Improved Ballistic Impact Resistance of Nanofibrillar Cellulose Films with Discontinuous Fibrous Bouligand Architecture

Abstract

Natural protective materials offer unparalleled solutions for impact-resistant material designs that are simultaneously lightweight, strong, and tough. Particularly, the Bouligand structure found in the dactyl club of mantis shrimp and the staggered structure in nacre achieve excellent mechanical strength, toughness, and impact resistance. Previous studies have shown that hybrid designs by combining different bioinspired microstructures can lead to enhanced mechanical strength and energy dissipation. Nevertheless, it remains unknown whether combining Bouligand and staggered structures in nanofibrillar cellulose (NFC) films, forming a discontinuous fibrous Bouligand (DFB) architecture, can achieve enhanced impact resistance against projectile penetration. Additionally, the failure mechanisms under such dynamic loading conditions have been minimally understood. In our study, we systematically investigate the dynamic failure mechanisms and quantify the impact resistance of NFC thin films with DFB architecture by leveraging previously developed coarse-grained models and ballistic impact molecular dynamics simulations. We find that when nanofibrils achieve a critical length and form DFB architecture, the impact resistance of NFC films outperforms the counterpart films with continuous fibrils by comparing their specific ballistic limit velocities and penetration energies. We also find that the underlying mechanisms contributing to this improvement include enhanced fibril sliding, intralayer and interlayer crack bridging, and crack twisting in the thickness direction enabled by the DFB architecture. Our results show that by combining Bouligand and staggered structures in NFC films, their potential for protective applications can be further improved. Our findings can provide practical guidelines for the design of protective films made of nanofibrils.

1. Introduction

Architected materials from nature with excellent mechanical and protective properties inspire the development of impact-resistant and lightweight synthetic materials [1–4]. The Bouligand structure is commonly found in structural design in nature that involves uniaxially arranged fibers/fibrils in a helicoidal form, with each layer rotating at a certain pitch angle ($\gamma$) from adjacent layers. This architecture can be widely found in fish scales, crustacean exoskeletons, bones, and many other natural materials, each with unique mechanical properties that cater to the specific functions necessary for the organism’s survival [3–5]. From a study on the fish scales of Arapaima gigas, one of the largest freshwater fish in the world, it was found that the scale has an inner layer that consists of mineralized collagen fibrils in a Bouligand structure. It helps minimize penetration damage from predators through various toughening mechanisms, such as crack twisting and fibril bridging [2, 6, 7]. In addition, the material’s natural flexibility also assists in the redistribution of compressive stresses [3]. Similarly, the dactyl clubs of stomatopods, e.g., mantis shrimp, can withstand immense stress from strong impact strikes against their prey, most often protected by mollusk shells. The dactyl club is composed of mineralized chitin nanofibrils organized in a Bouligand structure. The fact that the dactyl club can easily smash the mollusk shells without self-damage demonstrates the excellent impact resistance of the Bouligand structure. Recently, the Bouligand structure has led to impact-resistant materials design concepts that show promising applications in automobiles and body armor [8–12]. On the other hand, during the survival war between predators and preys, the mollusk shells also evolve excellent mechanical and protective properties that simultaneously achieve high mechanical strength and toughness as well as impact resistance [13–18]. Particularly, the inner layer of the mollusk shell, known as nacre, composes of nano-sized mineral platelets and a biopolymer matrix in a brick-and-mortar type of staggered arrangement. Nacre possesses excellent fracture toughness that is orders of magnitude greater than the constituents. It has been widely regarded as one of the best natural body armors due to its unique multiscale architectures [19–24].

Given the excellent performance of such natural materials with unique structures, tremendous efforts have been devoted to fabricating biomimetic materials by replicating or resembling the unique structures of natural materials. Previous efforts have applied different fabrication methods to resemble the Bouligand and other bioinspired structures [7, 25–29]. One of them 3D printed specimens with Bouligand structure, but they showed no improvements in critical failure energy and resisting crack initiation [28]. Another study prepared carbon fiber-reinforced epoxy specimens with a helicoidal layup similar to the Bouligand microstructure [29]. The plies in these specimens were manually cut and laid according to the layup specifications and then cured in an oven. Experimental transverse testing showed that specimens with lower interplay angles (pitch angles, $\gamma$) could sustain higher loadings with a 34% increase in peak loading for 19-ply laminates. Micro-CT scans further show transverse cracking and delamination along the helicoid climb forming a spiral pattern [29]. It is important to note that these aforementioned case studies resemble the Bouligand structure at the macroscopic scale. It shows the scalability of these structures for larger-scale real-world applications. However, it may not be able to leverage the enhanced performance by adopting such structures at similar length scale as those in natural materials and may lead to insufficient mechanical performance compared to natural materials.

