Investigation of Dynamic Impact Responses of Layered Polymer-Graphene Nanocomposite Films Using Coarse-Grained Molecular Dynamics Simulations

Abstract

Polymer nanocomposite films have recently shown superior energy dissipation capability through the micro-projectile impact testing method. However, how stress waves interact with nanointerfaces and the underlying deformation mechanisms have remained largely elusive. This paper investigates the detailed stress wave propagation process and dynamic failure mechanisms of layered poly(methyl methacrylate) (PMMA) - graphene nanocomposite films during piston impact through coarse-grained molecular dynamics simulations. The spatiotemporal contours of stress and local density clearly demonstrate shock front, reflected wave, and release wave. By plotting shock front velocity (U_s) against piston velocity (U_p), we find that the linear Hugoniot U_s – U_p relationship generally observed for bulk polymer systems also applies to the layered nanocomposite system. When the piston reaches a critical velocity, PMMA crazing can emerge at the location where the major reflected wave and release wave meet. We show that the activation of PMMA crazing significantly enhances the energy dissipation ratio of the nanocomposite films, defined as the ratio between the dissipated energy through irreversible deformation and the input kinetic energy. The ratio maximizes at the critical U_p when the PMMA crazing starts to develop and then decreases as U_p further increases. We also find that a critical PMMA-graphene interfacial strength is required to activate PMMA crazing instead of interfacial separation. Additionally, layer thickness affects the amount of input kinetic energy and dissipated energy of nanocomposite films under impact. This study provides important insights into the detailed dynamic deformation mechanisms and how nanointerfaces/nanostructures affect the energy dissipation capability of layered nanocomposite films.

Graphical Abstract

1. Introduction

Natural materials usually possess special hierarchical patterns that are key to their prominent mechanical properties, such as nacre [1–3], gecko feet [4], spider silk [5], and bone [6]. Nacre, found in the shiny interior of many mollusk shells, shows excellent impact resistance that protects the inner body from the attack of predators [3]. Standing out with superior levels of toughness, strength, and hardness, nacre has attracted paramount attention from researchers for the past twenty years [7–9]. The two constituents of nacre have been found to be inorganic aragonite and organic biopolymer. With a hierarchical structure, nacre possesses toughness that is much higher than any of its constituent phases [10]. Previous experimental studies have found that the structures at different levels contribute synergistically to excellent toughness and energy absorption during crack propagation [10–15].

The excellent properties of natural materials promote the advent of biomimetic materials. Considerable efforts have been devoted to preparing nanocomposites with similar architecture to that of nacre, seeking lightweight, high-toughness, and high-strength artificial materials [16, 17]. To alleviate the brittleness and poor impact resistance of glass, Yin et al. [18] proposed a laminated glass that duplicates the three-dimensional “brick-and-mortal” arrangement pattern of nacre. It shows that this nacre-like glass is two to three times more impact resistant than laminated glass and tempered glass while maintaining high strength and stiffness. Xie et al. [19] fabricated a nacre-mimetic nanocomposite comprised of silk fibroin and graphene oxide that exhibits hybridized dynamic responses arising from alternating nanoscale components with high-contrast mechanical properties. Apart from the fine architecture, abundant interfacial interactions also play a key role in the nacre’s unique mechanical properties [20]. Researchers have recently leveraged different interface interactions, such as π − π interaction and hydrogen bonding, to create strong and tough artificial nacre [21–23]. Among those hard and strong materials that have been used in nanocomposites, multi-layer graphene (MLG) sheets, with outstanding mechanical properties and large surface area, have shown great promise as the reinforcement of polymer-based nanocomposites and as the rigid phase for nacre-inspired nanocomposites [24–28].

