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Abstract

There is growing industrial and academic interest in manufacturing of biocomposite parts comprised of natural fibers in a thermoplastic matrix that begin as a commingled, unconsolidated preform. Unfortunately, little thermal property data exists in the literature for simulation/analysis of processes used to make parts (e.g., pultrusion, Automated Fiber Placement (AFP), and compression molding). In this paper, the authors explain how specific heat capacity and thermal conductivity values of both constituent materials and the biocomposite preform are measured in a direction transverse to the fiber length, and how the effect of entrained air is included. Thermal property values for hemp and flax fibers along with polypropylene and polyethylene filaments, measured both individually and combined into apparent values for the preforms, are compared with experimental values. Finally, determination of thermal properties for use in pultrusion simulation is explained as a case study.

Keywords

Thermoplastic biocomposites hemp flax thermal conductivity specific heat capacity

Introduction

Polymer composite materials consist of strong and stiff reinforcement fibers such as glass, carbon, aramid, or basalt encapsulated in a thermoset or thermoplastic resin matrix. The combination of these constituent materials provides superior mechanical properties (e.g., high specific strength and stiffness) and other advantages as compared to their homogenous counterparts. As such, the worldwide composites market, estimated to be worth $86 billion in 2020, is expected to increase at a compound annual growth rate (CAGR) of 6.6% from 2021 to 2028.¹ Strong natural bast fibers such as hemp and flax are also gaining in popularity for use in composites, because they offer specific mechanical properties similar to glass or basalt for many applications but as more sustainable alternatives. Accordingly, the market for such ‘biocomposites’ is expected to explode at a CAGR of 14.20%, from $21 billion in 2020 to $61 billion in 2028.² Another important trend in composites is that thermoplastic matrices are oftentimes preferred over thermosets because of their superior toughness, inherent bendability, better reprocessibility, and lower carbon footprint,³ although their use in biocomposites is quite limited.

The expected increased use of thermoplastic biocomposites in products (based on the aforementioned trends) will involve process simulation, but such analysis requires unique material properties due to the format of the raw materials. Since thermoplastic melt viscosities are commonly 3–4 orders-of-magnitude higher than those of uncured thermoset resins (e.g., epoxy), which makes reinforcement impregnation difficult, a common method that avoids this problem is to commingle fibers with thermoplastic filaments to melt in place and minimize impregnation distances. There are several manufacturing processes currently used to fabricate parts comprised of commingled, unidirectional tow comprised of natural fibers, thermoplastic filaments, and entrained air (Figure 1(a)) including pultrusion, automated fiber placement (AFP), and compression molding.⁴ Thermal analysis of these composite processes and related tooling requires heat transfer properties, particularly thermal conductivity and specific heat capacity, of the unconsolidated tow (fiber + thermoplastic filament + air) in a direction transverse to the direction of fibers and filaments.

Figure 1.

Schematics of (a) a unidirectional tow consisting of thermoplastic matrix filaments commingled with natural fibers and (b) a pultrusion process utilizing a commingled rope as input.

Related research on each of these processes in the context of thermoplastic biocomposites is as follows.

• Pultrusion, a continuous manufacturing process used to manufacture biocomposites with constant cross sections (cylindrical, rectangular), has been successfully demonstrated for thermoplastic composites and biocomposites such as graphite/PPS (polyphenylene sulfide),⁵ flax/polypropylene⁶ and, flax/polylactic acid (PLA).⁷ Thermoplastic composite pultrusion, shown schematically in Figure 1(b), differs from pultrusion of thermoset composites in that it uses: commingled tows as input; a preheating device for the input material; a heated die to finish melting the matrix then consolidate and ensure good fiber impregnation and consolidation; and an additional cooling die to impart dimensional stability to the final pultruded part by solidification.⁷ Linganiso et al. pultruded biocomposites of flax/PLA commingled yarn,⁷ and Van de Velde et al.⁸ and Angelov et al.⁹ worked with flax/polypropylene commingled yarn. Van de Velde concluded that flax fiber is a desirable reinforcement material due to its environmental advantages. Angelov⁹ found that for a particular pultrusion speed (24 cm/min) and die temperatures (230°C), the pultruded flax/PP profiles had comparable mechanical performance to those of compression-molded parts. Memon and Nakai¹⁰ also developed a pultrusion system for jute/PLA commingled yarn.

• Automated fiber placement (AFP), an advanced manufacturing process used to manufacture complex aircraft parts, uses a robotic/gantry system with an attached fiber placement head to heat and lay down multiple strips of thermoplastic composite tow onto a tool surface and simultaneously consolidate it. Adhesion between the tows is ensured by appropriate heating, compaction, and tow tensioning systems.¹¹ Lamontia et al.¹² developed a three-stage out-of-autoclave AFP layup specifically for thermoplastic matrices. The first hot line compactor establishes initial intimate contact and healing, the second compactor maintains temperature to complete healing of the polymer chains, and the third cold compactor chills the material and compresses voids.