Nanofibrillar cellulose (NFC) is a particularly promising building block to replicate the Bouligand and brick-and-mortar structures found in biomaterials at nanometer length scale. NFC, the elementary fibrils in the wood and plant biosynthesis process that consists of 36 cellulose chains arranged in Iβ crystal structure, can potentially self-assemble into the Bouligand structure [19, 30–34]. This self-assembly is a key characteristic of NFC that makes it advantageous for preparing bioinspired structural materials, which are promising for future structural and impact-resistant applications [35–41]. The $\gamma$ of these self-assembled Bouligand microstructures can be controlled by the conditions within the water solvent used [40, 42]. This is important to note because $\gamma$ can be an important design variable for desired functions. In addition, NFC has excellent mechanical properties comparable to Kevlar and other nanofibrils [19, 23].

It thus becomes critical to understand the underlying mechanisms and come up with design principles for structural materials made of NFC with enhanced impact resistance and other mechanical properties. In this regard, computer simulations offer great promise and can save significant time and costs compared to experiments. Our previous computational study provided insights into the dynamic failure mechanisms of a Bouligand-structured film made of continuous NFC. We found the impact resistance of such films strongly depended on $\gamma$, and a low $\gamma$ (18°–42°) resulted in improved impact performance due to greater nanofibril sliding, crack twisting, and impact stress delocalization [1]. In this previous study, we showed that greater fibril sliding could contribute to the higher impact resistance of Bouligand-structured film made of continuous NFC. However, the possible sliding events are intrinsically limited by the continuous nature of nanofibrils that span the whole film. It is reasonable to hypothesize that using relatively short, discontinuous nanofibrils can potentially promote the fibril sliding. By further conserving the critical crack twisting mechanisms by judicious selection of discontinuous sites and $\gamma$, the overall impact resistance of the CNC films can possibly be enhanced. A recent study partially validates this hypothesis by applying a hybrid Bouligand and nacreous staggered structures, named discontinuous fibrous Bouligand (DFB) architecture, and examining the fracture energy of 3D-printed single-edge notched specimens. The study showed that this DFB architecture achieves enhanced fracture resistance due to the hybrid toughening mechanisms of crack twisting and crack bridging [2]. Remarkably, other previous studies demonstrated that cracking twisting and crack bridging may coexist during the fracture process of natural materials with Bouligand structures [43–48]. A few other studies have also shown that hybrid designs that combine different microstructures can break performance tradeoffs and improve fracture toughness [7, 25, 26].

However, whether such hybrid designs by combining Bouligand and staggered structures could lead to enhanced impact resistance under localized projectile impact remains unknown, and how to design the structures to achieve the optimal impact resistance is a daunting experimental task as a larger number of design parameters can affect the final performance. This study systematically investigates the dynamic failure mechanisms and quantifies the impact resistance of NFC films that adopt a DFB architecture, i.e., staggered discontinuous NFC in each layer with a helicoidal layup, by leveraging coarse-grained molecular dynamics (CGMD) simulations. Specifically, we applied a previously developed CG model of NFC that successfully captures the mechanical properties of all-NFC materials under both quasi-static and dynamic deformation processes [1, 22, 49]. Our previous studies have demonstrated that CGMD offers a great advantage compared to continuum-scale simulations and all-atomistic (AA) MD simulations [50–55]. We also note that our selection of short and discontinuous NFC is motivated by the fact that NFC from wood and plant cellulose biosynthesis process generally have lengths in the range of 500–2000 nm. By carrying out ballistic impact MD simulations with explicit projectile and characterizing the ballistic limit velocity ($V_{50}$) and penetration energy ($\Delta E_k$), we examine the impact resistance of NFC films with DFB architecture depending on different geometric factors. We also characterize the deformation mechanisms that affect the impact resistance from simulation trajectories.

2. Methods and Materials

Our model system is illustrated in Fig. 1, where we highlight the simulation scheme, DFB architecture, and the CG model used for the NFC building block. As previously discussed, Bouligand-architectured films with continuous fibrils have been previously studied, and their mechanical properties under different loading conditions have been summarized [1, 49]. The difference between continuous NFC and discontinuous NFC is manifested at the red beads, where fibrils are disconnected by deleting the intra-fibril bonded interactions (bond and angle interactions). The length $L$ represents the whole length of the fibrils, and all the fibrils have constant $L$ in each simulation case. We alter $L$ for different cases and systematically study its effect on the impact resistance of the NFC films with DFB architecture. All the projectile impact simulations were carried out using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [56]. The simulation trajectories were visualized by the Visual Molecular Dynamics (VMD) program [57].

Figure 1.

Simulation schematic and structural design for NFC films with DFB architecture.

