Modeling the Rheological Characteristics of Flexible High-Yield Pulp-Fibre-Reinforced Bio-Based Nylon 11 Bio-Composite

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1 Journal of Encasulation and Adsortion Sciences, 015, 5, 1-10 Published Online March 015 in SciRes. htt:// htt://dx.doi.org/10.436/jeas Modeling the Rheological Characteristics of Flexible High-Yield Pul-Fibre-Reinforced Bio-Based Nylon 11 Bio-Comosite Robenson Cherizol 1,,3*, Mohini Sain 1,3, Jimi Tjong 1 Centre for Biocomosites and Biomaterials Processing, Faculty of Forestry, University of Toronto, Toronto, Canada Powertrain Engineering Research & Develoment Centre, Ford Motor Comany, Windsor, Canada 3 Deartment of Chemical Engineering & Alied Chemistry, University of Toronto, Toronto, Canada * robenson.cherizol@mail.utoronto.ca Received 13 January 015; acceted 30 January 015; ublished 3 February 015 Coyright 015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). htt://creativecommons.org/licenses/by/4.0/ Abstract The aim of this work was to develo a mathematical model to investigate the rheological characteristics of viscoelastic ul-fibre comosite materials. The rheological roerties of High-Yield Pul (HYP) reinforced bio-based Nylon 11 (Polyamide 11) (PA11) comosite (HYP/PA11) were investigated using a caillary rheometer. Novel redicted multihase rheological-model-based olymer, fibre, and interhasial hases were develoed. Rheological characteristics of the comosite comonents influence the develoment of resultant microstructures; this in turn affects mechanical characteristics of a multihase comosite. The main rheological characteristics of olymer materials are viscosity and shear rate. Exerimental and theoretical test results of HYP/PA11 show a stee decrease in aarent viscosity with increasing shear rate, and this melt-flow characteristic corresonds to shear-thinning behavior in HYP/PA11. The non-linear mathematical model to redict the rheological behavior of HYP/PA11 was validated exerimentally at 00 C and 5000 S 1 shear rate. Finally, redicted and exerimental viscosity results were comared and found to be in a strong agreement. Keywords HYP/PA11, Rheological Characteristic, Viscosity/Shear Rate, Modeling 1. Introduction Pul-fibre-reinforced thermolastic comosites are in high demand in the automobile, construction, and aero- * Corresonding author. How to cite this aer: Cherizol, R., Sain, M. and Tjong, J. (015) Modeling the Rheological Characteristics of Flexible High-Yield Pul-Fibre-Reinforced Bio-Based Nylon 11 Bio-Comosite. Journal of Encasulation and Adsortion Sciences, 5, htt://dx.doi.org/10.436/jeas

2 sace industries. Vegetable fibres are biodegradable and renewable; they consume less energy than glass fibres, and consequently they generate less ollution [1]-[3]. Other reasons for the high demand for the utilization of green fibres are their low density and good thermal and acoustic roerties. Pul fibres, moreover, do not abrade rocessing tools [] [3]. Materials from biological sources regrou natural olymers, so they can be exected to exhibit viscoelastic behavior. Aroriate rocessing and roduction conditions of olymer roducts are determined by their rheological characteristics. The bleached high-yield ul (HYP) fibres derived from hardwood that were used in this study are short crystalline fibres [4] [5]. Short-fibre-reinforced olymer comosites are extensively used in manufacturing industries due to their light weight and imroved mechanical roerties [5]. Hence, HYP has been used not only for its low lignin content, but also for its otential thermal stability and its strong adhesion when it is bonded with high-temerature engineering thermolastic olymers [4]-[6]. The study of the rheological behavior of viscoelastic olymer comosites is mostly limited to a two-hase fibre-olymer. The so-called interhase zone aears in the viscoelastic daming of olymer comosite rocessing [7]. This deformation significantly affects the redicted overall rheological characteristics of natural-fibrereinforced thermolastic comosites [8]. During rocessing, fibre-reinforced olymers are subjected to rigorous deformations that cause fibres to translate, agglomerate, bend, and rotate with the flow of the fibre matrix [7]-[9]. This strongly influences the rheological and mechanical roerties in different arts of the final roduct because of the close deendence of these roerties on the orientation