Ethylene maleated amorphous propylene compatibilized polyethylene nanocomposites: Stress and temperature effects on nonlinear creep

The effects of stress and temperature on the nonlinear creep behavior of linear low‐density polyethylene (LLDPE) nanocomposites reinforced with montmorillonite‐layered silicate (MLS) nanoclay and compatibilized with an amorphous maleated ethylene copolymer (amEP) is investigated. To study the effect of stress on the creep resistance of these materials, creep tests were conducted at different stress levels (10, 25, and 50% yield stress). The effect of temperature was examined by analyzing the creep and recovery of the films at temperatures in the range of ?100 to 25°C. The individual creep compliance curves for each stress level and temperature were fitted to both the Burgers model and the Kohlrausch‐Williams‐Watts (KWW) function. The results indicate that modification of the polyethylene results in a suppression of relaxation times but the temperature trends are reversed below the β transition temperature. Filled systems exhibited a distribution in relaxation times whose trend matched the relaxation time trends in both Burger and KWW models. POLYM. ENG. SCI., 50:1633–1645, 2010. © 2010 Society of Plastics Engineers     

Modeling of creep for multiwall carbon nanotube/epoxy nanocomposite

The effect of multiwall carbon nanotubes (MWCNTs) on creep of epoxy matrix was evaluated on the basis of short‐term creep‐recovery tests performed at different stresses and temperatures. Six different compositions of MWCNT and bisphenol A epoxy resin (0–3.8 wt % of MWCNTs) were investigated. Slight reduction of creep compliance, strain rate, and residual strain were revealed experimentally for nanocomposite comparing to the neat resin. The development of viscoelastic strain for creep stage was described by the use of time–temperature–strain superposition principle with the parameters obtained from the approximation of recovery stage using modified Schapery model. The model accounted for the effect of strain on the viscoelastic strain rate for recovery stage. Its application gave better results for approximation of a series of recovery curves at different temperatures and stresses than of time–stress superposition model. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

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     

A practical approach to modeling time‐dependent nonlinear creep behavior of polyethylene for structural applications

The purpose of this work is to develop a practical method for constitutive modeling of polyethylene, based on a phenomenological approach, which can be applied for structural analysis. Polyethylene is increasingly used as a structural material, for example, in pipes installed by trenchless methods, where the relatively low stiffness of polyethylene reduces the required installation forces, chemical inertness makes it applicable for corrosive environments, and adequate strength allows its use in sewer, gas, and water lines. Polyethylene exhibits time‐dependent constitutive behavior which is also dependent on the applied stress level resulting in nonlinear stress–strain relationships. Nonlinear viscoelastic theory has been well established and a variety of modeling approaches have been derived from it. To realistically utilize the nonlinear modeling approaches in design, a simple method is needed for finding a constitutive formulation for a specific polyethylene type. This paper presents such a practical approach to nonlinear viscoelastic modeling utilizing both the multi‐Kelvin element theory and the power law functions to model creep compliance. Creep tests are used to determine material parameters and models are generated for four different polyethylene materials. The corroboration of the models is completed by comparisons with results from different tensile creep, step‐loading creep, and load‐rate tests. POLYM. ENG. SCI., 48:159–167, 2008. © 2007 Society of Plastics Engineers     

Nonlinear tensile creep of linear low density polyethylene/fumed silica nanocomposites: Time‐strain superposition and creep prediction

The main objectives of the study were (i) to quantitatively describe the nonlinear viscoelastic creep of model nanocomposites, (ii) to construct the generalized compliance curve by means of the tensile compliance vs. internal time superposition for a pseudo iso‐free‐volume state, and (iii) to predict the compliance vs. real time curves for selected stresses. To this end, the free volume theory of nonlinear viscoelastic creep developed for thermoplastics and their blend was successfully employed. Linear low density polyethylene/fumed silica nanocomposites, showing notable enhancement of the creep resistance in proportion to the surface area of incorporated nanofillers, were taken as simple model materials. POLYM. COMPOS., 31:1947–1955, 2010. © 2010 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     

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     

Time dependent response of polycarbonate and microcellular polycarbonate

Microcellular polycarbonate is a novel cellular material with cells on the order of 10 μm in diameter and a cell density on the order of 10⁹ cells per cm³. In this study the room temperature creep response of microcellular polycarbonate is experimentally determined and compared with the creep behavior of polycarbonate. The viscoelastic response of polycarbonate and microcellular polycarbonate is characterized using Schapery's theory of nonlinear viscoelasticity. Polycarbonate exhibited a nonlinear creep response at stress levels above 24.13 MPa, while the nonlinear behavior in microcellular polycarbonate was initiated at lower stress levels. Creep strains of microcellular polycarbonate contain a significantly higher viscoplastic component compared with the unfoamed material.     

