By Maj. Levi Thomas, Maj. Ryan Kemnitz, Ryan Kinkade, Richard Nyquist, and Lt. Col. Derek Spear

U.S. Air Force Photo

Aircraft armor is typically heavy, but does it have to be? Many military missions today require heavy armor for enhanced survivability, but this “dead weight” also reduces aircraft performance in nearly every way. Additionally, while the geometry of traditional armor solutions has largely been limited to simple shapes, the increased accessibility of additive manufacturing (AM)—also referred to as 3-D printing—is presenting new possibilities for the types of geometries that can be made and fielded. These geometries include complex internal structures with increased strength-to-weight ratios. So, could such structures be employed to produce lighter, equally effective aircraft armor? In particular, could they be integrated into the load-bearing structure of the aircraft to save additional weight while also being able to retain their structural advantages under the high strain rates associated with ballistic impacts? If so, such a breakthrough could help mitigate the weight penalty associated with traditional aircraft armor and provide the military with a distinct edge in terms of aircraft survivability and performance.

Before AM structures can be considered for potential aircraft armor solutions, however, two pertinent questions must be answered:

  1. How do AM metals perform at the high strain rates present in ballistics?
  2. What internal structures are optimal for ballistic performance?

To address these questions, a research group at the Air Force Institute of Technology used an AM process to produce several armor samples with complex internal structures and, in collaboration with the 704th Test Group, tested their ballistic performance.


The complex internal structures discussed herein are visually similar to traditional honeycomb paneling—the lightweight structures made with a hexagonal internal layer often used in modern aircraft. Honeycomb paneling is an exception to the general truth that complex structures are more difficult to manufacture. That said, this paneling actually exhibits complexity in only two dimensions. Conversely, the next generation in lightweight structures with complex internal structure is a group called triply periodic minimal surface (TPMS). The internal structure of a TPMS can be thought of as a sine wave with periodicity in all three dimensions (see Figure 1), and these structures are subsequently “strong” in all three dimensions.

Figure 1. Illustration of One Type of TPMS Surface—the “Schwarz P” [1].

The first two TPMS shapes (Primitive and Diamond) were discovered by Hermann Schwarz in the 1860s, and several more (most notably the Gyroid) were discovered by Alan Schoen in the 1970s [2]. TPMS structures have been observed in natural settings. For example, Diamond structures have been found in beetle scales [3], and Gyroid structures have been found in butterfly wings [4]. However, these structures have also been found to be effective in man-made structures as well.

TPMS structures are uniquely suitable for modern part infills. The smooth continuity of TPMS structures results in reduced stress concentrations on AM parts [5]; and the TPMS construct can be tailored for different designs, mechanical requirements, and overall weight limitations, enabling optimized solutions for numerous applications, including the specialized field of aircraft armor.

Future helicopter designs, for example, could include bespoke TPMS layers integrated into a monocoque shell, providing lightweight armor as part of the structural skin. These TPMS layers would be implemented in aircraft structures in a “sandwich” configuration, between front and back plating, with the plating optimized for survivability against small-arms fire, for aerodynamics, or for structural strength.

Because of their periodic nature and smooth topology, TPMS structures are a competitive choice for part infills. Many TPMS infill types perform better under compression than traditional strut lattices [6]. Zhao et al. [5] found that TPMS structures of comparable geometry to body-centered cubic (BCC) lattices were superior to their strut-type counterparts under compression at 20% and 30% relative densities. The advantages of TPMS structures over strut-based structures stem from a reduction in stress concentrations as a result of the curvature [5].


Because a TPMS is without thickness, it can be represented in one of two structure types: sheet-type structures and skeletal-type structures. As illustrated in Figure 2, sheet-type structures are produced by simply thickening the surface itself, while skeletal-type structures are produced by filling a region defined by the surface. Because sheet structures have been shown to outperform skeletal structures of the same period and density, sheet structures were chosen for the testing described herein [6, 7].

Figure 2. Sheet and Skeletal Diamond Structures (Left); Sheet and Skeletal Gyroid Structures (Right).

TPMS structures promise significant structural advantages for lightweight applications, but much of the mechanical behavior of TPMS infills has yet to be characterized. Several recent studies have evaluated metallic TPMS structures in quasi-static compression [6–10]. Comparatively little, however, is known about their response to impact. Ballistic impact and response to high strain rates are critically important to characterize for applications such as aircraft armor.


All samples were additively manufactured through a form of laser powder bed fusion (LPBF) called selective laser melting (SLM). The SLM process involves using a laser to melt thin layers of metal powder. The laser is directed by computer instructions to melt areas of the powder bed, welding the metal powder into previously melted layers. Powder layer thickness, laser power, laser scanning speed, and laser scan spacing (or hatch spacing) are common user-varied parameters. After 3-D printing, all samples were removed from the metal build plates by wire electrical discharge machining (EDM). The samples were neither stress-relieved prior to removal from the build plate nor subjected to heat treatments after removal.