state of the fibres. Likewise, rheological roerties that are a function of the flow-induced fibre configuration in the matrix also influence the hysical roerties of fibre-reinforced olymer comosite [8] [9]. The effect of the interhasial zone has been already studied by Kaw and Besterfield [10] and Yeh [11] as a third constituent of the redictive models with resect to the elastic behavior of fibre-reinforced olymer comosites. Gohil and Shaikh [1] and Kari et al. [13] have investigated the interhasial effect in wood-fibre-reinforced olymer comosites. It was demonstrated that the interhase, considered as a homogeneous and isotroic material, has a significant effect on the loss factor and on the rediction of the elastic roerties of three hases: fibre, interhase, and olymer comosite. Other works by Lamnawar and Maazouz [14], and Larache and Agbossou [15] used theoretical and exerimental aroaches based on shear lag and shear modulus to show the role of the interhase in the elastic roerties of comosite materials. However, no studies have been found in the literature that consider these three hases in investigating the effect of the interhase on rediction of the rheological characteristics of viscoelastic ul-fibre-reinforced thermolastic olymer comosites. The rheological characteristics of such comosites are vital to their final mechanical roerties. Although natural-fibre-reinforced olymer comosites and their rocessing have been artially reviewed in several aers, models of their rheological behavior and analysis of the rheology-rocessing arameter relationshis have been neither investigated nor reorted. This study reorts on the state-of-the-art technology in the rheology of biocomosites from green-fibre olymers, including their viscoelasticity and comlex rheological behaviors as influenced by different conditions. Hence, an overview of the viscoelastic roerties of biomaterials derived from ul-fibre-reinforced thermolastic olymers is resented in order to analyze their rheological behavior as art of redicting the viscosity of olymer melts. Giesekus roosed a constitutive model based on a concet of configuration-deendent molecular mobility [16]-[18]. In this model, the viscoelastic comonent of the extra stress tensor is reresented with the arameters η, λ and α ; due to the highly nonlinear nature of the model equations, all the roerties need to be obtained numerically. Moreover, this model is only able to redict low load and low shear rate in the resence of fibre. The urose of this study, therefore, is to resent exerimental and redicted results of HYP/PA11 and to validate this novel rheological modeling aroach. First, we fully exlored the viscoelastic-olymer-based Giesekus constitutive model. Second, we introduced the fibre and interhasial hases in function of fibre diameter and asect ratio to the Giesekus model, considering the effect of fibre entanglement and agglomeration on the variation of the viscosity with shear rate. Finally, the model was validated by obtaining the exerimental data needed to evaluate the model s redictions.. Mathematical Model.1. Governing Equations The equations governing the flow are the mass and momentum conservation equations. ν = 0 (1)

3 ρ ν = + τ + ρg () where ν is the velocity vector, ρ the olymer melt density, τ the olymeric extra stress contribution, the ressure and g the gravitational velocity. For olymer melts exhibiting Newtonian rheology, τ takes the form T ( ) where μ is the melt viscosity and D u ( u) melts, the stress tensor deends on the deformation history... Assumtions τ = µ D (3) = + is the rate-of-strain tensor. For viscoelastic olymer The model was designed on the assumtion that it should describe rheological behavior as a function of the rate of deformation according to different conditions like fibre flexibility, interhasial zone and asect ratio, and anisotroic arameter. In addition, to obtain a closed-form analytical exression for the velocity distribution as a function of the viscoelastic arameters, the following assumtions were introduced: The flow of fibre-reinforced thermolastic comosites is assumed to be an incomressible fluid during the extrusion and injection molding rocesses; =, ν = 0 ; The isothermal viscosity laws are alied, i.e., the viscosity is only a function of shear rate; The comonents of the comosite are anisotroic, then nonlinear viscoelastic models; The flow is in a closed system and