Ultrasonic characterization of transversely isotropic epoxy/multiwalled carbon nanotube reinforced polyvinyl alcohol nanofiber mats nanocomposites

Abstract

Transversely isotropic materials’ mechanical properties are often determined using destructive testing methods. However, the data obtained from these tests are not sufficient for determining all mechanical properties of transversely isotropic materials. Thus, the aim of this study is to determine some elastic and mechanical properties of transversely isotropic nanocomposite materials, which are difficult to determine by destructive methods, using ultrasonic method. The polyvinyl alcohol (PVA) nanofiber mats reinforced with multi-walled carbon nanotubes (MWCNTs) at 1%, 3% and 5% ratios were produced using the electrospinning method. The resulting nanofiber mats were combined with epoxy resin (ER) with 5, 10 and 15 layers to form transversely isotropic ER/PVA-MWCNT nanocomposites. The effects of different MWCNT ratios and number of layers on the elastic constants and mechanical properties of materials were investigated using the ultrasonic pulse-echo overlap method. In addition, the morphologies of pure ER, PVA-MWCNT nanofiber mats and ER/PVA-MWCNT nanocomposites were evaluated by TEM and SEM analyses. According to the results obtained, in terms of some ultrasonic wave velocities (V_L11, V_L33, V_L45°, V_S12), elastic constants (c₁₁ and c₆₆), and mechanical properties (E₁, E₃, and μ₁₁), ER/PVA-MWCNT nanocomposites showed superior performance compared to pure ER. The most durable nanocomposite sample was determined as sample 3CPE-10, which contains 3% MWCNT and consists of 10 layers.

Introduction

Polymer matrix nanocomposites have gained a remarkable place in many engineering applications in recent years due to their superior properties such as lightweight, high strength, thermal stability, and electrical conductivity. In this context, epoxy resins (ER) have been a widely preferred matrix material, thanks to their excellent mechanical properties and chemical resistance. ¹ However, the brittle nature and limited toughness properties of pure epoxies have made it necessary to modify these materials with nano-reinforcements to improve their performance. ² Polymer matrix nanocomposite materials reinforced with carbon particles have found widespread applications in various sectors, including aerospace, defense, transportation, conductive films, fuel cells, transistors, displays, purification systems, textiles, and sports equipment.^3–5

Carbon nanotubes (CNT), particularly multi-walled carbon nanotubes (MWCNT), are widely used to enhance the performance of epoxy-based nanocomposites with properties such as high modulus of elasticity, electrical conductivity, and thermal conductivity.^6,7 The surface functionalization ⁸ and orientation of CNTs within the matrix ² can significantly affect the mechanical and electrical properties of nanocomposites. However, a challenge often encountered is the weak interfacial interaction between CNTs and polymeric matrices.^9,10 Similarly, in neat nanoparticle systems, the high surface area can lead to agglomeration in viscous polymers. This can result in insufficient thermal and mechanical properties in nanocomposites that use neat nanoparticles. To address this issue, it is recommended to modify the particle surface using various techniques to achieve better compatibility between polymer matrices such as epoxy resin and nanoparticles.^11–13 The electrospinning method offers numerous advantages, such as the ability to produce nanofibers with a high surface area-to-volume ratio, adjust fiber diameter, and incorporate various materials and additives. These advantages make it a valuable technique for achieving the desired properties in nanocomposite materials. In recent years, PVA nanofiber mats produced by the electrospinning method have been used to ensure uniform distribution of CNTs and achieve better bonding with the matrix. ¹⁴ Such hybrid structures, especially when manufactured in multiple layers, can exhibit transversely isotropic properties, offering directional mechanical performance.

In transversely isotropic materials, mechanical properties are often determined using destructive methods. ¹⁵ However, these static tests are very complicated, and the data obtained from these tests are not sufficient for determining all mechanical material properties. ¹⁶ In addition to destructive methods, ultrasonic testing as a non-destructive testing method has also been used for isotropic materials,^17–21 transversely isotropic materials,^16,22–26 and orthotropic materials.^27,28 Ultrasonic tests performed on such materials have revealed that ultrasonic methods provide more economical, repeatable, and accurate results than destructive testing methods such as tensile and indentation tests.^28–30 For instance, in the study conducted by Wong, Schmitt, ²⁵ the five independent elastic constants of sedimentary shales with transverse isotropic symmetry were measured using both ultrasonic methods and destructive static tests, and it was determined that the elastic constant values determined by static tests were much lower than the values determined by ultrasonic tests. New tellurite glasses were produced, and their density values were determined by El-Mallawany, Marzouk. ³¹ Furthermore, the longitudinal modulus, shear modulus, Poisson’s ratio, bulk modulus, and Young’s modulus values of these glasses were determined using the ultrasonic pulse-echo method at a frequency of 4 MHz. Oral and Ekrem ²⁴ produced ER/PVA nanocomposites with transverse isotropic symmetry. They determined elastic properties and anisotropy degrees of both neat ER and ER/PVA nanocomposites using longitudinal and transverse wave velocities. The research findings revealed a small degree of anisotropy in the dynamic Young’s modulus and a higher degree of anisotropy in the Poisson’s ratio. In another study conducted by Piekarczyk and Kata, ¹⁶ the material constants of anisotropic polycrystalline graphite and alumina (Al₂O₃) – hexagonal boron nitride (hBN) with transverse isotropic symmetry were calculated using ultrasonic method. In the study, it has been determined that as the porosity in graphite and the hBN content in Al₂O₃ increase, both the Young’s modulus and hardness values of the materials decrease.

Ultrasonic testing methods are an effective tool in determining the elastic properties of materials non-destructively. However, there are still difficulties in experimentally determining the five independent elastic constants of certain materials with transversely isotropic structures because of their very thin nature, the presence of discontinuities within them, and some velocities that are immeasurable in certain directions. ³² To determine the elastic constants and mechanical properties of a transversely isotropic material using the ultrasonic method, the densities of the materials, longitudinal ultrasonic wave velocities in the x (1) and z (3) directions, and longitudinal ultrasonic wave velocities at a 45° angle to the x–y plane need to be measured. In addition, shear ultrasonic wave velocities should also be measured, propagating in the z (3) and x (1) directions and vibrating the media particles in the x (1) and y (2) direction. Therefore, in cases where velocity measurements and certain material properties cannot be calculated due to various reasons, predictive methods (such as Theoretical Predictions and Experimental Data-Based Predictions) or computational approaches (including Modeling Approaches and Machine Learning and Data Mining) can be used to make these calculations. For instance, under the assumption of isotropy, if the longitudinal wave velocity in the 45-degree direction to the x–y plane (V_L45°) cannot be measured experimentally in a transversely isotropic material, then V_L45° in this material can be determined by taking the geometric mean of the experimentally measured ultrasonic longitudinal wave velocities (V_L11 and V_L33) propagating in the x (1) and z (3) directions and vibrating the media particles in the x (1) and z (3) directions. Additionally, using relationships between the elastic moduli of materials, some elastic constants that cannot be measured experimentally can be calculated with the help of experimentally measurable material properties. Finally, in some cases, certain material properties that cannot be measured in a particular material can be predicted on the basis of experimental data obtained from similar materials with similar characteristics.^24,25,33,34 However, it should be noted that such predictions may not be entirely precise and can involve a margin of error.