The dynamic mechanical behaviors and impact resistance of nacre-inspired nanocomposites have been of particular interest to researchers as well as the industry side because of the potential in advanced applications such as soft body armor and spacecraft shields [29–32]. Recent advances in experimental techniques have enabled impact tests of films at the micro or nanoscale, which allows for direct characterization of the dynamic mechanical properties of nanomaterials and nanostructures. Lee et al. [33] first developed the laser-induced projectile impact test (LIPIT) and reported the responses of nanocomposites with layered nanostructures consisting of glassy-rubbery block-copolymer to impact from hypervelocity micron-sized silica spheres. Later, with advanced LIPIT (α-LIPIT), studies also reported the high-strain-rate behavior of MLG over a range of thicknesses from 10 to 100 nanometers [34] and the ballistic impact behavior of thin elastomer films [35]. Xie et al. [19] recently employed the α-LIPIT to assess the dynamic mechanical behavior of nacre-mimetic nanocomposites using a 7.6 μm diameter silica projectile. Through the tests, the specific penetration energy was calculated, and microscopic images of the nanocomposite films post penetration were obtained for further analysis. Despite these recent advancements in experimental techniques, many of the investigations of microscale impact have been limited to postmortem analysis of impacted specimens, and little information is available for the extreme-rate impact dynamic process.

Besides experimental studies, computational methods have been instrumental in gaining insights into the dynamic deformation process and mechanical properties of bulk systems and nanocomposites. Grujicic et al. [36] employed a non-equilibrium molecular dynamics (MD) method to study various phenomena accompanying the generation and propagation of shock waves in polyurea. It was shown that the steady-wave planar shock profile and the shock Hugoniot relations in the material could be readily established from the simulation results. Their findings helped to understand the role of molecular-level characteristics in complex phenomena/processes, such as inelastic deformation and energy dissipation. Fu et al. [37] studied the shock response of polyethylene polymer modified by nanoparticles using coarse-grained (CG) MD simulations, in which they found a linear relationship between shock wave velocity and impact velocity. Xie et al. [38] performed a computational study on the mechanical behaviors of polyethylene under high-speed shock compression through MD simulations based on a united atom approach. The behaviors of shock wave propagations in the polymer were clearly presented. They also statistically analyzed the morphological evolution, which helped to elucidate the small-scale deformation mechanism. Dewapriya and Miller [39] recently studied the impact behaviors of a multilayer aluminum-polyurea nanocomposite with MD simulation and found such nanocomposite could achieve superior specific penetration energy. Additionally, computational studies have been carried out to understand the shock response or shock propagation and spallation in polymers, such as polyurea [40, 41], polyurethane [42], and polyethylene [43].

Despite these recent computational studies, the dynamic mechanical behaviors and specifically the stress wave propagation and failure mechanisms in nacre-inspired polymer nanocomposites, especially in thin-film configuration, are still not fully understood. Such understanding will be critical for the bottom-up design of nacre-inspired protective films. Our group recently investigated the dynamic mechanical behaviors of nacre-inspired layered nanocomposite films with a validated CG MD simulation approach [44]. Specifically, the mechanical properties and impact resistance of the MLG - poly(methyl methacrylate) (PMMA) nanocomposite films with different internal nanostructures were systematically studied under tensile loading and projectile impact, respectively. We have found that the elastic modulus, impact resistance, and dynamic failure mechanisms of such films depend on the internal nanostructures. Nevertheless, with a very small projectile and high velocity used, the systems were inevitably damaged under impact. The detailed shock wave propagation process in such layered nanocomposite films and the role of interfaces and nanostructures in this process have remained largely elusive.

This work addresses the shortcoming of the previous study by implementing piston impact tests on representative layered PMMA-graphene nanocomposite films, thus enabling us to examine the detailed shock wave propagation process plus the associated dynamic deformation and failure mechanisms. In addition, we also systematically investigate the dependence of the nanocomposite films’ energy dissipation capability on different internal and external factors through the quantification of a metric termed energy dissipation ratio.

2. Materials and Methods

We employ the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software (Aug7_2019 version) to carry out all the MD simulations [45]. The simulation trajectories are visualized using the Visual Molecular Dynamics software [46].

The CG models for both PMMA and MLG [47, 48] are employed to construct the layered nanocomposite films, with MLG being the rigid phase and PMMA being the soft phase.

