Dynamic Mechanical Behaviors of Nacre-Inspired Graphene-Polymer Nanocomposites Depending on Internal Nanostructures

Abstract

Nacre, a natural nanocomposite with a brick-and-mortar structure existing in the inner layer of mollusk shells, has been shown to optimize strength and toughness along the laminae (in-plane) direction. However, such natural materials more often experience impact load in the direction perpendicular to the layers (i.e., out-of-plane direction) from predators. The dynamic responses and deformation mechanisms of layered structures under impact load in the out-of-plane direction have been much less analyzed. This study investigates the dynamic mechanical behaviors of nacre-inspired layered nanocomposite films using a model system that comprises alternating multi-layer graphene (MLG) and polymethyl methacrylate (PMMA) phases. With a validated coarse-grained molecular dynamics simulation approach, we systematically study the mechanical properties and impact resistance of the MLG-PMMA nanocomposite films with different internal nanostructures, which are characterized by the layer thickness and number of repetitions while keeping the total volume constant. We find that as the layer thickness decreases, the effective modulus of the polymer phase confined by the adjacent MLG phases increases. Using ballistic impact simulations to explore the dynamic responses of nanocomposite films in the out-of-plane direction, we find that the impact resistance and dynamic failure mechanisms of the films depend on the internal nanostructures. Specifically, when each layer is relatively thick, the nanocomposite is more prone to spalling-like failure induced by compressive stress waves from the projectile impact. Whereas, when there are more repetitions, and each layer becomes relatively thin, a high-velocity projectile sequentially penetrates the nanocomposite film. In the low projectile velocity regime, the film develops crazing-like deformation zones in PMMA phases. We also show that the position of the soft PMMA phase relative to the stiff graphene sheets plays a significant role in the ballistic impact performance of the investigated films. Our study provides insights into the effect of nanostructures on the dynamic mechanical behaviors of layered nanocomposites, which can lead to effective design strategies for impact-resistant films.

1. Introduction

Developing impact-resistant films or barriers is crucial for military and aeronautic applications as resisting impact and dynamic load is imperative to the functionality, especially when human safety becomes a concern [1–3]. Another area of high importance is protective and shielding devices used in microelectronics, which may undergo accidental shocks during the service lives [4, 5]. There have been significant developments in commercial protective gears, including vehicle’s windshield, protective gears for sports [6, 7], and the military and aeronautic industry [2, 8–11]. Theoretical models for protective layered composites have been constructed to describe the mechanical response under high strain loading [12, 13]. Despite advancements in traditional protective materials systems, we expect significant or even revolutionary improvements in next-generation protective materials by integrating advanced nanomaterials and judiciously designed nanostructures [14].

It has been recognized that materials with feature sizes of nanometers exhibit unique properties compared to their macroscopic counterparts. For instance, metallic systems in nanometer size can achieve theoretical strength limits [15, 16] and metals with nanocrystalline grain structure also possess enhanced thermal-mechanical properties [17–20]. A recent study demonstrated that nanometer-thin multi-layer graphene (MLG) sheets have specific penetration energy ten times larger than bulk steel on an equal weight basis using novel microprojectile impact tests [21]. Moreover, ultrathin (less than 100 nm) polymer films have unique physical properties compared to their bulk counterpart [22–30]. A recent study found that semicrystalline polymer thin films achieve higher specific penetration energy than bulk protective materials and previously reported nanomaterials [22]. The reason was attributed to the effective strain delocalization during impact and the abundant viscoelastic and viscoplastic deformation mechanisms within the polymer thin films.

