Measurement and prediction of thermal conductivity for hemp fiber reinforced composites.
In the past few years, new research materials are being generated on the potential of cellulosic based fibers as reinforcement for plastics. All researchers who have worked in the area of natural fibers and their composites have agreed that these materials are claimed to offer environmental advantages such as lower pollutant emissions and lower greenhouse gas emissions. Moreover, natural fibers are low-cost fibers with low density and high specific properties [1, 2].
The properties of fiber-reinforced composites vary greatly, and depend upon their constituent materials, fiber orientation, and fiber volume fraction. Having an accurate knowledge about the material properties is essential if correct and meaningful process modeling is to be performed. Thermal properties such as thermal conductivity are important parameters to simulate the temperature variation inside the composite during a specific process. Thermal conductivity describes a material's ability to transport heat.
Mangal et al. studied the effect of volume fraction of pineapple leaf fiber on thermal properties of the composite using transient plane source technique . It was observed that increasing the fiber content in the matrix decreases the thermal conductivity and thermal diffusivity of the pineapple leaf fiber reinforced composite, which means that it could not provide the conductive path to the heat energy in the composite material. The theoretical values of thermal conductivity of composites were also obtained through Rayleigh-Maxwell and Meredith-Tobias models to compare with experimental data. Rayleigh-Maxwell model is applicable for a two phase dispersion of spherical particles in continuous medium for entire range of filler concentration in the composites . However, the Meredith-Tobias model does not consider the size and shape of the filler particles.
Sweeting et al. developed a new experimental method to determine the in-plane and though-thickness thermal conductivities of polymer matrix composites . The transient temperature gradient in the given direction is recorded using thermocouples and the result is processed numerically by an inverse approach to determine the directional thermal conductivity. The validation of the method was conducted using composites with known thermal properties, and excellent correlation was found between the known and determined thermal conductivities. The thermal conductivity and thermal diffusivity of oil-palm-fiber-reinforced untreated and differently treated composites using transient plane source technique at room temperature was studied by Agrawal et al. . They concluded that all the silane and alkali treatments of the fibers increased the thermal conductivity and thermal diffusivity of the composites in comparison with the acetylated composite. The silane treated fiber has higher polarity because of the formation of silonal group on the surface that results the higher thermal conductivity of the silane treated composites. The alkalization treatment removes impurities and increases the fiber surface adhesion characteristic with the resin and contribute to a higher thermal conductivity. The acetylation slightly increased the polarity of the fiber and, hence, the thermal conductivity of the composite increased marginally. Kalaprasad et al. analyzed and presented the thermal conductivity and thermal diffusivity of sisal-reinforced polyethylene, glass-reinforced polyethylene, and sisal/glass hybrid fiber reinforced polyethylene composites at high temperatures and with different fiber orientations . The difference between the thermal conductivity properties in parallel and perpendicular directions with respect to fiber length was maximum for sisal reinforced polyethylene as a result of the anisotropic nature of sisal fiber. An empirical equation was derived to explain the variation in thermal conductivity and thermal diffusivity with temperature.
In the present work, the thermal conductivity of the hemp fiber reinforced polymer composite at different volume fractions of the fiber is determined. The effect of fiber orientation in transverse and in-plane direction is investigated. To confirm the experimental results, the heating experiments are simulated by a finite element model (FEM) that incorporated the measured thermal conductivity and convection coefficients. Moreover, the experimental results of thermal conductivities of composites at different directions are compared with two reported models, E-S model and rule of mixture model, to describe the variation of the thermal conductivity versus the volume fraction of the fiber. The volume fraction of the fiber was obtained using Eq. 1.
An environmentally friendly thermoset water-based acrylic polymer was obtained from BASF Company, Ontario, Canada. The polymer is an aqueous solution of a polycarboxylic acid and a polyhydric alcohol as a crosslinking agent in water (52% water). The cure kinetic and conditions of the polymer were discussed in details in the previous papers [8, 9]. Hemp fibers in the form of randomly oriented and aligned were supplied by Hempline Company. The average fiber length was 9 cm and the diameter of the fiber was in the range of 10 to 300 [micro]m. Depending on the fiber diameter, the average tensile strength of the fiber was 250-1450 MPa . The randomly oriented and oriented fiber composites were prepared using the following process.