The model system builds upon the previously established bead-spring mesoscopic CG model of NFC [49]. Within this model, each CG bead represents three repeat units of the 36-chain structured (110) surface of NFC. The diameter of each CG bead is 3.4 nm, making its cross-sectional area equal to that of the NFC. Those CG beads interact with each other through bonded and non-bonded interactions. The bonded interactions include harmonic bonds and harmonic angles whose potential functions are shown below:

$$V_{bond}=k_b{(b-b_0)}^2\mathrm{f}\mathrm{o}\mathrm{r}b<b_{cut}$$ (1)

$$V_{angle}=k_{\theta }{(\theta -{\theta }_0)}^2$$ (2)

where $k_b$ is twice the spring constant, $b$ is the bond length, $b_0$ is the equilibrium bond length, $k_{\theta }$ is twice the bending spring constant, $\theta$ is the bending angle, and ${\theta }_0$ is the equilibrium bending angle which is set to 180°. For the bond potential, a cutoff $b_{cut}=3.27\mathrm{n}\mathrm{m}$ is set as the failure criterion corresponding to a failure strain of 5% based on prior MD studies [58]. The other values of bond potential parameters and angle potential parameters are determined through uniaxial tension and three-point bending tests on the AA model of NFC, respectively, according to the strain energy conservation approach. The values of those parameters can be found in Table 1. The non-bonded interaction is incorporated to account for the electrostatic and van der Waals effects. In this CG model, a Morse potential is employed to model the non-bonded interaction:

$$V_{nonbonded}=D_0[e^{-2\alpha \left(r-r_0\right)}-2e^{-\alpha \left(r-r_0\right)}]$$

where $D_0$ is the well depth, $\alpha$ controls the width of the potential well, $r$ is the distance between beads from different nanofibrils, and $r_0$ is the equilibrium distance. The values of the parameters in the Morse potential are determined by matching the interfacial properties between the CG and AA models and are presented in Table 1. Further, a cutoff distance $r_{cut}=6\mathrm{n}\mathrm{m}$ is set to consider only neighboring inter-fibril interactions and increase computational efficiency.

Table 1.

The parameter values used for the bond, angle, and non-bonded potentials.

Parameter	Value	Parameter	Value
b 0	31.14 Å	kb	260 kcal · mol−1 · Å−2
θ 0	180°	kθ	77000 kcal · mol−1 · rad−2
r 0	36 Å	D 0	240 kcal · mol−1
α	0.3 Å−1

Building upon the validated model of NFC, we construct representative NFC films using 11 layers (approximately 37 nm in thickness) of parallelly staggered NFC in each layer with left-handed helicoidal structures that are typical of chitin-rich shells of crustaceans and self-assembled NFCs [4, 30, 31, 43]. Specifically, a rotational angle, $\gamma$, about the axis normal to the layer plane is assigned starting from the bottom-most layer. In this study, the following $\gamma$ are considered: 0°, 18°, 30°, 45°, 75°, and 90°. We note that the number of layers and selected $\gamma$ are consistent with our previous study on continuous NFC film [1]. Discontinuous NFCs are constructed from continuous fibrils spanning the whole length of each layer by deleting the bonded interactions between the beads at the discontinuous sites (Fig. 1). We note that actual discontinuous sites can be larger than the ones considered herein. However, we believe the impact resistance of NFC films is mainly governed by the overlap length of nanofibrils when the size of defects is much smaller compared to the length of nanofibrils and the size of the projectile. Therefore, we believe the results in this study are generalizable to films with potentially larger defect sizes. There may have multiple discontinuous sites over the span of the impact region depending on the lengths and specific configurations selected in this study, which are discussed later.

We have selected four configurations regarding the location and distribution of discontinuous sites while keeping a unified length ($L=500nm$) for all nanofibrils. For the first three patterns (Fig. 2 (a)–(c)), adjacent nanofibrils in each layer have a 50% overlap length, and thus, the distance between discontinuous sites ($L_0$ in Fig. 1), e.g., the overlap length, is half of the fibril length $L$. The first configuration is denoted as Offset since we shift the discontinuous lines away from the impact site by 50% of the $L_0$ for each layer. The top view (Fig. 2 (a)) shows the discontinuous lines are offsite from the center of the film. We note that we further alter $L$ using the Offset configuration and study the influence of $L$ in the later part of this paper. The second configuration is denoted as Middle (Fig 2 (b)) as one line of discontinuous sites in each layer crosses the center of the impact zone. From the top view of the $\gamma =0°$ case, we can clearly see the discontinuous sites lying in the middle. For the third configuration, named Random Through-Thickness (TT) (Fig. 2 (c)), we shift the discontinuous sites for each layer collectively in-plane with a random distance between 0 and 50% of the $L_0$ based upon the Middle configurations. We note that the adjacent nanofibrils in each layer still have a 50% overlap length. This 50% overlap pattern can be seen from the top view of a specific layer in Fig. 2(c). In the last configuration, Random In-Plane (IP) (Fig. 2 (d)), we further introduce randomness for overlapping lengths between adjacent fibrils in-plane. In this case, the smallest overlap length governs the mechanical strength along the fibril direction for each layer [22]. Even though the four selected configurations cannot represent all possible configurations for NFC films, we believe such selections can help us to understand the effects of the location and distribution of discontinuous sites on the ballistic impact resistance of NFC films in this study.

