A method for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition: Energy‐Based Approach

A methodology for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition is proposed and validated by example of uniaxial creep of epoxy resin. Energy approach is applied for characterization of the region of linear viscoelasticity (LVE) and the threshold of LVE is given in the stress–strain representation as the master curve independent of time and temperature. Time‐ and temperature‐dependences of the stress threshold are calculated by extending LVE theory and time–temperature superposition principles (TTSP) to the energy relations. Reasonable agreement between experimental data and calculations is obtained. It is shown that number of tests required for characterization of LVE region in a wide range of test time and temperatures can be considerably reduced by applying the proposed methodology. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Nonlinear viscoelastic model for the prediction of double yielding in a linear low‐density polyethylene film

Tensile testing and tensile creep experiments for linear low‐density polyethylene in a thin‐film form were examined and analyzed in terms of a nonlinear viscoelastic model. The proposed model, based on two distinct thermally activated rate processes (Eyring models), was proved to describe the double‐yield‐point tensile behavior of the material tested. The required model parameters were evaluated from the corresponding creep‐strain curves, and this revealed the relationship between the main aspects of the inelastic behavior of polymers, that is, the monotonic loading and creep response. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 91: 3519–3527, 2004     

Tensile creep of a long‐fiber glass mat thermoplastic composite. I. Short‐term tests

This work is part of a larger experimental program aimed at developing a semi‐empirical constitutive model for predicting creep in random glass mat thermoplastic (GMT) composites. The tensile creep response of a long‐fiber GMT material has been characterized for 3‐ and 6‐mm thick material. Tensile tests showed that the variability within and between plaques are comparable with an overall variability of about 6% and 8% for the 3‐ and 6‐mm thick materials, respectively. The thicker material exhibited slightly higher variability and directional dependence due to greater flow during molding of the plaques. Short‐term creep tests consisting of 30 min creep and recovery, respectively, were performed over the stress range between 5 and 60 MPa. Three tests for determining the linear viscoelastic region were considered which showed that the 3‐ and 6‐mm thick GMT are linear viscoelastic up to 20 and 25 MPa respectively. The 6‐mm thick GMT consisting of a higher fiber weight fraction was linear over wider stress range. Furthermore, it was found that plastic strains were accumulated during creep, which suggests that a nonlinear viscoelastic–viscoplastic model would be more appropriate for long‐term creep at relatively high stresses, which will be presented in our companion paper. The magnitude of the plastic strains developed in the creep tests presented here was lower because a single specimen was loaded at multiple stress level over short durations. Hence, a nonlinear viscoelastic constitutive model has been developed for the two thickness materials. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Development of a creep‐free stress‐strain law for fire analysis of steel structures

This paper presents a practical procedure for obtaining creep‐free stress‐strain laws for steel exposed to fire, on the basis of codified stress‐strain laws that consider creep implicitly. The applicability of the proposed procedure has been tested on two commonly used stress‐strain laws for steel at elevated temperature, the Eurocode 3 law and a Ramberg–Osgood model, both of which have implicit consideration of creep. The simulation of two published steel coupon experiments on steel of grades S275 and S355 shows that both the Eurocode and Ramberg–Osgood stress‐strain laws produce inaccurate predictions of creep in fire at elevated temperatures. The proposed procedure was thereby used to extract the implicit creep according to the heating rates of the transient coupon tests and to derive the creep‐free stress‐strain laws. It has been shown that, by combining the creep‐free stress strain law obtained by the proposed methodology with an explicit creep model, a more realistic prediction of steel behaviour in the selected coupon test studies can be achieved. Copyright © 2015 John Wiley & Sons, Ltd.     