In this work, the composite was prepared employing a novel processing technique developed for natural fiber thermoset composites . Hemp fibers were formed on a perforated screen and the acrylic resin solution was circulated to impregnate the fibers with the solution (see Fig. 1). Vacuum filtration was applied to remove the excess solution. After circulation of the resin solution, the wet mat was displaced on a polyester sheet and then kept in the oven at 55[degrees]C for 48 hr to remove all moisture content. The mat would be ready for sheet molding process after the maturation period. Finally, to manufacture the composite the impregnated mat was cured at 180[degrees]C for 10 min using a hydraulic press to obtain the highest compaction. After the heating cycle, the composite was cooled inside the press to around 70[degrees]C using a water cooling system to prevent any blister formation due to any moisture content . The final composite was removed from the press and prepared for thermal conductivity measurements. Figure 2 shows the SEM micrographs of the oriented and in-plane randomly oriented composites.
[FIGURE 1 OMITTED]
Volume Fraction of Fiber
The volume fraction of fiber ([[upsilon].sub.f]) in the composite was determined using the following equation:
[[upsilon].sub.f] = [[[omega].sub.f] [[rho].sub.m]]/[[[omega].sub.m] [[rho].sub.f] + [[omega].sub.f] [[rho].sub.m]] (1)
where [[rho].sub.f] and [[rho].sub.m] are the densities of fiber and matrix and [[omega].sub.f] and [[omega].sub.m] are the weight fraction of fiber and matrix, respectively.
Because of anisotropic nature of the composite, the present work aims to measure the thermal conductivity in different principle directions to study the effect of fiber orientation on thermal conductivity of the composite. Three different experiments were applied to measure the transverse and in-plane thermal conductivity of oriented and randomly oriented composites. Figure 3 shows different samples used to measure the thermal conductivity. For transverse measurements, the samples were cut almost in 5 X 5 X 0.2 [cm.sup.3], and for in-plane measurements the dimensions of the samples were 5 X 1 X 1 [cm.sup.3].
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Thermal Conductivity Measurements
The method used to measure the thermal conductivity of composites has been adapted from a technique presented in Davidson and James work . To determine the thermal conductivity, the same apparatus was used. It consists of an electrically heated thin film (Kapton KHLV-202, low voltage heater, OMEGA) as the heat source sandwiched between two similar brick-shaped specimen halves (see Fig. 4). Two steel plates with the same dimension of the specimens were placed on either side of each specimen to create a uniform heating profile and prevent any convective thermal loss directly from the samples to the environment. Thermal compound (OT-201, High temperature conductive paste, OMEGA) was used to eliminate any thermal resistance between all components. The insulation was placed around the edges to create one-dimensional heat flow through the specimens. Prior to each measurement, a constant temperature gradient must be established across the specimen. This is done by imposing the homogeneous rate of heat flow that equals the electrical power P fed into the resistance heater. Because of the symmetry of the apparatus, the heat flow through each sample was assumed to be half the power consumed by the heater. The thermal conductivity of the sample is then calculated using Fourier law as:
[FIGURE 4 OMITTED]
k = [[J.sub.q]l]/[DELTA]T (2)
where k is the thermal conductivity of the sample [W [m.sup.-1] [K.sup.-1]], [J.sub.q] is the heat flux through the sample in W [m.sup.-2], in this case [J.sub.q] = P/2A, A is the cross-sectional area of the sample [[m.sup.2]], l is the thickness of the sample in the direction of the heat flow [m], and [DELTA]T is the temperature gradient across the sample [[degrees]C]. Two thermocouples were placed on both sides of one sample to monitor the temperature gradient at the surfaces and all were connected to a data acquisition system to record temperatures.
Specific Heat Capacity Measurement
To simulate the experimental method accurately, the specific heat capacity of the composites have to be determined. The evaluation of the specific heat capacity with temperature for hemp fibers was measured using a Differential Scanning Calorimeter (DSC) TA instruments DSC Q 1000 following well-established procedures . The specific heat capacity of the cured resin was obtained as well by a similar experiment. The variations of the specific heat capacity were measured in the range of 20-100[degrees]C.