Figure 3 shows a single build plate on which both types of armor samples were printed. Each of these samples was printed from a powdered nickel alloy, either AF9628 or Inconel. For the impact testing, six cylindrical TPMS projectile specimens were fabricated using three different cellular designs: Diamond, I-WP, and Primitive.

Figure 3. Armor and Projectile TPMS Samples Inside a 3-D Printer (Left) and Close-Up of the Build Plate (Right).


All ballistics testing was performed at the 704th Test Group’s Range A at Wright-Patterson AFB. Half-inch tungsten carbide ball bearings, simulating traditional 0.50-cal. rounds, were fired at the TPMS armor samples by a nitrogen-powered gas gun (shown in Figure 4). The projectile velocity was measured before and after impacting the armor to determine the kinetic energy absorbed. In the second set of testing, the TPMS structures were themselves loaded into the gas gun and fired at a rigid plate for impact testing. This test setup was used as a suitable substitute for the Taylor-impact (or Taylor-anvil) test, with the aim of determining the time-dependent mechanical properties of the TPMS structures.

Figure 4. Pneumatic Accelerator for Half-Inch Ball Bearings, Which Simulate 0.50-cal. Rounds.

Digital image correlation (DIC) was used to determine the impact velocity of the ball bearings and the TPMS projectiles. For the ball bearings, DIC was used to measure the speed of the bearing before and after impact. The TPMS projectiles used DIC to determine the strain subjected to the specimen due to impact loading by finding the change in length of the specimen through the imagery, as well as to determine the change in projectile velocity. The change in velocity was then used to calculate the force, and subsequently stress, on the specimen using the force impulse balance shown in equation 1.


From the perspective of survivability, aircraft armor must absorb and dissipate the kinetic energy of the projectile. The size of the projectile’s cross section gives an estimate of the area over which the armor directly acts to absorb the projectile energy. Not surprisingly, this quotient yields units of energy per area—similar to an energy flux—and is an important parameter in the design of aircraft armor (see equation 2).

The functional form of this energy flux shows that the difficulty of stopping a projectile goes with its mass, the square of its velocity, and the inverse of its cross-sectional area.

The more conventional method of characterizing armor from ballistic impacts is the ballistic penetration velocity—or V50—as described by the Department of Defense Test Method Standard MIL-STD-662F [11]. The V50 testing procedure, which seeks to determines the velocity at which a projectile has a 50% probability of penetrating an armor sample, accounts for the projectile size and velocity and provides a reliable and defensible way of comparing different armor types during a single test campaign. A good example of its use is the prior work of McWilliams et al., where AM titanium and aluminum lattice structures were compared to their wrought plate counterparts [12]. The V50 procedure may, however, not result in comparable and repeatable results when different projectile types (e.g., 0.223-cal., 0.30-cal., or 0.50-cal. rounds) are used for testing because the size and mass of the projectile are not controlled with this method. This so-called energy flux of the projectile is, therefore, also an important parameter to report in ballistics and armor-penetration testing.

An armor type is considered superior if it has enhanced ballistic performance at a given weight or mass. Because all testing for this effort was performed with identical ball bearings, we consider energy absorption as the benefit and relative density as the cost.

To summarize the test matrix, two materials (AF9628 steel and IN-716 Inconel), three TPMS types (Gyroid, Diamond, and I-WP), and relative densities ranging from 10 to 18% were tested. The cell width (or period) of the TPMS structures was held constant, and no heat treatments were applied.


At the highest relative density, the AF9628 armor completely (or almost completely) arrested the projectiles, thereby providing an estimate of the V50 [11]. The Gyroid TPMS fully arrested the slowest projectiles, but shots with higher entrance velocities penetrated with linearly increasing exit velocity. Due to the linear nature, we can estimate a lower bound for the V50 of the AF9628 Sheet Gyroid armor of 242 m/s (541 mph). We can likewise estimate an upper bound for the V50 for the of AF9628 Sheet Diamond armor of 259 m/s (579 mph) with the average of the seven projectile velocities, as only one of the recorded shots penetrated.

While velocity can be directly measured, it is ultimately the kinetic energy of the projectile that the armor must dissipate into strain work and heat to arrest the half-inch (0.50-cal.) tungsten ball bearing. Data from the 18% relative density tests provide a lower bound that these specific armor samples cannot reliably arrest a 0.50-cal. round with more than 525 J. Past this lower limit, we see what appears to be a linear increase in the kinetic energy absorbed by the armor with increasing projectile velocity. Additionally, these data represent the performance of samples of different relative densities (10% to 18%), materials, and structures.

Figure 5 shows the kinetic energy absorption profile and partitions the data into two groups based on the entrance velocity. Although the data are somewhat sparse, we observe two distinct linear relationships in ballistic performance. The strong R2 values in these two groupings indicate a high degree of correlation between relative density and energy absorption for that group of data.

Figure 5. Kinetic Energy Absorption Profile With Shots Grouped Based on Projectile Velocity.