Plastic deformation of low‐density polyethylene reinforced with biodegradable polylactide,Part 2: Creep characterization and modeling

The behavior of low‐density polyethylene (LDPE) and two blends prepared with polylactide (PLA) was determined by means of a novel video‐controlled testing method under stretching at constant true strain rate, under creep at constant true stress, and under creep at constant nominal stress. Most tests were performed at 23°C and 50°C. In this second part, the experimental data are modeled with the G'Sell‐Jonas phenomenological law expressing the axial true stress versus axial true strain and axial true strain rate. This model describes correctly the various deformation stages: (i) initial viscoelasticity, (ii) plastic yielding, and (iii) strain hardening up to rupture. It shows clearly the reinforcing effect of the PLA particles that increases the yield stress in stretching experiments and slows down the deformation kinetics under creep. It is shown how the local stress/strain behavior is related to the standard force/extension curves. Consequently, it is proposed that tensile tests at constant true strain rates should be systematically preferred to creep tests for the characterization of constitutive relations because they take much less time to be performed. POLYM. ENG. SCI., 2011. © 2010 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     

Critical stress of high‐density polyethylene during stress and photo‐oxidative aging

The long‐term photo‐oxidative aging behavior of high‐density polyethylene (HDPE) under different tensile stress was studied using a stress‐aging apparatus. The aging behavior was investigated through the methods of the surface morphology observation, gel content measurement, Fourier transform infrared spectroscopy, and creep behavior. It was found that stress has influence on the development of cracks and stress induces cracking through creep deformation. With increasing stress, the cracking time decreases in a reversed S‐shape curve way, and there is a critical stress near 7 MPa where the cracking time has a maximum decreasing rate. Meanwhile, the creep deformation increases rapidly when the stress exceeds the critical stress. The critical stress of HDPE is about 20–25% of breaking strength, and HDPE with low comonomer content has good dimensional stability when the stress is less than the critical stress, while HDPE with high comonomer content has a good performance when the stress exceeds the critical stress. This study may be useful for the rational selection of HDPE for the sheath material of bridge cable. POLYM. ENG. SCI., 55:2277–2284, 2015. © 2015 Society of Plastics Engineers     

Cyclic deformations of polypropylene with a strain‐controlled program

Experimental data are reported on isotactic polypropylene in uniaxial tensile cyclic tests with a strain‐controlled program (oscillations between fixed minimum and maximum strains). The following characteristic features of stress–strain diagrams are observed: (i) logarithmic decay in maximum and minimum stresses with number of cycles (cyclic softening), (ii) more pronounced reduction in minimum stress than in maximum stress (cyclic strengthening), (iii) independence of rates of decrease in maximum and minimum stresses of strain rate, (iv) decrease in hysteresis energy with number of cycles. To rationalize these observations, a constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers. Numerical simulation demonstrates that the model correctly describes experimental stress–strain curves and quantitatively predicts evolution of maximum and minimum stresses with number of cycles. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Evaluation of the derivatives of the strain energy function with respect to strain invariants for carbon black–filled EPDM

The experimental and theoretical investigation of the mechanical properties of an ethylene‐propylene‐diene terpolymer (EPDM) elastomer reinforced with carbon black was examined. The material constants of the testing material were determined by plotting the stress‐strain experimental curve in a reduced stress versus the inverse stretch diagram. The Ogden equation was used for the strain energy function to fit uniaxial experimental stress‐strain curves. The characterization of the material was examined using the contour maps of ?W/?I₁ and ?W/?I₂, i.e., of the derivatives of strain energy function with respect to strain invariants I₁ and I₂.     

Anisotropic continuum damage model for prediction of failure in flax/polypropylene fabric composites

An anisotropic continuum damage modeling approach was applied to model failure of a composite of unidirectional flax in a polypropylene matrix under quasi‐static tensile loading. Tensile, compressive and shear stiffness, and strength values of the composite were characterized according to ASTM standards, and the damage was quantified by optical microscopy. Based on the experimental strength and damage values, an anisotropic strain‐dependent material damage model was developed and implemented in the finite element program ABAQUS. This was combined with geometric models of the fabric composites incorporating the yarn geometry. Good agreement was observed between the experimental and numerical stress–strain curves, and the failure strength prediction by the model was within 3.1% of the experimental value. This study shows that combining a geometric model closely incorporating the actual geometry of a fabric composite with an experimentally determined material degradation model can yield good predictions of the mechanical behaviour of the composite. POLYM. COMPOS., 37:2588–2597, 2016. © 2015 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     