FEM SIMULATION OF HEATING EXPERIMENTS
The finite element analysis was applied to verify the temperature rise generated during the heating experiments. It was assumed that if the simulation of the experiment incorporating the measured thermal conductivity obtained by the method described in this paper produced accurate prediction of temperature rise in the sides of the composite, then the accuracy of the apparatus will be justified. The temperature distribution for the composite during the heating process was evaluated by solving the Fourier heat conduction equation :
[rho][C.sub.p] [[partial derivative]T/[partial derivative]t] = ([k.sub.x][[[[partial derivative].sup.2]T]/[[partial derivative][x.sup.2]]]) + ([k.sub.y][[[[partial derivative].sup.2]T]/[[partial derivative][y.sup.2]]]) + ([k.sub.Z][[[[partial derivative].sup.2]T]/[[partial derivative][z.sup.2]]]) (3)
where [rho] and [C.sub.p] are the density and specific heat capacity of the composite, respectively, and [k.sub.x], [k.sub.y], and [k.sub.z] are thermal conductivity coefficients in the main axes.
The half of the heat input from the heater was considered as a heat flux boundary condition for one side of the sample and the other side was transferring heat to the environment by convection. The heat transfer convection coefficient (h) was obtained from experimental results using the following equation:
[FIGURE 5 OMITTED]
q = [k.sub.z] [[DELTA]T/l] = h(T - [T.sub.air]) (4)
where h is the air heat convective coefficient, [T.sub.air] is the temperature of environment, and k, is the transverse thermal conductivity. On the rest of the boundary, the heat transferred assumed to be zero. The domain was divided into block elements using a software package: COMSOL 3.2. The schematic of the domain is presented in Fig. 5.
MODELING OF THERMAL CONDUCTIVITY
To date, several models for determining the thermal conductivity of polymer composites have been proposed. There are many types of composite systems in which a polymer is reinforced with unidirectionally arranged fibers. In those systems, the thermal conductivity of the composite is the highest. This is due to the anisotropic nature of fibers; while the conductivity is good along the fiber, the heat flow across the fiber is poor. On the other hand, if the alignment of fibers is perpendicular to the direction of thermal flux, the thermal conductivity will be the lowest.
The thermal conductivity of a fiber-reinforced plastic in the direction parallel to the fibers is well understood in terms of the conductivities of the fiber and matrix. In a unidirectional composite the thermal conductivities of composites in parallel conductions can be estimated from the rule of mixture:
[k.sub.c] = [[upsilon].sub.f] [k.sub.f] + (1 - [[upsilon].sub.f])[k.sub.m] (5)
where [[upsilon].sub.f] and [k.sub.f] denote the volume fraction and the thermal conductivity of fiber, respectively, while [k.sub.m] is the thermal conductivity of matrix .
A general expression for effective transverse thermal conductivities of unidirectional composites was derived by Zou et al. . The model was presented based on the thermal--electrical analogy technique for elliptical filament and square packing array unit cell model (E-S model). The dimensionless effective transverse thermal conductivity, [k.sub.e], the ratio of the thermal conductivity of the composite, [k.sub.c], to the thermal conductivity of matrix, [k.sub.m], were expressed as a function of the ratio of thermal conductivities of filler to matrix, [beta], filler volume fraction, [[upsilon].sub.f], and the geometry ratio of the filler, [rho] = a/b, where a and b are the axial lengths of the ellipse along the x-axis and y-axis, respectively :
[k.sub.e] = [k.sub.c]/[k.sub.m] = 1 - [1/c] + [[pi]/2d] - [c/[d[square root of ([d.sup.2] - [c.sup.2])]]]ln|[d + [square root of ([d.sup.2] - [c.sup.2])]]/c| (6)
where c = [square root of ([pi][rho]/[[upsilon].sub.f])]/2, d = [rho](1/[beta] - 1), [beta] = [k.sub.f]/[k.sub.m].
When [rho] = 1 (i.e., a = b), the present model can be simplified as the cylindrical filaments in a square packing array unit cell model.
According to Springer and Tsai in Ref. 7, the thermal conductivity for a unidirectional fiber composite with the heat flow making an angle (90 - [theta])[degrees] to the fiber direction is
[k.sub.c] = [k.sub.c.sub.[parallel]] [sin.sup.2][theta] + [k.sub.c[perpendicular to]] [cos.sup.2][theta] (7)
where [k.sub.c[parallel]] and [k.sub.c[perpendicular to]] are the thermal conductivities of the composite parallel and perpendicular to the fibers, respectively.
The above mentioned Eqs. 5-7 will be used to describe the variation of the thermal conductivity of the hemp fiber/acrylic composite versus volume fraction of the fiber.