• Compression molding uses heated matched molds and external pressure to melt and consolidate commingled thermoplastic composite tows and/or textiles into high-performance components. The combination of heat and pressure produces a composite part with low void content and high fiber volume fraction. Compression molding has been utilized to develop various biocomposite systems such as wood fiber/polypropylene,¹³ sisal/epoxy¹⁴ and jute/glass hybrid composites.¹⁵

To expand on the main point previously mentioned, effective tooling design using analytical and/or computational modeling for the aforementioned manufacturing processes involving a commingled natural fiber/thermoplastic filament material format requires accurate transverse thermal properties to predict the degree of fiber impregnation with thermoplastic resin. Discussion of such properties is sparse the literature. Accordingly, this paper focuses on this gap in knowledge by: (1) discussing the methodology and equipment used for determining thermal properties for a commingled format; (2) comparing different material models for estimating the combined properties of commingled fiber and matrix filaments; and (3) providing specific heat capacity and the transverse thermal conductivity of four specific biocomposite material systems – all combinations of two common recyclable thermoplastics, polyethylene and polypropylene, and the two strongest natural bast fibers, hemp and flax.

Background

Fibers from bast fiber plants, primarily hemp and flax, have been used as reinforcement in various composite systems as reflected in numerous research studies^6,16–19 related to the mechanical properties of the consolidated composite material. Hemp fiber-reinforced composites are considered an emerging market in the US since the production of hemp was only legalized in 2018 under the Farm Bill.²⁰ Flax was once one of the most important crops for US farmers, but it is now grown almost exclusively in North Dakota and Minnesota.²¹ Bast fiber-reinforced thermoplastics have many advantages over their thermoset counterparts such as low processing cost and design flexibility.¹⁵

There has been significant research on hemp- and flax-based thermoplastic composites and characterization of their mechanical properties ^{16–18,22–24} yet studies pertaining to the thermal properties are less prevalent. Volk et al.²⁵ pultruded large thermoplastic profiles of up to 40 mm diameter using glass fiber/PET commingled yarns. They were able to manufacture such large profiles only through careful die design and the selection of the processing parameters based on FEM thermal modeling. This further affirms the importance of the thermal properties of the flax/hemp commingled (unconsolidated) mix, irrespective of the manufacturing process used. Li et al.²⁶ attempted to determine the thermal conductivity and specific heat capacity of flax/polyethylene biocomposites prepared through extrusion where the thermal properties did not change significantly in the range of 170–200°C. The properties decreased with increasing fiber content. Aydin et al.²⁷ observed the effect of alkali treatment on Digital Scanning Calorimeter (DSC) thermograms of Flax/PLA based composites, but they failed to determine the specific heat capacity from the thermograms nor thermal conductivity. Kannan et al.²⁸ performed a similar study with Flax/polypropylene composites, yet the DSC analysis does not extend to the calculation of specific heat capacity and there is no mention of thermal conductivity analysis as well. Behzad and Sain²⁹ measured the thermal conductivities for hemp thermoset composite manufactured through a novel solution-based technique in both in-plane and transverse directions and their empirical conductivities showed good agreement with mathematical models. Their work focused on thermal conductivity of pure hemp fiber only. To the best of the authors’ knowledge, these are the only studies that provide information on the thermal properties of either hemp or flax fiber composites, and nothing in the literature discusses commingled yarns.

Experimental and theoretical plan

The experimental and theoretical plan addresses two specific thermal properties in the transverse direction only of comingled fibers comprising a porous preform with entrained air present: (1) specific heat capacity and (2) thermal conductivity. Both of these properties along with density are essential for both analytical and computational modeling of the aforementioned processes.

Materials used in this study were sourced domestically. The hemp and flax fibers were combed top roving from Living Dreams Yarn (Rainier, WA, USA). Polyethylene (PE) filaments with an average diameter of 0.13 mm were obtained from Berkley FireLine, USA. Polypropylene (PP) twine with an average diameter of 2.16 mm was obtained from HyperTough, Inc. The PP twine was eventually separated into individual filaments for testing. Low density PE and PP sheets of 1.75 mm, 3 mm and, 4.5 mm thicknesses made of the same polymer grade as the filaments were used to measure thermal conductivity of the virgin PP and PE with no porosity. For this study, natural fiber and thermoplastic filaments were commingled in a 50:50 ratio by volume, i.e. V_f = fiber volume fraction = V_m = matrix volume fraction = 50% when consolidated (i.e. no air).

Specific heat experimental procedure and analysis

The specific heat capacity of the materials is determined according to ASTM E1269 using a TA Q1000 DSC machine, where materials tested are heated at a specified rate in a controlled environment. All the materials are put in a DSC aluminum pan and sealed with an aluminum lid. The difference in heat flow in the test specimen pan and an empty pan is continuously monitored and recorded.