is driven only by alying load (zero ressure gradient, i.e., P = 0 ); The velocity field is steady and fully develoed, i.e., u u( y) Given the high viscosity of the olymer melt, inertia is negligible..3. Model Develoment A single Giesekus model derived from a Maxwell element would be sufficient to model the observed relaxationtime behavior, the shear stress, and the viscosity of olymer material. However, the strong nonlinear viscoelastic exression of shear viscosity in function of high shear rate of ul-fibre-reinforced olymer comosite required the extension of the model to include more arameters. Hence, in addition to the olymer hase, the fibre and interhase hases have been formulated into the Giesekus base model. The literature offers various concets for modelling change in the viscous roerties. It has been ointed out that only the viscous overstress and the strain rate are suitable deendencies for formulating a viscosity function. Figure 1 shows the surface area of the flexible HYP at different oints. Assuming that the fibre is flexible, when shear is alied the fibre is agglomerated at the oint of diameter D. The surface area of fibre before agglomeration is maximum, and is calculated as follows: At the agglomerated oint, the surface area is minimum, and we obtain: A A Max = πdl (4) Min πd 4 = (5) L Max Surface D Min Figure 1. HYP fibre of length L before load is alied: When load is alied, the fibre is entangled and agglomerated and has diameter D. 3

4 Assuming that the comosite material has three hases and that the fibre is flexible, the total stress or the stress of the comosite is reresented as: The shear stress of the olymer hase: τ = τ + τ + τ (6) c f int αλτ τ + λτ + ηγ = 0 (7) η where α is a model arameter attributed to anisotroic Brownian motion or anisotroic hydrodynamic drag on the constituent olymer molecules. It is required that 0< α < 1 as discussed by Giesekus [16]-[18]. The shear stress of the fibre hase: For L Ar =, we have D The shear stress at the interhasial hase: By rearrangement, we have τ f = πd 4 τ = f F ( D) + πd l F ( A ) πd r 0.75 Substituting Equations (7), (9) and (11) into (6) and rearranging it, we arrive at: L D σ f = (10) τ int σ f τ int = (11) Ar αλτ η = ηγ F σ 1+ λ τ τ f πd ( Ar 0.75) τ Ar Predicting the shear viscosity during the extrusion rocess and using the caillary rheometer involves a couled analysis of flow, shear rate, asect ratio, and interhasial effect. The resultant equation is highly nonlinear due to the viscosity, which deends on the shear rate, fibre asect ratio, and rocess arameters; these nonlinearities have been solved by the Newton-Rason method of numerical aroach. 3. Materials and Methods 3.1. Materials The matrix bioolymer bio-based Nylon 11, density 1.03, MFI 11, was sulied by Arkema, France. Asen HYP fibers were sulied by Tembec (Montreal, QC). The HYP is the tye used in wood-free rinting and in writing-aer grades and multile-coated folding-board grades; fibre length is 0.30 to 0.85 mm. Finally, the ul-fibre length was reduced by using a mechanical crib in order to investigate the asect ratio effect on the rheological behavior of the HYP/PA Exeriment The exeriment was rocessed using a Conical Twin Extruder. In the mixing method, the HYP fibre was dried at 80 C for 6hours and then added to the corresonding PA11 and well mixed before it was introduced to the extruder. The average temerature of the barrel was 00 C. (8) (9) (1) 4

5 3.3. Rheological Measurements The rheological measurements of the comosites melt-flow roerties were carried out in a twin-bore Rosand Caillary Rheometer model RH000 (the standard RH000 range suorts temeratures from 40 C to 500 C. The standard maximum force alied is 1 kn). The comosite samles for testing were cut into very small ieces, then laced inside the barrel and forced down into the caillary with the lunger attached to the moving cross-head. Reresentative steady-shear viscosity versus high shear rate is resented in the figures below for HYP/PA11, which was rocessed at the average extrusion temerature of 00 C. The aarent viscosity of the samle was obtained from steady-shear measurements for different fibre asect ratios, with the rate ranging from 50 to 5000 S 1. The rheology viscosity data resented in this aer reresent an average value of three measurements. 