RESULTS AND DISCUSSIONS
Specific Heat Capacity Measurements
The variation of specific heat capacity of hemp fiber and cured resin obtained from DSC measurements are shown in Figs. 6 and 7, respectively. Figure 6 shows that the specific heat capacity of fiber increases from 2.2 J [g.sup.-1] [K.sup.-1] to almost 3.4 J [g.sup.-1] [K.sup.-1] with increasing temperature from 20 to 100[degrees]C. The average variation of the specific heat capacity of fiber could be fitted quite well by a polynomial of the second order as
[FIGURE 6 OMITTED]
[C.sub.pf] = 5[e.sup.-6][T.sup.2] + 0.0149T + 1.78. (8)
Figure 7 shows that the specific heat capacity of the cured resin also increased linearly with temperature in the range of 20-100[degrees]C. The values vary from 1.98 J [g.sup.-1] [K.sup.-1] to 2.7 J [g.sup.-1] [K.sup.-1] approximately. These variations could not be neglected in the model and the following linear relationship can be fitted for the average heat capacity of the cured resin as
[C.sub.pr] = 0.011T + 1.5. (9)
To predict accurately the temperature variations in the composite the specific heat capacities of the composite materials are needed. Therefore, the evaluation of the specific heat capacity of the composite can be determined by combining Eqs. 8 and 9 using the rule of mixture as
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[C.sub.pc](T) = [v.sub.f][C.sub.pf](T) + (1 - [[upsilon].sub.f])[C.sub.pr](T) (10)
where [[upsilon].sub.f] is the volume fraction of the fiber.
Thermal Conductivity Measurements
Transverse Measurements. The measured transverse thermal conductivities of randomly oriented composites, [k.sub.c[perpendicular to]], (Fig. 3a) are displayed as a function of volume fractions of the fiber in Fig. 8. It is clear that as the volume fraction of hemp fiber increases the thermal conductivity of the composite decreases. Direct measurement of the thermal conductivity of fiber is extremely difficult. The uncured polymer contains high percentage of water that cannot be easily removed and for that reason it leads to the present of voids for a bulk of cured resin. Therefore, the calculation of thermal conductivity of the pure cured polymer is also doubtful. Hence, the transverse thermal conductivity of the fiber ([k.sub.[perpendicular to]]) and polymer have been evaluated by extrapolating the linear regression of thermal conductivity values of the composite to 100% fiber and 0% fiber. It is found that the thermal conductivities of fiber and polymer are 0.115 W [m.sup.-1] [K.sup.-1] and 0.42 W [m.sup.-1] [K.sup.-1], respectively. The behavior of the thermal conductivity of different composites can now be explained using the thermal conductivity values of fiber and polymer. As 50% of the polymer replaced by the hemp fiber, thermal conductivity value of the composite decreases from that of the matrix. Further increasing of the fiber content in the composites shows a decreasing behavior trend of the transverse thermal conductivity as compared with the thermal conductivity of polymer matrix. This behavior of polymer composites seems to be justified because the fiber filled in the polymer matrix has a lower thermal conductivity.
Each test was then simulated using a FEM. Applying the same amount of heat to the sample and employing the thermal conductivity and the heat transfer convection coefficient obtained from the experimental results, the temperature variation with time at different locations were obtained. To quantify the agreement between the measured temperature data and the predicted results, the temperature distribution in the hot and cold sides of the samples were compared with the experimental values (see Fig. 9). It can be observed that initially the temperature increases sharply and differences between the measured and predicted temperature is around 1-2[degrees]C up to almost 2 hr. At longer time, it reaches a plateau and the steady state temperature shows a very good agreement between the experimental and predicted results which can validate the thermal conductivity obtained from the experiment method.
[FIGURE 9 OMITTED]
Figure 8 shows the theoretical value of transverse thermal conductivity of composites obtained through the E-S model. Although the fibers are not remained directionally symmetric and the random orientations of fibers are visible in the composite, the model predicts the value of thermal conductivity in close agreement with the experimental values ([R.sup.2] = 0.99).
