Strain-Rate Dependent Behavior of Dispersed Nanocomposites

Abstract

With decreasing production costs, carbon nanomaterials have become common, scalable, and cost-effective additives in high-performance composites due to the potentially significant increases in mechanical, thermal, and electrical properties. The mechanical performance of carbon nanomaterial-reinforced matrix materials under high-strain-rate compressive conditions was investigated. This study compares neat epoxy-amine with 0.1 wt.% loadings of graphene or graphite dispersed in epoxy-amine. Quasi-static and high-rate testing was conducted using an Instron load frame and Split Hopkinson Pressure Bar (SHPB), respectively, to assess the material’s response to increasing strain rates via compressive loadings. No significant change in compressive strength was observed at quasi-static strain rates, with the 0.1 wt.% graphene sample showing no significant deviation from the neat resin at high strain rates. In contrast, the 0.1 wt.% graphite sample exhibited a substantial reduction in comparative compressive strength, decreasing by ~43% at 10² s⁻¹ strain rate and ~42% at 10³ s⁻¹ strain rate. While graphene may not significantly enhance stiffness at high strain rates, its ability to preserve ductility without introducing failure-prone features makes it a more effective additive for dynamic applications.

1. Introduction

Composite materials are widely used in applications requiring impact resistance and energy absorption due to their mechanical properties and design flexibility. The high strength-to-weight ratio, excellent damage tolerance, and ability to dissipate energy make composites ideal for use in industries such as automotive, aerospace, and defense. Fiber-reinforced composites in particular offer tailored performance by combining high-strength fibers with a ductile matrix, enabling effective load transfer and energy dissipation upon impact. These composites typically rely on the fibers to bear the load while the matrix provides protection, load transfer, and ductility. The matrix significantly influences the compressive strength, while the fibers largely determine tensile strength, and shear strength depends on the bonding between the matrix and fibers [1].

When a composite panel experiences a high-energy impact, the event generates complex stress waves and initiates several simultaneous failure mechanisms. The kinetic energy is dissipated through various damage processes, including rapid matrix cracking, interlaminar delamination, fiber fracture, and fiber pull-out [2,3,4]. Initially, the resin matrix develops micro-cracks and undergoes shear failure due to stiffness mismatches with the reinforcing fibers, often resulting in cracks aligned with the fiber direction. In high-speed impact scenarios, fiber damage becomes more pronounced as fibers may fail under tensile overload or separate from the surrounding matrix, dissipating energy through interfacial debonding [5,6]. The combination of these mechanisms determines whether the composite maintains its structural integrity or sustains significant damage. High-strain-rate testing of a neat matrix specimen enables the characterization of matrix-dominated behaviors that influence the earliest and most critical stages of the impact response.

Recent advancements in composite materials have focused on incorporating nanomaterials such as graphene and graphite into conventional matrices to enhance performance across a wide range of applications, including structural, thermal, and electrical properties. Graphene, a single layer of sp²-bonded carbon atoms arranged in a hexagonal lattice, is known for its mechanical, thermal, and electrical properties [7]. While mechanical enhancements are often the primary focus, improvements in functional properties such as thermal conductivity and electrical conductivity are also highly desirable. Incorporating graphene into composites leverages these attributes to enhance overall material performance. Additionally, graphene is lightweight and exhibits high stiffness, making it a desirable additive for enhancing composite properties [1]. Graphite, while chemically similar to graphene, consists of stacked graphene layers and is typically multiple orders of magnitude larger in scale. Its lower production cost and comparable benefits in certain applications make it a promising alternative or partial substitute for graphene in composite formulations [8,9].

Studies investigating the mechanical behavior of graphene-reinforced composites have shown that low loading levels, frequently around 0.1 wt.%, can significantly enhance the performance of these materials [10,11]. For instance, Bulut demonstrated that a 0.1 wt.% graphene nanoplatelet loading in basalt fiber/epoxy composites yielded the highest tensile strength [12]. Similarly, Vigneshwaran et al. found that composites with 0.1 wt.% graphene exhibited superior tensile strength and reduced strain, indicating better load transfer and bonding between the matrix and fibers [13]. These enhancements are attributed to nanoparticles’ ability to improve interfacial bonding [13,14], decrease frictional slippage [15], and delay crack propagation [14] during high-rate mechanical loading. Shadlou, Ahmadi-Moghadam, and Taheri found, for epoxy/graphene nanoplatelets (GNP) (wt.% 0, 0.25, 0.5, 1), that increasing the GNP content and the strain rate (0.01, 0.1, 1, 10 s⁻¹) resulted in higher compressive yield strength and modulus of elasticity, though the stiffening effect of GNPs was more significant at lower strain rates [16]. Additionally, the presence of nanoparticles in epoxy can induce various fracture mechanisms [9], highlighting the complex interactions that can both enhance and potentially compromise the mechanical integrity of the composite materials. Pol and Liaghat (2014) showed that, in glass/epoxy/nanoclay composites, at high strain rates from impact, nanoclay can serve as crack initiation sites and become brittle [14]. Shahjouei, Barati, and Tooski (2020) also noted that the agglomeration of GNPs can serve as sites of crack initiation [15]. Kim and Park (2020) found that a higher wt.% of graphene oxide (GO) resulted in decreased strength due to the clumping of GO [17].