Generally, the ability of a cellular structure to absorb energy during loading is found by determining the design’s toughness. In considering the ability of these TPMS designs to absorb energy, there are several characteristics to note from the stress-strain response curves obtained as part of this study. First, the lower-relative-density Diamond specimen exhibited a balance between the plateau stress and densification point, which indicates that, of the specimens tested, this specimen would likely have absorbed the most energy. The I-WP designs both had higher plateau stress values (shown in Figure 6), but they also showed much earlier densification than the Diamond. Finally, the Primitive design displayed the lowest plateau stress values of the designs but exhibited a delayed densification when compared to the other two designs. This result indicates that the Primitive design would perform better in energy-absorbing situations if the relative density, and subsequent mass, were not an issue.

Figure 6. Yield Curve From an Anvil Test.

The lattice toughness can be estimated by determining the stress-strain response of the projectile under a high strain rate impact. Toughness is calculated as the area beneath the stress-strain response curve from the initiation of loading to the densification strain. This numerical integration is implemented using the trapezoidal rule (shown in equation 3), where the incremental lower bound is shown as a, and the incremental upper bound is shown as b.

As there were limited data points collected at the high impact velocity, incremental stress values were estimated using a linear fit between the experimental data. The results indicate that the Diamond lattice provides the highest toughness value, even with a lower relative density than the other lattices. Due to the atypical response present in the second Diamond projectile, both Diamond specimens had a nearly identical toughness value even with a 5.48% difference in relative density. The I-WP lattice provided the next highest toughness values, with a lower spread in toughness than relative density. For a 5.60% increase in relative density, the toughness for the I-WP rose only 2.23%. Finally, the Primitive lattice toughness was the lowest of the three lattices tested under impact conditions. There was was expected with the closeness in relative density of the two specimens.


Prior to this work, sheet-type TPMS structures were shown to outperform those of the skeletal type. From among these sheet-type structures, Gyroid, Diamond, and I-WP were chosen for ballistic testing. This testing suggests that the Sheet Diamond structures are well suited for ballistics, as they exhibited better performance in terms of energy absorption. The relative density of the TPMS structures was shown to have a nearly linear effect on energy absorption over the range of densities measured in this investigation, supporting the possibility of custom-tailored armor designs to optimize increased ballistic performance or decreased weight.

Finally, two different materials with different mechanical properties were tested. Although samples from the materials were tested at different relative densities, the strong Pearson’s correlation coefficient found supports that they belong to the same data group in exhibiting a linear relationship between relative density and kinetic energy absorption capability. Although this finding does not downplay the significance of the material’s mechanical properties, it does show that the effect of relative density may be the more important factor.

In addition, the anvil-type impact testing of projectiles incorporating TPMS designs provided a measure of engineering toughness. The results from this testing allowed for a more detailed analysis of how the different designs were being loaded under impact conditions despite the fact that the time and spatial resolution of the camera were insufficient for detailed analysis. The two factors that must be considered in determining the ability of a design to absorb energy are the stress values of the response, primarily in the plateau region, and the densification point. As the curves show, the Diamond TPMS design balances these two factors, where the I-WP exhibits higher stress values and the Primitive design delays densification. The Diamond also exhibited the highest toughness values. The results found here support the results of the ballistic testing with TPMS armor plates as targets; the Diamond TPMS design will absorb more energy than the other designs examined across the tested velocity and relative density range.

This initial work has briefly explored some exciting new possibilities for lightweight aircraft armor solutions. Using the mathematical concept of a TPMS, AM armor samples were successfully produced and then ballistically tested under conditions representative of modern small-arms fire. Based on the positive performance demonstrated by some of these TPMS structures, a promising new option has been shown to exist for next-generation aircraft armor research, development, and acquisition.


Maj. Levi Thomas is an adjunct professor in the Department of Aeronautics and Astronautics at the Air Force Institute of Technology (AFIT). Specializing in high-speed optical experiments, his research and development experience has ranged from the Air Force Research Laboratory to the German Aerospace Center. Maj. Thomas holds a bachelor’s, master’s, and doctorate in engineering from the U.S. Air Force Academy, AFIT, and Purdue University, respectively.

Maj. Ryan Kemnitz is an assistant professor at AFIT, leading the metal additive manufacturing laboratory and conducting research in refractory metal alloy development. He holds a bachelor’s and master’s in mechanical engineering from the U.S. Air Force Academy and the University of Utah, respectively, and a doctorate in materials science from AFIT.

Mr. Ryan Kinkade is a recent graduate from AFIT with experience in additive manufacturing, high strain rate experimentation, and research on refractory metals. He holds a bachelor’s in mechanical engineering and a master’s in materials science from Wright State University and AFIT, respectively.

Mr. Richard Nyquist is a master’s student in aeronautical engineering at AFIT. He has three professional SolidWorks certifications and research experience in material science and robotics. He holds a bachelor’s in mechanical engineering from Cedarville University.

Lt. Col. Derek Spear is a recent graduate of AFIT, with his research focused on the time-dependent response of additively manufactured lattice structures for use in energy absorption applications under high strain rates. He has a bachelor’s in aeronautical engineering from the U.S. Air Force Academy; master’s degrees in aviation systems and aerospace engineering from the University of Tennessee and North Carolina State University, respectively; and a doctorate in aeronautical engineering from AFIT.


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