The detailed procedure of the DSC experiment is as follows. The DSC machine is purged with dry nitrogen throughout the experiment. The empty specimen holder plus lid is weighed to a precision of ±0.01 mg. Next, a sapphire standard (reference material) is put in the specimen holder and weighed to the same precision. The DSC chamber is heated from or cooled to a reference temperature of 40°C. The chamber is allowed to stay at this temperature for 5 min to ensure equilibrium. Next, the sapphire standard material along with the empty pan and lid is heated up to 320°C at a rate of 20°C/min. The thermal curve showing heat flow versus temperature is continuously recorded, as seen in Figure 2. The chamber remains at 320°C for 5 min to ensure equilibrium and then the thermal curve is terminated. The chamber is allowed to cool to ambient temperature. The same series of steps are followed for five test specimens of flax and hemp as bast fiber reinforcement, one test specimen of PP and PE as thermoplastic matrices (since they are already well characterized in the literature) and, one test specimen each of the four combinations of natural fibers and thermoplastic filaments.

Figure 2.

Typical DSC thermal curve (PMMA) as an example showing D_st at 75°C and D_s at 175°C.

Once the thermal curve is recorded, the specific heat capacity is calculated in the following manner. Data for temperatures between 30°C to 180°C at 10°C increments is recorded. Next, calorimetric sensitivity E, is calculated as per the ASTM standard using

E = [\frac{b}{60 D_{s t}}] [W_{s t} C_{s t} + ∆ W C_{c}]

(1)

where: b = heating rate, °C/min; C_st = specific heat capacity of the sapphire standard, J/(g*K); C_c = specific heat capacity of the specimen holder, J/(g*K); E = calorimetric sensitivity of the DSC apparatus;

D_{s t}

= vertical displacement between the specimen holder and the sapphire DSC thermal curves at a given temperature (see Figure 2), mW;

W_{s t}

= mass of sapphire, mg; and ∆W = difference in mass between the empty specimen holder and the standard specimen holder, mg, in cases where two sealed specimen holders have to be used.

Using the calorimetric sensitivity E, the specific heat capacity of the test specimen, C_s, at a specific temperature can be calculated using

C_{s} = \frac{60 E D_{s}}{W_{s} b} - \frac{∆ W C_{c}}{W_{s}}

(2)

where: C_s = specific heat capacity of the specimen, J/(g⋅K);

D_{s}

= vertical displacement between the specimen holder and the specimen DSC thermal curves at a given temperature (see Figure 2), mW;

W_{s}

= mass of specimen, mg; and ∆W = difference in mass between the empty specimen holder and the test specimen holder if the same holder is not used for both runs.

After obtaining the DSC curves of the individual materials, the Series, Parallel and Lewis-Nielson models, represented mathematically in equations (3)–(5) and primarily intended for thermally conductivity, are used to predict the specific heat capacities of the composites, and the predictions are compared against the experimentally obtained specific heat capacities of the four composite combinations.

S e r i e s m o d e l : \frac{1}{C_{c}} = \frac{V_{f}}{C_{f}} + \frac{({1 - V}_{f})}{C_{m}}

(3)

P a r a l l e l m o d e l : C_{c} = V_{f} C_{f} + (1 - V_{f}) C_{m}

(4)

L e w i s - N i e l s e n : C_{c} = C_{m} (\frac{1 + A B V_{f}}{1 - B ψ V_{f}})

(5)

where: C_c = specific of capacity of commingled fibers and matrix with no air, kJ/(kg⋅K); C_f = specific heat capacity of fibers, kJ/(kg⋅K); C_m = specific heat capacity of thermoplastic matrix, kJ/(kg⋅K);

V_{f}

= fiber volume fraction; A = 0.5 for uniaxially oriented fibers with the direction of heat perpendicular to the fibers³⁰; B =

(C_{f} / C_{m}) - 1 / (C_{f} / C_{m}) + A

;

ψ = 1 + V_{f} (\frac{1 - ϕ_{m}}{ϕ_{m}^{2}})

; and ϕ_m = 0.82 for uniaxial random type of packing.³⁰

Lastly, the specific heat of the commingled tows with unidirectional fibers is calculated using the rule of mixtures. Although the tow is modeled as a mixture of fiber and matrix in a particular volume ratio, there is a significant amount of air trapped in the system as previously mentioned. The effective area of air present in the composite preform (e.g., rope) cross section is calculated by subtracting the individual component (fiber and matrix) cross sectional areas from the total preform area as

A_{a i r} = A_{p} - \frac{m_{f}}{ρ_{f} L} - \frac{m_{m}}{ρ_{m} L} .