When the literature is examined, although there are many studies on the mechanical and thermal properties of carbon nanotube-reinforced polymer composites,^2,7,8 there appears to be a distinct gap in the comprehensive characterization of all elastic constants and mechanical properties of very thin transversely isotropic nanocomposites, especially by the ultrasonic method, produced by the electrospinning method. For example, Rathi and Kundalwal ⁶ examined the fracture toughness of MWCNT/ZrO2 hybrid-filled epoxy composites but did not map the materials to the fully elastic constant over ultrasonic velocities. Similarly, Oral and Ekrem ²⁴ performed ultrasonic characterization of ER/PVA nanocomposites, but in this study, the nanofiber phase was not enhanced with MWCNT. Recently published studies^1,14,35 emphasize the importance of the structure-property relationship in nanocomposites, but it does not offer a holistic characterization approach that combines material symmetry and ultrasonic methods.

In order to fill this gap, this study aims to experimentally determine the five independent elastic constants and mechanical properties of transversely isotropic ER/PVA-MWCNT nanocomposites by ultrasonic pulse-echo overlap method. To achieve this goal, the V_L45° values of the very thin ER/PVA-MWCNT nanocomposite materials were calculated using the ratios between the experimentally determined V_L45°, V_L11, and V_L33 velocities in similar transversely isotropic materials with comparable characteristics. Therefore, the calculated values of c₁₃, E₁, E₃, μ₁₁, and μ₃₁ for the ER/PVA-MWCNT nanocomposite materials produced in this study are semi-experimental and uncertain because they are determined using the semi-experimental V_L45° values. However, except c₁₃, E₁, E₃, μ₁₁, and μ₃₁ values, all other material properties were calculated using experimentally measured material densities and ultrasonic wave velocities.

Materials and Methods

Materials

The epoxy resin MGS-LR160 supplied from Hexion-USA, which has a density of 1130–1170 kg/m³ and viscosity of 700–900 mPa.s, was used as the matrix. The hardener MGS-LH160 supplied from Hexion-USA, which has a density of 960–1000 kg/m³ and viscosity of 10–50 MPa.s, was used as the curing agent. PVA (Density: 1190–1310 kg/m³, Melting point: 230°C, Molecular weight: 124 kg/mol) supplied from Merck-Germany was used for the production of PVA nanomats. The sodium dodecyl sulfate (SDS) (density: 1100 kg/m³, Melting point: 206°C, Molecular weight: 0.29 kg/mol) supplied from Merck-Germany was used as an anionic surfactant. The MWCNTs (Outer diameter: 15–25 nm, Inner diameter: 5–10 nm, Length: 10–20 μm) were supplied by Nanocyl SA-Belgium. The Polivaks supplied by the Poliya- Türkiye were used as releasing agents.

Preparation of PVA-MWCNT nanofiber mats and ER/PVA-MWCNT nanocomposites

Preparation of PVA-MWCNT nanofiber mats

The electrospinning method was used to produce the PVA-MWCNT nanofibers. First, 10 wt.% of PVA was added to 90 wt.% of neat water, and this PVA neat water mixture was heated to 80° C and mixed for 3 h at 400 r/min using a magnetic stirrer (C-MAG HS-10 series, Speed range: 100–1500 r/min, Temperature range: +50 to +500°C). Second, to prepare the SDS solution, 1 wt.% of SDS and 99 wt.% of neat water were mixed at 25°C for 10 min at 400 r/min using a magnetic stirrer again. Third, to reduce surface tension, 9 g of the PVA solution and 1 g of the SDS solution were mixed for 30 min at 400 r/min using a magnetic stirrer (C-MAG HS-10 series Models, Speed range: 100 to 1500 r/min, Temperature range: +50 to +500°C). Fourth, 99 wt.% of PVA-SDS solution and 1 wt.% of MWCNT were mixed in an ice bath for 5 min at 15-min intervals through an ultrasonic probe homogenizator (Bandelin HD 2070, Frequency: 20 kHz, Power:70W, Tip: KE 76, Amplitude setting range: % 25, Pulse cycle:-). ³⁶ Fifth, 4 mL of the last mixture obtained (99 wt.% of PVA-SDS solution + 1 wt.% of MWCNT) was loaded into a syringe-capillary tube with a tip of 0.8 diameter. Sixth, the electrospinning procedure was applied to the loaded mixture into the syringe-capillary tube by rotating the drum along the horizontal axis. For the electrospinning process, a 0.12 m gap between the spinneret and rotating collector was adjusted, and a feeding rate of 1.3 mL/h and a constant velocity of 5 mm/s as the collector rotation was performed by applying 25 kV between the spinneret and rotating collector at room temperature. Finally, the obtained PVA-MWCNT nanofiber mats were removed from the rotating drum and dried at 60°C under vacuum for 1 h. Thus, 99 wt.% PVA-SDS/1 wt.% MWCNT nanofiber mat abbreviated as 1CP was obtained (Figure 1). The fifth step was repeated with 97 wt.% PVA-SDS/3 wt.% MWCNT and 95 wt.% PVA-SDS/5 wt.% MWCNT to obtain 3CP and 5CP nanofiber mats, respectively.

Figure 1.

The diagram shows the synthesis flow chart of PVA-MWCNT nanofiber mats.

Preparation of the ER/PVA-MWCNT nanocomposites

The 1CP, 3CP, and 5CP nanofiber sheets had dimensions of 0.28 m × 0.30 m and were cut into pieces of size 0.008 m × 0.125 m. A chrome– nickel mold was used to produce the nanocomposites. To produce the ER/PVA-MWCNT nanocomposites, first, the 1CP nanofibers were placed into the mold as five layers. Second, the hardener was added to the epoxy resin. Third, epoxy resin with a hardener was syringed over the 1CP nanofiber mats in the mold up to wetting all nanofibers. Fourth, the molded resin was subjected to vacuum treatment at 0.6, 0.3, and 0.2 bar pressure for 10 min to remove air bubbles from the nanocomposite. Then, for the pre-curing process, the nanocomposite sample was vacuumed again for 24 h at room temperature under 0.2 bar pressure. Finally, for the final curing process, the obtained nanocomposite sample was placed in an oven at 80°C for 15 h. As a result, an ER/1CP nanocomposite sample abbreviated as 1CPE-5 was obtained. The same process was repeated for 10 and 15 layers of 1CP into the mold to produce 1CPE-10 and 1CPE-15 nanocomposites, respectively. The same process was repeated for 3CP and 5CP nanofiber mats to produce 3CPE-5, 3CPE-10, 3CPE-15, 5CPE-5, 5CPE-10, and 5CPE-15 nanocomposite samples. The nanocomposite samples and their abbreviations are listed in Table 1.

Table 1.

Descriptive abbreviations of pure epoxy resin (ER) and ER/PVA-MWCNT nanocomposite samples produced in this study.

Full name of the samples	Samples’ IDs	MWCNT ratio in PVA (%)	Number of PVA layers in samples
Epoxy resin	ER	0	0
Epoxy resin/PVA-MWCNT nanocomposites	1CPE-5	1	5
	1CPE-10	1	10
	1CPE-15	1	15
	3CPE-5	3	5
	3CPE-10	3	10
	3CPE-15	3	15
	5CPE-5	5	5
	5CPE-10	5	10
	5CPE-15	5	15

Measurements

Morphological measurements

To determine the interface between the PVA-MWCNT nanofibers and the neat ER matrix, scanning electron microscopy (SEM) was employed. SEM imaging of both the neat ER and ER/PVA-MWCNT nanocomposites was obtained at a voltage of 20 kV using a Hitachi-SU 1510 instrument (Tokyo-based Hitachi Corporation-Japan). In addition, high-magnification transmission electron microscopy (TEM) images of MWCNT-reinforced PVA nanofiber mats were obtained using a JEM-2100 electron microscope from Tokyo-based JEOL Ltd., Japan.

