Exploring acoustic properties of banana fiber composites with elastomeric filler through a computational approach

The constituents used in the fabrication of the composites are banana fiber (Plant family name : Musa Sapientum), TRP fillers, and epoxy binder. The banana fibers and TRP fillers were procured from a local vendors, while the CT/E—556 epoxy resin with polyamine hardener was supplied by M/s Composites Tomorrow, India. Raw banana fibers contain 61%–65% cellulose, 6%–18% hemicellulose, 5%–10% lignin, 3%–6% pectin, 1%–2% ash, and 2%–6% extractives [18, 40]. The banana fiber density was 1250kg m⁻³ and the average fiber diameter was 129 μm. The TRP fillers had a bulk density of 1016 kg m⁻³ and particle size > 400 μm. The epoxy resin had a density of 1200 kg m⁻³, with a resin to hardener mixing ratio of 10:1 by weight. The banana fibers were subjected to alkali treatment, in order to roughen the fibers and thus improve the adhesion between the binder and the fiber surface. The alkylation treatment breaks down the 'alkali sensitive hydrogen bonds' and forms new 'reactive hydrogen bonds', reducing the hydrophilicity of the banana fibers. Following alkylation, the hydrophilic components like lignin, hemicellulose, waxes and oils are removed from the fiber surface. The alkylation reaction of the fibers is shown in equation (1) [18].

$$\begin{eqnarray}&&{Fiber}-{OH}+{NaOH}\to {Fiber}-O-{Na}+{H}_{2}O\end{eqnarray} \tag{ 1 }$$

The alkali treated fibers are shown in 5(a), while the washed banana fibers are shown in figure 5(b). The TRP particles were quite coarse, and hence, ball milling was employed to reduce the size of the TRP fillers, and also to ensure uniformity in the grit shapes (figure 5(c). After ball milling, sieving was undertaken to filter the TRP fillers to the desired particle size of 70 μm as shown in figure 5(d). For the studies, five compositions were taken up as listed in table 2 and each composition was given a name 'NFC', indicating Natural Fiber Composite followed by a numeral for the particular composition. To prepare the specimens for the experiments on the impedance tube, suitable moulds were machined out of mild steel, on CNC machining centre shown in figure 6. Based on the fiber, filler and binder content in each composition, the constituents were weighed and placed meticulously inside the respective moulds line with release agent (for easy removal), followed by cold pressing on a compression moulding machine. Post-curing, the specimens were carefully extracted and taken up for the acoustic characterization on the impedance tube.

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Prior to conducting the computational analysis of the material, density values were determined using a combination of theoretical, experimental, and computational calculations. These density values played a crucial role in formulating accurate assumptions that facilitated a more comprehensive analysis of the results obtained from both the experimental and computational tests. To theoretically estimate the value of density of the specimens, the equations used were [41–43]:

$$\begin{eqnarray}&&{m}_{c}={m}_{f}+{m}_{m}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{W}_{f}+{W}_{m}=1\end{eqnarray} \tag{ 3 }$$

where,

$$\begin{eqnarray}{W}_{f}=\displaystyle \frac{{m}_{f}}{{m}_{c}}\ \&\ {W}_{m}=\displaystyle \frac{{m}_{m}}{{m}_{c}}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}{V}_{f}=\displaystyle \frac{{v}_{f}}{{v}_{c}}\ \&\ {V}_{m}=\displaystyle \frac{{v}_{m}}{{v}_{c}}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{V}_{f}=\displaystyle \frac{\tfrac{{W}_{c}}{{\rho }_{f}}}{\tfrac{{W}_{f}}{{\rho }_{f}}+\tfrac{{W}_{m}}{{\rho }_{m}}}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{V}_{m}=\displaystyle \frac{\tfrac{{W}_{c}}{{\rho }_{m}}}{\tfrac{{W}_{f}}{{\rho }_{f}}+\tfrac{{W}_{m}}{{\rho }_{m}}}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{\rho }_{c}{v}_{c}={\rho }_{f}{v}_{f}+{\rho }_{m}{v}_{m}\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{\rho }_{c}={\rho }_{f}{V}_{f}+{\rho }_{m}{V}_{m}\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{\rho }_{c}=\displaystyle \frac{1}{\tfrac{{W}_{f}}{{\rho }_{f}}+\tfrac{{W}_{m}}{{\rho }_{m}}}\end{eqnarray} \tag{ 10 }$$

For composites consisting of filler material,

$$\begin{eqnarray}&&{\rho }_{c}=\displaystyle \frac{1}{\tfrac{{W}_{f}}{{\rho }_{f}}+\tfrac{{W}_{m}}{{\rho }_{m}}+\tfrac{{W}_{r}}{{\rho }_{r}}}\end{eqnarray} \tag{ 11 }$$

Furthermore, the void content for the specimens was calculated using,

$$\begin{eqnarray}&&{void}( \% )=\displaystyle \frac{{\rho }_{{th}}-{\rho }_{{\exp }}}{{\rho }_{{th}}}\times 100\end{eqnarray} \tag{ 12 }$$