The CG model of MLG consists of a hexagonal lattice of beads in which each CG bead represents four carbon atoms, thus following a four-to-one mapping. The bond, angle, and dihedral potentials defined for the CG model are the following:

$$V_{\mathit{\text{bond}}}(d)=D_0{\left[1-e^{-\alpha \left(d-d_0\right)}\right]}^2\text{ for }d<d_{cut}$$ (1)

$$V_{\mathit{\text{angle;}}}(\theta )=k_{\theta }{\left(\theta -{\theta }_0\right)}^2$$ (2)

$$V_{\mathit{\text{dihedral}}}(\varphi )=k_{\varphi }[1-\text{cos}(2\varphi )]$$ (3)

$$V_{nb}(r)=4{ϵ}_{LJ}\left[{\left(\frac{{\sigma }_{LJ}}{r}\right)}^{12}-{\left(\frac{{\sigma }_{LJ}}{r}\right)}^6\right]\text{ for }r<r_{cut}$$ (4)

where d₀ = 2.8 Å is the equilibrium bond length, θ₀ = 120° is the equilibrium angle, and D₀ = 479.535 Kcal/mol, α = 0.99 Å⁻¹, d_cut = 3.5 Å, k_θ = 419.415 Kcal/mol, k_ϕ = 4.153 Kcal/mol, ϵ_LJ = 0.813 Kcal/mol, σ_LJ = 3.46 Å, and r_cut = 12 Å are constants calibrated to match the mechanical properties of MLG [47, 49]. We note that the Morse bond potential parameters were revised to match the MLG strength measured by nanoindentation [50]. The bonds that are stretched beyond d_cut are treated broken and subsequently deleted. We use the command ‘fix bond/break’ in LAMMPS package to account for potential bond breaking events during the simulation. The model has been shown to capture the elasticity, strength, and fracture properties of monolayer graphene and MLG very well. The CG model has been extensively used to study MLG’s dynamic failure behaviors under extreme rate deformations [51, 52].

The CG model of PMMA employs a two-bead mapping scheme for each monomer, with one bead representing the backbone group and the other one representing the side group. In addition, there are two types of bonds, two types of angles, and two types of dihedrals defined within the PMMA CG model [48]. The functional form of the force field and optimized potential parameters for the PMMA CG model can be found in the original study [48]. The CG model of PMMA has been shown to realistically capture the thermomechanical properties of PMMA, including those that emerge from nanoscale thin film configurations [44, 53–56]. We note that there is no bond-breaking criterion implemented in the model. Our previous studies have shown that bond breakage plays a negligible role under the highly localized projectile impact, mainly due to the shorter chain lengths used [56]. We anticipate the possibility and effect of bond breaking of the PMMA chains are even less for this piston impact loading implemented in this study.

We also use the Lennard-Jones potential to describe the interaction between PMMA beads and graphene beads:

$$V_{LJ}(r)=4{ϵ}_{gp}\left[{\left(\frac{\sigma }{r}\right)}^{12}-{\left(\frac{\sigma }{r}\right)}^6\right]$$ (5)

where r is the distance between a PMMA bead and a graphene bead, and the potential well depth ϵ_gp can be a measure of the interfacial interaction strength between the PMMA phase and graphene sheets. In this study, we change ϵ_gp to investigate the effect of the interfacial interactions on the dynamic impact responses of layered nanocomposite films.

The two nanocomposite films studied here differ in the thickness of alternating phases while conserving the total volume, as illustrated in Fig. 1. Specifically, Rep4 is made of four repetitive modules consisting of alternating 18 nm-thick PMMA and 18 graphene sheets, and Rep36 is made of 36 repetitions of thinner modules, which are 2 nm-thick PMMA and bilayer graphene sheets. In addition, both structures are caped with bilayer graphene sheets so that all the PMMA phases are confined at both ends. Therefore, the nanocomposite systems have 74 sheets of graphene and 72 nm-thick PMMA in total. We use a chain length of 100 monomers for the PMMA chains, consistent with our previous studies [44, 56, 57]. Both the Rep4 and Rep36 systems contain 193,344 CG beads, representing 1,176,576 atoms. The simulation box is set to be periodic in the in-plane direction of graphene sheets (XY-direction) and non-periodic in the thickness or Z-direction, i.e., representing finite-thickness films. We apply the piston impact along the Z-direction, which is also named the shock direction. The total thickness in the Z-direction is 100 nm, and we also include large empty domains on both sides of the film along the Z-direction to account for the potential deformation of the film. Both the sizes of the box in the X- and Y-direction are approximately 10 nm. We use relatively small sizes in the in-plane dimension of the system since we focus on the stress wave propagation along the shock direction. Moreover, our piston impact setup and the periodic boundary conditions allow us to minimize the influences from the sizes in the X- and Y-direction.