Creep behavior of PLA‐based biodegradable plastic exposed to a hydrocarbon liquid

This study explores the effect of hydrocarbon liquid on creep behavior of polylactic acid (PLA)‐based plastic. Evolution of the mechanical properties of the material was investigated experimentally by measurement of creep under tensile load. Tensile creep behavior was studied with a constant load over a temperature range from 30 to 50°C using specimens containing different levels of liquid. It was shown that the hydrocarbon liquid diffusion obeys the Fickian law of diffusion. The viscoelastic properties vary with temperature and these properties dramatically decrease above the glass transition temperature (T_g). Significant decreases in modulus and in the peak of tan δ were observed with an increase in liquid concentration at low temperatures. In contrast, at high temperatures, drier material recorded lower storage modulus. However, only small changes of T_g were recorded. Dependence of compliance on temperature was observed in the creep test at all levels of liquid content. With respect to drier samples, it was noted that the high liquid content material had a lower rate of increasing creep strain with temperature. Therefore, at elevated temperatures, higher creep strain of dry specimens was observed compared to those with a higher liquid content. The improvement of creep resistance and stiffening of material at high temperatures can be attributed to the significant increase of crystallinity fraction induced by liquid absorption. Understanding the effect of liquid diffusion in conjunction with temperature provides useful information for assessment of the potential use of this biodegradable plastic in load‐bearing applications exposed to an organic liquid. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Prediction of long‐term service performance of polymeric materials from short‐term tests: Creep and prediction of the stress shift factor of a longitudinal polymer liquid crystal

The material studied is a longitudinal polymer liquid crystal (PLC). The creep behavior of the PLC is examined in the region of nonlinear viscoelasticity. The creep compliance D curves at nine different stress σ levels, from 10 to 50 J.cm^?3 at a constant temperature are determined and shifted along the log time axis for σ_ref = 10 J · cm^?3 to produce the D versus t/a_σ master curve. A fairly general formula for stress shift factor a_σ based on free volume v^f and the chain relaxation capability (CRC) derived by one of the authors is applied. The formula predicts values that agree with the experimental ones within the limits of the experimental accuracy. Thus, experiments at several stress levels can serve for prediction of long‐term behavior from short‐term tests. The same value of the Doolittle constant B is obtained separately from temperature shift and stress shift experiments for the PLC.     

Tensile strain‐rate response of polymeric fiber composites

The tensile behavior of unidirectional glass‐fiber polymer composites was studied at three different strain rates. Tests were performed on 0° specimens as well as off‐axis specimens at 15°, 30°, 45°, and 90° with respect to the axis of tension. The nonlinear material behavior was modeled through a viscoplastic model based on a one‐parameter plastic potential function developed elsewhere. An effective stress‐effective plastic strain curve was constructed for each strain rate imposed and fitted with a power law. Thus, the tensile stress–strain curve could be predicted in a very accurate way for every strain rate examined and various types of off‐axis specimens. The strain rate‐dependent behavior is described through a scaling law, assuming that a model parameter is a function of the imposed strain rate. Predictions of the material response at strain rates different from those initially studied were found to be successful. POLYM. COMPOS., 26:572–579, 2005. © 2005 Society of Plastics Engineers     

Some aspects of the mechanical response of BMI 5250‐4 neat resin at 191°C: Experiment and modeling

The inelastic deformation behavior of BMI‐5250‐4 neat resin, a high‐temperature polymer, was investigated at 191°C. The effects of loading rate on monotonic stress–strain behavior as well as the effect of prior stress rate on creep behavior were explored. Positive nonlinear rate sensitivity was observed in monotonic loading. Creep response was found to be significantly influenced by prior stress rate. Effect of loading history on creep was studied in stepwise creep tests, where specimens were subjected to a constant stress rate loading followed by unloading to zero stress with intermittent creep periods during both loading and unloading. The strain‐time behavior was strongly influenced by prior deformation history. Negative creep was observed on the unloading path. In addition, the behavior of the material was characterized in terms of a nonlinear viscoelastic model by means of creep and recovery tests at 191°C. The model was employed to predict the response of the material under monotonic loading/unloading and multi‐step load histories. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Effect of processing and density on morphology and creep behavior of linear low‐density polyethylene