Density, and ultrasonic wave velocity measurements

Density measurements

Material densities were determined using a measurement system based on Archimedes’ principle. The analytical balance used for the density measurements had a capacity of 220 g and a readability of 0.1 mg (Radwag AS220/C/2, Radom, Poland) along with a density kit (Radwag 220, Radom, Poland). The density measurement process consists of three steps: first, the temperature of the water was introduced to the Radwag AS220 balance; second, the mass of the samples was measured in air; and third, the mass of each sample was measured in water. The semi-analytical balance then automatically calculates the density of each sample. To ensure the accuracy of the measurements, each measurement was repeated 10 times. The standard deviation values for density measurements were added to Table 2.

Table 2.

Experimentally measured void contents, average density (ρ, kg/m³) and ultrasonic wave velocity (V_L11, V_L33, V_L45°, V_S12, V_S31, m/s) values of pure ER and ER/PVA-MWCNT nanocomposite samples.

Samples	Void %	ρ Theoretical	ρ Measured	V L11	V L22	V L33	V L45°	V S12	V S31
E	0.76	1160.0	1151.5 ± 6.9	2690 ± 8	2690 ± 8	2690 ± 8	2690 ± 8	1189 ± 5	1189 ± 5
1CPE-5	0.96	1162.7	1154.6 ± 2.5	2862 ± 10	2859 ± 10	2640 ± 5	2691 ± 11	1292 ± 5	1137 ± 7
1CPE-10	1.08	1165.3	1152.9 ± 6.5	2886 ± 12	2889 ± 12	2662 ± 5	2714 ± 10	1302 ± 4	1164 ± 5
1CPE-15	1.16	1167.5	1151.1 ± 6.5	2859 ± 11	2864 ± 11	2637 ± 6	2689 ± 12	1290 ± 4	1150 ± 7
3CPE-5	1.29	1162.9	1148.1 ± 6.6	2880 ± 8	2884 ± 8	2656 ± 6	2708 ± 7	1300 ± 3	1148 ± 4
3CPE-10	0.89	1165.4	1155.1 ± 1.9	2899 ± 6	2896 ± 6	2674 ± 4	2726 ± 5	1308 ± 3	1143 ± 5
3CPE-15	0.85	1168.7	1158.9 ± 3.3	2891 ± 6	2888 ± 6	2667 ± 3	2719 ± 6	1305 ± 2	1139 ± 3
5CPE-5	1.72	1163.0	1143.4 ± 5.0	2850 ± 15	2856 ± 15	2629 ± 5	2680 ± 14	1286 ± 7	1136 ± 3
5CPE-10	1.51	1165.8	1148.5 ± 3.1	2880 ± 12	2888 ± 12	2656 ± 7	2708 ± 12	1300 ± 6	1161 ± 7
5CPE-15	1.01	1167.9	1156.2 ± 6.0	2846 ± 10	2840 ± 10	2625 ± 7	2677 ± 13	1285 ± 5	1137 ± 6

Theoretical density and void content measurements

First, the volumes of both the fiber and the matrix were calculated. For the calculation of fiber volume, the fiber thickness was calculated as 0.12 mm by measuring both between two glasses and using SEM images. The matrix thickness for each composite was calculated by considering the thickness of the casting mold as 0.90 mm. With these data, fiber volumes were calculated for each layer. ³⁷ The volume ratios (V_Vr) of the components in the composite are calculated in equation (1).

$$V_{Vr}=\frac{V_f}{V_m}$$

(1)

where, V_Vr refers to the fiber/matrix ratio, V_f refers to the volume ratio of the fiber, and V_m refers to the volume ratio of the matrix. “The Rule of Mixtures” principle was used to calculate the theoretical density of composite materials. This rule is based on using a weighted average of the densities of the components that make up the composite with their volume or mass ratios.

Within the scope of this study, the volume ratios of the components were preferred in the calculation of the theoretical densities of the composites. The theoretical densities of the composites (ρ_Theoretical) were calculated using equation (2).

$${\rho }_{theoretical}=\left(V_{Vr1}*{\rho }_1\right)+\left(V_{Vr2}*{\rho }_2\right)\dots$$

(2)

where, ρ_Theoretical, V_Vr1, V_Vr2,… and ρ₁, ρ₂, ρ₃,… are the theoretical density of the composite, the volume ratios of each component, and the density of each component in its pure state, respectively. After calculating the theoretical density, the following formula was carried out to measure the void contents of each composites.

$$Void\hspace{0.17em}content(\%)=\frac{\left({\rho }_{theoretical}-{\rho }_{measured}\right)}{{\rho }_{theoretical}}*100$$

(3)

where ρ_{_measured} and ρ_{_theoretical} are the actual density measured using Archimedes’ principle and the theoretical density calculated using equation (2), respectively.

Ultrasonic wave velocity measurements

Various techniques can be used to measure ultrasonic wave velocity, including pulse-echo, peak detection, through-transmission, cross-correlation, and phase measurement methods,^38,39 as well as the pulse-echo overlap method (PEOM). Among these techniques, PEOM is highly accurate for measuring ultrasonic wave velocity in materials. ³⁸ Therefore, in this study, ultrasonic wave velocities were measured at room temperature using the PEOM technique.

Ultrasonic wave velocity measurements were conducted using a 35 MHz frequency pulser/receiver generator (5800PR-Panametrics Olympus, USA), a 60 MHz frequency oscilloscope (GW Instek GDS–2062, Taiwan), a 10-MHz longitudinal wave contact transducer (V127-Panametrics Olympus, USA), and a 5-MHz shear wave contact transducer (V155-Panametrics Olympus, USA), as shown in Figure 2. The choice of coupling medium has a significant impact on the measurement of ultrasonic wave velocity. ⁴⁰ Therefore, glycerin (BQ Panametrics Olympus, USA) was used as the coupling medium for longitudinal wave velocity measurements, whereas shear wave coupling (SWC Panametrics Olympus, USA) was used for ultrasonic shear wave velocity measurements.

Figure 2.

Schematic diagram of the experimental setup used in density and ultrasonic wave velocity measurements of samples. The assembly includes a pulser/receiver generator (35 MHz), an oscilloscope (60 MHz), longitudinal (10 MHz), and shear (5 MHz) wave transducers.

Equation (4) was used to determine the velocity of ultrasonic waves propagating through the test sample after defining the time of flight between the backwall echoes.

$$\mathit{V}=\frac{\mathbf{2}\mathrm{\Delta }\mathit{d}}{\mathrm{\Delta }\mathit{t}}$$

(4)

where V represents the ultrasonic wave velocity, Δd denotes the thickness of the sample, and Δt indicates the time-of-flight between subsequent back wall signals on the flaw detector screen. To ensure the accuracy of the measurements, each measurement was repeated 10 times. The standard deviation values for both ultrasonic longitudinal wave velocity and shear wave velocity measurements were added to Table 2.

Measurement elastic properties of transversely isotropic nanocomposites

The elastic coefficients (c_ij) of transversely isotropic materials can be calculated using ultrasonic longitudinal and shear waves propagating in the appropriate directions of the material, and bulk density. Five independent elastic coefficients (c ₁₁ , c ₃₃ , c ₄₄ , c ₆₆ , and c ₁₃ ) have been defined for transversely isotropic materials.^16,41,42

To determine the elastic coefficients of the ER/PVA-MWCNT nanocomposites using PEOM, shear wave velocity (V _sij ) and longitudinal wave velocity (V _Lii ) values in the x, y, and z directions must be measured, where i and j indexes represent the propagation of waves and polarization directions of media particles, respectively. Moreover, for measuring V _L45° , the sample needs to be cut at an angle of 45° to the z (3) axis (Figure 3). However, because of the insufficient sample thickness, it was not possible to cut the samples at the required angle. Therefore, the approximate values of V _L45° for the ER/PVA-MWCNT nanocomposites were calculated using the velocity ratio. The velocity ratio is a useful parameter that depends on some variables such as pressure, porosity, and degree of consolidation and has been used in various applications, including estimating velocities, determining the degree of consolidation, and defining the pore fluid. ³³

Figure 3.