(6)

The air volume fraction for a preform is then

V_{a} = \frac{A_{a i r}}{A_{p}}

(7)

The area of the individual constituents are determined by dividing their mass by the corresponding density and the length. The specific heat capacity, C_p, can then be calculated using equation

C_{p} = C_{c} + V_{a} C_{a}

(8)

where: L = preform length, cm;

A_{a i r}

= apparent area of air, cm²;

A_{p}

= cross sectional area of commingled preform (including air), cm²;

m_{f}

= mass of fibers, g;

m_{m}

= mass of thermoplastic matrix, g;

ρ_{f}

= density of fibers, g/cm³;

ρ_{m}

= density of thermoplastic matrix, g/cm³;C_p = specific heat capacity of the commingled preform including air, kJ/kg.K; C_a = specific heat capacity of air, kJ/kg.K; and

V_{a}

= volume fraction of the trapped air.

Thermal conductivity experimental procedure and analysis

The apparent transverse thermal conductivity of the four composite preform combinations were experimentally measured using a procedure adopted from the work of Pashayi et al.,³¹ which is similar to ASTM D5470-17. Since the term “thermal conductivity” is applicable only to homogeneous materials, the term “apparent thermal conductivity” is used for heterogeneous materials such as unconsolidated and consolidated composites. Here, a custom-built test apparatus consisting of two temperature-controlled platens sandwiching a test specimen, as shown in Figure 3(a), is used. Since the specimens containing natural fibers are difficult to contain within the platen area, the correct amount of material is weighed and contained within an insulative acrylic fixture, which is essentially a frame. The thickness of the fixture essentially determines the gap between platens and, hence, the volume fractions during testing. With this apparatus, the experimental transverse thermal conductivity (k) value of any individual materials or commingled mixes are determined. Next, the experimentally obtained transverse k-values of the commingled mixes are compared to predictions from various composite thermal conductivity models. The literature provides various mathematical models for determining the apparent thermal conductivity of a composite including Series, Maxwell, Russel, and Lewis-Nielson.^26,30 The mathematical representation of each model are provided in equations (9), (10), (11) and (12)

S e r i e s m o d e l : \frac{1}{k} = \frac{V_{f}}{k_{f}} + \frac{({1 - V}_{f})}{k_{m}}

(9)

M a x w e l l : k = k_{m} (\frac{k_{f} + 2 k_{m} + {2 V}_{f} (k_{f} - k_{m})}{k_{f} + 2 k_{m} - V_{f} (k_{f} - k_{m})})

(10)

R u s s e l l : k = k_{m} (\frac{V_{f}^{\frac{2}{3}} + \frac{k_{m}}{k_{f}} (1 - V_{f}^{\frac{2}{3}})}{V_{f}^{\frac{2}{3}} - V_{f} + \frac{k_{m}}{k_{f}} (1 + V_{f} - V_{f}^{\frac{2}{3}})})

(11)

L e w i s - N i e l s e n : k = k_{m} (\frac{1 + A B V_{f}}{1 - B ψ V_{f}})

(12)

where: k_f = isotropic thermal conductivity of fiber material, W/m⋅K; k_m = isotropic thermal conductivity of thermoplastic matrix, W/m⋅K;

B = (k_{f} / k_{m}) - 1 / (k_{f} / k_{m}) + A

; and A,

ψ

, and

ϕ_{m}

are the same as before.

Figure 3.

(a) Thermal conductivity experimental setup, (b) schematic showing various thermal and electrical components, and (c) equivalent thermal resistance circuit.

The detailed procedure for determined k-values involves recording the platen temperatures and voltage of the DC power source continuously. Referring to Figure 3(b), the top platen at temperature T_H is heated with an electrical resistance heater connected to a regulated DC power source. The voltage across the heating coil is V_H (in volts), and the corresponding resistance is $R_{H}$ (in Ω). The current, $I$ , flowing in the circuit is measured by introducing an electric resistor in series with the coil, where the voltage and the resistance across the resistor are V_R (in volts) and $R_{R}$ (in Ω), respectively. The bottom plate temperature, T_C, is recorded but not controlled. Temperatures T_C and T_H are measured using thermocouples. This apparatus allows measurement of the thermal impedance between the platens. The thermal impedance is the sum of the contact resistance (aka interface resistance) between the platens and the specimen, and the thermal resistance of the specimen itself. The apparent thermal conductivity is obtained from the slope of the thermal impedance versus specimen thickness curve; hence, multiple specimen thicknesses (typically 3) must be tested to create this curve. This is explained by the following equations: the first to calculate current I through each thermal impedance modeled as two resistors in series; and the second to calculate the power (P or ${\dot{Q}}_{h}$ ) applied to the coil after substituting in $R_{H}$ .