Creep characterization of vapor‐grown carbon nanofiber/vinyl ester nanocomposites using a response surface methodology

The effects of selected factors such as vapor‐grown carbon nanofiber (VGCNF) weight fraction, applied stress, and temperature on the viscoelastic responses (creep strain and creep compliance) of VGCNF/vinyl ester (VE) nanocomposites were studied using a central composite design (CCD). Nanocomposite test articles were fabricated by high‐shear mixing, casting, curing, and post curing in an open‐face mold under a nitrogen environment. Short‐term creep/creep recovery experiments were conducted at prescribed combinations of temperature (23.8–69.2°C), applied stress (30.2–49.8 MPa), and VGCNF weight fraction (0.00–1.00 parts of VGCNF per hundred parts of resin) determined from the CCD. Response surface models (RSMs) for predicting these viscoelastic responses were developed using the least squares method and an analysis of variance procedure. The response surface estimates indicate that increasing the VGCNF weight fraction marginally increases the creep resistance of the VGCNF/VE nanocomposite at low temperatures (i.e., 23.8–46.5°C). However, increasing the VGCNF weight fraction decreased the creep resistance of these nanocomposites for temperatures greater than 50°C. The latter response may be due to a decrease in the nanofiber‐to‐matrix adhesion as the temperature is increased. The RSMs for creep strain and creep compliance revealed the interactions between the VGCNF weight fraction, stress, and temperature on the creep behavior of thermoset polymer nanocomposites. The design of experiments approach is useful in revealing interactions between selected factors, and thus can facilitate the development of more physics‐based models. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42162.     

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     

Prediction of creep of polymer concrete

Polymer concrete possesses viscoelastic properties conditioned by relaxation processes in the polymer binder. Their acceleration with an increase of temperature (principle of time–temperature equivalence) is used in predicting the long‐term creep of polymer concrete. Physical aging of the polymer binder influences the creep of polymer concrete. To predict the long‐term creep accounting for the aging process, an attempt to improve the time–temperature equivalence principle was undertaken. As a result of the experimental study of polyester resin‐based concrete and its structural components (a resin unfilled and filled with diabase flour), it has been established that the changes in the creep compliance of the material follow according to the principle of the time–aging time equivalence with the reduction function depending on aging temperature. To predict the long‐term creep of polymer concrete, a function of the time–temperature–aging time reduction was applied. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 1949–1952, 1999     

Stress relaxation in low‐shrink‐force polyolefin films

The morphology and stress relaxation of coextruded five‐layer LLDPE (linear low‐density polyethylene)/EVA (ethylene‐vinyl‐acetate) copolymer films were studied. Increasing VA (vinyl acetate) content in EVA causes a decrease of shrink tension in the films, which can be explained by a decrease in amount of crystallinity. The relaxation time spectrum of the coextruded crosslinked LLDPE/EVA films is similar to the relaxation time spectrum of crosslinked LLDPE film at room temperature. However, at elevated temperatures, an additional peak appears on the spectrum of coextruded film. The cause of this peak is temperature‐ and stress‐induced recrystallization of EVA during the relaxation test. This recrystallization was confirmed with DSC and wide angle X‐ray analysis. Polym. Eng. Sci. 44:1716–1720, 2004. © 2004 Society of Plastics Engineers.     

On‐line opto‐viscoelastic analysis of polypropylene fibres using multiple‐beam Fizeau fringes in transmission and a modified creep device

A creep device attached to an automated multiple‐beam Fizeau system in transmission was modified with a designed digital ruler. This device allows on‐line measurements of fibre length during creep experiments in terms of an analogue voltage value. The influence of sustained stress values on creep deformation and optical properties (n^||, n^? and Δn) for polypropylene (PP) fibres was studied interferometrically. The opto‐viscoelastic properties of PP fibres were determined for three different values of constant applied stress of 11.536, 18.717 and 25.905 MPa, at room temperature. Also, the variations of the cross‐sectional area and Poisson's ratio were studied during creep extensions. The compliance curves were obtained as a function of both time and applied stresses. Empirical formulae are suggested to describe the creep compliance curves for PP fibres, and the constants of these formulae were determined and described at each applied stress. A Kelvin chain was used to model the mechanical behaviour of the PP fibres under study. The effect of strain on the mean refractive indices, orientation function density and crystallinity was investigated as a result of the recorded data. Microinterferograms are given for illustration. The modified creep device with the designed digital ruler enables one to obtain instantaneous automatic accurate recording of fibre length values during creep experiments. Calculation of refractive indices, orientation function and crystallinity shows a difference in material behaviour at small stresses from that at higher stresses which may be attributed to different strain rates caused by different stresses. Copyright © 2010 Society of Chemical Industry     