The sample geometry and coordinate system required for ultrasonic wave velocity measurements in a transverse isotropic material are shown schematically. Wave propagation directions (i) and polarization directions (j) are defined for measurements V_L11, V_L33, V_S31, V_S12, and V_L45°.

As an example, previous studies have shown that the longitudinal wave velocity (V _L ) to shear wave velocity (V _S ) ratios in limestone and sandstone are 1.9 and 1.8, respectively. ³⁴ Furthermore, it has been reported that the ratio of V_L45° to V_L11 in some transversely isotropic materials is approximately 0.94. ²⁵ Therefore, in this study, the value of V_L45° in transversely isotropic ER/PVA-MWCNT nanocomposites was estimated using the experimentally measured V_L11 value and a ratio of 0.94. For further information on the use of velocity ratios to predict ultrasonic velocities, please refer to Lee. ³³

Table 3 presents the orientation of ultrasonic wave propagation and the particle vibration direction used for calculating the elastic constants of transversely isotropic materials.

Table 3.

Description of the ultrasonic wave velocities required to calculate the elastic constants of a transverse isotropic material. ²⁴

Ultrasonic wave velocity (m/s)	Direction of propagation and type of wave	Direction of the particle vibration
VL11	Longitudinal wave traveling in the x-direction	x-axis
VL33	Longitudinal wave traveling in the z-direction	z- axis
VS31	Shear wave propagating along the z direction	x- axis
VS12	Shear wave propagating along the x-direction	y-axis
VL45̊	Longitudinal wave propagating at an angle of 45°	45° to axis of symmetry

The connection between the density (ρ), elastic constants, and ultrasonic wave velocities of transversely isotropic materials is expressed by equation (5). ²⁵

$$\begin{array}{l}{\mathit{c}}_{\mathbf{11}}=\mathit{\rho }.{{\mathit{V}}_{\mathit{L}\mathbf{11}}}^{\mathbf{2}}\\ {\mathit{c}}_{\mathbf{33}}=\mathit{\rho }.{{\mathit{V}}_{\mathit{L}\mathbf{33}}}^{\mathbf{2}}\\ \begin{array}{l}{\mathit{c}}_{\mathbf{44}}=\mathit{\rho }.{{\mathit{V}}_{\mathit{S}\mathbf{31}}}^{\mathbf{2}}\\ {\mathit{c}}_{\mathbf{66}}=\mathit{\rho }.{{\mathit{V}}_{\mathit{S}\mathbf{12}}}^{\mathbf{2}}\\ {\mathit{c}}_{\mathbf{13}}=\mathit{\rho }.\left({{\mathbf{2}.\mathit{V}}_{\mathit{L}\mathbf{45}°}}^{\mathbf{2}}{{-\mathit{V}}_{\mathit{L}\mathbf{11}}}^{\mathbf{2}}-\mathbf{2}.{{\mathit{V}}_{\mathit{S}\mathbf{31}}}^{\mathbf{2}}\right)\end{array}\end{array}$$

(5)

Equation (6) ²⁵ was employed to calculate the Young’s modulus (E₁ and E₃), Poisson’s ratios (µ₁₁ and µ₃₁), and shear modulus (G₃₁) of the ER/PVA-MWCNT nanocomposites investigated in this study.

$$\begin{array}{l}{\mathit{E}}_{\mathbf{1}}=\frac{\mathbf{4}{\mathit{c}}_{\mathbf{66}}\left({\mathit{c}}_{\mathbf{11}}{\mathit{c}}_{\mathbf{33}}-{{\mathit{c}}_{\mathbf{13}}}^{\mathbf{2}}-{\mathit{c}}_{\mathbf{33}}{\mathit{c}}_{\mathbf{66}}\right)}{\left({\mathit{c}}_{\mathbf{11}}{\mathit{c}}_{\mathbf{33}}-{{\mathit{c}}_{\mathbf{13}}}^{\mathbf{2}}\right)}\\ {\mathit{E}}_{\mathbf{3}}=\frac{\left({\mathit{c}}_{\mathbf{11}}{\mathit{c}}_{\mathbf{33}}-{{\mathit{c}}_{\mathbf{13}}}^{\mathbf{2}}-{\mathit{c}}_{\mathbf{33}}{\mathit{c}}_{\mathbf{66}}\right)}{\left({\mathit{c}}_{\mathbf{11}}-{\mathit{c}}_{\mathbf{66}}\right)}\\ \begin{array}{l}{\mathit{\mu }}_{\mathbf{11}}=\frac{\left({\mathit{c}}_{\mathbf{11}}{\mathit{c}}_{\mathbf{33}}-{{\mathit{c}}_{\mathbf{13}}}^{\mathbf{2}}-\mathbf{2}{\mathit{c}}_{\mathbf{33}}{\mathit{c}}_{\mathbf{66}}\right)}{\left({\mathit{c}}_{\mathbf{11}}{\mathit{c}}_{\mathbf{33}}-{{\mathit{c}}_{\mathbf{13}}}^{\mathbf{2}}\right)}\\ {\mathit{\mu }}_{\mathbf{31}}=\frac{{\mathit{c}}_{\mathbf{13}}}{\mathbf{2}\left({\mathit{c}}_{\mathbf{11}}-{\mathit{c}}_{\mathbf{66}}\right)}\\ {\mathit{G}}_{\mathbf{31}}={\mathit{c}}_{\mathbf{44}}\end{array}\end{array}$$

(6)

The standard deviation values of elastic constant measurements and elastic modulus measurements were added to Tables 4 and 5.

Table 4.

Elastic constant values (c₁₁, c₃₃, c₄₄, c₆₆, c₁₃, unit GPa) of pure ER and ER/PVA-MWCNT nanocomposite samples, calculated using equation from the measured density and wave velocities.

Samples	c 11 (GPa)	c 33 (GPa)	c 44 (GPa)	c 66 (GPa)	c 13 (GPa)
ER	8.33 ± 0.05	8.33 ± 0.05	1.63 ± 0.01	1.63 ± 0.01	5.08 ± 0.14
1CPE-5	9.46 ± 0.15	8.04 ± 0.10	1.49 ± 0.05	1.93 ± 0.03	4.29 ± 0.04
1CPE-10	9.60 ± 0.14	8.17 ± 0.11	1.56 ± 0.04	1.96 ± 0.02	4.26 ± 0.03
1CPE-15	9.41 ± 0.15	8.00 ± 0.13	1.52 ± 0.04	1.92 ± 0.03	4.19 ± 0.04
3CPE-5	9.52 ± 0.12	8.10 ± 0.10	1.51 ± 0.06	1.94 ± 0.02	4.29 ± 0.07
3CPE-10	9.71 ± 0.12	8.26 ± 0.11	1.51 ± 0.05	1.98 ± 0.03	4.44 ± 0.06
3CPE-15	9.69 ± 0.13	8.24 ± 0.10	1.50 ± 0.05	1.97 ± 0.02	4.44 ± 0.06
5CPE-5	9.29 ± 0.19	7.90 ± 0.16	1.48 ± 0.06	1.89 ± 0.04	4.19 ± 0.03
5CPE-10	9.52 ± 0.15	8.10 ± 0.12	1.55 ± 0.05	1.94 ± 0.03	4.23 ± 0.03
5CPE-15	9.37 ± 0.14	7.97 ± 0.10	1.50 ± 0.04	1.91 ± 0.03	4.21 ± 0.04

Table 5.