I = \frac{V_{H}}{R_{H}} = \frac{V_{R}}{R_{R}}

(13)

P = \frac{V_{H}^{2}}{R_{H}} = \frac{V_{H} V_{R}}{R_{R}}

(14)

Additionally, the apparatus inherently loses heat to ambient air by natural convection, and this can be modeled as a loss resistance that is measured by running an experiment on the apparatus with no specimen loaded. The loss resistance, $R_{l o s s}$ , is considered to be in parallel with the interface thermal resistance and specimen thermal resistance, $R_{int}$ , and specimen thermal resistance, $R_{s p e c i m e n}$ . The loss resistance calculated previously using this apparatus is usually in the range of 211–235 K/W. The thermal resistance between the low temperature copper platen and the underlying aluminum base plate is $R_{s i n k}$ . Therefore, the total thermal impedance in the system (R_total), shown schematically in Figure 3(c), is given by

\frac{1}{R_{t o t a l}} = \frac{1}{R_{l o s s}} + \frac{1}{R_{int} + R_{s p e c i m e n} + R_{int} + R_{s i n k}}

(15)

The rate of heat transfer between two surfaces is equal to the temperature difference divided by the total thermal resistance between two surfaces. Therefore, $R_{t o t a l}$ is obtained by running an experiment on the specimens and determining the slope of the resulting plot of temperature differential $∆ T = T_{H} - T_{C}$ vs. power (P). For example, the ∆T vs. P curve for a Flax specimen is shown in Figure 4(a). Here, the heater voltage (V_H), resistor voltage (V_R), and the platen temperatures (T_H &T_C) are recorded at intervals of 0.25 V to calculate the power P. The resistance of the resistor is equal to 78.2 Ω. The interface resistance is included twice to account for the two interfaces present between the top platen and the specimen and the specimen and bottom platen. Next, it is assumed that the two interface resistances are equal to each other and the sum of these resistances along with $R_{s i n k}$ is assumed to be a constant ( $R_{I n t e r f a c e 2})$ . Now we can simplify equation (15) to

R_{s p e c i m e n} + R_{I n t e r f a c e 2} = \frac{R_{t o t a l} R_{l o s s}}{R_{l o s s} - R_{t o t a l}}

(16)

Figure 4.

(a) Temperature difference versus Power plot (b) Contact resistance versus thickness plot.

R_specimen is equivalent to $\frac{t}{(k A)}$ , where k is the apparent thermal conductivity, t is the thickness of the specimen, and A is the cross-sectional area. After substituting for $R_{s p e c i m e n}$ , the apparent thermal conductivity can be extracted from the slope of the following straight-line equation

(\frac{1}{k A}) t + R_{I n t e r f a c e 2} = \frac{R_{t o t a l} R_{l o s s}}{R_{l o s s} - R_{t o t a l}}

(17)

An illustrative plot for a Flax specimen is shown in Figure 4(b). The error bars reside within the markers. For obtaining a best-fit line, specimens of varying thickness need to be tested. In equation (17), the two unknowns are $R_{t o t a l}$ and $R_{I n t e r f a c e 2}$ (intercept). Therefore, at least two specimens of different thickness have to be tested, although a third specimen was also tested in our case to validate the values obtained from the first two specimens. Since the presence of air cannot be neglected in the specimens, the true apparent thermal conductivity for a material devoid of air is determined through regression wherever necessary. This approach for predicting the true value, taken from Behzad and Sain,²⁹ is particularly helpful in predicting the true conductivity values of natural fibers such as hemp and flax. For instance, if the empirical measurements of a natural fiber specimen with entrapped air yields a conductivity value of k₁ for a volume fraction of V₁, then for a volume fraction of 100% the true conductivity k₁₀₀ will be given by

k_{100} = k_{1} (\frac{100}{V_{1}})

(18)

Three experiments were performed for the natural fibers, since fibers may show high thermal property variability. In addition, one experiment each was conducted for the two thermoplastic matrices and the four combinations of the composite mix. Lastly, similar to specific heat capacity, the thermal conductivity of the commingled fibers, k, can be calculated as

k_{p} = V_{c} k_{c} + V_{a} k_{a}

(19)

where: k_p = thermal conductivity of the commingled preform, W/m⋅K;

k_{c}

= thermal conductivity of the composite specimen without air, W/m⋅K;

k_{a}

= thermal conductivity of the air, W/m⋅K;

V_{c}

= volume fraction of the preconsolidated composite material (matrix + fibers); and

V_{a}

= volume fraction of air.

Results and discussion

Experimental results related to specific heat capacity and thermal conductivities values for the four different biocomposite material combinations along with comparison with model predictions are presented and discussed in this section.