Figure 1.

Schematics of the layered graphene-PMMA nanocomposite films. (a) Rep4 consists of 4 repetitive modules of 18-nm thick PMMA phases and 18 graphene sheets; (b) Rep36 consists of 36 repetitive modules of 2-nm thick PMMA phases and bilayer graphene sheets. With another bilayer graphene cap at the right end, the total thicknesses of Rep4 and Rep36 are equal.

After constructing the structures and defining the forces fields, we carry out MD simulations to investigate the dynamic impact response of the nanocomposite films. First, the energy of the system is minimized using the conjugate gradient algorithm. Then, we apply the NVE ensemble in the first equilibration process for 200 ps. After that, an annealing process under the NPT ensemble is then performed with the pressure along the X- and Y-direction being kept at zero to relax the in-plane pre-stresses. The detailed temperature history for the annealing process is following: (i) equilibrating at the initial temperature of 300 K for 200 ps, (ii) increasing the temperature from 300 K to 600 K in 200 ps, (iii) staying at 600 K for 200 ps, (iv) decreasing the temperature from 600 K to 300 K in 200 ps, and (v) equilibrating at 300 K for another 400 ps. After the equilibration process, we implement the piston shock impact under the NVE ensemble as follows. First, we treat bilayer graphene sheets at the left end as a rigid body. Then, we apply a constant piston velocity, U_p, on the rigid bilayer graphene for 20 ps. This process resembles a piston impact while also allowing us to control the total momentum applied to the system [58, 59]. After that, the imposed velocity and the rigid body constraint are removed. The simulation continues running for 80 ps, during which we output the stress and density profile along the shock direction for further analysis.

3. Results and Discussion

3.1. Internal Stress Wave Propagation Process

We plot the normal stress in the shock direction (σ_zz) and the density (ρ), as a function of z-axis coordinates and time, in 2D contours, respectively. Figure 2 shows the spatiotemporal σ_zz contour and density contour of Rep36 for U_p = 1 Km/s and ϵ_gp = 0.4 Kcal/mol. In the two contours, horizontal axes represent the z coordinate of each cross-section in the current configuration, and vertical axes correspond to the time. In this way, the contours reflect the values of the longitudinal tensile stress or the density value corresponding to each cross-section at a specific time. We note that negative stress indicates compressive stress, while positive stress corresponds to tensile stress.

Figure 2.

The spatiotemporal contours of (a) stress in the shock direction (σ_zz) and (b) density (ρ) of the Rep36 system with U_p = 1 Km/s and ϵ_gp = 0.4 Kcal/mol. The shock front, release wave, and reflected wave are marked in (a).

In Fig. 2(a), the stress contour clearly exhibits the shock front, reflected wave, release wave, and piston movement, similar to previous studies on other systems [40, 42]. The wave propagation characteristics also show up correspondingly in the density contour. In the wave propagation process of Rep36, the shock front initiates and then propagates along the longitudinal direction until it encounters the right end face (REF). At the REF, the shock front is reflected and returns as a tensile reflected wave. It encounters another tensile wave, the release wave [60], at a specific time and position. The cross-section at which the two tensile waves encounter each other experiences high tensile stress and is likely to initiate the crazing deformation in the PMMA phase, i.e., spallation [43].