Comparison of elastic moduli (E₁, E₃, G₃₁, unit GPa), Poisson’s ratios (μ₁₁, μ₃₁) and anisotropy degree (E₁/E₃, μ₁₁/μ₃₁) values of pure ER and ER/PVA-MWCNT nanocomposites.

Samples	E 1 (GPa)	E 3 (GPa)	G 31 (GPa)	µ 11	µ 31	E 1 /E 3	µ 11 /µ 31
ER	4.49 ± 0.05	4.49 ± 0.05	1.63 ± 0.02	0.378 ± 0.035	0.378 ± 0.035	1.00	1.00
1CPE-5	5.64 ± 0.10	5.60 ± 0.15	1.49 ± 0.05	0.463 ± 0.004	0.285 ± 0.004	1.01	1.62
1CPE-10	5.75 ± 0.09	5.80 ± 0.13	1.56 ± 0.03	0.470 ± 0.005	0.278 ± 0.003	0.99	1.69
1CPE-15	5.63 ± 0.08	5.66 ± 0.14	1.52 ± 0.03	0.469 ± 0.004	0.280 ± 0.004	0.99	1.68
3CPE-5	5.68 ± 0.09	5.67 ± 0.15	1.51 ± 0.06	0.465 ± 0.005	0.283 ± 0.007	1.00	1.64
3CPE-10	5.77 ± 0.08	5.70 ± 0.14	1.51 ± 0.05	0.459 ± 0.007	0.288 ± 0.007	1.01	1.59
3CPE-15	5.76 ± 0.09	5.68 ± 0.13	1.50 ± 0.05	0.459 ± 0.006	0.288 ± 0.006	1.01	1.59
5CPE-5	5.54 ± 0.13	5.53 ± 0.18	1.48 ± 0.06	0.465 ± 0.004	0.283 ± 0.004	1.00	1.64
5CPE-10	5.70 ± 0.10	5.74 ± 0.16	1.55 ± 0.05	0.470 ± 0.003	0.279 ± 0.003	0.99	1.68
5CPE-15	5.59 ± 0.09	5.59 ± 0.16	1.50 ± 0.06	0.466 ± 0.004	0.282 ± 0.004	1.00	1.65

Measurement of the elastic characteristics of neat ER

Equation (7) is used to calculate the elastic properties of neat ER because it is an isotropic material with a well-defined mathematical relationship between elastic constants and ultrasonic wave velocity.^43,44 This relationship is commonly used and has been established in previous studies. ⁴⁵

$$\begin{array}{l}\mathit{L}=\mathit{\rho }{{\mathit{V}}_{\mathit{L}}}^{\mathbf{2}}\\ \mathit{G}=\mathit{\rho }{{\mathit{V}}_{\mathit{S}}}^{\mathbf{2}}\\ \begin{array}{l}\mathit{E}=\mathbf{2}\mathit{G}\left(\mathbf{1}+\mathit{\mu }\right)\\ \mathit{\lambda }=\mathit{\rho }\left({{\mathit{V}}_{\mathit{L}}}^{\mathbf{2}}-\mathbf{2}{{\mathit{V}}_{\mathit{S}}}^{\mathbf{2}}\right)\\ \mathit{\mu }=\frac{\mathit{L}-\mathbf{2}\mathit{G}}{\mathbf{2}\left(\mathit{L}-\mathit{G}\right)}\end{array}\end{array}$$

(7)

where V _L , V _S , L, G, E, λ, μ, and ρ denote the longitudinal and shear wave velocities, longitudinal and shear moduli (also known as Lame’s second constant), Young’s modulus, Lame’s first constant, Poisson’s ratio, and density of the specimens, respectively.

Isotropic materials have consistent physical properties in all directions. As a result, for isotropic materials, the relationship between longitudinal and shear wave values is such that V _L = V _L11 = V_L45° = V _L33 , V _S = V _S12 = V _S31 . In addition, the elastic constants specified in equation (5) and the elastic modulus provided in equation (6) will produce the elastic modulus values given in equation (7) for isotropic neat ER, with L = c ₁₁ = c ₃₃ , G = G ₃₁ = c ₄₄ = c ₆₆ , λ = c ₁₃ , E = E ₁ = E ₃ , and µ = µ ₁₁ = µ ₃₁ .

Results and Discussion

Polyvinyl alcohol (PVA) nanofiber mats reinforced with multi-walled carbon nanotubes (MWCNTs) at weight percentages of 1%, 3%, and 5% were produced, and these nanofiber mats were added to neat ER with 5, 10, and 15 layers to obtain transversely isotropic ER/PVA-MWCNT nanocomposites. The neat ER and ER/PVA-MWCNT nanocomposites’ morphology was investigated using TEM and SEM images shown in Figures 4 and 5. The commented results of both the elastic constants and mechanical properties determined by the measured densities, ultrasonic longitudinal and transverse wave velocities of neat ER, and the produced nanocomposites are given in Tables (2-5) and presented in Figs (6-11).

Figure 4.

TEM images of MWCNT-doped PVA nanofibers: (a) homogeneous dispersion in MWCNT at 1 wt, (b) homogeneous dispersion in MWCNT at 3 wt, (c) agglomeration and degradation in MWCNT at 5 wt. Scale bar: 500 nm.

Figure 5.

SEM images of materials taken at 10,00 KX magnification: (a) 1CP (1% MWCNT) nanofiber mat, (b) 3CP (3% MWCNT) nanofiber mat, (c) 5CP (5% MWCNT) nanofiber mat, (d) Pure epoxy resin (Neat ER) fracture surface, (e) 1CPE-15 nanocomposite fracture surface, (f) 3CPE-15 nanocomposite fracture surface, (g) 5CPE-15 nanocomposite fracture surface.

Figure 6.

Comparative graph of measured density (ρ) and ultrasonic longitudinal wave velocity (V_L11, V_L33, V_L45°) values of pure ER and ER/PVA-MWCNT nanocomposites.

Figure 7.

Comparative graph of measured ultrasonic shear wave velocity (V_S12, V_S31) values of pure ER and ER/PVA-MWCNT nanocomposites.

Figure 8.

Comparative graph of elastic constant values (c₁₁, c₃₃, c₄₄, c₆₆, c₁₃) of pure ER and ER/PVA-MWCNT nanocomposites calculated using equation (5).

Figure 9.

Comparative bar graph of Young’s modulus values (E₁, E₃) of pure ER and ER/PVA-MWCNT nanocomposites calculated using equation (6).

Figure 10.

Comparative graph of shear modulus (G₃₁) and Poisson’s ratio (μ₁₁, μ₃₁) values of pure ER and ER/PVA-MWCNT nanocomposites calculated using equation (6).

Figure 11.

Young’s modulus ratio (E₁/E₃) and Poisson’s ratio (μ₁₁/μ₃₁) values showing the degree of anisotropy of pure ER and ER/PVA-MWCNT nanocomposites.

Morphological Results

In the TEM images shown in Figure 4(a) and (b), it is clearly seen that 1% and 3% by weight MWCNTs are uniformly distributed in the PVA nanofiber. It can be seen that there is less number of MWCNTs in 1% MWCNT-doped PVA compared to 3% MWCNT-doped PVA nanofiber.

