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Application of the “Theory of Mixtures” to Temperature – Stress Equivalency in Nonlinear Creep of Thermoplastic/Agro-fibre Composites
Abstract
The viscoelastic characterization of agro-filler based plastic composites is of paramount importance for these materials' long-term commercial success. To predict creep, it is imperative to derive a relationship between deformation, time, temperature, and stress. This work is the harbinger in modelling of the nonlinear creep behaviour of two-phase materials, where an extended "theory of mixtures" has been used to describe all the creep related parameters. The stress- and temperature-related shift factors were estimated in terms of the activation energy of the constituents. The combined effect of temperature and stress on creep strain was accommodated in a single analytical function where the interaction was shown to be additive. The model was validated under rigorous conditions and is unique because it describes creep not through curve fittings, but in terms of the creep constants of the constituents. This constitutive model is not only a vanguard in the prediction of long term creep of many biocomposites but also in the modelling of creep under step loading of temperature.
... Pramanick et al. 66 worked on developing a model to study the nonlinear behaviour of creep in polymer composites of the two-phase system where they used an extended 'theory of mixtures' to describe the creep phenomenon. it is interesting to mention that the effect of temperature and stress on the creep deformation of the individual constituents can be fitted in combination in a single analytical function where the interaction is additive. ...
The growth in applications of natural fibre polymer composites (NFPCs) has increased the importance of understanding time-dependent viscoelastic properties such as creep resistance, stress relaxation, and fatigue, all of which are covered in this chapter. The fundamentals of measurement of these properties are discussed, and the use of short- and long-term prediction of creep resistance of the NFPCs to achieve adequate long-term performance is outlined. The effects of the interfacial interaction between natural fibres and polymers on fatigue and stress relaxation properties of the NFPCs are explored.
There is a growing interest in developing foamed TPO since replacing solid TPO will reduce material cost and fuel usage. In this paper, various talc contents are added into a TPO matrix, consisting of PP blended with a metallocene-based polyolefin elastomer. The effect of talc on TPO foams blown with N2 is studied using the batch foaming simulation system. The influence of N2 content and processing conditions on cell nucleation behaviour is discussed.
More than ever before, thermoplastic polyolefin (TPO) is actively used for interior and exterior applications in the automotive industry. Foamed TPO parts use far less material than their solid counterparts and, thereby, reduce material cost, weight, and fuel usage. However, foamed TPO is not yet in mainstream use because the appropriate foaming technology is not yet well developed. The literature reports the use of carbon dioxide (CO2) as a blowing agent for TPO;1–3 there is, however, little research on the use of nitrogen (N2) as a blowing agent, despite nitrogen's numerous advantages. In this study, various talc contents were added to a TPO matrix consisting of polypropylene blended with a metallocene-based polyolefin elastomer. The effect of talc on the TPO foams blown with N2 was studied with a batch foaming simulation system. The simulated results were compared actual foam extrusion results. The influence of the N2 content and processing conditions on the cell nucleation behavior is discussed. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010
Starting with specific constitutive equations, methods of evaluating material properties from experimental data are outlined and then illustrated for some polymeric materials; these equations have been derived from thermodynamic principles, and are very similar to the Boltzmann superposition integral form of linear theory. The experimental basis for two equations under uniaxial loading and the influence of environmental factors on the properties are first examined. It is then shown that creep and recovery data can be conveiently used to evaluate properties in one equation, while two-step relaxation data serve the same purpose for the second equation. Methods of reducing data to accomplish this characterization and to determine the accuracy of the theory are illustrated using existing data on nitrocellulose film, fiber-reinforced phenolic resin, and polyisobutylene. Finally, a set of three-dimensional constitutive equations is proposed which is consistent with nonlinear behavior of some metals and plastics, and which enables all properties to be evaluated from uniaxial creep and recovery data.
An approach to modeling the mechanical behavior of fiber reinforced and unreinforced plastics with an evolving internal state is described. Intrinsic nonlinear viscoelastic and viscoplastic behavior of the resin matrix is taken into account along with growth of damage. The thermodynamic framework of the method is discussed first. The Gibbs free energy is expressed in terms of stresses, internal state variables (ISVs), temperatureand moisture content. Simplifications are introduced based on physical models for evolution of the ISVs and on experimental observations of thedependence of strain state on stress state and its history. These simplifications include use of master creep functions that account for multiaxial stresses, environmental factors and aging in a reduced time and other scalars. An explicit representation of the strains follows, which isthen specialized to provide three-dimensional homogenized constitutiveequations for transversely isotropic, fiber composites. Experimentalsupport for these equations is briefly reviewed. Finally, physicalinterpretation of some of the constitutive functions is discussed usingresults from a microcracking model as well as molecular rate process andfree volume theories. It is shown that the present thermodynamicformulation leads to a generalized rate process theory that accounts for abroad distribution of thermally activated transformations in polymers.