Figure 2.

Different configurations considered in this study: (a) top view of the Offset configuration film ($\gamma =30°,$ $L=750\mathrm{n}\mathrm{m}$), (b) top view of Middle configuration film ($\gamma =0°$, $L=500\mathrm{n}\mathrm{m}$), (c) top view of the top layer and side view of the film for the Random TT configuration ($\gamma =0°$, $L=500\mathrm{n}\mathrm{m}$), (d) top view of the top layer and side view of the film for the Random IP configuration ($\gamma =0°,$ $L=500\mathrm{n}\mathrm{m}$). The beads representing fibril ends or discontinuous sites are highlighted.

We define an impact region of the NFC film that has a diameter of 1,000 nm. We note that a fibril length of 2,000 nm in the Offset configuration is identical to a continuous nanofibril case as the discontinuous sites will be all outside of the impact region. An explicit projectile is also created above the center of the impact region of the NFC film. The projectile is in a spherical shape with a diameter of 160 nm and consists of CG beads that are arranged in a cubic diamond pattern. The density of the projectile is 3.53 $g/c{m}^3$. The interactions between the projectile beads and the NFC beads are modeled by a 12–6 Lennard Jones (LJ) potential [50]:

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

where $r$ is the distance between a projectile bead and a Bouligand bead. The two parameters, ${\epsilon }_{LJ}$ and ${\sigma }_{LJ}$, are chosen to be 20 kcal/mol and $4nm$, respectively. Our previous study shows that the value of ${\epsilon }_{LJ}$ has a negligible influence on the ballistic impact response of the Bouligand structure, but a high value may bring more noise to the force responses at high impact velocities [59]. Such settings are consistent with our previous study on continuous NFC films [1].

During the impact process, the NFC beads outside of the impact region are fixed, resembling the clamping boundary condition in previous experiments [60]. The NVE (microcanonical) ensemble is adopted during the impact process. The projectile is set rigid as there is no obvious deformation of the projectile during such micro-ballistic impact tests [20]. An initial velocity perpendicular to the film is given to the projectile to initiate the impact process. In determining the $V_{50}$ of the different NFC films, a series of initial velocities are assigned to the projectile in the trial tests, and we look for the lowest velocity to fully penetrate the film, which is our selection of $V_{50}$. To calculate $\Delta E_k$, we use impact velocities that are higher than $V_{50}$ of the films. Specifically, we have used three velocities, 400 m/s 500 m/s, and 1000 m/s, to measure $\Delta E_k$. For the purposes of measuring $V_{50}$ and $\Delta E_k$ with higher reliability, multiple simulations have been run for each case, and we use the average values in the figures and include the standard deviations as error bars.

3. Results and Discussion

In this section, we first study the effect of different configurations and identify a more representative one (Offset) for detailed examinations of the deformation mechanisms. We then highlight a few cases that show enhancement in impact resistance over the continuous fibril case. Next, we analyze the effects of pitch angle ($\gamma$), fibril lengths ($L$), and other factors on the dynamic deformation mechanisms of NFC films under projectile impact and discuss their roles in altering the failure mechanisms and impact resistance. Our previous study has shown that NFC films with different $\gamma$ show non-negligible differences in film density ($\rho$) [1]. Therefore, we use the specific ballistic limit velocity ($V_{50}/\rho$) and penetration energy ($\Delta E_k/\rho$) to assess the impact resistance of different NFC films.

3.1. Effect of different configurations on impact resistance and the role of impact velocities.

Projectile impact simulations were first conducted on all four configurations as they provide a wider scope of impact failure mechanisms to study within the NFC films. By comparing their performance in terms of $V_{50}/\rho$ and $\Delta E_k/\rho$, we aim to determine a suitable initial impact velocity for assessing $\Delta E_k/\rho$ of different films and look into the influence of specific configurations on the films’ impact resistance.

