Dynamic mechanical behavior of multilayer graphene via supersonic projectile penetration

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Science  28 Nov 2014:
Vol. 346, Issue 6213, pp. 1092-1096
DOI: 10.1126/science.1258544


Multilayer graphene is an exceptional anisotropic material due to its layered structure composed of two-dimensional carbon lattices. Although the intrinsic mechanical properties of graphene have been investigated at quasi-static conditions, its behavior under extreme dynamic conditions has not yet been studied. We report the high–strain-rate behavior of multilayer graphene over a range of thicknesses from 10 to 100 nanometers by using miniaturized ballistic tests. Tensile stretching of the membrane into a cone shape is followed by initiation of radial cracks that approximately follow crystallographic directions and extend outward well beyond the impact area. The specific penetration energy for multilayer graphene is ~10 times more than literature values for macroscopic steel sheets at 600 meters per second.

Graphene: A miniature bulletproof vest?

To stop a speeding projectile, you need a combination of strength and toughness so that the impact doesn't just pierce the stopping material. The material also needs to dissipate the absorbed kinetic energy. Lee et al. measured the response of multilayer graphene to the projection of microbullets using miniaturized ballistic tests. The findings confirm graphene's exceptional strength and stiffness.

Science, this issue p. 1092

Graphene, the atomic monolayer building block of graphite, is known for its exceptionally high intrinsic strength and stiffness arising from the two-dimensional (2D) hexagonal lattice of covalently bonded carbon atoms. Recently, graphene’s in-plane Young’s modulus (Y) was measured to be more than 1.0 TPa using atomic force microscope nanoindentation (1). Because tensile mechanical stresses in a material cannot be transmitted faster than the speed of sound [c ~ (Y/ρ)1/2, where ρ is the density of the material], the nonequilibrium local stress arising from the inertial effect becomes important under dynamic conditions accompanying high–strain-rate, predominantly tensile loading (2). In this regard, the relatively low density (~2200 kg m−3) of graphene (3), along with its high modulus, leads to a superior in-plane speed of sound (c ~ 22.2 km s−1), implying that concentrated stresses applied under extreme conditions can rapidly be delocalized.

Nanoindentation has served as an effective technique to study the tensile mechanical properties of monolayer graphene. It is inherently a low-speed test (<<1 m s−1), but strain rates can reach ~105 to 106 s−1 for very thin samples (4), whereas most high-speed, high–strain-rate mechanical characterization techniques, such as split-Hopkinson pressure bar (5) and ballistic tests (6), are inappropriate for testing very thin specimens. To address high-speed and high–strain-rate tensile-dominated penetration of thin films, we improved our laser-induced projectile impact test (LIPIT) (7). In this advanced LIPIT (or “α-LIPIT”), a single micrometer-size solid silica sphere (or “μ-bullet”) is fired at a high speed (<3 km s−1) with a high aiming accuracy (<1.1° deflection) toward a thin film. The velocity of the μ-bullet is measured before and after penetration to determine the energy lost during the test. We employed multilayer graphene (MLG) membranes in a range of thicknesses (10 to 100 nm, equivalent to 30 to 300 graphene layers) to apply localized, very–high–strain-rate tensile deformation (~107 s−1) at a specific area. As the thickness of the MLG membranes (h) is always considerably less than the diameter (D) of a μ-bullet (D/h ≥ 40), the high–strain-rate in-plane tensile behavior of MLG can be assessed from the thickness-dependent characteristics of the energy required for projectile penetration through the membrane.

The MLG membranes are prepared by mechanical exfoliation of highly ordered pyrolytic graphite (grade SPI-1, SPI Supplies; fig. S1), as shown in Fig. 1A. A silica μ-bullet [D = 3.7 ± 0.02 μm, based on imaging by scanning electron microscopy (SEM)] is propelled by expanding gases created by the laser ablation of a gold film (~50 nm thick). A 20-μm-thick elastomeric layer of cross-linked polydimethylsiloxane is used to confine the ablation products, eliminates the temperature rise of the μ-bullet, and diminishes the strength of the shock waves propagating through air. The impact speed (vi) is measured (with the reproducibility of vi within ± 2%) using a triple-exposure photograph of the moving μ-bullet with ± 10 m s−1 error, where the time gap between the three exposures is achieved by employing different travel distances for each laser pulse (fig. S2). The residual speed (vr) of the μ-bullet is similarly measured after the μ-bullet has traveled a certain distance (d) beyond the membrane (Fig. 1B). An average thickness (have) of the impact area was determined using a thickness-dependent optical transmittance measurement (fig. S3) given by an analytical formula (8) and the optical parameters of graphite (9). An additional postpenetration image allowed identification of the penetration area (Fig. 1C).