Designing nanocomposites with unique nanostructures is another promising strategy to equip material systems with excellent impact resistance and protective capability. In this regard, natural biomaterials provide great inspiration for the nanostructure and hierarchical structures that usually combine a stiff, robust phase and a soft, dissipative phase. Various hierarchically structured biomaterials have demonstrated mechanical properties surpassing those of the individual constituents by orders of magnitude [31–33]. The Bouligand structure, found in crustacean and beetle exoskeletons [34–36], fish scales [37, 38], and mantis shrimp dactyl clubs [39], have been shown to exhibit high impact tolerance and strength [40]. Our recent study has revealed the unique role of nanostructural features in the impact resistance of Bouligand films made from high aspect ratio nanofibers [40]. Another widely studied natural material - nacre, the inner layer of a mollusk shell - features layered arrangements of hard and soft phases forming a brick-and-mortar type of structure. It is known to be an outstanding example that has a high specific strength and toughness [41, 42]. By imitating its multi-layer structure arrangement in nanoscale, structural materials with high mechanical performance can be fabricated [43–46]. Mechanical properties of the nacre-inspired nanocomposites have been studied widely using experiments [44, 45] and simulations [26, 46, 47]. Experiments have shown the outstanding stiffness and fracture toughness contributed to the nacre-like layered structure [44, 45]. Computational studies, particularly molecular dynamics (MD) simulations have also been applied to analyze the mechanisms underlying the excellent mechanical properties of such nanocomposites. Recent studies have shown that the nanoconfinement effect on the (bio)polymer phase by the adjacent stiffer layers plays a role in the enhanced mechanical property of materials with nacre-inspired structures [26, 48, 49]. Specifically, the nanoconfinement effect increases the strength, toughness, and interfacial interaction strength of the polymer phase within the thin nanocomposite films [26, 49]. Although the in-plane mechanical properties of the nacre-inspired nanocomposites have been widely studied, the out-of-plane mechanisms of these nanocomposites have yet to be fully understood. These mechanisms are directly relevant to the design of nanocomposites that can possess excellent impact resistance.

Experimental tests with impact loading have been conducted toward understanding the out-of-plane deformation mechanisms and dynamic failure behaviors [21, 50]. However, it is difficult to track the deformation process in detail under dynamic loading, especially at high strain rates, since the period of deformation is very short and the state of stress is highly localized. Recent advances in computational studies have enabled high-velocity impact simulation tests of ultrathin films at the nanoscale level [48, 49, 51–57]. This study attempts to understand the dynamic response of nacre-inspired nanocomposite films under ballistic impact. The studied nanocomposite systems are comprised of hard phases - MLG sheets - and soft phases - polymethyl methacrylate (PMMA). The systems adopt a layered structure with changing layer thickness while conserving the total system volume. We utilize previously developed coarse-grained (CG) models of MLG and PMMA used in molecular dynamics (MD) simulations [58, 59]. The models have been validated to capture the mechanical properties and failure behaviors of both MLG and PMMA [46, 48, 60–62]. Particularly, we have used these CG models to study their dynamic failure behaviors using ballistic impact simulations and provide insights into the nanoscale ballistic response of individual nanoscale thin films [63–65].

Building upon our previous studies on the nacre-inspired MLG-PMMA nanocomposites [26, 46] in this study, we first characterize the effect of nanostructures on mechanical properties through uniaxial tensile deformation and free vibration tests induced by nanoindentation. Through the characterization, we highlight the unique nanoconfinement effect in these nanocomposite systems. Then, we investigate the dynamic failure mechanism of nacre-inspired nanocomposites under ballistic impact in the through-thickness direction. We find that the main failure mechanisms and the impact resistance of studied nanocomposites depend on the structural arrangements of MLG and PMMA phases and their thickness.

2. Methods and Material Systems

2.1. Overview of the coarse-grained models

We construct the nanocomposite films with the brick-and-mortar structure of alternating MLG and PMMA phases using previously developed CG models of MLG and PMMA. The CG model of the MLG sheets employs a 4-to-1 mapping scheme that conserves the hexagonal symmetry [59]. The model has been shown to capture the anisotropic mechanical response and orientation-dependent interlayer shear behavior of MLG [59]. The CG model of the PMMA adopts a two-bead mapping scheme for each monomer, in which one represents the side chain methyl group and the other one represents the backbone group [58]. This CG model captures the thermal and mechanical properties of the PMMA, including the ones that emerged from nanoscale thin film configurations [26, 30]. We note that the CG model of PMMA does not include bond-breaking criteria in the system. A previous study has shown that the dominant failure mechanisms of PMMA films consisting of only short chains under ballistic impact are the interchain pull-out or disentanglement, and bond stretching in the polymer chains is not significant [46].

