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Determination of Material Constants for Nonlinear Viscoelastic Predictive Model
Abstract
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.
... [13][14][15] Creep testing has also been performed predominately in flexure for relatively short durations, usually for the purpose of comparing manufacturing parameters. [16][17][18][19] A few studies have conducted longer flexural creep tests up to 90 days. 9,10 Flexure response, however, is mechanically complex due to both the material's bimodal behavior and its nonlinear constitutive response. ...
... For creep response, Schapery's model can be reduced to a hyperbolic sine and a time-dependent power-law. 17 The time-and stress-dependent strain is expressed as ...
... Several other authors have used the hyperbolic sine term to describe stress-strain behavior of WPCs due to a monotonically increasing load. 5,20,34 The derivation of a time-dependent power-law supports the widespread empirical use of this form after its introduction by Findley et al. 31 A few authors 17,21 have demonstrated the successful use of Schapery's theory to describe both the quasistatic and time-dependent behavior of WPCs. Since the quasi-static ramp tests were conducted relatively quickly, the time-dependent term in equation (1) was negligible for these tests, and the ''instantaneous'' strain of the materials becomes ...
The thermoplastics within wood–plastic composites (WPCs) are known to experience significant time-dependent deformation or creep. In some formulations, creep deformation can be twice as much as the initial quasi-static strain in as little as 4 days. While extensive work has been done on the creep behavior of pure polymers, little information is available on the mechanical effects of mixing polymers with large amounts of wood-based or other bio-based fillers. As producers seek to develop structural WPC products that may be subjected to sustained loads, it is imperative that this creep behavior be understood. We characterized the quasi-static and time-dependent deformations of seven WPC formulations (primarily polypropylene, and polyethylene) in tension and compression. The quasi-static, mode-dependent response of the material to a linearly increasing strain was found to be well described by an exponential function coupled with a linear term. For most formulations, significant differences between the tension and the compression behaviors were not exhibited below 50% of the tensile capacity. The long-term creep response of the material was found to conform well to a time-dependent power-law (Findley, Shapery, etc.) at various stress levels for both loading modes.
... enhanced crystallinity due to stretching under a tensile load, microcracking, aging). Schapery (1969) presents a general form for the time-dependent non-linear compliance obtained from thermodynamic considerations, as follows (Lin et al., 2004): ...
... A vertical shift (related to structure changes) as well as an horizontal shift (related to changes in the distribution of retardation times) may be required to superimpose compliance curves obtained at different levels of stress, even if measurements are made at constant temperature. The permanent deformation also increases with stress level as shown by Lin et al. (2004). These authors offer a good reference for the determination of non-linear material constants (equation 8.11) from experimental data fitting. ...
... Both stress and temperature-related shift factors and the interactions thereof would be predicted with this theory. We have shown in our previous work that deck-board materials made of wood/plastics exhibit a Schapery type of nonlinear behaviour 18,19 under ambient conditions. We also emphasize that our goal is to predict long term performance, so all the shift factors will also be validated for rigorous long-term experiments. ...
... So it was imperative to determine the stress related constants (g 1 , g 2 , a σ etc.). This issue was taken up in detail in our previous paper 18,19 and will be mentioned cursorily. It must be mentioned that all the shift factors relate to a reference condition. ...
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.
... enhanced crystallinity due to stretching under a tensile load, microcracking, aging). Schapery (1969) presents a general form for the time-dependent non-linear compliance obtained from thermodynamic considerations, as follows (Lin et al., 2004): ...
... A vertical shift (related to structure changes) as well as an horizontal shift (related to changes in the distribution of retardation times) may be required to superimpose compliance curves obtained at different levels of stress, even if measurements are made at constant temperature. The permanent deformation also increases with stress level as shown by Lin et al. (2004). These authors offer a good reference for the determination of non-linear material constants (equation 8.11) from experimental data fitting. ...
... W.S.Lin et. al. [4] the purpose of this study was to determine these creep related material constant for 60% wood flour reinforced extruded thermoplastic material and build linear and nonlinear viscoelastic behaviour of that samples. Sourabh P. Sawant et. ...
... Studies of the influence of the outdoor natural climate conditions on the flexural and creep properties of WPCs showed that these properties are degraded after exposure to the sun for 2-6 months, so that the strain produced by the material is higher than that at room temperature after 6 months; then, due to the decrease in the temperature, humidity, and ultraviolet intensity, the strain generated by the material is smaller than that at room temperature [9]. In addition to the temperature, humidity also affects the creep behavior, so that an increase in the humidity will accelerate the creep of WPCs [10]. ...