Fig. 3 compares the impact resistance of NFC films with different configurations and constant $L=500nm$. Fig. 3 (a) plot $V_{50}/\rho$ results and Fig. 3 (b)–(d) show $\Delta E_k/\rho$ results at three different initial impact velocities for all different configuration cases considered herein. We find that $V_{50}/\rho$ results (Fig. 3(a)) exhibit similar trend to $\Delta E_k/\rho$ at impact velocity of 400 m/s (Fig. 3(b)). We also find that the energy absorption level of the films cannot be discriminated against under an impact velocity of 1000 m/s (Fig. 3(d)). This is due to under high-velocity projectile impacts, films primarily absorb energy through local tearing around the projectile rim and fragmentation within the projected volume, while energy absorbed through other failure mechanisms is negligible. This phenomenon happens when the films are not able to delocalize the high stress at the impact site to a larger deformation zone before local penetration [51]. By considering $V_{50}/\rho$ as an intrinsic impact resistance characteristic, our results show that $\Delta E_k/\rho$ at lower initial impact velocity reflects the intrinsic impact resistance of NFC films. This observation is consistent with our previous study on 2D materials and polymer thin films [51]. Therefore, we select the initial impact velocity of 400 m/s to compare $\Delta E_k/\rho$ of NFC films with different structures in the rest part of this study.

Figure 3.

$V_{50}/\rho$ (a) and $\Delta E_k/\rho$ of NFC films with different DFB configurations and constant $L=500nm$ at initial impact velocity of 400 m/s (b), 500 m/s (c), and 1000 m/s (d). The error bars mark the standard deviations from five simulation runs.

Then, we investigate how different configurations affect discontinuous films’ impact resistance. Fig. 3 (a) and (b) show that the Offset configuration films have higher $V_{50}/\rho$ and $\Delta E_k/\rho$ than films with other configurations at a large range of pitch angles considered herein, and films with the Middle configuration have the worst performance in terms of $V_{50}/\rho$ and $\Delta E_k/\rho$. These results indicate that the Offset configuration can best lead to enhanced impact resistance in general. Intriguingly, films with Random TT and Random IP configurations are superior at lower pitch angles like 0° and 18°. By examining the simulation trajectories, we find that Random TT and Random IP films uniquely utilize fibril breaking near the edge of the film to absorb energy, as shown in Fig. 4 (a) and (b). Additionally, the Random TT film shows crack bridging mechanisms in the through-thickness direction as the discontinuous sites are randomly shifted among different layers. Furthermore, it is expected that more fibril sliding events can occur in the Random IP film at small pitch angles as the smaller overlap length can lead to smaller energy barriers of fibril sliding. We should also note that the superior performance of Random IP and TT configurations compared to the Offset at lower pitch angles may also be due to the specific $L$ used herein, when the fibril sliding and crack bridging mechanisms aforementioned contribute significantly to the intrinsic impact resistance. With a different $L$, their contribution likely changes, and the effect of configurations on impact resistance can be altered as well.

Figure 4.

Top view of films with (a) Random TT and (b) Random IP configurations with $\gamma =0°$ and $L=500\mathrm{n}\mathrm{m}$. The insets highlight the failure mechanisms – edge cracking, through-thickness crack bridging, and fibril sliding – present in these two configurations.

Because the Offset configuration outperforms other configurations in a broader range of $\gamma$ and has a more deterministic fibril overlap length and structural pattern, we focus on the Offset configuration in the next section. Specifically, we conduct a thorough investigation into the effects of $L$ and $\gamma$ and expand the discussions on the roles of different failure mechanisms in the subsequent sections.

3.2. Impact resistance of NFC films with Offset configuration.

We characterize and compare the impact resistance of NFC films with Offset configuration and varying $L$ in the range of 50–1750 nm. Specifically, we measure $V_{50}/\rho$ and $\Delta E_k/\rho$ at 400 m/s of different films and investigate the detailed failure mechanisms during the ballistic impact process. To compare the impact resistance of NFC films with DFB architecture and those with continuous nanofibrils, i.e., consisting of Bouligand architecture only (from our previous study [1]), we can examine whether the DFB architecture with hybrid Bouligand and staggered structures has an advantage over Bouligand architecture only.

The explicit values and trends of $V_{50}/\rho$ and $\Delta E_k/\rho$ for NFC films with DFB architecture with different $L$ (x-axis) and $\gamma$ (different colors in the legend) are shown in Fig. 5 (a) and (c). In Fig. 5 (b) and (d), we further plot the normalized $V_{50}/\rho$ and $\Delta E_k/\rho$ values, where the values in Fig. 5 (a) and (c) are scaled by the corresponding values of continuous NFC films that were obtained in our previous study [1]. Thus, a normalized value larger than 1 indicates better performance in impact resistance. It is worth noting that for the shortest $L=50\mathrm{n}\mathrm{m}$ (i.e., $L_0=25nm$) used in this study, the overall impact resistance of NFC films with DFB architecture still achieves 50%~80% of that of continuous NFC films. Our previous study showed that with $L_0=25nm$, unidirectional NFC nanopaper can achieve approximately 50% of the stiffness and strength of the continuous counterparts [49]. We note that additional factors, such as Bouligand structures in the thickness direction and offset configurations, can also contribute to the overall impact resistance of NFC films made of relatively short nanofibrils. This observation further demonstrates the effectiveness of DFB architecture in achieving excellent impact resistance despite using relatively short nanofibrils.