Table 3 compares the densities of the compositions. The presence of voids and defects within the material, can lead to discrepancies between the experimental density and the theoretical density. Theoretical values may also deviate from computational values due to the omission of factors such as particle length and diameter, fiber and filler orientation, and the uniformity of their distribution. Furthermore, neither the theoretical nor computational values account for variations in the length and diameter of fibers or fillers. To analyze the distribution of the banana fibers and TRP fillers within the specimens, and the void content, optical microscopy was taken up using the Olympus BX53M optical microscope on NFC-1, NFC-3 and NFC-5 as representative compositions. Figure 7 shows the micrographs of the compositions NFC-1, NFC-2 and NFC-5. NFC-1 showed a high concentration of banana fibers as it contained 53 wt.% of banana fibers, and least void content among the compositions of ∼5.55%. NFC-2 showed a higher number of voids, with a lesser distribution of banana fibers compared to NFC-1, with the highest void content of ∼14.8% among all compositions. It was conclusive from the micrographs of NFC-5, about the presence of only TRP fillers, although some voids were present, the void content being ∼9.3%.

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The acoustic tests were conducted using a BSWA Tech SW422 Impedance Tube setup (figure 9) following ISO 10 534-2:1998 [44]. Two 100 mm and 30 mm diameter specimens were used to obtain transmission loss readings across a frequency range of 63-6300 Hz under environmental conditions using $\tfrac{1}{4}$ inch microphones of sensitivities 55.6 mV/Pa, 56.2 mV/Pa, 56.9 mV/Pa and 55.6 mV/Pa [45] respectively as seen in figure 9. The specimens used in the experiments are shown in figure 8. Transmission Loss of a particular material indicates the effectiveness of a material when used as an acoustic barrier. The portion of transmitted incident energy is called the power transmission coefficient of sound, represented by the symbol τ. Transmission loss can be expressed as follows [46, 47],

$$\begin{eqnarray}&&{TL}=10\mathrm{log}\left(\displaystyle \frac{1}{\tau }\right)\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&\tau =\displaystyle \frac{{I}_{{transmitted}}}{{I}_{{incident}}}\end{eqnarray} \tag{ 14 }$$

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The RVE approach is a fundamental concept in the study of composite materials, including filled composites considered in the current study. The RVE approach is used to analyze the behavior of composite materials at the macroscopic level by considering a smaller, representative volume that captures the essential features of the micrsotructure of the composite [48]. This microstructure includes the arrangement, distribution, and properties of both the matrix material and the filler particles. By analyzing the behavior of the RVE, one can derive effective macroscopic properties of the composite material, such as its elastic modulus, density, and other mechanical properties [49]. Ansys Material Designer^® was used to develop the RVE unit cells for each of the compositions and obtain the orthotropic properties. For instance, in case of the NFC-1 composition, a Random Fibre Matrix RVE unit cell (fiber volume fraction = 0.53, orientation tensor = 0.333, aspect ratio = 155:1, fiber diameter = 0.13 mm) was constructed as shown in figure 10. The corresponding material properties of banana fibre, L12-K6 epoxy, and tyre rubber particles used for this study have been summarised in table 4. The orthotropic elasticity of each composite was determined using periodic boundary conditions. Once the data was acquired, it was subsequently imported and loaded into the Engineering Materials tab for modal and harmonic acoustics analysis. Similarly, this procedure was repeated for the other compositions.

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One of the popular tools for analysis of sound transmission loss is the Ansys Harmonic Acoustics^® Module, which has been used in the current work. In this tool, one needs to define the physics region (the composite plate in this case being analyzed), and the acoustics region (enclosure) before and after the physics region, in which sound waves propagate. The inlet and outlet ports have to be defined with respect to the measurement of the transmission loss function. The numerical model for analysing transmission loss was based on the SW422 Impedance Tube setup. The setup consisted of a 100 mm disc and a 30 mm disc, with the impedance tube modelled using the enclosure feature. The discs were placed at the centre of the enclosure, and the air enclosure for the 100 mm disc had a diameter of 100.5 mm and a length of 300 mm. To maintain a constant aspect ratio of disc diameter to the tube length, the enclosure for the 30 mm disc was made 30.5 mm wide and 90 mm long [3].

The specimen was classified as the physics region, while the air enclosure around the specimen was the acoustics region. The lateral surface of the enclosure was assigned as the radiation boundary. The input and output ports were selected as the left and right faces of the enclosure to measure the transmission loss, as seen in figure 11. The FE model was based on the impedance tube experimental setup, the schematic being shown in figure 12. For each composition, natural frequencies were obtained using six modes from the modal analysis module. To calculate the surface velocity, equation (15) was used [53], where 'a' represents the speed of sound, γ is the adiabatic index (=1.4), the gas constant (R) with the temperature (T) ∼299 K.

$$\begin{eqnarray}&&a=\sqrt{\gamma {RT}}\end{eqnarray} \tag{ 15 }$$

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Corresponding to the experimental setup, a frequency range of 63–1300 Hz for the 100 mm setup and 1300–6300 Hz for the 30 mm setup was used for the simulation. An element sizing of 3–3.5 mm for the physics region and 4–4.5 mm for the acoustic region was employed. The mesh metrics (table 5) were optimised to obtain accurate results within a reasonable time frame of 10–12 hours. The comparison of experimental and computational transmission loss values with percentage errors are depicted in table 6.