The Split Hopkinson Pressure Bar (SHPB) is used to create dynamic loading conditions and can provide insights into composite behavior under high strain rates. The SHPB is a tool used to measure the response of materials to high-strain-rate impacts, which is crucial for understanding performance in dynamic environments [18]. Graziano, Dias, and Petel noted that composites tested in SHPB exhibited higher compressive modulus and strength at high strain rates due to limited polymer chain mobility, emphasizing the role of both the polymer matrix and the additives in determining dynamic performance [19]. Additionally, Hosur et al. note that samples in compression tested through the thickness of the laminate rather than in the direction of fiber orientation are dominated by the properties of the matrix [20].

Building on this foundation, this study aims to explore the effects of different compressive strain rates on non-fiber-reinforced epoxy resin (control), epoxy resin with graphene, and epoxy resin with graphite. High-rate and quasi-static compressive behavior of epoxy/carbon nanomaterial composite samples with low loadings (0.1 wt.%) of graphene and graphite were tested using the SHPB and a load frame, respectively. By focusing on quasi-static and high-rate compression, this work seeks to fill the knowledge gap regarding how small additions of graphene and graphite influence matrix behavior under dynamic conditions. Comparing the results of graphene- and graphite-reinforced composites with neat resin will help in understanding the significant differences in compressive properties, which may be attributed to variations in particle size, morphology, and their interactions with the epoxy matrix. Whether graphite could serve as a viable, cost-effective substitute for graphene in a variety of loading rates for high mechanical performance applications was also considered.

2. Materials and Methods

2.1. Materials

Figure 1 shows the components of the epoxy resin. The epoxide was a diglycidyl ether of bisphenol F (DGEBF) (EPON 862) (Figure 1a) and the amine curative was an unmodified aliphatic amine, triethylenetetramine (TETA) (EPIKURE 3234) (Figure 1b). The graphene was xGnP Graphene Nanoplatelets (Grade C) from XG Sciences with an average surface area of 750 m²/g. The graphite was High Purity Natural Crystalline Flake Graphite from Barite World, with an average surface area of 16 m²/g. All materials were used as received.

2.2. Sample Preparation

Nano-carbon/matrix test cylinders were fabricated using a silicone mold with a nominal dimension of 0.5 inch in diameter and 0.5 inch in height for an aspect ratio of 1:1. Nanoparticles were added to epoxy at 0.1 wt.% loadings and mixed using an overhead paddle mixer at 800 rpm for 2 min immediately before infusion or casting. Samples were cured at room temperature for a minimum of 60 days, then polished on a double-sided planetary lapping and polishing machine to ensure the pucks’ faces were parallel and without imperfection.

2.3. Material Characterization

2.3.1. Quasi-Static Compression

An Instron A357385 load frame with a 250 kN load cell and parallel compression platens was used to characterize the quasi-static compression behavior of composite pucks at a series of strain rates from 10⁻³ s⁻¹ to 10⁰ s⁻¹. Strain rates were determined based on the 12.7 mm (0.5 inch) height of the specimen and calculated in increasing orders of magnitude starting at 10⁻³ s⁻¹ through 10⁰ s⁻¹ for quasi-static strain rates. This system is equipped with a video extensometer, which was used to accurately measure the compressive strain at the sample via tracking dots. A minimum of three samples were tested for each loading at each strain rate.

2.3.2. High-Rate Compression

To characterize the effect of strain rate on composite matrix materials at higher strain rates, an SHPB was used at rates from 10² s⁻¹ to 10³ s⁻¹. As seen in Figure 2, the SHPB system consists of a 10 ft incident bar, a 10 ft transmission bar, and a 2 ft striker, all constructed from 1-in diameter C300 steel. The striker length and various copper pulse shaper geometries were optimized to ensure sample failure while creating incident pulses that achieved constant strain rates and dynamic stress equilibrium [21]. The strain gauges and oscilloscope recorded the strain, velocity, and stress states of the two bars, enabling the derivation of the sample’s mechanical properties. Air pressure was modulated to obtain the desired strain rates. Strain rates were calculated after each test, as velocity is driven by air pressure in the system. A minimum of five samples were tested for each loading at both strain rates.