The TEM images in Figure 4(c) show that when 5% by weight MWCNTs are added to PVA nanofibers, the MWCNTs aggregate and disrupt the nanofibers. According to TEM images, the addition of 5% MWCNT caused the strength and toughness of the obtained ER/PVA-MWCNT nanocomposites to decrease, as it both disrupted the PVA fibers and caused agglomeration on the PVA fibers. ⁴⁶ Similar results are found in the literature. For example, it has been stated that in increasing proportions of MWCNTs in the matrix, due to their high aspect ratios and specific surface areas, the strong van der Waal interaction force causes the agglomeration of CNTs in the epoxy matrix. ⁶

Figure 5 provides 10 KX magnified SEM images of neat ER, MWCNT-doped PVA nanofiber mats, and 15-layer ER/PVA-MWCNT nanocomposites, along with the TEM image of 3% MWCNT-reinforced PVA nanofibers. In Figure 5(a)–(c), the addition of MWCNTs reduced the nanofiber diameters. In addition, it has been determined that PVA nanofibers with 1% by weight of MWCNT have diameters ranging from 150 to 335 nm, those with 3% by weight of MWCNT have diameters ranging from 90 to 310 nm, and PVA nanofibers with 5% by weight of MWCNT have diameters ranging from 45 to 140 nm.

From the SEM images provided in Figure 5(e)–(g), it is possible to observe the interactions between the fibers and the epoxy matrix, including the wrapping, breaking, pulling, and bridging of the fibers. As shown in Figure 5(d), the fracture surface of epoxy exhibits typical brittle fractures and river-like flow lines. Reinforcing epoxy resin with nanofibers enhances both its mechanical properties and changes the morphology of fractured surfaces. The actions of MWCNT-reinforced nanofibers, such as delamination from the matrix, pulling from the epoxy, bridging of cracks deflection, and blunting, play a significant role in increasing the fracture toughness of composite materials.^47,48

Void Content, Density and Ultrasonic Wave Velocity Results

The densities and ultrasonic wave velocities (longitudinal and shear) of neat ER and the ER/PVA-MWCNT nanocomposites are given in Table 2, Figures 6 and 7. Table 2 summarizes the measured values of void content, density, ultrasonic longitudinal, and shear wave velocity of the neat ER and ER/PVA-WCNT nanocomposites.

The density value was determined to be 1151.3 kg/m³ for neat ER, whereas the density values ranged from 1148.1 kg/m³ to 1158.9 kg/m³ for the ER/PVA-MWCNT nanocomposites. The highest density value was determined to be 1158.9 kg/m³ for the 3CPE-15 sample. The obtained density results agree well with the related literature.^49–51 In addition, the density value of most of the obtained nanocomposites was determined to be lower than that of the neat ER. This can be attributed to air bubbles that could exist between the PVA-MWCNT nanofiber mats and epoxy resin during the molding process. Because the density of PVA varies between 1190 and 1310 kg/m³, the density of neat ER varies between 1130 and 1170 kg/m³ and the density of MWCNT varies between 2000 and 2600 kg/m^{3 51}. Therefore, the density of the nanocomposite formed by adding MWCNT to PVA by electrospinning and adding these nanofiber mats to neat ER would be higher than that of neat ER. However, the air gaps inside the composites, which are thought to cause the density of the nanocomposites to decrease, were not allowed to affect the ultrasonic measurement results. During ultrasonic velocity measurements, ultrasonic probes were moved on the material surfaces to detect parts without air gaps, and measurements were made in these parts.

As shown in Table 2, Figures 6 and 7, the longitudinal wave velocity values of the obtained nanocomposites, V_L11, V_L33, and V_L45°, changed from 2846 to 2899 (m/s), 2625 to 2674 (m/s), and 2680 to 2726 (m/s), respectively. The shear wave velocity values of the obtained nanocomposites, V_S12 and V_S31, changed from 1285 to 1308 (m/s) and 1136 to 1164 (m/s), respectively. The highest V_L11 (2899 m/s), V_L33 (2674 m/s), V_L45° (2726 m/s), and V_S12 (1308 m/s) values were determined for the 3CPE-10 nanocomposite sample, whereas the highest V_S31 (1164 m/s) values were measured for the 1CPE-10 nanocomposite sample.

All ultrasonic velocities of ER/PVA-MWCNT nanocomposite materials have higher values than neat ER except for the longitudinal wave velocity (V_L33) propagating in the z (3) axis and polarized in the z (3) axis and the transverse wave velocity (V_s31) propagating in the z (3) axis and polarized in the x (1) axis. A remarkable result of this research is that the highest longitudinal and transverse wave velocities were measured in the samples using 10 layers of PVA-MWCNT in all three types of nanocomposites. It can be stated that the 3CPE-10 sample gave the best progress results compared with neat ER. Because compared with neat ER, there has been an increase of 0.3% in ρ, 7.8% in V_L11, 1.3% in V_L45, and 10% in V_S12 values in the 3CPE-10 sample.

The density and velocity values (V_L22 ≈ V_L11) given in Table 2 reveal the transversely isotropic structure of the ER/PVA-MWCNT nanocomposites, which also confirms the SEM image data. As can be seen from Table 2, Figures 6 and 7, ultrasonic longitudinal and shear wave velocity values differ according to the direction. The order of longitudinal wave and shear wave velocities in different directions for nanocomposites obtained in this research, from high to low, is determined as follows: V_L11 > V_L45° > V_L33 and V_S12 > V_S31. This velocity behavior observed in ER/PVA-MWCNT nanocomposites with transverse isotropic symmetry is similar to that observed in other materials with similar symmetry.^24,25

Estimation of the elastic constants

The elastic constant values of the neat ER and ER/PVA-MWCNT nanocomposites obtained by equation (5) are tabulated in Table 4 and plotted in Figure 8.

As seen from Table 4 and Figure 8, except for c₁₁ and c₆₆, the elastic constants of the ER/PVA-MWCNT nanocomposites are lower than those of the neat ER. It is clear from Table 4 that the values of c₁₁, c₃₃, c₄₄, c₆₆, and c₁₃ elasticity constants change from 9.29 to 9.71 GPa, 7.90 to 8.26 GPa, 1.48 to 1.56 GPa, 1.89 to 1.98 GPa, and 4.19–4.44 GPa, respectively. The elastic coefficient values obtained for the ER/PVA-MWCNT nanocomposites are compatible with those calculated by the ultrasonic method for polycrystalline graphite with transverse isotropic symmetry by Piekarczyk and Kata. ¹⁶ On the other hand, the obtained elastic modulus values for the ER/PVA-MWCNT nanocomposites agree with those obtained for the ER/PVA nanocomposites with 5, 10, and 15 layers of neat PVA Oral and Ekrem. ²⁴ However, in the study conducted by Oral and Ekrem, ²⁴ the elastic constants generally increased with the number of PVA layers within the matrix, whereas in this research, as observed in Table 4 and Figure 8, the number of PVA-MWCNT layers within the matrix increased up to 10 and then decreased when increased from 10 to 15. When the elastic coefficients of all three types of nanocomposites are examined, the nanocomposites formed with 10 layers of PVA-MWCNT nanofiber mats (1CPE-10, 3CPE-10 and 5CPE-10) have the highest values. Therefore, the most suitable PVA-MWCNT layer ratio in such composites is 10 layers.

On the other hand, when all the nanocomposite samples obtained were compared, it was determined that the 3CPE-10 sample had the highest elasticity coefficient values, except for the c₄₄ coefficient. In addition, compared with neat ER, increases of 16.56% and 21.47% were observed in the c₁₁ and c₆₆ coefficient values of the 3CPE-10 sample, respectively. These results support the interpretation of the velocity values obtained for 3CPE-10.