In-plane Measurements. The measured in-plane thermal conductivities of oriented composites, [k.sub.c[parallel]], (Fig. 3b) are plotted as a function of volume fraction of fibers in Fig. 10. It can be noticed that unlike transverse measurements, as the volume fraction of hemp fibers increases the in-plane thermal conductivity of the oriented composite increases. By extrapolating of the thermal conductivity values of the composite to 100% fiber and 0% fiber, the longitudinal thermal conductivity of the fiber ([k.sub.[parallel]]) and the thermal conductivity of polymer were obtained to be 1.48 W [m.sup.-1] [K.sup.-1] and 0.42 W [m.sup.-1] [K.sup.-1], respectively. As it is obvious, there is a significant difference in thermal conductivities in the longitudinal and transverse directions of the fiber. Since natural fibers consist of crystalline cellulose lattice that are radially arranged around its axis, they are highly anisotropic, which give less thermal resistance along the axis compare with across the axis. Moreover, the number of fiber walls in plane oriented direction would be much less than the number of fiber walls in transverse direction. Therefore, there are more fiber walls to cross in the transverse direction and consequently more resistance to the heat flow.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
The predicted values for the in-plane oriented thermal conductivity obtained from the rule of mixture model (Eq. 5) were shown in Fig. 10. It is found that the obtained values of thermal conductivities are in good agreement with the experimentally measured values ([R.sup.2] = 0.95).
Figure 11 shows the experimental in-plane thermal conductivities of random oriented composites, [k.sub.c], (Fig. 3c). In this case, fibers are oriented in different angles (from 0 to 90[degrees]) with the direction of the heat flow. It can be seen that as the fiber volume fraction increases, the thermal conductivity also increases, which indicates that fibers are mostly oriented in the same direction of the heat flow. The thermal conductivity of the polymer was obtained by extrapolating a linear regression of experimental values ([R.sup.2] = 0.92) to 0% fiber and compared with other values that were determined in the above mentioned experiments (Table 1). Comparison of the results obtained in different experiments shows approximately the same value for the thermal conductivity of polymer which validates the experimental data. The small deviation could be due to the experimental errors. Inserting the in-plane thermal conductivity of randomly oriented composites, [k.sub.c], the in-plane thermal conductivity of in-plane oriented composite, [k.sub.c[parallel]], and the transverse thermal conductivity of the composite, [k.sub.c[perpendicular to]], at different volume fractions into Eq. 7, the average of the fiber angles with heat flow direction in randomly oriented composite at different volume fractions of fiber obtained to be around 31[degrees].
An empirical equation was developed to describe the variation of the in-plane thermal conductivity of randomly oriented composite, [k.sub.c], with volume fractions of fiber through linear regression of the experimental values. It can be expressed by the following linear relationship ([R.sup.2] = 0.92).
[k.sub.c] = 0.72[[upsilon].sub.f] + 0.40. (11)
A simple method has been employed to measure the transverse and in-plane thermal conductivities of hemp fiber reinforced composites. The transverse and in-plane thermal conductivities for oriented and randomly oriented composites for different volume fractions of fiber were investigated. Experimental results show that the orientation of fibers has a significant effect on the thermal conductivity of composites. For transverse direction, because of the lower transverse thermal conductivity of the fiber compare with the polymer as the volume fraction of fibers increases, the thermal conductivity of the composite decreases. On the other hand, for in-plane direction, because of the higher longitudinal thermal conductivity of fiber compare with polymer, the thermal conductivity of oriented composites enhanced with increasing the volume fraction of fiber. To validate the experimental results, the heating experiments for thermal conductivity measurement were simulated using a FEM that incorporated the measured thermal conductivity and the heat transfer convection coefficients along with specific heat capacity from DSC measurements and density. Predicted temperatures show close agreement with experimental data, which confirm the obtained thermal conductivity. Moreover, the experimental results of thermal conductivities of composites at different directions were compared with two different models (E-S model and rule of mixture model). Good agreement between theoretical and experimental results has been found. An empirical relationship was obtained for the in-plane thermal conductivity of randomly oriented hemp fiber composites.
The assistance of S.R. Davidson for providing the experimental set-up and performing the thermal conductivity measurements is gratefully acknowledged. Authors are thankful to NCE Auto21, Canada, for their financial support in this work.
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T. Behzad, (1) M. Sain (2)
(1) Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, Toronto M5S 3E5, Canada
(2) Faculty of Forestry, University of Toronto, 33 Willcocks Street, Toronto M5S 3B3, Canada
Correspondence to: M. Sain; e-mail: firstname.lastname@example.org
Contract grant sponsor: NCE Auto21, Canada.
TABLE 1. Estimated thermal conductivities of fiber and polymer. Thermal conductivity (W [m.sup.-1] [K.sup.-1]) Direction of measurement Fiber Polymer Transverse measurement 0.115 0.423 In-plane oriented measurement 1.48 0.427 In-plane randomly oriented measurement -- 0.405