Application of time‐temperature superposition to energy limit of linear viscoelastic behavior

The energy approach for evaluation of the limits of linear viscoelastic (LVE) behavior is considered. The approach of Foux and Bruller based on the Reiner‐Weissenberg dynamic theory of strength is developed for the temperature effect. Value of the stored energy at the limit of LVE is considered as the material characteristic independent on loading conditions and temperature. Time–temperature superposition principle is extended for the energy calculations. Curves of the stored energy calculated for different temperatures are shifted to each other in the logarithmic time axes similarly as creep compliance and relaxation modulus curves in creep and tension tests, respectively. Temperature is considered as a factor that accelerates transition form linear to non‐LVE at the same stored energy threshold. This is proved by example of polyvinylchloride by comparing temperature dependences of the stress limits of LVE determined in two independent test series: tensile creep and constant strain rate tests. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Mechanical properties and creep behavior of rotationally moldable linear low density polyethylene‐fumed silica nanocomposites

Rotationally moldable linear low density polyethylene (LLDPE) is one of the most popular materials used for rotational molding. Yet, incorporation of additives is necessary to improve the mechanical, visco‐elastic, thermal as well as melt flow properties of LLDPE. In this article, the influence of fumed silica (FS) nanoparticles on the mechanical properties viz. tensile, flexural, and impact strengths of rotationally moldable LLDPE is investigated. The microstructural studies using SEM were conducted to study the dispersion of FS in LLDPE and correlated with the mechanical properties of the nanocomposites. Dynamic mechanical analysis (DMA) were also carried out to find the time–temperature dependent mechanical properties viz. storage modulus (E '), loss modulus (E ”), and tan delta between 1 and 8 wt% of FS. DMA studies were extended to perform accelerated stepped isothermal creep studies to find out the influence of FS in creep strains. POLYM. COMPOS., 38:421–430, 2017. © 2015 Society of Plastics Engineers     

Long-term creep behavior of polypropylene/fumed silica nanocomposites estimated by time–temperature and time–strain superposition approaches

Nonlinear viscoelastic creep was studied on polypropylene/fumed silica nanocomposites. The free-volume theory of nonlinear viscoelastic creep was successfully applied to obtain generalized creep master curves using a tensile compliance vs. internal time superposition in the region of nonlinear viscoelasticity. Concurrently, a time–temperature superposition approach was also adopted for the construction of creep master curves. A good agreement between the time–strain and the time–temperature superposition approaches was assessed by comparing the master curves obtained from the two data reduction methods. Both approaches evidenced a remarkable stabilizing effect induced by the nanoparticles that was observed especially for higher creep stresses and at increased temperatures and, considering the correspondent superposition principle, at long loading times. At the same time, both storage and loss moduli measured through dynamic mechanical analyses, were enhanced in all nanocomposites. Activation energy values obtained from the analysis of dynamic multi-frequency tests were in good accordance with those referred to creep tests.     

Impression creep of PMR‐15 resin at elevated temperatures

The polyimides formed from the polymerization of monomeric‐reactants (PMR) approach have been increasingly used as matrix materials in fiber‐reinforced composites on aerospace and space structures for high temperature applications. The performance of PMR‐based structures depends on the mechanical durability of PMR resins at elevated temperatures, including creep and stress relaxation. In this work, the creep behavior of PMR‐15 resin was studied using the impression technique in the temperature range of 563–613 K and the punching stress range of 76–381 MPa. It was found that there existed a steady state creep for the creep tests performed at temperatures of 563 K and higher, from which a constant impression velocity was calculated. The steady state impression velocity increased with temperature and punching stress with the stress exponent in the range of 1.5–2.2. The average of the apparent activation energy of the PMR‐15 was calculated as 122.7 ± 6.1 kJ/mol. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

An alternative approach to estimating parameters in creep models of high‐density polyethylene

Polyethylene (PE) is increasingly used in structural applications due to its light weight and rust‐resistant nature. With growing demand for the use of PE as a structural material, there is a need for mathematical models that describe the mechanical behavior of this material. Curve fitting using a linear time‐dependent model is a common approach for modeling creep of PE at the macrostructural level. However, besides the point estimates of the model parameters and the (visual) fit of the model to experimental data, little else is learnt from the curve‐fitting approach. This work presents a rigorous statistical approach for modeling creep compliance of PE. Four high‐density PE resins used over a wide range of applications are studied. Linear viscoelastic modeling using the multi‐Kelvin element theory is examined in two forms: model linear in parameters and model nonlinear in parameters. With the application of valid statistical techniques, complex relationships between model parameters, largely unstudied before, are observed, such as evidence of a high degree of correlation among material parameters of the creep model. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers.     

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.