Wood–plastic composite (WPC) materials are mainly used as flooring in buildings or as structural load-bearing plates, and will undergo creep deformation during use, resulting in structural failure and safety problems. Therefore, this work adopted the orthogonal test method to carry out creep tests on wood–plastic composites. We used the range method and variance analysis method to process the creep data and analyze the influence of the load, temperature, and relative humidity on the creep strain in specimens of wood–plastic composites. The results showed that the creep strain of the WPC specimens changed significantly with a change in the load stress, while a change in relative humidity had no significant effect on the creep strain. When the relative humidity was increased from 55% to 65%, the creep strain increased by 0.03%, but when the temperature was increased from 30 °C to 35 °C, there was no significant difference in the creep strain. However, when the temperature was increased from 30 °C to 40 °C and from 35 °C to 40 °C, a significant difference in the creep strain of the WPC specimens was observed.
... Several researchers have used the linear, power law, and other empirical models to establish the relationship between independent factors (time and temperature) and dependent factors ( creep strain and stress relaxation) of fiber-reinforced composite (Lin et al., 2004). Information on creep and stress relaxation analysis of materials may be fuzzy and insufficient most times, hence the need to adopt modeling in this research to develop better assumption and satisfactory description of creep theories, analysis and application. ...
... In the this stage the researchers study nonlinear viscoelastic by modifying the same linear theory like Schapery theory to be applied to nonlinear viscoelastic behavior as increasing to study the material behavior at high stress and high temperatures where the linear viscoelasticity not give a good accuracy to describe that behavior at this 29 condition. Many of models were built according to modified linear theory to describe the nonlinear theory by using software analyzing according to FE method. ...
... 67 it was suggested that the model could also incorporate environmental variations such as relative humidity, time, stress and temperature. Lin et al. 68 carried out the creep and recovery testing in the flexural bending mode for 60% wood flour reinforced extruded HDPE composites to determine the creep related material constants for the nonlinear viscoelastic model. ...
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.
... defi nes stress effects on the instantaneous elastic compliance g 1 is the transient compliance factor with a similar meaning to g 0 g 2 is the factor that accounts for the infl uence of loading rate on creep a σ is a horizontal time scale shift factor relating to the viscoelastic response as a function of time and stress. It shifts the creep data parallel to the time axis relative to a master curve for creep strain versus time n is the index that determines the shape of the creep curve ε p is the plasticity that occurs during creep. ...
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.
... The linear viscoelastic range can be determined by an isochroneplotting strain versus stress at a specific time. Long-term creep compliance is one performance criteria commonly used to evaluate composite materials [Lin et al. 2004]. ...
... In linearly viscoelastic materials, the creep compliance is independent of stress; a condition that may exist at low stresses. Long-term creep compliance is one performance criteria commonly used to evaluate composite materials (Lin et al., 2004). ...
... While creep rupture clearly pres ents the greater danger, deflection concerns may have a larger impact on the viability and acceptance of the material. It has been shown that even at relatively low stresses WPC structural members may experience exces sive deflections given enough time, while few attempts have been made to estimate their long-term deflection (Kobbe 2005, Lin et al. 2004. The current standards for WPC mechanical properties test the creep recovery and creep rupture of the material in flexure only (ASTM 2004). ...
The polymers within wood-plastic composites (WPCs) are known to experience significant time-dependent deformation, or creep. While extensive work has been done on the creep behavior of pure polymers, little infor mation is available on the effects of mixing the polymers with large amounts of wood or other bio-based fillers. As the market increases for structural WPC products that may be subjected to sustained loads, it is imperative that this creep behavior be understood. This study character izes the time-dependent deformation of two WPC formu lations [polypropylene and high-density polyethylene (HDPE)] in tension, compression, and flexure. It was found that the power law (Findley, Shapery, etc.) fits the data at various stress levels and loading mechanisms, for both formulations. This means that the deformation rate linearly decreases in log-log space and, after 400 d of testing; almost all the tests that have not failed remain in primary creep. The time-dependent constants associ ated with the power law and their stress dependencies are also presented.
... It is imperative to deal with the effect of these factors, when they occur concomitantly. We have shown in our earlier work that creep of HDPE-rice husk deck-boards show nonlinear behavior with respect to stress [5] and follow the power law. Authors have proven that pure HDPE creep exhibits nonlinear behavior under stress [6]. ...