The high wave velocity (and hence high stiffness) in the plane of the mats (1–2 plane: high V11, S12, 11, c₆₆) indicates that the MWCNT-reinforced PVA nanomats create a strong, reinforcing network within that plane. Conversely, the lower properties out-of-plane (3-direction: lower L33, S31, c₃₃, c₄₄) suggest that the bonding between the individual nanomats and the epoxy matrix is the weaker link, acting as a compliant layer. This is characteristic of layered, transversely isotropic materials. The 10-layer configuration seems to be the optimal balance between in-plane reinforcement and through-thickness properties, minimizing void content.

Elastic modulus and poisson’s ratio

In this part of the research, the elastic moduli, Poisson ratio, and degree of anisotropy values of neat ER and ER/PVA-MWCNT nanocomposites obtained using equation (6) are given in Table 5 and Figures 9–11 and are interpreted. According to Table 5 and Figure 9, the values of E₁ for the ER/PVA-MWCNT nanocomposites were determined to be between 5.63 GPa and 5.75 GPa, 5.68 GPa and 5.77 GPa, and 5.54 GPa and 5.70 GPa for the 1CPE, 3CPE, and 5CPE groups nanocomposites, respectively. In addition, the values of E₃ for the ER/PVA-MWCNT nanocomposites were determined to be between 5.60 GPa and 5.80 GPa, 5.67 GPa and 5.70 GPa, and 5.53 GPa and 5.74 GPa, for the 1CPE, 3CPE, and 5CPE groups nanocomposites, respectively. Thus, the values of both E₁ and E₃ are higher than those of neat ER. Compared to Young’s modulus values of the neat ER (4.49 GPa), an increase of between ∼23.4 % and ∼28.5% and between 23.2 % and ∼29.2% was observed in E₁ and E₃ values of the ER/PVA-MWCNT nanocomposites, respectively.

One of the important results of Young’s modulus values of the obtained nanocomposites is that E₁ and E₃ values are very close to each other. The Young’s modulus values (E₁ and E₃) obtained for ER/PVA-MWCNT nanocomposites support the Young’s modulus values of the nanocomposites obtained by adding unmodified PVA to neat ER by Oral and Ekrem. ²⁴

The Young’s moduli of neat PVA, neat ER, and neat MWCNT were determined to be 0.108 GPa, ⁵² 4.49 GPa, and 1–2.4 TPa,^53–55 respectively. Therefore, it is clear from these values of Young’s modulus that the factor causing the higher Young’s modulus values of the ER/PVA-MWCNT nanocomposites is the very high Young’s modulus of MWCNTs. This finding supports density value variations.

It is clear from Table 5 and Figure 10 that the shear modulus (G ₃₁ ) values of all obtained nanocomposites are lower than those of the neat ER. Because the shear modulus of the neat ER was 1.63 GPa, the value of G ₃₁ ranged between 1.49 GPa and 1.56 GPa, 1.50 GPa and 1.51 GPa, and 1.48 GPa and 1.55 GPa for the 1CPE, 3CPE, and 5CPE groups of the ER/PVA-MWCNT nanocomposites, respectively. These results are in good agreement with the results of c₄₄ and prove the shear wave velocity (V_S31) values given in Table 2. These lower values of G₃₁ (or C₄₄) and V_S31 may be due to the weak shear bonds that existed between the ER and PVA-MWCNT nanofiber mats toward the z (3) axis or a higher ratio of air gaps may occur between the ER and PVA-MWCNT nanofiber mats. On the other hand, the shear modulus values obtained for the ER/PVA-MWCNT nanocomposites produced in this research are very close to the shear modulus values of the ER/PVA nanocomposites produced in the research conducted by Oral and Ekrem, ²⁴ but they are lower. The highest G₃₁ values for ultrasonic velocities, Young’s modulus, and elasticity coefficients were obtained for the nanocomposites formed when 10-layer PVA-MWCNT nanofiber mats were added to neat ER.

Figure 10 presents the variation of the Poisson’s ratios (µ₁₁ and µ₃₁) with increasing MWCNT ratio in PVA and PVA–MWCNT nanofiber mat layers. As shown in Table 5 and Figure 10, compared to the Poisson’s ratio of the neat ER (0.378), µ₁₁ values of all ER/PVA-MWCNT nanocomposites are higher while µ₃₁ values of all ER/PVA-MWCNT nanocomposites are lower. The µ₁₁ values of the 1CPE, 3CPE, and 5CPE group nanocomposites ranged from 0.463 to 0.470, 0.459 to 0.465, and 0.465 to 0.470, respectively. The µ₃₁ values of the 1CPE, 3CPE, and 5CPE group nanocomposites ranged between 0.278 and 0.285, 0.283 and 0.288, and 0.279 and 0.283, respectively. Poisson’s ratio provides essential information about the binding forces that hold the components of a composite material together, which is similar to other elasticity moduli and coefficients. ⁵⁶ Although it may not apply to auxetic materials, a decrease in Poisson’s ratio in many engineering materials is interpreted as an increase in the cross-linking density in that material.^19,56,57 According to this conclusion, an increase in the µ₁₁ values of nanocomposites obtained compared with neat ER indicates a weakening of transverse bonds in the x (1) direction. In contrast, a decrease in µ₃₁ values implies an increase in transverse bonds in the z (3) direction. Recently, the properties of different materials, such as Poisson’s ratio, have also been calculated using destructive methods. ⁴⁶ However, because these destructive tests subjected the produced nanocomposites to uniaxial loading in only one direction, Poisson’s ratio could only be determined in the x (1) direction. For instance, Poisson’s ratio values for ER/PVA-MWCNT nanocomposites were determined to be between 0.193 and 0.231 in the research carried out by Yıldırım, Ataberk. ⁴⁶ Additionally, the value of Poisson’s ratio determined as 0.378 for neat ER using the ultrasonic method in this research was determined as 0.187 by Yıldırım, Ataberk. ⁴⁶ Poisson’s ratio and other material properties in nanocomposite materials are influenced by factors such as the material components, their compatibility, and the discontinuities that can occur within them. Therefore, the differences in Poisson’s ratio values obtained with these different techniques may be attributed to the inability to detect discontinuities in materials during non-destructive tests and the ability to conduct tests in areas of materials that do not contain discontinuities when using ultrasonic methods.

Compared with the neat ER, the values of E₁, E3, and µ₁₁ in 1CPE-10 increased from 4.49 to 5.75 GPa (∼28%), 4.49 to 5.80 GPa (∼29%), 0.378 to 0.470 (∼24%), respectively. The values of E₁, E₃, and µ₁₁ in 3CPE-10 increased from 4.49 to 5.77 GPa (∼29%), 4.49 to 5.70 GPa (∼27%), 0.378 to 0.459 (∼21%), respectively. The values of E₁, E₃, and µ₁₁ in 5CPE-10 increased from 4.49 to 5.70 GPa (∼27%), 4.49 to 5.74 GPa (∼28%), 0.378 to 0.470 (∼24%), respectively. Finally, when compared to all nanocomposites obtained, the highest elastic modulus values are achieved in the case of 10-layer PVA-MWCNT samples. For example, the highest E₁ (5.77 GPa) value was obtained in 3CPE-10, the highest E₃ (5.80 GPa) and G₃₁ (1.56 GPa) values were obtained in 1CPE-10, the highest µ₁₁ (0.470) value was obtained in 1CPE-10 and 5CPE-10, and the highest µ₃₁ (0.288) value was obtained in 3CPE-10 and 3CPE-15. On the other hand, in comparison to neat ER values, a general decrease was seen in G₃₁ and µ₃₁ values of nanocomposites. For example, the highest decrease was seen in G₃₁ (∼9%) values of 5CPE-5 samples. In addition, the highest decrease was seen in µ₃₁ (∼27%) values of the 1CPE-10 sample. Thus, considering the density, ultrasonic speed, elastic coefficients, and elasticity modulus obtained compared with neat ER, using 10 layers of PVA-MWCNT nanofiber mats neat ER is the most appropriate composition ratio to obtain the best durable ER/PVA-MWCNT nanocomposites.