Figure 5.

The absolute (a) and normalized (b) $V_{50}/\rho$ values of the NFC films with DFB architecture. The absolute (c) and normalized (d) $\Delta E_k/\rho$ values of the NFC films with DFB architecture at an initial impact velocity of 400 m/s. The error bars mark the standard deviations from five simulation runs.

Interestingly, most NFC films with DFB architecture and pitch angles ranging from 18° to 72° and $L$ larger than 750 nm show improved impact resistance than the corresponding continuous NFC films. Despite less than 10% enhancement, the results here are remarkable as we demonstrate discontinuous nanofibril assemblies can achieve greater impact resistance against localized, high-speed projectile impact than continuous fibril assemblies. This is counterintuitive as continuous (long) fibrils normally possess superior mechanical properties than discontinuous (short) fibril assemblies. Previous studies show that discontinuous nanofibril/platelet assemblies can approach the mechanical strength and toughness of the continuous nanofibril/platelet assemblies as the length of nanofibril/platelet increases [49, 61]. Nevertheless, our study further demonstrates that by using discontinuous nanofibrils and adopting a DFB architecture, we can improve the impact resistance of NFC films compared to films made of continuous nanofibrils. Next, we look into the underlying mechanisms that explain the improved impact resistance.

3.2.1. Mechanisms that lead to the improved impact resistance of NFC film with DFB architecture.

When films undergo projectile impact, the presence of discontinuous sites allows the initiation of local cracks due to local high stress concentrations and fibril sliding starting at the discontinuous sites. Additionally, we have observed several toughening mechanisms, such as crack bridging and crack twisting, during the project penetration process in NFC films due to the hybrid design of Bouligand and staggered structures, as illustrated in Fig 6. We believe these toughening mechanisms contribute to the improved impact resistance of NFC films with DFB architecture compared to films with continuous fibrils. Previous studies showed that crack twisting and crack bridging were the two main toughening mechanisms, and the inclusion of discontinuous sites essentially increases the possibility for these failure mechanisms to occur [2, 45, 46]. It is important to note that these failure mechanisms are strongly correlated with each other, and some of them can happen simultaneously.

Figure 6.

(a) Bottom view (i.e., view from the back side) of the NFC film with Offset configuration, $\gamma =30°,$ and $L=750\mathrm{n}\mathrm{m}$. (b) A detailed sectional view of the film shows the deformation away from the impact site. (c) Demonstration of the long-twisted crack path due to crack twisting. (d) The enlarged schematic diagram highlights fibril sliding and crack bridging mechanisms.

More specifically, intralayer fibril sliding can initiate at discontinuous sites that are away from the impact site due to the development of the impact-propagation zone [51]. Such sliding events can help dissipate impact energy through inter-fibril frictions. Fibril sliding events may lead to intralayer crack opening within NFC films, which usually involve the crack bridging mechanism resulting from the staggered nanofibrils (Fig. 6 (d)). We note crack bridging mechanism promotes impact resistance of the films by dissipating additional impact energy when cracks propagate [62, 63]. In addition, crack bridging mechanisms also exist in interlayer deformation. As shown in Fig. 6 (d), when the cracks propagate in the top layer as fibrils sliding, the fibrils in the layer below also function as bridges to decelerate the crack opening while dissipating energy. Moreover, interlayer fibril sliding and intralayer fibril sliding may compete with each other to occur, where the outcome is also influenced by the geometric factors of the films (i.e., $L$ and $\gamma$), as discussed later. Previous studies have similarly shown that crack bridging mechanism alleviate stress from crack tips which allows stable growth of cracks instead of immediate propagation in an unstable (often catastrophic) fashion [54][56].