The investigated system consists of alternating MLG and PMMA phases with designed thickness, and one repetition module includes an MLG phase and a thin PMMA film. The number of repetitions (n) is adjusted to conserve the total volume of the nanocomposites, which have 26 layers of graphene sheets and 24 nm thick of the PMMA phase in total. The repetition modules (MLG + thin PMMA film) are stacked in a repetitive manner, and the schematic diagrams of the investigated structures are shown in Fig. 1. Specifically, each repetition module contains N layers of graphene sheets, where N = 24/n, and PMMA film with a thickness of 24/n nm. The system is then being capped with an additional two layers of graphene sheets at the bottom surface, therefore, equaling 26 layers of graphene sheets in total. The PMMA phases consist of blocks of polymer chains with a chain length of 100 monomers per chain.

Figure 1.

(a) Schematics of the CG models utilized in this study and nacre-inspired nanocomposite films with different numbers of repetitions in (b)-(i). We also add the schematics of impact simulation with a sharp-nosed projectile (b) and a blunt-nosed projectile (c) in the Gra1 film. All systems share the same coordinate.

We use ‘Gra’ to illustrate the default setting where the thicker MLG (N≥2) is on top. They will be impacted first during the ballistic impact simulations. In Fig. 1, the number following Gra is the number of repetitions - n. Alternatively, we use PMMA(n) to illustrate the setting that the cap bilayer graphene sheets and the adjacent PMMA phase experience the impact first. As most of the nanocomposite films studied are not symmetric based on the central plane, these notations enable us to describe the impact responses with projectile impact from both directions. We note that the Gra12 system is symmetric to the central plane of the film as bilayer graphene sheets are separated by 2 nm thick PMMA films. As a result, Gra12 is identical to the notation of PMMA12.

The total length of the system (along y-direction) is approximately 85 nm. The width of the system (along x-direction) is 42 nm. Periodic boundary conditions are applied at x- and y-directions. Because of this, we usually only show the side view of the systems. Vacuum spaces are introduced at the upper and lower end of the box along z-direction to isolate the nanocomposite system for analysis.

2.2. CG-MD simulation protocols

All the simulations were carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) molecular dynamics package [66], and the simulation trajectories were visualized using the Visual Molecular Dynamics (VMD) software [67]. The system is first equilibrated using NVE ensemble with a Langevin thermostat at 300 K for 0.2 ns. Then, an annealing process is conducted using direct heating and cooling down under NPT ensemble throughout the entire process. This entire equilibrium process is conducted in a total period of 1.2 ns. It is done by first equilibrating the system at 300 K for 0.2 ns, and then heating it up to 600 K within 0.2 ns. After the system has reached 600 K, it is further equilibrated at such temperature for another 0.2 ns to allow the prestress within the PMMA layer to fully relax. 600 K is well beyond the glass transition temperature (T_g) of PMMA - 380 K as measured in the previous study [46]. Finally, the system is cooled down to 300 K using 0.2 ns and stays at 300 K for 0.4 ns. To maintain a stable layered structure during the process, we have constrained both ends of the graphene sheets along x-direction to their initial positions by applying a tethering force to the graphene beads in the end regions. The tethering force on both ends of the graphene sheets resembles the clamped boundary conditions used in experiments. We use such constraints to not only maintain a uniform layered structure during the equilibrium process, but also serve as fixed boundary conditions when the film is impacted by the projectile in the subsequent simulations. The equilibration procedures resemble our previous studies [46, 65]. This process has been shown to fully equilibrate the nanocomposites as the potential energy of the systems reaches a plateau after this process. Details are included in the Supplemental Information (SI).

After equilibration, three types of non-equilibrium MD (NEMD) simulations, including uniaxial tensile deformation, nanoindentation, and ballistic impact simulations, were carried out in this study. The uniaxial tensile simulations adopt a constant-strain-rate deformation along the x-direction of the system (Fig. 2b). The strain rate is 5×10⁸ s⁻¹, similar to previous studies using MD simulations [26, 68]. We use uniaxial tensile simulations to explore the elastic modulus of the films along the in-plane direction and the nanoconfinement effect from MLG on the PMMA phase. The nanoindentation simulations apply an implicit indenter using the command provided in LAMMPS (Fig. 2a). Specifically, a cylindrical shape indenter with a radius of 0.3 nm and length along y-direction equaling to the system’s width is applied to press downward on the target surface (i.e., indenting in the z-direction). The indenter was then removed after reaching a certain depth, allowing the film to vibrate freely without interference. The free vibrating frequency of the investigated film was then measured by tracking the z-displacement at the centroid of the film. Different indent depths were tested to ensure that the vibrating frequency keeps as constant. The film vibration frequency also allows us to analyze the dependence of mechanical properties of the nanocomposite films on their nanostructures.