When looking at the degree of anisotropy from Table 5 and Figure 11, Young’s modulus ratios (E₁/E₃) ranged from 0.99 to 1.01, and Poisson’s ratios (μ₁₁/μ₃₁) ranged from 1.59 to 169. Similarly, Oral and Ekrem ²⁴ reported anisotropy ratios of 0.93–0.99 and 1.71–2.03 for E₁/E₂ and μ₁₁/μ₃₁ in the ER/PVA nanocomposites, respectively. These findings about anisotropy degree reveal that there is no significant difference in terms of Young’s moduli, but there is a significant difference in terms of Poisson ratios. In the related literature, different ratios were reported for G ₁₁ /G ₃₁ ratio in London clay as 1.50, ⁵⁸ sedimentary shales as 1.24, ²⁵ Gault clay as 2.25, ⁵⁹ and for E₁/E₃ in sedimentary shales as 1.70, ²⁵ and stiff Gault clay as 3.96. ⁵⁹ Therefore, in places where these materials will be used, they must be positioned in the correct positions and exposed to loads. Although the close values of E1 and E3, the ratio E1/E3 being very close to 1, and the data in Figure 9 might suggest that the resulting composite materials are isotropic, the data in Figures 4 and 5, significant differences between VL11 and VL33, VS12 and VS31, and μ11 and μ31, confirm that the composites produced in this study can be considered as transversely isotropic materials.

The results obtained in this study are in general agreement with previous research on similar nanocomposite systems and demonstrate the advantage of the ultrasonic method. For instance, Rathi and Kundalwal ⁶ reported that a 1.0 wt% MWCNT/ZrO₂ hybrid filler loading yielded an approximately 68% increase in the tensile strength of nanocomposites compared to pure epoxy. In our study, an increase of approximately 28%–29% in Young’s modulus values (E₁ and E₃) was observed in the 10-layer sample containing 3% MWCNT (3CPE-10) compared to the pure epoxy. This difference can be explained by the fact that in the study of Rathi and Kundalwal, ⁶ the mechanical properties were measured by uniaxial tensile test, while in our study, the average stiffness of the material in both cardinal directions (1 and 3) was measured by ultrasonic method. Similarly, Oral and Ekrem ²⁴ reported an overall increase in elastic constants in pure PVA nanofiber-reinforced epoxy composites when the number of layers increased from 10 to 15. However, in our MWCNT additive system, optimum properties were obtained in 10 layers, while some decrease was observed in 15 layers. This suggests that the challenges that are likely to arise in interfaces and dispersion homogeneity as the number of layers increases become more pronounced in the presence of MWCNT.

The results of this study reveal that MWCNT supplementation has a bidirectional effect on the mechanical behavior of ER/PVA nanocomposites. The marked improvement in properties (E₁, c₁₁, c₆₆) in isotropic plane 1-2 of the material can be interpreted as an indication that MWCNTs are effectively dispersed within the nanofibers and throughout the plane, strengthening the charge transfer mechanism. In contrast, the observed decrease in the shear modulus (G₃₁) in the three direction and the associated elastic constant (c₄₄) indicates the presence of weak shear bonds at the interface between the nanofiber layers and the epoxy matrix. This may be due to microscale air gaps that cannot be completely eliminated despite vacuum infusion during sample preparation, or due to a chemical incompatibility between PVA and epoxy. Thus, the resulting nanocomposite exhibits a hybrid structure that is ‘strengthened' in the isotropic plane but somewhat ‘attenuated' in the direction perpendicular to this plane. This finding clearly highlights the critical importance of interfacial engineering and interlayer adhesion in the design of transverse isotropic composites, as well as strength. Furthermore, the 5% performance reduction in MWCNT samples cannot be explained solely by agglomeration; The overload disrupting the nanofiber morphology, breaking the charge distribution continuum, may also have played a significant role in this behavior. Therefore, in future studies, the optimization of chemistry and manufacturing parameters to improve the interface will be key to fully unlocking the potential of this material class.

The mechanical performance of the ER/PVA-MWCNT nanocomposites developed in this study is critical to evaluate their potential in lightweight construction applications. For instance, the Young’s modulus value of ∼5.77 GPa measured in the 3CPE-10 sample exhibits superior rigidity compared to Nylon 6 (∼2–4 GPa), ⁶⁰ a widely used engineering plastic, while its density (∼1155 kg/m³) is notably lower than that of conventional metals like aluminum (∼2700 kg/m³), ⁶¹ providing a significant advantage in terms of specific strength (strength/density). This combination of properties suggests that these materials may be a suitable candidate for weight reduction targets, particularly in the automotive and aerospace sectors. Its transverse isotropic nature allows meeting different mechanical demands in different directions with a single material; for example, a drone may behave differently in one direction where high rigidity is required (E₁) and another direction where flexibility is required in the fuselage. On the other hand, although the results of this study demonstrate the superior mechanical performance of ER/PVA-MWCNT nanocomposites at room temperature, their long-term stability and durability under different environmental conditions (e.g., moisture, thermal cycles, UV radiation) that these materials will be exposed to in actual application scenarios such as automotive and aerospace require critical consideration in the context of the manufacturing methodology adopted. Therefore, it is recommended that future studies systematically study long-term performance degradation through periodic ultrasonic monitoring and mechanical testing combined with accelerated aging tests (humidity, temperature, UV).

In conclusion, the main objective of this study, the fully elastic characterization of transverse isotropic nanocomposites, has been successfully achieved thanks to the ultrasonic method. The findings revealed not only the properties of the material in a particular direction, but also five independent elastic constants in all directions and the mechanical properties derived from them, providing a comprehensive data set that could not be obtained by destructive methods. This proves that the ultrasonic method is an extremely valuable and complementary tool for the mechanical characterization of fine-structured and anisotropic materials.^6,24

Conclusions

In this study, transversely isotropic ER/PVA-MWCNT nanocomposites were obtained by incorporating PVA-MWCNT nanofiber mats produced by electrospinning method into epoxy resin with different layer numbers. Measurements by the ultrasonic pulse-echo overlap method have shown that some of the elastic constants and mechanical properties of these nanocomposites are higher compared to pure epoxy. In particular, the structure, which contains 3% MWCNT and consists of 10 layers, exhibited the highest strength. Furthermore, although the degree of anisotropy in terms of Young’s modulus is low, marked differences in Poisson’s ratios have been observed. The ability to predict some unmeasurable wave velocities with data from similar materials makes an important contribution to non-destructive characterization. In this context, it is proposed to perform similar ultrasonic analyses for materials with different isotropic and anisotropic structures. Although electrical conductivity is beyond the scope of this study, it is well known in the literature that MWCNTs confer this property. Therefore, by optimizing electrical conductivity in future studies, these nanocomposites have the potential to be used not only as structural elements, but also in multifunctional applications such as electromagnetic interference shielding or self-heating composite fins.