Fig. 1 The microballistic experiment.

(A) Scheme of the experiment. PDMS, polydimethylsiloxane. (B) Side-view image of a moving μ-bullet taken by triple exposure at time steps t1 to t3. (C) MLG membrane on a sample holder after α-LIPIT. Three separate impact test regions are highlighted by green backlight. (D) Schematic illustration of penetration steps: (i) prepenetration stage; (ii) conic deformation stage; (iii) fracture stage; and (iv) postpenetration stage, showing the film morphology after penetration and relaxation. Scale bars in (B) and (C), 50 μm.

The schematic in Fig. 1D depicts the series of events during penetration accompanying the kinetic energy loss of a μ-bullet (ΔEk). As the μ-bullet impacts a strike face area (As = πD2/4), an elastic wave radially propagates at c and a conic deformation of the MLG membrane follows with a radial speed of its base, vc, which is generally slower than c (step ii). The primary force is axisymmetric tension with a strong radial gradient and results in the cone shape. Typically, three to six cracks are initiated near the center of As and propagate outward in the radial direction (step iii), resulting in the creation of the same number of petals. The transferred momentum to the MLG membrane induces creasing and folding of each triangular-shaped petal at its base while the elastic extension of the membrane is rapidly relaxed along the radial direction via snap-back (step iv). The longest crack from the impact center is defined as the maximum crack distance, Lmax, which we use as the estimation of the final radius of the conic deformation due to the reduction of the tangential stress. ΔEk is composed of two terms, the net energy to penetrate a membrane (Ep) and the energy loss due to air drag (Eair). Ep depends on various energy dissipation mechanisms including elastic stretching of the membrane, fracture, and heating, as well as the kinetic energy transfer to the membrane petals and membrane debris.Embedded Image (1)As the mass of a μ-bullet, m is calculated to be 5.0 ± 0.1 × 10−14 kg, based on the measured diameter D and the density of silica (1900 kg m−3) provided by its vendor (microParticles GmbH). The incident Ek is 9 nJ at 600 m s−1 and 21 nJ at 900 m s−1 while ΔEk is in the range of 1 to 5 nJ. The measured deceleration by air drag (aair) is ~0.6 × 108 m s−2, assuming constant deceleration, which yields Eair = maaird ~1.07 nJ for d ~ 350 μm (the travel distance of a μ-bullet after penetration when we take the triple exposure). Therefore, the primary contribution to the kinetic energy loss is the net energy to penetrate a MLG membrane (Ep) under our experimental conditions.

The MLG membranes had a typical lateral grain size of ~10 μm. Due to the stress concentration at the impact site, the grain boundary effects (10, 11) (if any; see the supplementary materials) would occur only if the grain boundaries exist within As. As the ratio, D/h is quite large (40 to 350), the mechanical response of the MLG film depends primarily on its in-plane tensile strength under a high strain rate. A typical penetration hole features a set of petals (Fig. 2). The area directly beneath the μ-bullet impact shows extensive damage through complex, fine-scale fractures, folding, delamination, and loss of parts of the membrane (indicated by the yellow arrowheads). As the initiation of the radial cracks may not be exactly at the impact center, asymmetric shaped petals are often observed (e.g., Fig. 2, A and D). The damage area is thus much wider than As, in strong contrast to the observed behavior of polycrystalline gold and amorphous, glassy poly(methyl methacrylate) (PMMA) membranes, in which penetration results in a circular hole with an area of ~As (see figs. S6 and S7). Correspondingly, a much smaller penetration energy is measured.

Fig. 2 Representative penetration features of MLG membranes.

(A and B) SEM images of petals, radial cracks, folds, and snap-back damage to the petal tips and (C) the adjacent crack-pair angle distribution for vi = 600 m s−1. (D and E) SEM images and (F) the adjacent crack-pair angle distribution for vi = 900 m s−1. The inset in (F) shows the armchair (red) and zigzag (green) directions. The circles in the SEM images show As. Scale bars in (A), (B), (D), and (E), 5 μm.