The acoustic transmission loss (TL) values of various compositions of the composite were classified across three frequency ranges for ease of behaviour analysis, namely low (67–400 Hz), medium (400–1900 Hz), and high (1900–6300 Hz). The results displayed in figures 13 and 14 showed that, in the low-frequency range, the composition NFC-4 had the lowest average TL value of 2.25 dB, while NFC-3 exhibited the highest average TL value of 24.37 dB, with a peak maximum of 27.13 dB. Moving on to the medium frequency range, the TL values of NFC-2 and NFC-4 showed a drastic increase, although they still had the lowest TL values. NFC-1 and NFC-3 had similar peaks (33–34 dB) and average (25–27 dB) TL values, which were higher than the other compositions. Additionally, NFC-5 demonstrated a significant increase in TL values compared to the low-frequency range. Finally, for the high-frequency range, the TL value for NFC-3 deteriorated slowly, while those for NFC-1 and NFC-5 continued to increase steadily. NFC-5 had the highest peak maximum of 46.73 dB at 3150 Hz within the high-frequency range. NFC-4 consistently exhibited the lowest TL values throughout the high-frequency range, with a minimum TL of 16.24 dB and a maximum of 36.88 dB. Overall, NFC-1 and NFC-5 show a steady rise in TL throughout the test range, whereas NFC-3 and NFC-4 showcase a wide range of TL values over the entire frequency spectrum.

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The transmission loss values obtained from the computational model increase with frequency compared to the undulations gradually noticed in the experimental values. This variation can be attributed to the computational model assuming ideal conditions for the enclosure and the specimen. The uncertainties in weather and atmospheric disturbances can also contribute to the variation in results. Multiple iterations were carried out to maximise the number of data points obtained for the transmission loss readings, and the values obtained were plotted against the experimental readings in figure 15 as a logarithmic trendline, as TL is a logarithmic quantity. NFC-3, followed by NFC-5 and NFC-1, shows the closest approximation of results between the experimental and computational values with a standard deviation of 1.82–3.51% throughout the entire frequency range. Meanwhile, NFC-2 and NFC-4 show a maximum deviation between the two results with a standard deviation in the range of 18.76–25.18%. The same can be observed by noting the point of convergence for each of the compositions. From figure 15, the convergence for NFC-1 and NFC-5 occurs between ∼2000–3000 Hz, and NFC-3 shows a near parallel plot for both the results with a difference of 1 dB at the beginning of the plot. Conversely, the plot for NFC-4 shows a convergence at ∼6000 Hz at the very end of the plot, with a significant divergence observed in the low-frequency range. Meanwhile, the plot for NFC-2 showed no convergence within the frequency range studied in this experiment. However, it displayed a moderate divergence in the logarithmic plots for the low and medium-frequency ranges, followed by minimum deviation in the high-frequency zone. This deviation can be attributed to the fact that NFC-4 shows extremely low values of TL in the low-frequency range, as shown by the data obtained from the experimental analysis. Nevertheless, the data points in the medium and high-frequency ranges for the experimental and computational plots for NFC-4 show moderate deviation upon close observation, indicating that this disruption from standard patterns may be due, but not limited to, the high variation in density between the simulated and experimental values as discussed in section 3.3.

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Additionally, the mean TL values for all compositions were calculated and plotted as a polar plot (figure 16). Through this plot; we can note that NFC-1, NFC-3 and NFC-5 show the best acoustic characteristics in terms of mean Transmission Loss. The TL values obtained from this research align with the findings from previous studies, further validating the efficacy of these materials in sound insulation applications [54]. Previous research showed banana fibre to exhibit a maximum TL of 23 dB, while coir demonstrated a slightly lower TL of 20 dB. On the other hand, particle boards exhibited the highest TL value among the investigated materials, with a remarkable 36 dB. Other synthetic composites yielded a TL range of 30 dB. These results are consistent with previous research, highlighting the inherent sound-dampening capabilities of both natural and synthetic composites.

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The modal analysis was taken up on Ansys to discern the first six modes for the various compositions. The specimens were modelled as 100 mm and 30 mm as per the specifications of the impedance tube setup. The first six mode shapes for the 100 mm configurations of NFC-1 can be seen in figure 17. Mode shapes for the remaining compositions were similar, with a slight variation in the values of the frequencies, as seen in table 7. Another additional observation was that modes 2 and 3 and 4 and 5 showed the same values of frequencies with a 90^o phase difference.

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