4. Results and Discussion The novel nonlinear viscoelastic material model was exlored in order to simulate the nonlinear rheological behavior of HYP/PA11. In this study, both exerimental and redictive results on HYP/PA11 were investigated in order to understand the ower, validity, and caabilities of the novel rheological model develoed. The detailed rheological roerties are the major focus of this work Exerimental Results Rheological characteristics of the olymer, fibre, and interhasial hases influence the final characteristics of the resultant microstructure of comosite materials; these characteristics in turn affect the mechanical roerties of a multihase olymer comosite system. Exerimentally, the aarent viscosity as function of the steady-shear rate of HYP/PA11 at 00 C is shown in Figure (as noted, these results are the average of three different exerimental tests). As noted, the comosite material used in the exerimental study had a fibre length of 0.73 mm, and the exeriment was conducted at 00 C. The exerimental results showed that the aarent viscosity of HYP/PA11 comosite decreases with increasing shear rate. This decrease in the shear viscosity with the increase in shear rate corresonds to the seudolastic fluid characteristic of the comosites. This seudolastic behavior (also referred to as shear-thinning behavior) lotted in Figure is mainly influenced by the orientation of the olymer molecules, the agglomeration of the flexible fibre, and the entanglements within the olymer chains in the caillary rheometer. Due to the flexibility of HYP, when shear is alied to the material the orientation of the fibre changes its configuration from rectangular to sherical; such modifications are roduced in the fibre length and the surface area of the fibre once the orientation is comleted at high shear rate. On the other hand, the chain agglomerations are roduced simultaneously with collasing one chain onto another chain. The entanglement of the chains followed by agglomerations, as well as the entanglements within the chains, are caused by the Brownian motions and low relaxation of HYP. The high shear-thinning behavior obtained for HYP/PA11 can be also associated to the thermal degradation of HYP during the rheological testing. The molten olymers tend to arrange themselves with their major axes in the direction of shear, and thereby oints of entanglement are reduced. 800 Shear viscosity (Pa.S) Shear rate (s -1 ) Figure. Shear viscosity vs. shear rate of HYP/PA11 at 00 C. 5

6 As a result, the viscosity decreases. In other words, in this case of non-newtonian flow behavior of olymer melts, the decrease in viscosity when the shear rate is increased by alying load is associated with high shearthinning behavior and with viscoelastic characteristics of biocomosite materials. However, at very high shear rates (from 3000 to 5000 S 1 ), the molten HYP/PA11 showed a less restrained decrease in aarent viscosity. Such high decrease in the shear viscosity is associated with high shear-thinning behavior. This non-newtonian behavior is associated with the alignment and the orientation of the fibre in the olymer chains and the effect of the fibre asect ratio. At low as at high shear rates, the formation of agglomerates is evident; therefore HYP molecules are comletely oriented due to the good green-hyp disersion in the bio-based PA11 matrix. This means that the breakage of the fibre length allows the maintenance of an accurate fibre-asect ratio when the diameter of flexible HYP is ket unchangeable during the rocess. The shorter length of the fibres will also suort their alignment in the direction of the flow, thus reducing the fibre-fibre collisions and leading to a higher decrease in the aarent viscosity. 4.. Variation of the Viscosity with a Function of Shear Rate of HYP Reinforced PA11 at Various Temeratures The variation of the aarent viscosity in function of the shear rate of HYP-reinforced PA11 at various temeratures was investigated and the rheological test results are resented in the Figure 3. The rheological conditions were ket constant while different tests were run for 190 C, 00 C, and 10 C. The aarent viscosity of the HYP/PA11 deended on the rate of shear at which it was measured and resented. The shearing effects decreased as the temerature increased; that is, the HYP/PA11 became more non- Newtonian in the higher temerature region. At higher temerature the reduction of the shear viscosity was more ronounced at intermediate shear rate, while for 190 