Crack twisting is another failure mechanism observed in a large portion of NFC films during projectile penetrations. Previous studies indicate that crack twisting is generated by small pitch angles between adjacent layers that direct cracks to propagate along longer paths and thus enhance the impact resistance of Bouligand architectures [62, 64, 65]. The twisted cracks follow the fibril orientations in Bouligand architectures. In the NFC films with DFB architecture, we find that the introduction of discontinuous sites that are interconnected but along different orientations because of pitch angles has the potential to further increase the twisted crack paths. Fig. 6 (b) demonstrates that as fibrils slide in the top layer, which results in the in-plane crack, the fibrils in the adjacent layer also start to slide following the orientation of discontinuous sites and lead to a crack opening in that layer. Then, the crack opens in the next layer by following the same pattern so on and so forth, which creates a twisted crack with elongated crack paths, as illustrated in Fig. 6(c). In summary, we find that in the NFC films with DFB architecture, fibril sliding across different layers triggers a combination of crack bridging and twisting mechanisms, which enable enhanced energy dissipation. Based on the findings here, we hypothesize that the enhancement in impact resistance by adopting DFB architecture can be potentially increased when the system size becomes even larger and additional hierarchies are introduced to the NFC films. We plan to test this hypothesis in our future study.

3.2.2. Effect of fibril lengths.

In this section, we discuss the effect of fibril lengths ($L$) on the energy dissipation of the NFC films with DFB architecture. According to Fig. 5 (b) and (d), for all pitch angles, both $V_{50}/\rho$ and $\Delta E_k/\rho$ at 400 m/s increase drastically as $L$ increases from 50 nm to 750 nm and then saturate for larger $L$. The normalized $V_{50}/\rho$ and $\Delta E_k/\rho$ follow a similar trend, and certain $\gamma$ lead to better performance than the corresponding films with continuous NFC, as discussed in previous sections. In this section, we mainly discuss the reasons that contribute to improved impact resistance as $L$ increases initially.

The stress distribution of a film under projectile ballistic impact was previously experimentally studied [66], and these experiments show that as a projectile makes initial contact with the film, the stress exerted on the impact site is the greatest. The magnitude of stress decreases radially towards the edge of the film. When $L$ is small (i.e., below 200 nm), the impact site consists of high-density discontinuous sites. Therefore, the film easily falls apart, and its impact resistance is significantly lower. Shown in Fig. 7 (a)–(d), the number of discontinuous sites within the developed impact propagation zone during impact decreases as $L$ increases from 50 nm to 750 nm and then completely disappears with a further increase of $L$. This likely explains the saturation of $V_{50}/\rho$ and $\Delta E_k/\rho$ beyond $L=750\mathrm{n}\mathrm{m}$. We thus term $L=750\mathrm{n}\mathrm{m}$ as the critical $L$ in terms of impact resistance in our case. From the simulation trajectory, we also find that more significant fibril sliding away from the impact site can be observed as $L$ becomes larger than 250 nm. Also, the fibrils tend to slide for longer distances in films with larger $L$. Moreover, films with larger $L$ lead to longer twisted crack paths, which further enhances energy dissipation capability. In summary, NFC films with shorter fibrils (relative to the size of the projectile) mainly exhibit local deformation and penetration under the projectile impact, and the energy dissipation capability is limited. However, when the fibrils become significantly longer compared to the impact propagation zone, the NFC films can activate additional failure mechanisms such as fibril sliding, crack twisting, and crack bridging to enhance the energy dissipation capability.

Figure 7.

Bottom views of NFC films with Offset DFB configuration under an initial impact velocity of 400 m/s. In (b)-(d), the deformations away from the impact site are highlighted in the insets. The $\gamma$ and $L$ are specified for each film.

3.2.3. Effect of pitch angles.

In this section, we discuss the effect of pitch angle ($\gamma$) on energy dissipation of the NFC films with DFB architecture. We focus on the films with $L$ that exceed the critical $L$ as the $V_{50}/\rho$ and $\Delta E_k/\rho$ results saturate for larger $L$ and show low standard deviations. We note that for these cases, the defects are away from the impact site and are scattered in terms of both intralayer and interlayer for non-0° $\gamma$ cases. Fig. 5 shows that $\gamma$ plays a key role in the energy dissipation of the films, but unlike the effect of $L$, there is not a clear trend for impact resistance of the films with increasing $\gamma$. This finding is nontrivial as it cannot be simply explained by the concentration of defects and their proximity to the impact site. Specifically, films with $\gamma$ ranging from 18° to 72° exhibit consistently higher $V_{50}/\rho$ and $\Delta E_k/\rho$. Among these, the film with $\gamma =30°$ shows the greatest $V_{50}/\rho$ and $\Delta E_k/\rho$, while the films with 0° pitch angle have the worst impact resistance. We note that our previous study with continuous fibrils showed similar results [5, 63]. Also, the normalized $V_{50}/\rho$ and $\Delta E_k/\rho$ at 400 m/s exceed 1 for films with $\gamma$ ranging from 18° to 72° and $L$ exceeding the critical $L$, as discussed previously. From our results, 30° is found to be the optimal $\gamma$ for NFC films with DFB architecture. It is worth mentioning that when DFB architecture is subjected to different loadings, the optimal $\gamma$ may vary [2, 67, 68].