The viscoelastic characterization of agro-filler based plastic composites is of paramount importance for the material’s long-term commercial success. To predict creep, it is important to derive a relationship between deformation, time, temperature, relative humidity, and stress. Since temperature shift can interfere with stress shift in creep, the predictive model should incorporate the relationship between these two shifts. Rice husk-HDPE beams were subjected to creep and recovery in the flexural mode and stress/time/temperature-related creep behavior of the same was studied. Temperature-related creep constants and shift factors were determined for the material and the constants were compared against theoretical two-phase constants. 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. This means that the stress equivalency of temperature is possible. This constitutive equation can predict creep in the long run. Although stress dependency is nonlinear, temperature dependency is linear and thermorheologically complex. The ‘single-phase’ material behavior (creep constants) was also compared with a ‘two-phase’ predictive model, where the creep constants were estimated with the ‘theory of mixtures’.
... It is imperative to deal with the effect of these factors, when they occur concomitantly. We have shown in our earlier work that creep of HDPE–rice husk deck-boards show nonlinear behavior with respect to stress [5] and follow the power law. Authors have proven that pure HDPE creep exhibits nonlinear behavior under stress [6]. ...
The viscoelastic characterization of agro-filler based plastic composites is of paramount importance for the material’s long-term commercial success. To predict creep, it is important to derive a relationship between deformation, time, temperature, relative humidity, and stress. Since temperature shift can interfere with stress shift in creep, the predictive model should incorporate the relationship between these two shifts. Rice husk-HDPE beams were subjected to creep and recovery in the flexural mode and stress/time/temperature-related creep behavior of the same was studied. Temperature-related creep constants and shift factors were determined for the material and the constants were compared against theoretical two-phase constants. 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. This means that the stress equivalency of temperature is possible. This constitutive equation can predict creep in the long run. Although stress dependency is nonlinear, temperature dependency is linear and thermorheologically complex. The ‘single-phase’ material behavior (creep constants) was also compared with a ‘two-phase’ predictive model, where the creep constants were estimated with the ‘theory of mixtures’.
... Their approach is very attractive since it requires little computational effort. Authors like Lin et al. (2004), Papanicolaou et al. (2004) and Pramanick and Sain (2006) used their approach successfully. Lee and Knauss (2000) and Nordin and Varna (2006b), amongst others, have pointed out that ideal creep-recovery tests cannot be performed in practice: a tensile machine requires some time to apply a given load to a sample. ...
Schapery-type constitutive theories for nonlinearly viscoelastic materials have been used extensively within the literature. Most of the applications are 1D but some 3D applications can be found. Most of the 3D applications are thermodynamically inconsistent extensions of the 1D constitutive theory. This paper shows and illustrates how thermodynamically admissible Schapery-type constitutive theories can be generated. In addition, a new 3D constitutive theory is introduced. A new data reduction procedure for obtaining the material parameters, which does not rely on creep–recovery tests, is introduced. The procedure leads to material parameters that are thermodynamically admissible and considers the whole mechanical response rather than particular values, as in most data reduction procedures. This procedure is tested on a thermoplastic material and the constitutive theory
thus obtained is compared with data from other load histories.
Gluten plays a key role in determining the unique baking quality of wheat by conferring water absorption capacity, cohesivity, viscosity and elasticity of the dough. In spite of being relatively minor constituents, water-soluble pentosans (WSP) have the capacity to significantly affect the properties of dough and the final baked product. An understanding of their rheological properties in relation to their interaction would be therefore highly desirable in order to understand the physical and chemical mechanisms responsible for variations in bread making quality.Gluten and WSP were extracted from defatted whole wheat flour. Rheological behavior of the hydrated gluten–WSP samples was studied using creep-recovery test and dynamic measurements. For gluten samples, the dynamic moduli increased with the increase in NaCl concentration. The WSP had significant impact on this behavior, hence strengthening the network at any ionic strength, as shown by the increase of storage (G′) and loss (G″) moduli. The gluten–WSP samples were most strengthened when water level was 50%, which was determined by creep tests and oscillating measurement. The gluten–WSP mixture was also less sensitive to the thermal treatment than the glutens alone, as shown by the lower magnitude of variation of G′ and G″ with temperature.
Agro-based plastic composites are being used as deck boards and other load-bearing materials. In these composites, both fibers and plastics contribute to creep when they carry loads. However, the existing literature concentrates on creep prediction and characterization of composites as a single-phase material. In our study, an attempt is made to develop a generic creep prediction model that describes the creep behavior of composites with the constituents’ creep behavior. The ‘theory of mixture’ for composites is extended to describe the creep behavior of this material, which is two phase. This model is validated for HDPE-rice husk composites with power-law-Boltzmann’s superposition principles. The model works well not only to describe creep, but also its nonlinearity. The model is generic enough for extending it to incorporate varying environmental conditions, such as time and temperature. This is the first model to describe creep for a two-phase bio-based composite. This study is a vanguard in correlating Schapery’s ‘single-phase’ model with a ‘two-phase’ model, where the same is validated for step-loading situations.
