypropylene/clay nanocomposites under tension and retraction

Observations are reported in relaxation tests under tension and retraction on polypropylene/clay nanocomposites with various contents of filler. A two‐phase constitutive model is developed in cyclic viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters in the stress–strain relations are found by fitting the observations. Ability of the constitutive equations to describe characteristic features of the time‐dependent behavior of nanocomposites under cyclic deformation is confirmed by numerical simulation. POLYM. ENG. SCI., 2013 © 2012 Society of Plastics Engineers     

Uniaxial time‐dependent ratcheting behavior of bronze powder filled polytetrafluoroethylene at room and high temperature

A series of tensile and ratcheting experiments for cold compaction polytetrafluoroethylene (PTFE) and bronze filled PTFE (PTFE/bronze) were conducted with Dynamic Mechanical Analyzer (DMA‐Q800) at room and high temperature (473 K). The effects of peak stress‐holding time, creep, recovery, mean stress history, stress‐rate history, and pretension on the ratcheting behavior of PTFE/bronze were investigated. It is found that longer peak stress‐holding time leads to larger ratcheting strain accumulation. In the meantime, the ratcheting strain accumulates more rapidly at high temperature and the influence of temperature is more obvious than that of the additive fraction of bronze. Creep strain produced during the uploading and the stress‐holding time only partially recovers in the unloading process. Moreover, prior lower stress rate enhances the deformation resistance and restrains the ratcheting of subsequent cycling at higher stress rate. The ratcheting strain in the subsequent cyclic loading at lower mean stress is also restrained by previous cyclic loading at higher mean stress. Finally, the elastic modulus increases and the ratcheting strain is restrained apparently after the pretension. In addition, the elastic modulus and ratcheting strain of the PTFE/bronze with both pretension and recovery are smaller than those with pretension but without recovery. POLYM. ENG. SCI., 54:1571–1578, 2014. © 2013 Society of Plastics Engineers     

Effect of Compressive Stress on Fatigue of Alumina under Uniaxial Cyclic Loading

The effect of compressive stress on fatigue behavior of alumina was investigated under uniaxial cyclic loading. Experimental data for alumina tension specimens under uniaxial tension–unloading and tension–compression cyclic loadings were compared. This comparison suggests that compressive stress is effective in advancing the crack growth under tension–compression cycling.     

Cyclic interaction between normal and shear stresses of an epoxy polymer—Experiments and model predictions

This investigation focuses on the axial‐torsional loading interaction of an epoxy polymer, Epon 826/Epi‐Cure Curing Agent 9551. Thin‐walled tubular specimens were subjected to combined constant tensile (or shear) stress and cyclic shear (or tension) loading schemes. Pure tensile creep and shear creep tests were also performed to compare the creep deformation to that with superimposed cyclic shear or cyclic tension. Test data clearly showed that cyclic shear (or cyclic tension) have a readily discernible effect on the tensile (or shear) creep deformation. Similarly, a superimposed constant tensile (or shear) load affects the hysteresis responses in cyclic shear (or cyclic tension). A nonlinear constitutive model developed by the authors was used to simulate the observed normal‐shear stress interaction. Due to the inclusion of an effective stress parameter in its nonlinear function, this model was able to account for the normal‐shear coupling effect. However, the incorporation of a general loading/unloading rule led to inaccurate simulation of the observed oscillatory creep response. A modification of the general rule was proposed and better predictions on both the cyclic and the creep responses could be obtained. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Systematic experimental study on mechanical behavior of PVB (polyvinyl butyral) material under various loading conditions