Figure 2.

Schematic diagrams for (a) nanoindentation and (b) uniaxial tensile testing on the Gra12 film. The nanoindentation simulation consists of an implicit indenter indenting on the film, then removed after it reaches a certain indent depth, allowing the film to vibrate freely. The tensile testing simulation applied an increasing strain with a constant strain rate of 5×10⁸ s⁻¹ along the in-plane direction of MLG (x-direction).

Lastly, we investigate the impact responses and dynamic mechanical behaviors of the MLG-PMMA nanocomposites. We perform high-velocity impact tests with both block- and cylindrical-shape projectiles (shown in Fig. 1). The block shape represents a blunt-nosed projectile, and the cylindrical shape is used as a sharp-nosed projectile. The projectiles are comprised of beads in a diamond lattice with the mass of the beads of 96 g/mol and a lattice parameter of 0.72 nm. The density of the projectiles is approximately 3.4 g/cm³. Both projectiles are periodic along the y-axis. The blunt-nosed projectile has a square shape at the x-y plane with a width of 8 nm. The sharp-nosed projectile has a cylindrical shape with a radius of 4.53 nm, which leads to the same mass as that of the block projectile. According to the outcome of previous experiments [21], the projectile shows no observable deformation. Therefore, the projectile is treated as a rigid body in the impact simulations. We use 12-6 LJ potential with ɛ_LJ = 0.813 kcal/mol and σ_LJ = 0.346 nm to describe the interactions between the projectile and the graphene and PMMA beads. Our previous study uses the same parameters of the LJ potential, and it has shown that the interaction between the projectile and film does not significantly affect the impact response [16]. After the equilibration process of the system, a downward impact velocity, V₀, normal to the x-y plane, is assigned to the projectile to initiate the impact process. We also let the projectile impact on both the top and bottom surfaces of the nanocomposites, as the nanocomposite film is not symmetric to its central plane. For brevity, the Gra(n) films are renamed to PMMA(n) when the projectile first impacts the bilayer graphene cap, as the thicker PMMA phase is closer to the strike-face. We systematically analyze the deformation processes of the nanocomposite films from the trajectories under NEMD simulations.

3. Results and Discussion

3.1. Nanoconfinement effect

Results from uniaxial tensile simulations are first presented, which characterize the elastic properties of different nanocomposite films along the in-plane direction. Figure 3 shows typical stress-strain relationships during the tensile deformation of nanocomposites with different repetition numbers (n). The mechanical responses of the entire system are presented in Fig. 3a, in which three typical structures are compared. Even though we only show three cases for better clarity, we confirm that the other structures show a similar trend. There is an increasing trend of the elastic modulus with increasing n. Specifically, Young’s modulus of Gra12 rises more than 5% compared to the Gra1 structure. Even though it seems that this is a minor increment, considering the large volume fraction of the graphene phase, which is also a constant for all the systems here, this is still a non-negligible increment in the elastic modulus of the nanocomposites herein. The increase of the elastic property indicates the nanoconfinement effect on the PMMA phase from the adjacent graphene sheets. The nanoconfinement effect is further illustrated by comparing the stresses originated from the polymer phase only, as shown in Fig. 3b. With a decrease in thickness on each PMMA phase (i.e., increasing n), both the elastic modulus and general stress levels at the given deformation of the PMMA phase increase, indicating a stiffer and stronger behavior. The observation of the significant difference between Gra1 and Gra12 agrees with previous studies that the elastic moduli of polymer thin films are enhanced by the nanoconfinement effect, which can be tuned by increasing cohesive interaction between polymer and graphene sheets or other substrates [24, 26, 30, 48]. Additionally, the nanoconfinement effect can be tuned by changing the thickness of polymer films under confinement [25, 27–29].

Figure 3.

(a) The stress-strain relationships of the entire system under uniaxial tensile deformation, where the elastic responses of the films show slight differences. (b) The stress-strain relationship of the polymer phase and thinner polymer phases (larger n) show stiffer and stronger behavior.