In this study, creep/recovery behavior of wood flour/polypropylene (PP) composite was compared with solid wood and PP. Wood flour–PP composite samples (strips with 10 mm thickness and 70 mm width) were made using a laboratory twin-screw extruder. Short-term flexural creep tests at 30% of ultimate bending load were performed using flexural creep equipment. Total time to complete every test was 120 min (60 min creep and 60 min recovery). Creep parameters (relative creep, fractional deflection, creep rate, etc.) were measured for all creep test samples. The result showed that the relative creep in wood–plastic composite (WPCs, with or without coupling agent) is significantly higher than solid wood and lower than PP. Also, it was observed that the creep rate in WPC (with or without coupling agent) is significantly lower than plastic, but is approximately equal to solid wood. The use of coupling agent decreased relative creep and fractional deflection in wood flour–PP composite panels. Findley creep model predicted creep strain with a high acceptable accuracy for studied materials.
The dispersion of filler in resin is an important factor which determines the mobility of a compound in a molder and also the mechanical properties of molded products in wood/plastic composite, especially with high wood filler content. In this report, the dispersion of components in the melt-mixture of a compound in response to the size of cellulose filler and resin content was examined for compounds with a high content of cellulose in polypropylene by the evaluation of viscoelasticity using a cone rheometer, and the following conclusions were obtained: (1) The viscoelasticity measured by a cone rheometer was dependent on the dispersion state of the compound, and it was confirmed that the presented evaluation method of viscoelasticity affords information relevant to the dispersion state of filler in a compound; (2) On the basis of the viscoelastic evaluation of compounds with different resin contents, a model for the distribution of cellulose and resin is proposed in terms of the tangle of fibers; (3) Viscoelastic analysis showed that cellulose size has an influence on the tangle of fibers; (4) The results of viscoelasticity and mechanical properties of molded products suggested that an important factor determining the tangle of fibers is the average aspect ratio. The proposed analysis of viscoelasticity presents a simple technique for estimating the dispersion state of a compound with high filler content, which is hardly possible by conventional fluid evaluation methods. POLYM. ENG. SCI., 48:168–176, 2008. © 2007 Society of Plastics Engineers
Ice-core and snow samples collected on Belukha glacier, Russian Altai mountains, were analyzed for n-alkanes by gas chromatography. On the basis of the total concentrations (T-HCs), carbon preference index (CPI) values and the plant wax contributions (WaxC n), it is suggested that mountain glaciers on the Asian continent received higher loading of n-alkanes from natural and anthropogenic sources than the Greenland ice sheet. It appears that the loading and variation of n-alkanes on glaciers in the Altai are approximately the same as those of the mountain in general, because the concentrations, CPI values and WaxC n percentages of n-alkanes in Sofiyskiy glacier, also in the Russian Altai, are at the same levels as or slightly greater than those in ice-core and snow samples from Belukha glacier. It seems that the n-alkanes on Belukha glacier are derived mainly from higher plant wax and petroleum exhaust other than from diesel engines. Vertical profiles of T-HCs and CPI values of n-alkanes show that the non-WaxC n portions and T-HCs have recently increased with a decrease in CPI values on Belukha glacier. A similar trend of n-alkanes was reported for Sofiyskiy glacier, indicating that the influence of human activities has gradually increased around the Altai.
To improve our understanding of the wood composite hot-pressing process, viscoelastic consolidation of wood flake mats was investigated in terms of constituent flake properties and mat formation. A fundamental model of mat stress relaxation was developed based on the compressive stress relaxation of wood flakes and Poisson distribution of flake overlaps formed in the mat. Both stress relaxation and creep of wood flakes and flake mats at ambient condition were experimentally tested and analyzed. The results showed that the stress relaxation of wood flakes at different levels of compression follows linear double logarithmic relationships with varying slopes or rates of stress relaxation. The mat stress relaxation model was validated by comparing the model predictions with the experimental data. Like stress relaxation, creep of flakes also varies with the level of compression. Due to porosity difference, creep of flake mats is not quantitatively comparable to creep of flakes in terms of relative creep strain. Instead, relative creep compaction ratio of mats is comparable to that of wood flakes.
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.
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.