Short- and long-term tensile creep tests of high-density polyethylene (HDPE) have been performed at different stress levels under an ambient temperature of 20°C. The effects of stress and physical ageing on the creep compliance are studied. The short-term creep data show that the distribution of relaxation times of HDPE is shifted even by a very low stress. Acceleration of creep can be realized by applying high stresses, and a momentary master curve of creep compliance can be constructed using the time-stress superposition principle. At low stresses, though the material exhibits strong non-linearity, the ageing rate μ is found to be independent of stress. A unified non-linear creep relation is obtained that incorporates the physical ageing effect and predicts the long-term creep behaviour with good agreement with experiments.
Rice husk based plastic composites are increasingly being used as deck-boards, railings and other load-bearing materials. Since this material typically contains 40% plastic, and plastics creep with respect to time when they carry load, creep is an important issue here. So the viscoelastic characterization of this material and the prediction of creep as a function time is of paramount importance for the material's long-term commercial success. Creep is a time related deformation but it can also be affected by the stress level and environmental conditions, such as time and temperature. In order to predict the creep of this composite, it is important to derive a relationship between deformation, time, temperature, relative humidity and stress. Nonlinearity can exist in the stress, temperature, and moisture related deformation. In this study, hollow extruded rice husk -HOPE beams were subjected to creep and recovery in flexural mode and the stress related nonlinear creep behaviour of the same was studied phenomenologically. Both linear and non-linear region constants were determined with modified models, and a predictive model was developed. These constants will be used to define, model and predict long-term creep deformation.
This paper finalizes research on graded Douglas-fir 2 by 4 beams subjected to constant bending loads of various levels and durations. Compared to results for testing in a controlled environment, results confirm that load duration did not appear to be shortened by tests in an uncontrolled environ-ment, at least extending out to 12-plus years. By the same comparison, relative creep was considerably increased, however. The extended data also confirm that no evidence was found for a threshold below which stress levels for lumber can be maintained indefinitely. Based on the finalized prediction equations of this study and those of two previous studies, a factor of 2.0 for a 10-year load duration is more appropriate for Douglas-fir bending allowable properties than the 1.62 factor currently recommended. Also, bending deflections due to creep doubled sooner than commonly accepted. This research is important to structural engineers and code groups respon-sible for the safe design of wood structures when establishing new design criteria for load duration and deflection limits.
The response of nonlinear viscoelastic creep of neat and carbon fiber-reinforced Polyether-etherketone (PEEK) and epoxy resin at different temperature was studied using Schapery's constitutive equation. As reinforced materials, the laminates [904]s and [±454]s were investigated. For comparisons reasons, the same type of experiments was conducted on the respective neat polymers. The results show that the linear viscoelastic limit is shifted to lower values with increasing temperature. This was observed for neat polymers as well as for the [±454]s laminates. On the other hand, for the [904]s laminates, the influence of the temperature on the linear viscoelastic limit seems to be relatively restricted. Besides, for all resins and laminates studied, it is shown that the influence of temperature on the nonlinearity of the instantaneous material response is significantly lower than that on the transient nonlinearity.
Creep in the nonlinear zone of wood plastic composite can be described by a few material constants. The purpose of this study was to determine these creep related material constants for 60% wood flour reinforced extruded HDPE samples. Creep and recovery data in flexural bending mode were analyzed. Schapery's theory was used to simulate creep data. The creep related material constants varied according to the stress level. The experiment was short term and the values of these constants will be used to characterize, simulate, and model long-term creep under varying temperature and moisture in our ongoing project.
Wood fibre reinforced polypropylene composites of different fibre content (40, 50 and 60% by weight) have been prepared and wood fibres (hard and long fibre) were treated with compatibiliser (MAH-PP) to increase the interfacial adhesion with the matrix to improve the dispersion of the particles and to decrease the water sorption properties of the final composite. Results indicated that impact properties were affected by moisture content. The Charpy impact strength decreased and maximum force was increased with increasing of moisture content. With the addition of MAH-PP (5% relative to the wood fibre content), damping index decreased around 145% for hard wood fibre–PP composites at 60 wt.% wood fibre content. Long wood fibre–PP composites showed more impact resistance than hard wood fibre–PP composites. Short term flexural creep tests were conducted to investigate the creep behaviour of wood fibre–PP composites. Three experimental parameters were selected: the addition of compatibiliser, temperature and wood fibre content. The addition of MAH-PP, increased creep modulus that means reduced the creep. The extent of creep resistance (creep modulus and creep strength) decreased with increasing temperature. It was also found that wood fibre content has a great effect on creep resistance which is increased with increasing wood fibre content.