The nanoconfinement effects dependent on nanostructures can also be observed from the free vibration frequency results of the films. The obtained frequency value is positively related to Young’s modulus of the film. This trend resembles the relationship between the resonance frequency f and the elastic modulus E on a continuum beam predicted theoretically [69, 70]

$$f=\sqrt{EI/A{l}^3}$$ (1)

where I is the second moment of area, A is the cross-sectional area, and l is the effective length of the system. For all the investigated systems in this study, they have the same length l and similar moment of inertia I and cross-sectional area A. In addition, the system is periodic and uniform in the width direction (y-direction) and thus can be simplified as a 2D beam system. Eq. (1) shows that f positively depends on E, with a power of 0.5. This aligns with our result (see Table 1), in which the power value is fitted as ~0.57. The deviation might be due to the slight difference in thickness of the system after equilibration processes and the different densities of the graphene and PMMA phases. Nevertheless, the increasing trend of both f and E with increasing n clearly demonstrates the nanoconfinement effect within the nanocomposites. Our study shows that the internal nanostructures can tune the in-plane stiffness of layered nanocomposite films. Our results also indicate that the in-plane stiffness of films can be explored and compared through vibrational analysis.

Table 1.

The mean value and standard deviation (S.D) of Young’s modulus (E) and free vibration frequencies (f) of different films.

Film Gra(n)	E (GPa) Mean (S.D.)	f (GHz) Mean (S.D.)
1	246.9 (1.8)	4.55 (0.07)
2	248.0 (1.8)	4.61 (0.08)
3	252.0 (1.8)	4.75 (0.08)
4	252.2 (2.1)	4.76 (0.04)
6	255.8 (2.3)	4.86 (0.07)
8	257.8 (2.1)	4.87 (0.04)
12	260.8 (1.5)	5.03 (0.06)

3.2. Influence of projectile shape on ballistic impact behavior

We first compare the responses of investigated nanostructured films under high-velocity impact from either sharp-nosed or blunt-nosed projectiles. We find that except for the Gra1 case, which has no repetitive features, the responses for other cases are similar under the impact of the two types of projectiles. For the Gra1 case, the major difference between the two cases is in the failure mechanisms of the top and bottom faces. The difference is attributed to the different stress concentrations upon impact and the shape of stress waves propagating through the thickness direction.

Figure 4 shows the dynamic failure of the Gra1 system upon impact from both blunt-nosed and sharp-nosed projectiles with the same impact velocity. At this point, both projectiles rebound and show similar residual velocity after impacting the film. Localized failure in the top layers of both systems is observed upon impact due to the immense stress localized on the strike-face. Relatively more fragments can be observed in the sharp-nosed projectile system as the resulted localized stress in the top graphene sheets is higher than the case in the blunt-nosed projectile system (Fig. 4).

Figure 4.

The different failure mechanisms in the Gra1 system for (a) blunt-nosed and (b) sharp-nosed projectile with V₀=4000 m/s at different time frames. The graphene cap layers at the bottom are fractured under the impact of the blunt-nosed projectile but not in the sharp-nosed projectile case.

Even though the projectile rebounded, a compressive stress wave keeps propagating downward for both cases. We observe a similar crazing-like deformation within the PMMA layer in both cases. Such deformation mechanisms will be discussed in detail in section 3.4. Interestingly, we find that under the blunt-nosed projectile impact, the bottom bilayer graphene cap is destroyed by the stress wave, despite that not all graphene sheets at the strike side are fractured. This behavior is similar to our previous work illustrating the spalling-like failure of MLG under blunt-nosed projectile impact [64], where cracks can localize in the bottom section of MLG. We have shown that this type of failure is due to the reflection of the planar shape of the compressive stress wave into a tensile wave. In addition, the planar stress wave experiences limited attenuation during propagation, although the interfaces between graphene and PMMA will lead to a certain level of stress wave dissipation. Such dissipation at interfaces is also reflected in the fact that the spalling-like failure does not show up in nanostructures with a higher number of repetitions.