In the case of Rep4, there is significant decay in the shock front as it propagates across PMMA/MLG interfaces. This phenomenon is mainly attributed to the wave reflections that happen at those interfaces. In addition, we find that wave reflections lead to multiple wavefronts and subsequent superpositions. To better illustrate this process, we name all the interfaces inside the nanocomposite film in such a manner (as marked out in Figure 3(a)): IF1 is the interface between the left-most MLG phase and the left-most PMMA phase, IF2 is the interface between the PMMA phase and the next MLG phase, and so on. When the generated shock front (the bold red dashed arrow W1) propagates to IF2, part of the shock front gets reflected and then propagates backward. We mark this reflected wave as W3. The other part of W1 transmits through IF2 and propagates forward, and we mark this transmitted wave as W2. After a short time, W2 encounters IF3 and the transmitted part is marked as W4, which moves toward IF4. The reflected wave at IF4 is marked as W6. In the meantime, W3 propagates backward and then encounters IF1 again. W5 is the reflected portion by IF1, which transmits through IF2 and becomes W7. Interestingly, W7 and W6 arrive at IF3 at the same time. This coincidence comes from the fact that W2, W4, and W6 (shown in pink arrows) travel the same distance as W3, W5, and W7 (shown in white arrows) do. Subsequently, the reflected part of W6 (marked as W8) and the transmitted part of W7 (marked as W9) at IF3 become superposed and propagate forward as W10. Similar phenomena happen at other IF (i.e., IF4-IF7). As a result, the original shock front is divided into multiple wavefronts which propagate to the REF at different times. Figure 3(a) shows that the strongest wavefront is the one reaching REF secondly. Its reflected wave by REF is named the major reflected wave since it is the strongest among all the REF-reflected waves.

Figure 3.

The spatiotemporal contours of (a) tensile stress (σ_zz) and (b) density (ρ) of the Rep4 nanocomposite film with U_p = 0.2 Km/s and ϵ_gp = 0.8 Kcal/mol. W1 (wave #1) represents the initial shock front. The following dashed pink, white, and red lines showcase the shock wave reflection and superposition processes. The black arrows represent the release wave propagation and the corresponding processes.

A release wave is also generated when the enforced moving constraint on the piston is withdrawn. This release wave, which behaves as a tensile wave [60], experiences similar reflections and superpositions at the interfaces as the shock wave does. The release wavefront also divides into multiple wavefronts propagating to REF at different times. We can see in Figure 3(a) that the strongest release wavefront is the one arriving at REF secondly. More interestingly, we find at the location where the two tensile wavefronts meet, i.e., the major reflected wavefront and release wavefront, PMMA crazing develops, as marked by the two black circles in Figure 3(a) and (b), respectively. We also showcase the simulation snapshot of the PMMA crazing as an inset in Figure 3(b). During such crazing deformation, the sliding of chains is much easier to be activated than chain breaking [61–64], which further justifies our practice that no bond-breaking criterion is implemented in the PMMA CG model.

Figure S1 in the Supporting Information (SI) shows that the in-plane stresses, σ_xx and σ_yy, in the MLG phase of Rep4 exhibit tensile stress characteristics as the initial compressive stress wave propagates through, in contrast to compressive stresses in all three directions in the PMMA phase. This unconventional behavior can be explained by the negative Poisson’s ratio of MLG under out-of-plane loading. The negative Poisson’s ratio of MLG has been illustrated in previous studies using first-principles calculations and molecular dynamics simulations [65–67]. To further showcase the influence of negative Poisson’s ratio of MLG on its dynamic impact response, we apply similar piston impact loading to a pure MLG plate. Again, in-plane tensile stresses are developed in the wake of the impact. The results are included in Figures S2 and S3 in the SI. It should also be noted that the zigzag high-stress bands observed in Rep4 are not obvious in the case of Rep36. One possible reason is that the distance between two neighboring MLG phases in Rep36 is much shorter than that in Rep4, and the reflections of waves occur at a much higher frequency in Rep36 than in Rep4, which makes it harder to identify the wave propagation paths as well as the associated high-stress bands.

To further show that the wave propagation process and mechanisms identified in Fig. 3 are independent of the film thickness, we conduct an additional simulation on a film with a thickness double that of the Rep4 film (twice the repetitive modules while keeping the same module thickness) under the same impact loading condition. The results are shown in Fig. S4 in the SI. We observe a very similar wave propagation process, including wave reflections and superpositions within the PMMA phase and across the whole nanocomposite film. It demonstrates that the wave propagation process described above is representative of such layered nanocomposite films. We also observe that there is no polymer crazing developed in this thicker system. It is probably because the tensile stresses generated by the reflected and release waves have been weakened due to more interfaces and longer propagation paths in this thicker system. The fact that polymer crazing develops in the thinner film while not in the thicker film under similar piston impact loading also indicates the intrinsic energy dissipation due to interfaces within the layered nanocomposite films.