Specific heat capacity

DSC runs for five specimens each of hemp and flax fibers performed over a temperature range of 40–320°C (see Figure 5) allow characterization of their composition (primarily cellulose, lignin and hemicellulose for fibers) or melt behavior (for polymers). Both hemp and flax fibers are primarily comprised of semicrystalline cellulose (65–75 wt%) .³² According to Kabir et al.,³³ hemicellulose degrades at a lower temperature range (25–290°C) as compared to lignin (150–420°C) and cellulose (250–350°C). At least three specimens for flax showed a drop around 150°C, which indicates hemicellulose decomposition. A second drop near temperatures of 200°C shows the onset of cellulose and lignin decomposition. Hemp fibers show a similar trend where the first drop in three specimens occurred at around 150–170°C indicating hemicellulose decomposition. A second drop in the temperature ranges of 230–260°C indicates cellulose and lignin degradation. Lastly, sharp drops for two of the hemp specimens at ∼120°C might indicate the release of bonded water, as was also observed by Han et al.³⁴ The thermal curves obtained for the four materials from the DSC equipment are shown in Figure 6. The average of the data obtained from the five specimens of both natural fibers is shown in the thermal curves of Flax and Hemp in Figures 6(a) and (b). From Figures 6(c) and (d), the melting point of the plastics can be determined by the steep drop in the heat flow. Polyethylene shows a melting point between of 130–132°C, which agrees well with 134°C obtained by Mathot et al.³⁵ in their DSC study. The melting point of polypropylene is estimated to be around 165°C. This melting peak is comparable with the peak obtained by Mucha et al.³⁶ in their polypropylene DSC study. The calorimetric sensitivity, E, distance D_s, and specific heat capacity C_s of each material at various temperatures based five specimens are provided in Table 1.

Figure 5.

DSC curves for all five specimens of (a) flax and (b) hemp fibers along with the average curve.

Figure 6.

DSC curves for (a) flax (average), (b) hemp (average), (c) PE, and (d) PP.

Table 1.

Data obtained from DSC experiments.

Temperature (°C)	Calorimetric Sensitivity, E	D_s (mW)				Specific Heat, C_s (kJ/g⋅K)				Weight of Specimen (mg)
Temperature (°C)	Calorimetric Sensitivity, E	Hemp	Flax	PE	PP	Hemp	Flax	PE	PP	Hemp	Flax	PE	PP
40	2.84	0.788	1.445	1.741	2.855	1.266	1.673	2.600	3.282	6.266	8.158	5.6	7.37
50	1.08	2.309	3.369	3.509	4.920	1.391	1.504	1.983	2.147
60	0.99	2.521	3.636	3.779	5.353	1.397	1.494	1.963	2.148
70	0.97	2.695	3.903	3.907	5.606	1.457	1.566	1.990	2.206
80	0.97	2.882	3.965	4.027	5.765	1.544	1.588	2.051	2.267
90	0.97	3.083	4.049	4.160	5.884	1.636	1.616	2.116	2.310
100	0.97	3.275	4.172	4.348	6.004	1.726	1.660	2.212	2.356
110	0.97	3.441	4.339	4.686	6.151	1.807	1.723	2.391	2.417
120	0.97	3.572	4.547	5.658	6.385	1.864	1.794	2.889	2.503
130	0.97	4.139	4.793	6.529	6.866	2.130	1.884	3.344	2.695
140	0.97	4.166	5.087	7.651	7.903	2.143	1.989	3.927	3.104
150	0.97	4.159	6.521	28.21	9.899	2.136	2.497	14.58	3.884
160	0.97	4.139	6.842	18.81	13.13	2.128	2.611	9.704	5.155
170	0.97	4.861	7.111	4.785	18.34	2.460	2.704	2.426	7.199
180	0.97	4.652	7.485	4.353	8.907	2.361	2.834	2.199	3.481
190	0.96	4.673	7.678	4.717	7.450	2.369	2.900	2.384	2.906
200	0.96	4.653	8.347	4.845	7.424	2.361	3.139	2.450	2.896
210	0.96	4.653	7.410	5.050	7.437	2.349	2.791	2.540	2.883
220	0.96	4.640	6.967	5.221	7.469	2.351	2.643	2.637	2.905
230	0.96	4.577	6.385	5.333	7.513	2.325	2.441	2.698	2.926
240	0.96	6.051	5.802	5.439	7.568	2.994	2.227	2.740	2.935
250	0.96	4.735	5.289	5.508	7.625	2.393	2.049	2.780	2.961
260	0.96	5.075	4.831	5.563	7.681	2.554	1.890	2.812	2.987
270	0.96	4.626	4.534	5.612	7.733	2.351	1.788	2.841	3.012
280	0.97	4.578	4.422	6.011	7.785	2.335	1.753	3.054	3.039
290	0.97	4.499	4.341	5.899	7.869	2.299	1.725	2.995	3.072
300	0.97	4.305	4.093	5.860	7.904	2.215	1.641	2.982	3.093
310	0.97	3.962	3.726	5.824	7.906	2.068	1.519	2.983	3.114
320	0.98	3.613	3.307	5.781	7.879	1.922	1.381	2.988	3.132

The experimentally determined specific heat capacities for the four materials with respect to the temperature and curve fits of this data for use in process simulation are shown in Figure 7. Fourth-order polynomials fit the natural fiber data most accurately.

H e m p : C_{h e m p} (T) = (- 1.197 \times 10^{- 10}) T^{4} + (- 7.263 \times 10^{- 8}) T^{3} + (2.675 \times 10^{- 5}) T^{2} + (5.765 \times 10^{- 3}) T + 0.9856

(20)

F l a x : C_{f l a x} (T) = (6.507 \times 10^{- 9}) T^{4} + (- 4.98 \times 10^{- 6}) T^{3} + (1.242 \times 10^{- 3}) T^{2} + (- 1.105 \times 10^{- 1}) T + 4.584

(21)

Figure 7.