3. Results and Discussion

3.1. Compression Characterization

Compression testing was used to characterize the strain-rate sensitivity of neat and filled resin specimens at exponentially increasing strain rates. Figure 3 shows the characterization of neat resin at increasing strain rates, which serves as the baseline for this series of experiments. Consistent with the established trends reported in the literature, a substantial increase in material strength is observed with increasing strain rates [19,22,23]. As seen in Figure 3, this strain-rate dependency suggests a dynamic strengthening mechanism in the neat resin due to limited time for molecular or structural rearrangement at elevated strain rates [19]. The neat resin data shown in Figure 3 will serve as a reference for comparison against nanoparticle-filled resins, enabling a comparative analysis of their mechanical performance at varying strain rates. Strain rates are displayed in ascending order from 10⁻³ s⁻¹ to 10³ s⁻¹, excluding 10¹ s⁻¹.

3.1.1. Quasi-Static Compression

The quasi-static compression test results shown in Figure 4 and Figure 5 compare the compressive strength of neat resin with 0.1 wt.% graphene and 0.1 wt.% graphite, respectively. Both the 0.1 wt.% graphene and 0.1 wt.% graphite have comparable ultimate compressive strength to the neat resin at the same given strain rate. However, a ~22% comparative increase in compressive modulus at 10⁻² s⁻¹ for both the 0.1 wt.% graphene and 0.1 wt.% graphite shows better stiffness in the nanoparticle matrix composites when compared to the neat matrix. The relevant modulus and compressive strength data can be found in Appendix A.

3.1.2. Split Hopkinson Pressure Bar

Figure 6 illustrates the high-rate compression behavior of neat resin, 0.1 wt.% graphene, and 0.1 wt.% graphite samples tested using SHPB. The neat resin serves as the baseline for comparison, demonstrating the expected stress–strain response under high strain rates. The 0.1 wt.% graphene sample closely mirrors the baseline behavior, showing no significant difference in compressive performance. In contrast, the 0.1 wt.% graphite exhibits a substantial decrease in mechanical properties when compared to the neat resin. At a strain rate of 10² s⁻¹, the modulus and compressive strength of the graphite-loaded specimen are reduced by 43% and 54%, respectively. Similarly, at a strain rate of 10³ s⁻¹, the modulus shows a 41% reduction, while the compressive strength decreases by 50%. The relevant modulus and compressive strength data can be found in Appendix A.

3.1.3. Strain-Rate Comparison

For Figure 7, Figure 8 and Figure 9, the compressive behavior is represented as an increase or decrease in performance of each mechanical property as compared to neat resin, where 0% (blue line) is the performance of the neat epoxy resin. Note that the graphs do not reflect absolute values but rather values relative to the neat resin at individual strain rates. When comparing the results of compression testing across quasi-static and high-rate regimes, there is a notable deviation between the behaviors of graphene- and graphite-filled epoxy systems.

As shown in Figure 7, the compressive modulus exhibits a notable increase at the 10⁻² s⁻¹ strain rate for both graphene- and graphite-loaded samples. However, this improvement was not observed across all other quasi-static strain rates, with 10⁻³ s⁻¹ and 10⁻¹ s⁻¹ more closely aligning with neat resin. The neat resin had a lower modulus, while the graphene- and graphite-loaded samples remained more consistent across 10⁻³ s⁻¹ to 10⁻¹ s⁻¹ (see Appendix A). Under high-rate loadings, 0.1 wt.% graphite samples experienced significant reductions in both compressive strength and stiffness compared to the neat resin, while the 0.1 wt.% graphene loading followed much closer to the trends of the neat resin.

Both graphene- and graphite-loaded nanocomposites exhibit similar mechanical behavior to the neat resin in quasi-static loading conditions; however, at high strain conditions, graphene-loaded nanocomposites exhibit similar behavior to the neat resin, while graphite shows a significant decrease in strength and modulus comparatively. Under dynamic loadings, the larger graphite particles become detrimental to performance. With all other variables held constant, a larger-sized defect is known to have a higher maximum stress at the crack tip when compared to a smaller-sized defect [7]. Additionally, nanoclay and graphene-adjacent materials can agglomerate [14,15,17] and serve as crack initiation sites [14,15]. The graphite is expected to result in a nanocomposite that is more susceptible to failure due to its larger size because graphite’s size and morphology likely promote stress localization and facilitate crack initiation when compared to graphene.