In summary, the PMMA/MLG interfaces in the nanocomposites have two effects on the shock wave propagation process. First, the abundant interfaces can lead to reflections of the incident shock front. Through a series of reflections and superpositions, it generates multiple wavefronts which reach the free surface at the other end at different times. The wavefronts are then reflected by the free surface and become tensile stress waves, among which the strongest one is the major reflected wave. When the fronts of the major reflected wave and release wave meet, it can potentially result in crazing deformation in the PMMA phase. Second, the reflections at the interfaces tend to increase the overall wave propagation distance and can enhance the dissipated energy during the stress wave propagation process after impact loading.

3.2. Hugoniot U_s – U_p Relationship

When homogeneous materials are subject to an impact, the relationship between the shock front velocity U_s and the piston velocity U_p, i.e., the Hugoniot U_s − U_p relationship, follows [68]:

$$U_s=c_0+k{U}_p$$ (6)

where c₀ is the bulk sound speed; k is the slope of the Hugoniot.

It reveals that U_s and U_p have a linear relationship for homogeneous material systems. Previous experimental and computational studies have indeed observed linear U_s − U_p relationship for different polymer systems at a relatively small velocity regime (< 3 km/s) [69–71]. We plot their shock velocity U_s against piston velocity U_p in Fig 4 for the studied PMMA-graphene layered nanocomposite films. It turns out that the linear relationships between U_s and U_p still holds for both Rep4 and Rep36. This is a surprising result given that the nanocomposite systems considered herein are highly heterogeneous (we show in Figure S5 in the SI that the pressure and density profiles of the systems at a given time are very inhomogeneous, totally different from the bulk polymer systems reported before) and we have observed complex stress wave propagation and reflection mechanisms. This result demonstrates that the linear Hugoniot U_s − U_p relationship may be valid for a broader range of systems than those studied before.

Figure 4.

Shock front velocity (U_s) vs. piston velocity (U_p) for both Rep4 and Rep36. The dashed lines are the fitted linear trends.

3.3. Dependence of Energy Dissipation Capability on Different Factors

3.3.1. Influence of piston velocity on energy dissipation efficiency

Typical curves of energy evolution with time during the impact are shown in Figure 5, including the total energy and potential energy of the nanocomposite system. The total energy of the system keeps increasing when the piston is forced to move at a constant velocity, indicating the input kinetic energy from the piston impact. After the velocity constraint on the piston is removed, the total energy remains constant. We define the difference between the initial total energy and the final total energy as the input energy from the piston impact. Similarly, the nanocomposite film’s potential energy also increases and reaches its peak, which marks the maximum amount of energy absorbed by the nanocomposite system. Afterwards, the potential energy decreases as the elastic energy quickly converts back to kinetic energy, mainly through the center-of-mass motion of the film. However, the potential energy does not return to its initial value. Instead, it shows a permanent increase, and the energy increment corresponds to the part of energy that is dissipated by irreversible (or plastic) deformation of the PMMA phase and/or at the interface. Therefore, we use it as the dissipated energy in the following discussions. We note that energy dissipation can also be in the form of local temperature increases in the film. We neglect this part of energy dissipation since the capability of our CG models to capture the thermal properties has not been validated. Even though we only focus on the energy dissipation related to the dynamic deformation of the system, our study still provides important insights into this essential part of energy dissipation, which has been challenging to quantify in traditional experimental characterizations.

Figure 5.

(a) Evolutions of a nanocomposite film’s total and potential energy under piston impact and the definitions of input energy and dissipated energy. (b) The energy dissipation ratio of Rep4 under different U_p with ϵ_gp = 0.8 Kcal/mol. (c-e) The snapshots of the nanocomposite film at the end of impact under different U_p: 0.125 Km/s, 0.25 Km/s, and 1.5 Km/s.