A constitutive model consisting of a combination of the Schapery nonlinear viscoelastic heredity integral and a nonlinear viscoplastic functional employed by Zapas and Crissman is described. Material constants associated with the constitutive models are measured for graphite-bismaleimide (IM7/5260) composites at elevated temperatures and stress levels. These results are then combined with classical lamination theory, so as to predict the response of a multi-angle laminate to cyclic thermomechanical loadings. Predictions are favorably compared with measurements obtained during a 50-hr test involving ten 5-hr loading cycles.
This report presents data on the creep response of a polymeric composite that is a candidate material for automotive applications. The above data were used to establish the basis for the mechanical characterization of the material's response over a wide range of stresses and temperatures, as well as under cyclic loading and due to exposure to distilled water. A constitutive model based upon fundamental principles of irreversible thermodynamics and continuum mechanics was employed to encompass the above mentioned database and to predict the response under more complex inputs. These latter tests verified the validity of the model.
The results of creep and recovery experiments are reported for two types of polyethylene—one a linear high density homopolymer, and the other an ethylene-hexene copolymer. Data were obtained at temperatures in the range 23°C to 57°C and creep times of 10 s to 4.33 × 105 s. In order to approximate constant true stress conditions, all of the experiments were carried out at the same value of applied stress (4 MPa) and the change in strain during creep was in all cases less than 2 percent. Comparison of these results with the results from earlier work on an ultra high molecular weight polyethylene shows that there is a great similarity in the behavior of all three materials, and the behavior of all three can be described quite well by a one-dimensional equation consisting of two terms—one a hereditary term and the other a plasticity term. It is further shown that to a very good approximation the idea of time-temperature superposition can be applied to the description of the hereditary term.
Two sets of dynamic mechanical property data and some stress relaxation data for semicrystalline, linear polyethylene are treated by data reduction methods previously described. These data can be represented by a master plot of reduced modulus versus reduced frequency and two sets of temperature-dependent shift factors. The first of these factors reflects the change of viscoelastic relaxation times with temperature. The second represents a separable change of modulus with temperature which applies over the entire time or frequency range of the experiments. This change is larger and in the opposite direction to that found applicable in the behavior of noncrystalline plastics and rubbers. The two sets of dynamic data show the same frequency–temperature dependence which can be represented by an activation energy of 22 kcal./mole. Small differences in the modulus–temperature dependence are attributed to differences in molecular weight or annealing conditions. The stress relaxation data superposes to a curve in good agreement with the dynamic data but with a factor of 20 difference in time scale. This difference is attributed to the finite strains used in the stress relaxation measurements. Such strains might be expected to increase free volume in simple extension deformations and so accelerate the relaxation.
Creep, the deformation over time of a material under stress, is one characteristic of wood-filled polymer composites that has resulted in poor performance in certain applications. This project was undertaken to investigate the advantages of blending a plastic of lower-creep polystyrene (PS) with high-density polyethylene (HDPE) at ratios of 100:0, 75:25, 50:50, 25:75, and 0:100. These various PS–HDPE blends were then melt blended with a short fiber-length wood flour (WF). Extruded bars of each blend were examined to measure modulus of elasticity and ultimate stress. Increasing the ratio of WF increased modulus of elasticity in all composites, except between 30 and 40% WF, whereas the effect of WF on ultimate stress was variable, depending on the composite. Scanning electron microscopic images and thermal analysis indicated that the wood particles interacted with the PS phase, although the interactions were weak. Finally, creep speed was calculated by using a three-point bending geometry with a load of 50% of the ultimate stress. Creep decreased only slightly with increasing WF content but more significantly with increasing PS content, except at pure PS. The WF/75PS–25HDPE blend showed the least creep. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 418–425, 2001
Creep behaviour of unmodified and functionally modified thermoplastic-wood fibre composites was studied. For PVC, PE and PP-based composites creep is strongly dependent on the amount of load, time and temperature. A small rise in the temperature above ambient temperature increased creep significantly for PVC-woodfiber composites. Instantaneous creep resistance of woodfibre-filled PP is higher than that of PE-based composites. PP and PE-based wood composites were modified with maleic and maleimide compounds. Maleic or maleimide modification of woodfibre improved transient creep behaviour of PP-woodfibre composite but it did not show practically any effect on instantaneous creep. A mathematical model has been proposed to predict creep behaviour of PVC, PP an PE-based wood fiber composites. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 260–268, 2000
An extensive set of stress relaxation and constant strain rate tests for characterizing the mechanical responses of a medium density polyethylene and a high density polyethylene that are commonly used in natural gas distribution piping is described and analyzed. The development of coherent master curves for the relaxation modulus, maximum stress, and the time-to-failure for pressurized pipes through a combination of both horizontal and vertical shifting is presented. The relaxation data are used to develop a nonlinear Viscoelastic material model. The model is assessed by making comparisons of the predicted stress-strain response with the measured response in the constant strain rate tests.