C, the reduction of the shear viscosity reached a maximum at higher shear rates (from 3000 to 5000 S 1 ). This characteristic is due to the fact that the HYP-reinforced PA11 fibres were agglomerated and entangled at low temerature and low and intermediate shear rate; this made flow deformation difficult (at this oint this rheological behavior is called near-newtonian). At high shear rate, the shearing effects increased while the effect of temerature was less ronounced, and flow deformation was mostly dominated by the shearing effect. However, from 3000 to 5000 S 1 all the aarent viscosity variations in function of shear rates followed the same rate of deformation for different temerature rofiles; this corresonds to shear-thinning behavior Effect of Fibre Content on the Rheological Behavior of HYP/PA11 The effect of the fibre content on the rheological characteristics of the comosite was investigated. Figure 4 shows the exerimental results for 10%, 0%, and 30% HYP/PA11. These curves are tyical of seudolastic materials, which show a decrease in viscosity with increasing shear rate. At high fibre content, the material offers higher shear viscosity even for high shear rate. In general, the incororation of fibres in olymer systems increases the viscosity and increases further with fibre content. The difference is not very significant for 10% and 0% fibre for intermediate and high shear rate. At low HYP content, the shear viscosity was exected to increase raidly with increasing concentrations of the fibres because of the raidly increasing interactions between articles as they become acked more closely to each other. Nevertheless, at very high fibre content, random anisotroic structures of fibres in the olymer melt were created. The increase in shear viscosity was found to be more redominant at lower shear rates where fibre and olymer molecules were not comletely oriented Effect of the Fibre Asect Ratio on the Rheological Proerty The results from the study of the effect of the asect ratio of flexible ul-fibre-reinforced bio-based Nylon 11 are resented below in Figure 5. At low fibre asect ratio, the decrease in viscosity as a function of the shear rate was greater for both low and high shear rate. Contrarily, at higher fibre-asect ratio the shear viscosity shows a moderate decrease for low and intermediate shear rate. At low and intermediate shear rate, the viscosity curves are slightly decreased and the distance between each viscosity curve remains large. However, at high shear rate the viscosity lots are tightly close. This is because fibre agglomeration and entanglement are not ronounced at high shear rate or frequency, due to the comlete 6

7 degree Shear rate (s -1 ) Figure 3. Variation of the viscosity with a function of shear rate of HYP/PA11 at various temeratures. Shear viscosity (Pa.s) Shear viscosity (Pa.s) Figure 4. Shear viscosity vs. shear rate of HYP/PA11 at 00 C. 00 degree 10 degree Shear rate (s-1) 10%BCTMP/PA11 0%BCTMP/PA11 30%BCTMP/PA11 Figure 5. Shear viscosity vs. shear rate of HYP/PA11 at 00 C. orientation of the fibre and olymer molecules. Much as with high fibre content, the increase in shear viscosity is found to be greater at lower shear rates, where fibre and olymer molecules are not comletely oriented Predicted Results In this section, the numerical lot below shows the results of the mathematical redictive model for reresenting the rheological characteristics of the material and the influence of rocessing conditions on the material s resultant microstructure. 7

8 To verify the alicability of the formulated viscoelastic-material model, certain rheological tests were simulated and comared with the exerimental data. The comarisons show that the newly develoed rheological viscoelastic-material model is caable of simulating not only the deendence of shear viscosity on the material s shear rate, but also the variation in the sloe of the material s rheological resonses. The shear viscosity curve observed for HYP/PA11 is deicted in Figure 6 for 30% HYP fibre. Figure 6 shows that HYP/PA11 biocomosite acts as a seudolastic fluid and that the shear viscosity lots have a tendency to decrease for high shear rates. The various assumtions considered in these models, in fact, were well fitted to the fluid s actual behavior. The fibre-agglomeration effect considered when the model was first conceived is a rimary contribution to the originality