In contrast, under the impact of the sharp-nosed project, the bottom bilayer graphene sheets do not show failure. The sharp-nosed projectile system forms an expanding wave originated from the impact site. The wave propagates with a sphere-shaped wavefront, as illustrated in our previous continuum-level simulations showing the wave shape [64]. This leads to faster attenuation of the compressive waves. The more significant extent of fragmentation at the top surface further lowers the intensity of the compressive wave. As a result, the bottom bilayer graphene cap remains intact.

In addition, the same pattern is not observed in cases where the projectile first impacts the PMMA side as the PMMA phase on the strike side constantly dissipates the kinetic energy of the projectile, leaving a much weaker compressive wave which is insufficient to lead to spalling-like failure. It indicates that the prerequisites for spalling-like failure are a stiff and less-dissipative medium at the strike side to generate a strong compressive wave and a planar shape wavefront.

Despite the different failure mechanisms observed at the bottom graphene cap layers, we find that the cap layer breakage does not affect the impact resistance, i.e., the V₅₀ of the investigated films. This is because graphene cap layers contribute minimally to the total ballistic performance of the system, which will be discussed in section 3.4. We also note that the different failure mechanisms at the bottom graphene cap layers only occur in a narrow velocity window. The Gra1 film shows similar responses under both projectiles at other V₀. These results are included in the SI (Fig. S3–s5).

Furthermore, we compare blunt-nosed projectile vs. sharp-nosed projectile impact for Gra2 (Fig. S6) and Gra3 (Fig. S7) cases in the SI, which also show consistent responses. As a result, the influence of projectile shape only appears within a small V₀ range in the Gra1 case.

3.3. Influence of the strike face on the impact responses of asymmetric films

Comparison of dynamic mechanical behaviors during the ballistic impact of pure graphene, Gra1, and PMMA1 are shown in Figure 5. These snapshots correspond to impact by a blunt-nosed projectile with a V₀ of 4000 m/s. We have already discussed the spalling-like failure in Gra1 in section 3.2. Our simulations on pure graphene (i.e., 26 graphene sheets) also show the stress-induced failure mechanisms at the bottom section, similar to our previous study [64]. We also observe that some of the graphene sheets fracture at both ends, where strictly clamped boundary conditions are enforced. These localized failures are due to the stress concentrations resulted from in-plane propagated waves. We have previously shown that the film size needs to be large enough to eliminate the in-plane wave-induced failure [64]. Our choice of the width of the systems is limited by computational resources. We note that the finite size MLG used in this study would lead to the deteriorated impact resistance of MLG. However, comparing the dynamic failure of pure graphene and nanocomposite systems, as in Fig. 5a and 5b, we find that by adding a dissipative soft polymer phase, the deterioration from finite in-plane size is greatly alleviated. This highlights the role of the soft phases in nacre-inspired nanocomposites in resisting impact.

Figure 5.

The trajectories of (a) pure graphene structure with 26 layers of graphene sheets, (b) Gra1 structure, and (c) PMMA1 structure under the impact of the blunt-nosed projectile with V₀ = 4000 m/s. The arrow on the projectile indicates its moving direction.

We then compare the different behaviors of PMMA1 and Gra1. When the project impacts the bulk MLG phase first for the Gra1 case, the polymer phase does not significantly contribute to the absorption of kinetic energy. Figure 5b shows that the projectile bounces off from the strike-face before voids within the PMMA phases are observed. A major portion of the kinetic energy from the projectile is absorbed by the strike-face, graphene sheets, which resulted in bond breakages and delamination of the top graphene surface. The thick PMMA film, however, transfers a small portion of the energy from the shock wave induced by the strike to the bottom of the structure and creates a spalling effect. The effect occurs much later than the initial strike since the compressive wave speed slows down in the polymer phase. Conversely, when the PMMA film is on the strike-face, the polymer phase provides natural resistance to the projectile, of which the kinetic energy dissipates significantly as it penetrates through the polymer film (Fig. 5c). When impacting on the PMMA side, under the same V₀, the graphene sheets underneath PMMA1 stay intact, and the films show a much better impact resistance compared to the Gra1 case. This observation agrees with recent studies that the viscoelastic deformation of the PMMA film contributes greatly to dissipating the energy when positioned as the strike-face [49, 54–56]. The projectile can rotate during the penetration process. This rotation is highly dynamic and depends on the internal nanostructures, as shown in the SI (Fig. S2). We have confirmed that the rotation of the projectile does not affect our evaluation of the impact resistance of different films.