In Figure 8, graphene, graphite, and neat resin showed similar compressive strength across quasi-static rates (10⁻³ s⁻¹ to 10⁰ s⁻¹). In contrast to the improvements noted in compressive modulus at 10⁻² s⁻¹, the incorporation of nanoparticles provided relatively small to non-existent changes to the compressive strength at low strain rates when compared to the neat resin. At high strain rates, graphite-filled specimens showed clear reductions in comparative strength, with 54% at 10² s⁻¹ and 50% at 10³ s⁻¹, when compared to the neat resin. This is likely due to stress concentrations introduced by the larger graphite flakes and their reduced aspect ratio when compared to graphene. This aligns with prior studies reporting that micron-scale fillers and nanoparticles can intensify local stresses and act as fracture initiation sites under dynamic conditions [9,15,19,24]. Graphene-loaded specimens, however, demonstrated strength values closer to those of the neat resin, maintaining structural integrity even at elevated loading rates. This performance is likely due to the smaller size and higher aspect ratio of graphene platelets, which promote effective stress transfer while minimizing their function as critical flaws within the matrix [8].

Figure 8 represents the strain at break values of the nanoparticle-filled matrix as compared to the neat resin performance, where data points below the neat resin baseline indicate more brittle behavior, and those above the line indicate more ductile behavior than the neat resin. Note that the strain at break in this case is denoted as the strain at maximum compressive strength. At low strain rates (10⁻³ s⁻¹ and 10⁻² s⁻¹), both graphene- and graphite-filled samples exhibited notable decreases in strain at break relative to the neat material. However, as the strain rate increased, the performance of the graphene-filled samples became more closely aligned with the neat resin, while graphite-filled samples demonstrated a more pronounced decline. Although 0.1 wt.% graphite showed only a 9% reduction at 10⁰ s⁻¹, performance fell sharply at both higher and lower strain rates. This trend suggests a shift from ductile behavior, dominated by polymer chain mobility, to brittle failure mechanisms at high rates, where stress concentrations around graphite flakes drive failure [9,19].

The more consistent performance of graphene-filled samples suggests better stress distribution and reduced localization during dynamic loading [9,16]. At moderate strain rates, graphite flakes can bridge microcracks and temporarily improve ductility. However, beyond an optimal threshold, they become failure initiators [12]. In contrast, graphene exhibits a more stable strain-at-break response due to its smaller size, which reduces the likelihood of large-scale defect formation [9,16]. Scanning electron microscopy (SEM) of graphene and graphite is shown in Appendix B. While graphene may not significantly enhance stiffness at high strain rates, its ability to preserve comparative ductility without introducing failure-prone features makes it a more effective additive for dynamic applications.

4. Conclusions

Quasi-static and dynamic compressive testing was carried out on neat and filled epoxy nanocomposites at 0.1 wt.% graphene and 0.1 wt.% graphite loadings. The quasi-static loadings were conducted using an Instron load frame at rates from 10⁻³ s⁻¹ to 10⁰ s^−1, and high-rate testing was conducted on a Split Hopkinson Pressure Bar at rates from 10² s⁻¹ to 10³ s⁻¹. The quasi-static compression tests revealed minimal changes in compressive strength of 0.1 wt.% loaded nanocomposites when compared to neat resin, suggesting that the material’s performance remains relatively consistent under lower strain rates. However, under high-rate compression, substantial deviations were observed for the graphite-filled specimen, with both modulus and compressive strength significantly reduced. These findings indicate that while the introduction of graphene and graphite additives does not actively detract from quasi-static compressive strength relative to neat resin, graphite introduces weakness at high strain rates.

The poor high-rate performance observed in the graphite-filled composite can be attributed to differences in particle size and morphology, which influence the chain density and load transfer characteristics of the matrix. Graphite particles, being larger, can disrupt the epoxy network, creating stress concentrations and reducing the overall integrity of the composite under dynamic loading. In contrast, the nanoscale dimensions of graphene allow it to better integrate within the polymer matrix without significantly compromising the polymer crosslinks, enabling it to maintain mechanical strength and comparative ductility across different strain rates [9,16]. Nanomaterial selection in composite design is important, particularly for applications subjected to high-strain-rate conditions where particle-matrix interactions play a critical role in determining performance.