We think it is also important to understand why NFC films with $\gamma =0°$ and 90° exhibit lower energy dissipation and fail to outperform their continuous film counterparts. For $\gamma =0°$, the Offset configurations give rise to aggregated discontinuous sites through the thickness. Therefore, the discontinuous sites function as major defects in the films and lead to little resisted crack opening through the thickness, as illustrated in Fig. 8 (a). Therefore, NFC films with DFB architecture at $\gamma =0°$ show poor impact resistance. Our results indicate that it might be a good design strategy to disperse fibril ends or defects within films instead of making them aggregated to achieve better impact-resistant films. For $\gamma =90°$, where fibrils align perpendicularly in the thickness direction, the adjacent layers have minimal crack bridging or twisting effects since fibrils in adjacent layers only interact through weak inter-fibril adhesions along the crack opening direction, as shown in Fig. 8 (b). By visualizing the simulation trajectory, we only observe significant fibril sliding in the top two layers while localized penetration in other layers. Moreover, we find that the cracks stop propagating in twisted paths, and instead, they grow in vertically straight paths [23, 69]. Therefore, minimal interlayer crack bridging, less fibril sliding, and the lack of crack twisting mechanism collectively lead to the limited energy dissipation capability of the $\gamma =90°$ cases.

Figure 8.

(a) The illustrated crack path for $\gamma =0°$ film, where discontinuous sites are at the same location for adjacent layers, leading to little resisted crack opening through the thickness. (b) The illustrated crack path for $\gamma =90°$ film, where the interlayer crack bridging only comes from weak inter-fibril adhesions along the crack opening direction.

Conversely, we find that NFC films with $\gamma$ ranging from 18° to 72° utilize a combination of fibril sliding, crack bridging, and crack twisting to enhance their energy dissipation. With increasing $\gamma$ in this range, we also notice a competition between fibril sliding and crack twisting mechanisms. Specifically, as fibril sliding becomes more significant in a specific layer, more energy is dissipated through this intralayer mechanism. At the same time, through-thickness twisted cracks become less likely to happen, leading to a reduction of energy dissipation in the thickness direction. When $\gamma =30°$, we see the largest fibril sliding magnitude across the layers (shown in Fig. 7(c)), and in the meantime, significant crack twisting is observed across the layers. Therefore, we postulate that the optimal performance in $\gamma =30°$ is attributed to the fact that it has the most effective combination of fibril sliding, crack bridging, and crack twisting mechanisms.

4. Conclusion

NFC is a promising bio-derived building block to construct impact-resistant films with bioinspired structures. Our study demonstrates that using discontinuous cellulose nanofibrils and adopting specific DFB architecture for the NFC film can outperform the continuously long fibrils in terms of impact resistance against projectile impact. The specific requirements for the DFB architecture found in this study include achieving critical $L$ and adopting certain configurations that minimize the discontinuous sites (defects) within the impact site as well as applying an optimal $\gamma$. We find that the Offset configuration is generally superior to other configurations considered in this study, and the critical $L$ is 750 nm, which is correlated with the size of developed impact propagation zone upon the projectile impact. With $L$ larger than 750 nm, the $V_{50}/\rho$ and $\Delta E_k/\rho$ values start to saturate. We also find that among all the $\gamma$ considered, $\gamma =30°$ usually gives rise to the highest $V_{50}/\rho$ and $\Delta E_k/\rho$. By looking into the deformation mechanisms during the projectile impact, we find that the DFB architectures utilize a combination of fibril sliding, crack bridging, and crack twisting to enhance their energy dissipation. Also, there seems to exist internal competition between different mechanisms, particularly between fibril sliding and crack twisting. The optimal architectures identified in this study ($L\ge 750\mathrm{n}\mathrm{m}$ and $\gamma =30°$) are found to possess the best combination of different mechanisms.

Following this study, we have identified additional work that needs to be done to achieve a comprehensive understanding of the structure-property relationship of NFC films with DFB architecture. First, additional simulations with varying projectile sizes and shapes are needed to fully understand how the critical $L$ is correlated with the projectile size and other geometrical factors. We note that theoretical relationships used in our previous studies can be utilized to unravel such size dependences [49, 51, 61]. Second, additional configurations, such as Offset in the thickness direction and Random in both IP and TT, can be considered to see if they offer even better impact resistance against projectile impact. Lastly, it would be interesting to examine other mechanical properties, such as toughness and flexibility, and check whether DFB architecture shows any advantages in improving these properties.

Overall, we believe our study demonstrates the improved ballistic impact resistance of NFC films with hybrid DFB architecture and unravels the underlying mechanisms. The insights from this study have the potential to guide the future design of protective films made of nanofibrils.