of this study. Accordingly, both redicted and exerimental results showed how the flexibility and entanglement of HYP fibre contributed to the change in the fibre s total surface area and the resultant influence on the rheological characteristics of HYP/PA11 comosite. The entanglement and agglomeration of the fibre are manifested at high shear rate, where the decrease in the fibre s surface area increases the material s shear viscosity and consequently shows a non-newtonian behavior. Figure 6 demonstrates that the flexibility and diameter of the ul fibres affects the viscoelasticity of the resultant comosite. Another observation is that the interhase interaction also influenced the viscosity behavior with the changing shear rate of HYP/PA11, together with the change in the asect ratio, which was mostly resent in the interhase. The interhase interaction in seudolastic fluid behavior is significant in the study of the shear viscosity with the increase in shear rate of high-fibre-content reinforced olymer comosite. The observed decrease in the shear viscosity of comosite material from the lot ma of the redicted model is associated with the high degree of seudolasticity due to erfect disersion of high-yield ul fibre into the comosites; this gives rise to the good reinforcing effect of HYP on PA Model Validation In this section, the comarisons between the theoretical redictions and exerimental measurements are detailed. In the exeriments, the shear viscosity was determined to be a function of high shear rate while olymer flow rate and rocessing temerature were ket constant. Exerimental and redictive results from HYP/PA1 are shown in Figure 7. The average shear viscosity at the initial shear rate was about 800 Pa s for 00 C for low fibre asect ratio and about 1000 Pa s for intermediate and high fibre asect ratio, and at this oint the melt exhibited both exerimentally and redictively a shift from Newton to non-newtonian rheological characteristics. However, as the shear increased, HYP/PA11 showed highly non-newtonian behavior, corresonding to high shear-thinning behavior. The accuracy of the redictive model derived from the exerimental testing results and used for calculating the revious shear viscosity was high. Exerimentally and mathematically, the shear viscosity as function of steady-shear rate of HYP/PA11 at 00 C is shown in Figure 7 (where Ex. = exeriment and M. = modeling): Ar1, Ex. Ar, and Ex. Ar3 reresent the fibre asect ratio 1,, and 3; and Ar1 < Ar < Ar3. Desite the discreancy between the values for viscosity obtained by the redictive model and those from exeriments from 000 to 500 S 1, the agreement between the model s redictions and exerimental data is remarkable given the simlicity and accuracy of the model, the exactitude of the material roerties and arameters, and the fitness of the roosed boundary conditions. At both low and high shear rate, good agreement is Shear viscosity (Pa.s) Shear rate (s -1 ) Figure 6. Prediction of shear viscosity vs. shear rate of HYP/PA11 at 00 C. 8

9 100 Shear viscosity (Pa.s) Ex. Ar1 Ex. Ar Ex. Ar3 M.Ar1 M. Ar M. Ar3 Figure 7. Shear viscosity vs. shear rate of HYP/PA11 at 00 C. evident from the results; hence, this novel mathematical redictive rheological model is well fitted to the extrusion of viscoelastic biocomosite materials. From 3000 to 5000 shear rate both exerimental and redictive results show a regular decrease on the shear viscosity, which may be due to the fact that fibre distribution and orientation are comlete, and that the viscosity is mainly deendent on the mobility of the olymer chains in the comosite structure. The model s lot of shear viscosity versus shear rate is evidence that the model is alicable to mathematically reresenting the rheological behavior of a variety of natural fibre-reinforced thermolastic viscoelastic comosite materials. 