To also take the input energy into account, we further define a new metric - dissipation ratio, which is computed as the ratio of the dissipated energy to the input energy, to compare the energy dissipation efficiency of the layered nanocomposite films depending on U_p and other factors.

Figure 5(b) shows the results of input energy, dissipated energy, and dissipation ratio depending on U_p for ϵ_gp = 0.8 Kcal/mol. The input energy depends quadratically on U_p. The dissipated energy also increases with U_p, but the increment rate is slower than that of input energy, especially for high U_p. As a result, the dissipation ratio first goes up and then goes down as U_p increases. It reaches its maximum value at around U_p = 0.25 Km/s. This is an interesting observation as it shows that the energy dissipation efficiency of the nanocomposite films maximizes at a moderate U_p. Next, we examine the underlying reason for the maximal value of the dissipation ratio at U_p = 0.25 Km/s. We showcase the deformation patterns of Rep4 at three different U_p as labeled (c)-(e) in Figure 5(b). Specifically, Figure 5(c) shows a snapshot of the nanocomposite at the end of the impact at U_p = 0.125 Km/s, in which little crazing deformation is observed. Nevertheless, we note that a certain amount of energy is still dissipated through unrecoverable deformation within the system, including but not limited to polymer intra-chain buckling, inter-chain sliding, and dissipative friction at interfaces. As U_p increases to 0.25 Km/s, a snapshot (Figure 5(d)) shows that certain zones in the PMMA phase start to develop observable crazing deformation. Crazing can dissipate a large amount of energy, and thus it leads to a significant rise in the dissipation ratio. At U_p = 1.5 Km/s, where U_p is far beyond the critical U_p, PMMA phase experiences extensive crazing deformation, as shown in Figure 5(e). Meanwhile, the total dissipated energy through PMMA crazing no longer keeps up with the quadratic increase of the input energy. Consequently, the energy dissipation ratio decreases as U_p continues to increase.

We conclude that the large crazing deformation of the PMMA phase plays a crucial role in the energy dissipation process of the layered nanocomposite films. The layered nanocomposite films can achieve the optimal impact energy dissipation efficiency at a moderate U_p when PMMA crazing deformation emerges.

3.3.2. Influence of ϵ_gp on energy dissipation

To understand the influence the interfacial interaction on the energy dissipation capability, we change the value of ϵ_gp from 0.4 to 3.0 Kcal/mol, which corresponds to the value of interfacial energy from 0.14 to 1.45 J/m². This range is similar to experimentally measured interfacial energy values [72]. We then carry out the simulations and calculate the dissipation ratio for each case. The plot of the dissipation ratio against ϵ_gp is shown in Figure 6(a). Under the condition of constant piston velocity (U_p = 1 Km/s), there is a critical ϵ_gp around 0.5 Kcal/mol, below which the dissipation ratio is significantly lower. Moreover, when ϵ_gp is larger than the critical value, the dissipation ratio becomes independent of ϵ_gp. In fact, the critical ϵ_gp value corresponds to the transition of dynamic failure modes from the interfacial separation between PMMA/MLG phases to PMMA crazing, informed by the simulation trajectories after impact. Figure 6(b) and 6(c) shows the cases of ϵ_gp = 0.4 Kcal/mol and ϵ_gp = 0.6 Kcal/mol, respectively. We note here that the critical value of ϵ_gp also depends on U_p. For instance, the existence of the critical ϵ_gp is expected to only happen for U_p that can activate the crazing deformation within nanocomposite films with stronger interfacial interaction, i.e., larger than the critical U_p. Therefore, the influence of U_p should also be considered when examining the impact of nanofiller-matrix interfacial interactions on the energy dissipation of nanocomposite films.

Figure 6.

(a) Energy dissipation ratio of Rep4 for different ϵ_gp. (b-e) Simulation snapshots at the end of impacts for different ϵ_gp values: 0.4 Kcal/mol, 0.6 Kcal/mol, 2.0 Kcal/mol, and 3.0 Kcal/mol.

3.3.3. Influence of the layer thickness

Lastly, we compare the energy dissipation behaviors of Rep4 and Rep36, which have the same volume of each phase but different layer thicknesses. Specifically, the thicknesses of both the MLG phase and PMMA phase in Rep4 are eight times larger than those in Rep36. By comparing the difference between Rep4 and Rep36, we explore the influence of the nanolayer thickness on the dynamic mechanical behaviors of layered nanocomposite films.