The results obtained from our simulations provide valuable insights into the design strategy of protective thin films. When designing a protective nanostructured film using alternating soft and hard phases, a more confined structure leveraging the nanoconfinement effect from the hard phase to the soft phase should be considered if the design target is higher in-plane stiffness. Adding a viscoelastic phase (i.e., polymeric thin film) on top of stiff plates can significantly improve the impact resistance. This design strategy can have great potential as it does not require any disassembly procedure yet still achieves a significant enhancement on ballistic impact resistance.

3.4. Effect of nanostructures on impact resistance and deformation mechanisms

This section looks into the effect of nanostructures on the impact resistance of the studied MLG-PMMA films and the associated deformation mechanisms.

To quantitatively compare the impact resistance of films with different nanostructures, V₅₀ are measured and analyzed first. V₅₀ is usually referred to as the lowest velocity that fully penetrates the target with a 50% possibility. The variation in residual velocity (V_r) of the projectile versus the impact velocity (V₀) is shown (Fig. 6). The V_r is captured as the approximate constant velocity of the projectile after the perforation process. A positive value indicates a full penetration during the test, whereas a negative one indicates the projectile rebounded from the film. In our computational study, the V₅₀ is approximated as the V₀ value corresponding to zero V_r, which can be numerically determined by the cross point between V_r = 0 line and the linear interpolation between two consecutive data points. Our results show that the V₅₀ of the films is independent of the shape of the projectiles. We include all the V₀ − V_r data for all the nanostructured films in Fig. S9 in the SI.

Figure 6.

Residual velocity (V_r) vs. impact velocity (V₀) relationships of different films for (a) blunt-nosed projectile and (b) sharp-nosed projectile.

All the nanocomposite films show an improvement on V₅₀ comparing to the pure graphene sheets in Fig. 6. Our results indicate that positioning a thick polymer film on top of the stiff MLG phase as the strike face (as in the case of PMMA1) leads to the most significant improvement in ballistic resistance. The PMMA1 has the highest V₅₀ among all films and is roughly 50% higher comparing to that of Gra1. As illustrated in the previous section, the PMMA film at the strike-face significantly dissipated the impact energy, which allows the graphene sheets underneath to stay intact. The Gra1 exhibits the lowest V₅₀ among all the investigated nanocomposite films, as the viscoelastic behavior of the PMMA film does not contribute to the resistance provided by the graphene sheets on the strike-face, at least in the nanocomposite films studied herein (Fig. 5b). For Gra8 and Gra12, however, they do not show a significant difference with projectile impacting on different sides. This is because the effects of strike-face and finite sizes become diminished for these structures as they become more symmetric, and the films exhibit gradual and sequential failure during the perforation.

We note that even though our study indicates that using two single bulk PMMA and MLG phases while making the PMMA film on top achieves the highest V₅₀, such design leads to unbalanced structures and a tradeoff from decreasing in-plane performance, as shown in Section 3.1. In addition, limited by the system size, higher repetitions only result in very thin PMMA phases. As a result, only the PMMA1 case shows the obvious ‘dragging’ effect of the polymer phase. If the total thickness increase to micro-sizes, the polymer phases for higher repetition structures may also play a considerable role in dissipating energy. Combined with other deformation mechanisms (to be discussed next) and direct nanoconfinement effect, higher repetitions might perform better under impact when the film thickness reaches micron sizes. We also note that the projectile impact simulations only generate insights into the localized impact failures, while the large-area impact, such as blast, can be better studied using other types of simulations [71, 72]. We will leave these aspects to our future study.

Next, we discuss the deformation mechanisms in layered nanocomposites that potentially contribute to energy dissipation/absorption capability under impact loading conditions. Our simulation trajectories reveal interesting deformation mechanisms within the nanostructured films after a projectile impacted them with low to medium velocity. In those cases, the strike-face stays intact or experiences minimal crack or failure. We note that those cases are also ideal cases for protection barriers under impact loading and are predominant loading scenarios of various biomaterials during the life period of the living organisms.