Specific heat capacity versus temperature for (a) flax, (b) hemp, (c) polyethylene, and (d) Polypropylene.

Other than a spike in C near the polymer’s melting point (correlated to the latent heat), a linear data fit suffices for most of the temperature range.

P E : C_{P E} (T) = (2.816 \times 10^{- 4}) T + 3.234

(22)

P P : C_{P P} (T) = (2.242 \times 10^{- 3}) T + 2.6656

(23)

A mathematical method adopted from the work of Franquet et al.³⁷ can be used to capture the spike in specific heat in the thermoplastic’s phase change region by allowing indirect incorporation of the latent heat information into the specific heat capacity using

C (T) = C_{s, p c m} + ({C_{l, p c m} - C}_{s, p c m}) (\frac{T_{a} - T_{m}}{T_{a} - T}) + L_{f} (\frac{T_{a} - T_{m}}{{(T_{a} - T)}^{2}}) if T < T_{m}

C (T) = C_{l, p c m} if T \geq T_{m}

where:

C_{p c m} (T)

= the temperature dependent specific heat capacity of the phase change material, kJ/kgK;

C_{s, p c m}

= specific heat capacity of the solid state of the material (could be a function of temperature as well), kJ/kgK;

C_{l, p c m}

= specific heat capacity of the liquid state of the material (could be a function of temperature as well), kJ/kgK with the average of the values obtained from the DSC run used in this case;

T_{a}

= melting temperature of the pure PCM, K (e.g., 165°C or 438 K for PP);

T_{m}

= the end temperature of non-isothermal melting for the PCM This last temperature is usually calculated through a set of experiments involving DSC. The literature shows that the phase transition for PP takes place over a 5°C range, so a value of T_m = 165 + 5= 170°C = 443 K will be used for an example calculation. Finally,

L_{f}

= latent heat of fusion, kJ/kg.

Although validity of the Franquet method needs to be studied further, it is demonstrated for PP in Figure 8.

Figure 8.

Complete Specific heat capacity curve fit for PP after incorporating latent heat (L_f) indirectly using Franquet method.

The experimental and model-based specific heat capacity curves for all four composite combinations are shown in Figure 9. All three mathematical models (Series, Parallel, Lewis-Nielson) fail to predict the experimental data accurately, although the Series model comes the closest in general. Li et al.²⁶ found that the specific heat capacity of the composite mix decreases as the fiber percent increases. Therefore, at a 50% fiber volume fraction, the specific heat capacity of the composites was considerably lower than the pure matrix materials and hence the result obtained in this study fits the trend observed by others. Since the Series, Parallel, and Lewis-Nielsen models were originally developed to predict the thermal conductivity of a composite,³⁰ and there is a lack of similar studies comparing experimental values to the mathematical predictions, this indicates that these models are not appropriate predictors for combined specific heat capacity. Therefore, the authors suggest that experimentally obtained specific heat capacity values be used for process simulation instead.

Figure 9.

Specific heat capacities of the composite mix along with the mathematical model predictions for (a) hemp/PP, (b) hemp/PE, (c) flax/PP, and (d) flax/PE.

Apparent thermal conductivity

In this experimental study, the thermal conductivities of the four commingled materials (flax, hemp, polyethylene, and polypropylene) were measured and compared to other values in the literature (see Table 2). The authors were not able to find experimentally determined thermal conductivity of dry, aligned hemp fibers in the literature, and the measured value closely aligns with the predicted value from Behzad and Sain.²⁹ The thermal conductivities of hemp and flax are very similar, since both of them are bast fibers. Using the four mathematical models listed in The Experimental and Theoretical Plan and a V_f = 50%, the mathematical predictions are calculated. Next, three specimens of each of the four composite material combinations were experimentally determined using the same procedure. The measured thermal conductivity values, k_p, of the commingled fibers, predicted values using the five different models, and difference between experimental and simulation results are provided in Table 3. Similar to the findings of Kalaprasad et al.,⁴⁰ the comparison shows the series model providing the closest overall agreement to experimental values across all the four material combinations with errors ranging from 3-12%. Hence, the series model predictions should be used for apparent thermal conductivity values in subsequent analyses. The Lewis-Nielson model predicted the thermal conductivities of PP composites even better than the series model, but it was worse for the PE composites.

Table 2.

Measured thermal conductivities of the constituent materials.

Material	Apparent thermal conductivity, k (W/m⋅K)±1σ	Conductivity values from the literature (W/m⋅K)
Flax	0.113 ± 0.001	0.119²⁶
Hemp	0.112 ± 0.001	0.115²⁹
Low density polyethylene	0.316 ± 0.002	0.25–0.32³⁸
Polypropylene	0.225 ± 0.001	0.224³⁹

Table 3.