Creep behavior of 40‐ and 80‐μm‐thick films of linear low‐density polyethylene with four different densities produced by blowing and casting processes was investigated at room temperature (RT) and 70°C. As a criterion for ductile creep failure, strain‐to‐failure was chosen, which amounts to the maximum elongation characterized by necking of the whole sample. At RT under the stress of 8 MPa, strain‐to‐failure increases by one order of magnitude (from 0.08 to 0.80) with a decrease in density from 0.930 to 0.902 g/cm³. Processing effects creep deformation much less significantly in comparison with density. It is found that under loading at RT, some amount of orthorhombic phase in films with the densities of 0.902 and 0.912 g/cm³ transforms into the monocline phase. The intensity of a peak of this phase near the angle 2θ of 19.5° does not depend on the test duration. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

Viscoelastic constitutive model for uniaxial time‐dependent ratcheting of polyetherimide polymer

Based on the experimental observations, a cyclic nonlinear viscoelastic constitutive model was proposed to describe the uniaxial time‐dependent ratcheting of polyetherimide (PEI) polymer under tension–compression and tension–tension cyclic loading. The model was constructed by extending the nonlinear viscoelastic Schapery model (Schapery, Polym. Eng. Sci., 9, 295 (1969)). The extension emphasized the changes of parameter functions used in the original model, which enabled the model to describe the ratcheting of polymer material. Comparing the simulations with corresponding experimental results, the capability of the extended model to predict the uniaxial time‐dependent ratcheting of PEI was verified. It is shown that the extended model can reasonably describe the uniaxial time‐dependent ratcheting of the polymer under the tension–compression and tension–tension cyclic loading with different peak‐holdings, stress rates, and stress levels. POLYM. ENG. SCI., 52:1874–1881, 2012. © 2012 Society of Plastics Engineers     

Hyperelastic model analysis of stress‐strain behavior in polybutadiene/ethylene‐propylene diene terpolymer nanocomposites

Micromechanics of elastomer nanocomposite samples based on polybutadiene (BR), ethylene‐propylene diene terpolymer (EPDM) hyperelastic matrixes prepared via melt compounding was investigated using uniaxial tensile analysis. Constitutive hyperelastic models, including Polynomial, Yeoh, Ogden, Arruda‐Boyce, and Van der Waals were used to determine material parameters in incompressible isotropic elastic strain‐energy functions on the basis of a nonlinear least squares optimization method by fitting the data obtained from uniaxial classic experiments. Effect of nanoclay (0, 3, 5, 7, and 10 phr) content on the simulation accuracy was investigated. Simulation results compared with the experimental data suggested that the Ogden model as the most consistent model investigated here. J. VINYL ADDIT. TECHNOL., 23:21–27, 2017. © 2015 Society of Plastics Engineers     

基于DIC的BFRC受压损伤特性及本构模型研究

采用数字图像相关(DIC)技术对玄武岩纤维混凝土(BFRC)受压过程中试件表面应变场进行计算,分析了试件表面水平应变云图变化情况,得到了BFRC受压损伤演化规律;通过对水平应变场统计分析,利用应变场标准差统计指标定义损伤演化因子,得到不同纤维掺量下BFRC损伤演化曲线;同时,基于应变等效原理及损伤演化因子,推导出BFRC单轴受压损伤本构模型,通过对比试验与模型曲线,发现两者吻合较好,该模型在峰值应变之前可有效描述BFRC单轴受压下损伤演化过程;对比曲线发现玄武岩纤维可有效提高混凝土峰值应力及峰值应变,提高其变形能力,并具有延缓损伤作用.