As shown in Fig. 7, unique crazing-like deformations are observed in the soft PMMA phases after the impact of the sharp-nosed projectile. We note that the deformation mechanisms are very similar using the blunt-nosed projectile, and corresponding results are included in the SI (Fig. S8). After the projectile impacts on the strike-face, a compressive wave forms and propagates downwardly. Due to the relatively slow wave propagation speed and wave reflections at the polymer/graphene interface, heterogeneous deformation arises in the thickness direction of the films. Specifically, when the compressive wave propagates downwardly, the upper layers become relaxed first and vibrate upwardly and towards the projectile direction, while the bottom part of the film is still deformed downwardly due to the influence from the compressive wave. This effect induces tensile stress to certain confined PMMA phases, which lead to microvoid formations. The microvoids expand in the x-direction that is normal to the stress wave, and they eventually develop into crazing-like deformation zones [73–75]. The impact energy from the projectile is effectively dissipated during the development of the crazes, which involves significant interchain sliding within the PMMA phase. Through this source of energy dissipation, the vibration of the films is significantly damped. Similar deformation can be observed on all investigated films with the layered nanostructure (Fig. 7). The crazing-like deformation in the PMMA phases is separated by the stiff graphene sheets and happens in multiple PMMA phases. The stiff graphene sheets maintain the integrity of the whole film and prevent it from falling apart. Our simulation models also show good adhesion between graphene and PMMA, which prevents the interfaces from complete delamination.

Figure 7.

Crazing-like deformation in nanolayered films of (a) Gra12, (b) Gra8, and (c) Gra6 under low- to medium-velocity impact from the sharp-nosed projectile with V₀ = 2000 m/s.

To summarize the key deformation mechanisms, the viscoplastic behavior of the PMMA films dissipates a significant portion of energy, which is further enhanced by the crazing-like deformation developed in multiple layers of PMMA, while the stiff graphene sheets provide overall robustness of the structure and avoid total failure of the film. We expect that these observe deformation mechanisms would improve the energy dissipation capability of layered nanostructures in protective applications.

We note that such crazing-like deformation is not observed when the film is under a higher velocity impact (i.e., V₀ larger than 4500m/s). When under such high strain loading, the projectile can start penetrating the film before the crazing-like deformation within the PMMA phase occurs. The perforation process significantly dissipates the impact energy, hindering the global vibration of the nanocomposite films. It also breaks the integrity of the PMMA phases, which limits the formation of the microvoids.

4. Conclusion

In this work, we conduct CGMD simulations on nacre-inspired MLG-PMMA nanocomposite films and investigate their mechanical properties and dynamic failure mechanisms. We focus on the effect of nanostructure and layer thickness on elastic modulus, impact resistance, and deformation mechanisms.

We find that films with a more confined structure (i.e., decreasing layer thickness and higher number of repetitions) yield higher elastic modulus through uniaxial stretching and out-of-plane free vibration simulations. The enhancement is attributed to the nanoconfinement effect on the nanoscale thin PMMA films from adjacent stiff graphene sheets.

We then use ballistic impact simulation to study the dynamic failure mechanisms and the impact resistance of different nanostructured films, indicated by the V₅₀ value. We observe that although the V₅₀ of the investigated films impacted by sharp-nosed or blunt-nosed projectiles are very much identical, the blunt-nosed projectile can lead to an early spalling-like failure at the bottom surface of a single repetition structure. When the repetition number increases, the films fail by sequential penetration instead. Interestingly, for single repetition film, we also observe that the V₅₀ differs significantly depending on the strike-face. By placing the PMMA phase on the top of the MLG, the viscoelastic behavior of the PMMA drastically drags the projectile during penetration, resulting in higher V₅₀. In contrast, by placing the PMMA film under the MLG phase, MLG experiences direct impact from the projectile instead. The influence of the stress waves and finite boundary condition leads to a much lower V₅₀ eventually. We further study the deformation mechanisms of layered nanocomposite films under the low-velocity impact. We find that the nacre-inspired layered nanocomposites develop crazing-like deformation within the polymer phases, significantly dissipating the impact energy. This deformation mechanism can be potentially leveraged in the future design of nanostructured protective films.

In conclusion, our work illustrates that the internal nanostructure of the nacre-inspired, layered MLG-PMMA nanocomposite films plays a significant role in the mechanical properties and dynamic failure mechanisms. More importantly, the observations and results from this work provide important insights into potential design strategies of protective thin films.