Many independent penetration experiments (47 events for vi = 600 m s−1 and 43 events for vi = 900 m s−1) were carried out for statistical analysis (figs. S4 and S5). The average apex angles (θA in Fig. 1D) of petals for the 600– and 900–m s−1 projectile velocities are 83 ± 21° (for 107 cracks) and 70 ± 23°(for 93 cracks), respectively, indicating that the higher tangential stresses induced at 900 m s−1 were relaxed through more radial cracks. Despite the in-plane isotropic elastic nature due to the approximate sixfold symmetry of graphene (12), the preferential crack propagation directions Embedded Image (the armchair direction) and Embedded Image (the zigzag direction) cause preferred angles between adjacent cracks to be a multiple of 30° (13). Correlation to the underlying crystallographic orientation of the membrane is noted in the distribution of the angle between adjacent cracks displaying preferences for small multiples of 30° (Fig. 2, C and F).

Transmission electron microscopy (TEM) was carried out on snap-back portions of the petal regions of thin (have ~ 10 nm) fractured membranes (Fig. 3). The bright-field TEM image shows complicated local folding of the membrane near the penetration (Fig. 3, A and B). The higher-magnification dark-field image shows bend contours and moiré fringes (upper left and left center regions in Fig. 3C, resulting from the interference of electrons scattered from superposed folded MLG regions; see diffraction pattern insets in Fig. 3C). In the extensively folded region nearest the impact origin, a fine-scale mosaic structure is evident in both the electron diffraction pattern and dark-field images due to the deformation resulting from the rapid elastic relaxation (i.e., petal snap-back).

Fig. 3 Damage features of a thin MLG membrane.

(A) Bright-field TEM micrograph of the impact region (have ~ 10 nm) for vi = 900 m s−1. (B) Higher magnification of the petal apex area indicated by the red arrowhead in (A). (C) Three dark-field TEM micrographs are overlaid to show bend contours, rotation-tilt moiré fringes, and a fine-scale mosaic texture resulting from snap-back and membrane folding. The two diffraction patterns show (C1) a typical hexagonal spot pattern of the undeformed film and (C2) the altered, multireflection-satellite spot pattern from near the impact region. The red and blue regions correspond to imaging with Embedded Image, and the green region corresponds to Embedded Image. Scale bars, (A) 5 μm; (B) and (C), 0.5 μm. The voidlike features at the upper left in (A) are a result of residual water-soluble polymer from film preparation.

Despite a relatively wide fluctuation in Lmax, its lower limit is well fit by 0.1have + D/2 (Fig. 4A). The film thickness inhomogeneity is represented by the coefficient of variation (CV) of the local thicknesses measured over a circular area (radius r = Lmax). MLG membranes that have CV > 10% in the impact area clearly lead to a greater fluctuation of Lmax. The radial speed of the circumferential base of the expanding cone-shape deformation region of a membrane can be approximated by vc ≅ 1.23c[vi/21/2c)]2/3 and thus scales with the cube root of the in-plane speed of sound in the material (14). Values for vc correspond to 1950 and 2560 m s−1 for impacts of 600 and 900 m s−1, respectively. An empirical estimation of deformation parameters is then possible by setting the lower limit of Lmax to the maximum radius of the cone, because the tangential tensile stress (Fig. 1D) is the origin of the radial cracks. For example, assuming a simple 1D model for a 900–m s−1 impact to a 50-nm-thick MLG membrane, we estimate the penetration time tpLmax/vc ~ 3 ns; the 1D-approximate average maximum tensile strain εmax ≅ (vitp/Lmax)2/2 = ~6%, close to the lower boundary of the reported failure strain range, 5 to 25% (1, 15, 16); and the 1D-approximate average tensile strain rate as given by the maximum strain divided by the penetration time or Embedded Image s−1. A further discussion of the estimation of strain and strain rate is available in the supplementary materials.

Fig. 4 Analyses of microballistic results.

(A) Maximum crack distances in MLG membranes of various thicknesses for the two different penetrator velocities. (B) Kinetic energy changes of a μ-bullet versus thickness after penetration of MLG membranes. Colors in (A) and (B) represent the thickness inhomogeneity (via CV) of the film in the impact area. (C) Specific penetration energy of MLG, PMMA, and gold membranes compared with macroscopic materials at various impact velocities. The density of each material is represented by a logarithmic color scale. Error bars denote SD.

From Eq. 1, ΔEk(have) can be fit with a linear function (Fig. 4B), where the y-intercept value corresponds to Eair. Therefore, the intrinsic energy dissipation of a MLG membrane is given by Ep(have) = 0.026have and 0.030have for the two velocities we employed, and a similar trend is also found in macroscopic ballistic tests (17, 18). For D/have >> 1, Ep can be expressed by two terms, Embedded Image, where the first term represents the minimum inelastic energy transfer to target material within As and Ed represents all of the other energy dissipation mechanisms. The specific energy dissipation, Embedded Image, which is insensitive to material density by taking account of the mass within Ashave, is given by Embedded Image, where Embedded Image is the specific delocalized penetration energy. Embedded Image is thus a figure of merit to evaluate the impact energy delocalization ability of a material as more sample mass beyond As contributes to the energy dissipation, whereas the material-independent energy dissipation term, Embedded Image, serves as a baseline.