Figure 7 shows the comparison of input energy and dissipated energy of both Rep4 and Rep36 for the whole range of ϵ_gp. We observe that the input energy from the piston show differences in the two nanocomposite films despite the fact that the input momentum is kept constant. This is because the overall mechanical properties of the two nanocomposite films and their dependence on ϵ_gp are both different. In the case of Rep4, the input energy shows a moderate uptrend with ϵ_gp while the dissipated energy mildly oscillates about a steady value except for the ϵ_gp = 0.4 Kcal/mol case, in which the failure is dominated by the interfacial separation, as shown in Fig. 6(b). In the case of Rep36, ϵ_gp shows a much more significant influence on both the dissipated and input energy compared to Rep4. We note that the influences of ϵ_gp on both energy indexes are positive. In other words, larger ϵ_gp leads to greater dissipated energy and greater input energy, even though the quantitative effects are different. Such differences in sensitivity to ϵ_gp between Rep4 and Rep36 are attributed to the number of interfaces of unit volume inside the nanocomposite films. There are more PMMA/MLG interfaces in Rep36, and in the meantime, the PMMA layers are much thinner. Our previous studies have shown that the nanoconfinement effect of graphene sheets on polymer films becomes more prominent as polymer films become thinner [44, 53]. The results here show that the stronger nanoconfinement effect in Rep36 also leads to a stronger dependence on ϵ_gp.

Figure 7.

Comparison of input and dissipated energy between Rep4 and Rep36 for a range of ϵ_gp values at U_p = 1 Km/s.

We note that the dissipation ratio of the nanocomposite films can also depend on other factors, including but not limited to film total thickness, duration of the impact pulse, and pulse shapes, which can be more complex than the one used in this study. The modeling and simulation approach proposed herein has the unique advantage of investigating these dependence relationships compared to other approaches, and we plan to address these in our future studies. The unveiled relationships from modeling and simulation can be potentially validated by the α-LIPIT and Kolsky bar testing experiments and also provide valuable guidance to the design and characterizations.

4. Conclusions

This paper investigates the dynamic mechanical behaviors and failure mechanisms of PMMA-graphene nanocomposite films using CG MD simulations. We have illustrated the detailed shock wave propagation process through the spatiotemporal contours of σ_zz and density. The presence of PMMA/MLG interfaces gives rise to complex wave reflection and superposition behaviors within the nanocomposite films. The PMMA phase crazing deformation has been shown to initiate at the location where the fronts of the two critical tensile waves, i.e., the major reflected wave and the major release wave, meet when U_p reaches a critical value. The activation of PMMA crazing significantly enhances the dissipated energy of the nanocomposite films under impact. By using a dissipation ratio, computed as the ratio of the dissipated energy to the input kinetic energy, we find that the maximal dissipation ratio also happens approximately at the critical value of U_p. This finding can be used as a design principle for nanocomposite-based protective films for the most efficient energy dissipation. In addition, we find that there is a critical ϵ_gp that corresponds to the transition of failure/deformation modes between interfacial separation and PMMA crazing. Moreover, the energy dissipation behaviors of Rep4 and Rep36 show different dependence on the change of ϵ_gp, which is mainly attributed to their difference in the number of interfaces per unit volume or layer thickness. In summary, the results from this study provide important insights into not only the detailed deformation mechanisms of nacre-inspired layered nanocomposite films but also the design strategies of nanocomposite films with excellent impact resistance.

More importantly, the intriguing observations and results from this study open up fruitful topics to look into in our future work. For instance, we find that the linear Hugoniot U_s − U_p relation still applies to the layered nanocomposite films, and the anisotropic MLG sheets result in different stress development patterns in the MLG and PMMA phases. Additionally, the authors plan to integrate the insights from the presented MD modeling approach and summarize them into constitutive relationships of layered nanocomposite systems under dynamic loading conditions. Such effort will build upon our previous demonstration of multiscale modeling of other heterogeneous material systems [73, 74].