The short- and long-term creep behaviors of ultra-high-molecular-weight polyethylene (UHMWPE) systems (compression-molded UHMWPE sheets and self-reinforced UHMWPE composites) have been investigated. The short-term (30–120 min) creep experiment was conducted at a load of 1 MPa and a temperature range of 37–62°C. Based on short-term creep data, the long-term creep behavior of UHMWPE systems at 1 MPa and 37°C was predicted using time–temperature superposition and analytical formulas. Compared to actual long-term creep experiments of up to 110 days, the predicted creep values were found to well describe the creep properties of the materials. The creep behaviors of the UHMWPE systems were then evaluated for a creep time of longer than 10 years, and it was found that most creep deformation occurs in the early periods. The shift factors associated with time–temperature superposition were found to increase with increasing temperature, as per the Arrhenius equation. The effects of temperature, materials, and load on the shift factors could be explained by the classical free volume theory. © 1998 John Wiley & Sons, Inc. J Biomed Mater Res, 40, 214–223, 1998
This article presents data on the creep response of a polymericcomposite that is a candidate material for automotive applications. Theabove data established the basis for the mechanical characterization ofmaterial''s response over a wide range of stresses and temperatures, aswell as under cyclic tensile loading. A constitutive model based uponfundamental principles of irreversible thermodynamics and continuummechanics was employed to encompass the abovementioned database and topredict the response under more complex inputs. These latter testsverified the validity of the model.
This study considers the time-dependent response of a woodthermoplastic composite. The extruded material under considerationconsists of wood flour embedded in a high-density polyethylene (HDPE)matrix. The characterization study is based on a series of creep andrecovery tests. Stiffness reduction (i.e. damage) and permanentdeformation was observed in the material when the creep stress amplitudeexceeded a threshold value. The damage and permanent strains were foundto depend on creep stress amplitude and duration. The permanentdeformation was more efficiently accommodated by considering the coupontotal strain, however. A nonlinearly viscoelastic model is presentedthat incorporates damage and permanent deformation effects. Damage wasmodeled by considering an effective stress. The model is shown tocompare favorably with the experimental creep/recovery data as well astwo-step load history verification tests.
This article presents an overview of time dependence in the mechanical properties of materials, and of the methods to describe it.
An account is given on natural and man-made cellulose fiber reinforced plastics. Possible applications of this material group are detailed. A survey is also discussed about physical and chemical treatment methods that improve fiber matrix adhesion, as well as their results and effects on the physical properties of composites. The results show that natural fibers can be processed with the already commonly applied methods: glass mat thermoplastic matrix (GMT, sheet moulding compound (SMC) or bulk moulding compound (BMC).
According to the well-known Schapery’s formulation, the nonlinear viscoelastic response of any material is controlled by four stress and temperature dependent parameters, g0g1, g2 and aσ, which reflect the deviation from the linear viscoelastic response. Based on Schapery’s formulation, a new methodology for the separate estimation of the three out of four nonlinear viscoelastic parameters, g0, g1 and aσ, was recently developed by the authors. In the present article, a further development of the previously developed methodology is attempted leading to an analytical estimation of the fourth nonlinear parameter, g2, which additionally includes the viscoplastic response of the system. Thus, a full nonlinear characterization of the composite system under consideration is achieved. The validity of the integrated model was verified through creep-recovery experiments, applied at different stress levels to a unidirectional carbon fibre reinforced polymer.
The short- and long-term creep behaviors of ultra-high-molecular-weight polyethylene (UHMWPE) systems (compression-molded UHMWPE sheets and self-reinforced UHMWPE composites) have been investigated. The short-term (30-120 min) creep experiment was conducted at a load of 1 MPa and a temperature range of 37-62 degrees C. Based on short-term creep data, the long-term creep behavior of UHMWPE systems at 1 MPa and 37 degrees C was predicted using time-temperature superposition and analytical formulas. Compared to actual long-term creep experiments of up to 110 days, the predicted creep values were found to well describe the creep properties of the materials. The creep behaviors of the UHMWPE systems were then evaluated for a creep time of longer than 10 years, and it was found that most creep deformation occurs in the early periods. The shift factors associated with time-temperature superposition were found to increase with increasing temperature, as per the Arrhenius equation. The effects of temperature, materials, and load on the shift factors could be explained by the classical free volume theory.
Thesis (M.S.)--Washington State University, 2001. Includes bibliographical references.
Computer-produced typeface. Thesis (M.S.)--Washington State University, 1999. Includes bibliographical references.
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