Statistical values of Embedded Image for MLG, PMMA, and polycrystalline gold were determined from the fitted slopes of Ep versus have (Fig. 4B and figs. S6E and S7C). From this data (see square data points in Fig. 4C), MLG exhibits the highest Embedded Image (or Embedded Image), namely 1.26 MJ kg−1 (or 0.86 MJ kg−1) at 900 m s−1, compared with 0.58 MJ kg−1 (or 0.19 MJ kg−1) for gold and 0.52 MJ kg−1 (or 0.08 MJ kg−1) for PMMA. We also calculated Embedded Image from previous macroscopic ballistic tests of several materials: PMMA (19), aluminum (20, 21), steel (22, 23), and Kevlar KM2–polyvinyl butyral (PVB) composite fabric (24). These macroscopic tests used a millimeter-scale spherical steel projectile to penetrate a thin sheet (0.4 < h < 6 and 1 < D/h < 20) without appreciable deformation of the projectile (table S1). The overall trend of Embedded Image is quite similar, despite the large differences in the microscopic α-LIPIT and traditional macroscopic tests and the huge range in tensile modulus, strength, and density among PMMA, aluminum, and steel. This implies that the principal energy dissipation mechanism for the three macroscopic materials is the kinetic energy transfer from the projectile to the target material within As (i.e., to the mass ρAsh), which results in a dishing process (25). This is why the Embedded Image values of PMMA and gold from α-LIPIT also follow this trend and indicate a good correspondence between the micro- and macroscopic high–strain-rate evaluation methods for these materials, which also display localized penetration via a dishing process.

However, the two highly anisotropic layered materials—the Kevlar KM2-PVB composite fabric and the MLG membrane—deviate strongly from this trend. The Kevlar KM2-PVB composite is an armor-grade laminate made of strong, stiff polyaramid fibers (strength ~ 4 GPa, Y ~ 84 GPa, c ~ 7.6 km s−1) embedded in PVB resin (26). The planar fourfold symmetric high-stiffness woven polyaramid multilayer fabric shows an extensive conelike deformation under ballistic impact, and the higher Embedded Image (or Embedded Image) values (see blue triangles in Fig. 4C) can be understood by the contribution of large sample mass well beyond the impact area to energy absorption (27). Similarly, the superior value of Embedded Image for MLG (see green squares in Fig. 4C) can be explained by its ability to simultaneously be stiff, strong, and elastic, stretching into a cone shape due to the force imparted by the forward moving projectile. As a result, the Embedded Image values of the MLG membrane (0.92 and 0.86 MJ kg−1 for 600 and 900 m s−1) substantially surpass those of steel (0.08 and 0.11 MJ kg−1) at the same vi. Therefore, the MLG demonstrates specific delocalized penetration energy 8 to 12 times higher than that of steel due to the strong delocalization behavior at these impact speeds. As the higher delocalization effect results in a wider penetration hole, this tendency could be disadvantageous in certain aspects such as multi-hit capability. However, this potential weakness of MLG will be substantially relieved when the crack propagation is deflected by forming a composite.

Our microscopic ballistic results reveal that the superior in-plane speed of sound, high strength, stiffness, and structural anisotropy make MLG an extraordinary armor material exhibiting excellent impact energy delocalization under a supersonic penetration event. Because material far beyond the strike face area can also consume kinetic energy from the μ-bullet while the MLG membrane sustains high dynamic tensile stress, the μ-bullet effectively experiences a higher areal density material. As large-scale production of graphene-based composite materials is becoming possible (28), other graphene-like materials are being studied (29), and the results suggest opportunities for the use of ordered anisotropic nanocomposites for surprising mechanical applications. The good correspondence between the micro- and macroscopic projectile penetration tests, especially in the measured specific energy absorption, suggests that the microballistic method with its high-energy resolution may offer an effective means for the exploration of high–strain-rate physics of various materials, as well as practical advantages in rapid, high-throughput testing.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S7

Table S1

Reference (30)

References and Notes

  1. Acknowledgments: This work was funded by the Defense Threat Reduction Agency under contract 1-12-10008 and the Welch Foundation grant C-1716.
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