The mechanical behavior of polyvinyl butyral (PVB) significantly influences crashworthiness and energy mitigation abilities of windshields in terms of pedestrian safety. In this article, mechanical characteristics of PVB are experimentally studied. First, tension and compression experiments on PVB specimen are carried out under various quasi‐static loading rates. Fundamental mechanism of rate‐dependent behavior is investigated. Besides, dynamic tension and compression experimental data are compared to investigate the mechanical behavior of PVB in a whole strain rate region and it is found that PVB behaves as a visco‐elastic material under compressive loadings in both quasi‐static and dynamic situations; however, in tension experiments, stress–strain curves of PVB under dynamic loadings are elasto‐plastic while those under quasi‐static loadings are visco‐elastic. Considering all the unique characteristics of PVB's behavior, constitutive models are then established based on Zhu‐Wang‐Tang model mathematically. Further, unit volume energy absorption of every experiment in quasi‐static tension and compression are calculated as well as the stress intensify factor. In addition, visco‐elasticity part in the constitutive model is employed. Results may offer useful experiment data and important constitutive characteristics of PVB material to further studies of automotive crashworthiness and pedestrian protection. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Uniaxial ratchetting and low-cycle fatigue failure behaviors of adhesively bonded butt-joints under cyclic tension deformation

Ratcheting and low-cycle fatigue failure behaviors of the adhesively bonded hollow cylindrical butt-joints has been experimentally investigated. A series of uniaxial cyclic tension experiments were carried out under stress-controlled mode. The effects of stress amplitude, mean stress and cycle time on the uniaxial ratcheting response, fatigue damage variable evolution and fatigue life of the adhesively bonded butt-joints were analyzed. The results show that the ratcheting strain, ratcheting strain rate and fatigue damage variable all increase with the increase of stress amplitude and mean stress. The shorter cycle time results in the increase of fatigue damage variable and the degradation of the stiffness of the adhesive material. It is also found that the increase of stress amplitude and mean stress can reduce the low-cycle fatigue life. Meanwhile, the fatigue life increases with the increase of cycle time for the adhesively bonded butt-joints.     

Uniaxial ratchetting behavior of vulcanized natural rubber

Most of rubber engineering components endure cyclic loading during their service, and a nonzero mean stress during cyclic loading may cause an accumulation of strain which is known as ratchetting phenomenon. In order to study the ratcheting effect of rubber, a series of uniaxial ratchetting experiments were conducted on vulcanized natural rubber (NR). The effects of cyclic stress amplitude, mean stress and their histories on ratchetting behavior were studied, respectively. The uniaxial ratchetting behavior of natural rubber depends greatly on the stress amplitude and mean stress. The ratchetting strain rate greatly increases with the stress amplitude or mean stress increased. Experimental results reveal that the rubber material exhibits a strong memory of the previous high loading history, and such memory plays a significant role on the subsequent ratchetting. The ratchetting behaviors of the rubber exhibit little sensitive to the applied cyclic stress rate except for the initial strain. POLYM. ENG. SCI., 48:191–197, 2008. © 2007 Society of Plastics Engineers     

橡胶材料非线性高弹-粘弹性本构模型

本文提出的修正Zener模型,即以非线性弹簧与粘壶代替原来的线性弹簧与粘壶,得到一种适合橡胶材料在单轴作用下的非线性高弹-粘弹性本构模型。该模型可同时描述加载、卸载及应力松弛行为。模型将应力分解为弹性应力与粘性应力。弹性应力由Yeoh高弹性模型得到;粘性应力由加载及卸载过程的瞬时应力通过积分变换得到。此外考虑到应力松弛的作用,因此将粘性应力分解成两部分：一是在加载、卸载过程所用时间内由应变的改变所导致的粘性力;二是在该时间内由应力松弛所产生的反作用力。最后,将实验结果与该模型的计算结果进行对比,结果表明计算结果与实验结果具有良好的一致性,说明该本构模型可靠、合理。     

Correlation between uniaxial and shear creep of thermoplastics

Creep data in uniaxial tension, compression and shear on PVC, PMMA, and PP sheet were used to test analytical correlating procedures. It was shown that shear and uniaxial creep could be closely related using the concept of shear stress and shear strain on octahedral planes. This correlating procedure was only effective if due allowance was made for the different creep response in simple tension and compression for each of these materials. It was also shown that the relationship between the viscoelastic creep moduli and strain ratio, which is stress and time dependent, has the same form as the analogous relationship between the linear elastic constants.