5. Conclusion In this study, a novel rheological model for viscoelastic materials was develoed in order to redict rheological roerties and then comared with exerimental results on HYP/PA11. This nonlinear rheological model was develoed for constant material arameters, simultaneously considering viscous, elastic, and inertial nonlinearities and interhasial hase variables and arameters. The redictive results indicated that the develoed model well suorts the determination of rheological characteristics of the investigated material, such as viscosity and shear stress. In addition, the rheological model was lausibly demonstrated and validated based on the exerimental results of shear viscosity versus shear rate. Both exerimental and redictive results showed high shearthinning behavior on HYP/PA11 associated with a high degree of seudolasticity due to the good disersion of HYP into PA11 and the orientation of the flexible fibre effects in the direction of the molten PA11. The model was validated for different fibre asect ratios and high shear rate, u to 5000 S 1. Due to its consistency and its high redictive ability, the model may be alied in rheological studies and investigations of viscoelastic materials, articularly in the automobile, construction, and aerosace industries. Acknowledgements This work was carried out with the suort of Mitacs funding; the University of Toronto and the Ford Motor Comany financially suorted this study. References Shear rate ( S -1 ) [1] Pervaiz, M. and Sain, M. (003) Carbon Storage Potential In natural Fibre Comosites. Resources, Conservation and Recycling, 39, htt://dx.doi.org/ /s (0) [] Bourmaud, A. and Baley, C. (009) Rigidity Analysis of Polyroylene/Vegetal Fibre Comosites after Recycling. Polymer Degradation and Stability, 39, htt://dx.doi.org/ /j.olymdegradstab [3] George, J., Sreekala, M.S. and Thomas, S. (001) A Review on Interface Modification and Characterization of Natural Fiber Reinforced Plastic Comosites. Polymer Engineering Science, 41, htt://dx.doi.org/10.100/en [4] Gu, R. and Kokta, B. (010) Mechanical Proerties of PP Comosites Reinforced with BCTMP Asen Fiber. Journal of Thermolastic Comosite Materials, 3, htt://dx.doi.org/ /

10 [5] Bajai, P. (01) Brief Descrition of the Pul and Paer Making Process. Biotechnology for Pul and Paer Processing, [6] Thomen, H. (001) Modeling the Physical Processes in Natural Fiber Comosites during Batch and Continuous Pressing. Oregon State University, Corvallis. [7] Plackett, D., Torgilsson, R. and Andersen, T. (010) Influence of Fiber Tye, Fiber Mat Orientation, and Process Time on the Proerties of a Wood Fiber/Polymer Comosite. International Journal of Polymeric Materials, 51, htt://dx.doi.org/ / [8] Uhlherr, P.H.T., Guo, J., Zhang, X.M., Zhou, J.Z.Q. and Tiu, C. (005) The Shear-Induced Solid-Liquid Transition in Yield Stress Materials with Chemically Different Structures. Journal of Non-Newtonian Fluid Mechanics, 15, htt://dx.doi.org/ /j.jnnfm [9] Liu, Y.J., Xu, N. and Luo, J.F. (000) Modeling of Interhases in Fiber-Reinforced Comosites under Transverse Loading Using Boundary Element Method. Journal of Alied Mechanics, 67, 41. htt://dx.doi.org/ / [10] Kaw, A. and Besterfield, G. (1998) Effect of Interhase on Mechanical Behavior of Comosites. Journal of Engineering Mechanics, 117, htt://dx.doi.org/ /(asce) (1991)117:11(641) [11] Yeh, J.R. (199) The Effect of Interface on the Transverse Proerties of Comosites. International Journal of Solids and Structures, 9, htt://dx.doi.org/ / (9)90005-e [1] Gohil, P. and Shaikh, A. (010) Analytical Investigation and Comarative Assessment of Interhase Influence on Elastic Behavior of Fiber Reinforced Comosites. Journal of Reinforced Plastics and Comosites, 9, [13] Kari, S., Berger, H., Rodriguez, R.R. and Gabbert, U. (005) Comutational Evaluation of Effective Material Proerties of Comosites Reinforced by Randomly Distributed Sherical Particles. Comosite Structures, 71, [14] Lamnawar, K. and Maazouz, A. (008) Rheology at the Interface and the Role of the Interhase in Reactive Functionalized Multilayer Polymers in Coextrusion Process. American Institute of Physics, 978, [15] Larache, M., Agbossou, A., Pastor, J. and Muller, D. (1994) Role of Interhase on the Elastic Behavior of Comosite Materials: Theoretical and Exerimental Analysis. Journal of Comosite Materials, 8, [16] Deshande, K. (004) k-version of Finite Element Method for Polymer Flows using Giesekus Constitutive Model. Ph.D. Thesis, University of Kansas, Lawrence. [17] Hosseinaliour, S., Tohidi, A. and Shokrour, M. (01) A Review of Dough Rheological Models Used in Numerical Alications. Journal of Comutational and Alied Research in Mechanical Engineering, 1, [18] Giesekus, H. (198) A Simle Constitutive Equation for Polymer Fluids Based on the Concet of Deformation-Deendent Tensorial Mobility. Journal of Non-Newtonian Fluid Mechanics, 11, htt://dx.doi.org/ / (8)

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