Commingled composite thermal conductivities.

Composite system	k_p±1σ (W/mK)	Series		Parallel		Maxwell		Russell (W/mK)		Lewis-Nielson (W/mK)
Composite system	k_p±1σ (W/mK)	Value (W/mK)	% difference	Value (W/mK)	% difference	Value (W/mK)	% difference	Value (W/mK)	% difference	Value (W/mK)	% difference
Hemp/PP	0.151 ± 0.000	0.156	3	0.172	14	0.168	11	0.169	12	0.154	2
Flax/PE	0.157 ± 0.000	0.163	4	0.213	36	0.200	28	0.203	30	0.180	15
Hemp/PE	0.155 ± 0.000	0.172	12	0.217	41	0.206	34	0.208	35	0.180	17
Flax/PP	0.157 ± 0.000	0.148	6	0.168	7	0.162	3	0.164	4	0.154	2

Case study: Commingled fiber properties for pultrusion preform

To demonstrate how transverse material properties are determined for a practical situation, a case study involving commingled thermoplastic matrix/natural fiber rope preforms intended for pultrusion is discussed. The final cross-sectional diameter and area for V_f = 50% and complete consolidation are 1.00 cm and 0.785 cm², respectively. In this case, total cross-sectional area of the matrix filament and natural fiber are both A_c = 0.785(0.5) = 0.393 cm². The required mass of each constituent material, m_c, for the unconsolidated preform of length L, is related by the equation $m_{c} = A_{c} L ρ_{c}$ , where ρ_c = constituent density. The preform length for all material combinations was L = 0.91 m (3’). The theoretical cross-sectional area of air, $A_{a i r}$ , is calculated using equation (6), where A_p is based on the preform dimensions. The diameter of the preforms was empirically determined at three separate positions along their length using calipers. Examples of commingled fibers preforms for all four commingled composite systems are shown in Figure 10, and their corresponding volume fractions are calculated in Table 4.

Figure 10.

Homemade commingled fibers from left to right: Flax/PP, Hemp/PP, Hemp/PE, and Flax/PE.

Table 4.

Volume fractions for unconsolidated commingled fibers.

Composite system	A_p (cm³)	A_air (cm³)	V _f = V _m	V _air
Hemp/PE	2.41	1.62	0.16	0.67
Hemp/PP	1.99	1.19	0.19	0.60
Flax/PE	1.67	0.88	0.24	0.53
Flax/PP	1.92	1.13	0.21	0.59

Using volume fractions from Table 4, the thermal properties of the commingled ropes are calculated using the previously described analysis. Although, the specific heat capacity can be calculated at any temperature, examples are provided for 40°C and 120°C in Table 5. Thermal conductivity at room temperature is provided.

Table 5.

Specific heat capacities and thermal conductivity for unconsolidated, commingled composite preforms.

Composite system	C_p at 40°C (kJ/g⋅K)	C_p at 120°C (kJ/g⋅K)	$k$ (W/mK)
Hemp/PE	1.14	1.34	0.081374
Hemp/PP	1.51	1.47	0.051056
Flax/PE	1.30	1.47	0.065029
Flax/PP	1.61	1.48	0.060979

Conclusion and future work

Thermal properties transverse to fiber direction (Figure 1) are arguably the most important model parameters required for analysis and simulation of composite manufacturing processes that involve commingled fiber and thermoplastic filament (e.g., pultrusion, AFP, and compression molding). Furthermore, interest in natural fibers combined with thermoplastics is growing, but there is little prior art on these thermal properties or how they are measured. In this paper, ASTM standard-based methods for measuring transverse C and k of commingled, unconsolidated, and porous mixes of natural fiber and thermoplastic filament in the presence of air are explained in detail. Specific heat capacity of flax and hemp, which initially increases then eventually decreases with temperature rise, is captured by a fourth-order polynomial curve fit; whereas values for PP and PE show a slight linear increase with temperature and a sharp spike during phase transition at their melting points. Unfortunately, constituent property and volume fraction data combined into an apparent C for the preform using series, parallel, and Lewis-Nielson models does not match experimental values. Hence, experimental data for the apparent C-values should be used in simulation instead. Experimentally measured k-values for the same commingled and unconsolidated preforms closely match those found in the literature. As expected, constituent data combined into an apparent k for the preform using a series model (one of five examined) closely matches experimental values. Finally, apparent thermal properties are determined from constituent properties as a case study for use in a pultrusion simulation.

Future work related to thermal properties for these types of composite manufacturing processes includes: (1) experimental characterization of a wider range of natural and synthetic reinforcement fibers and thermoplastic matrices (including bioplastics) and (2) a similar study on thermal properties along the fiber direction.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Empire State Development’s Division of Science, Technology and Innovation (NYSTAR) in New York State through their Centers for Advanced Technology program [Contract #C140134].

ORCID iDs

Daniel Walczyk

Amogh Wasti

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