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# Turning Bullets into Baseballs

Scientists at Southwest Research Institute are developing a better body armor to protect law enforcement and military personnel.

 As part of a program for the U.S. Army, SwRI engineers are examining ceramic and backing fabric materials, as well as new geometries, to help reduce the weight of body armors. In this photo, a number of ceramics and fabrics used in modern armors surround two sectioned aluminum targets. The targets illustrate how an armor-piercing round sheds its copper jacket as it penetrates an aluminum alloy.

Which would you rather have hit you?

• A 5-ounce baseball traveling at 130 miles per hour (good fastball pitchers today throw at about 100 mph), or

• a 9.7-gram, 0.30-caliber bullet as it exits the barrel of a rifle at 1,875 mph?*

*A bullet slows as it travels through the air. Its speed is 1,600 mph at 200 yards and 1,350 mph at 400 yards, corresponding to baseball speeds of 110 mph and 95 mph.

 Senior Research Scientist Dr. James D. Walker of the Materials and Structures Division specializes in terminal ballistics, particularly large-scale computational physics simulations and analytical modeling of penetration and shaped charge events.

When a person is hit by a moving object, the object transfers its momentum to that person. Newtonian physics dictate that momentum is conserved, meaning it cannot be lost. The momentum transferred from the object to the person is the "push" that can knock us over. Momentum equals the mass of the object multiplied by its velocity. The lighter the object, the faster it needs to travel to have the same momentum as a heavier object. Therefore, a baseball moving at 130 mph and a rifle bullet moving at 1,875 mph will have an equally hard impact.

Common sense says that, painful as the choice may be, we would much rather be hit by the baseball. The problem with the bullet hitting you is that it travels at such high speeds that it can penetrate an individual and cause considerable damage. The baseball, on the other hand, is larger and slower, and stays outside the body. That, in fact, is the only difference. Otherwise, the ability of the two impacts to knock us over is about the same. The challenge for body armor designers is to convert a bullet's impact to the equivalent of a blunt blow.

Thus the role of body armor, or bullet-proof vests, is clear. We cannot stop momentum transferred by the bullet to the person -- that is a fundamental, conserved quantity -- but we can place protective armor between the person and the bullet so that it does not puncture the person.

Body armor should be designed so that it adds enough material to deform the bullet and slow it down so that, by the time the momentum reaches the wearer, the bullet impacts like a baseball hitting skin. Such an impact will leave bruises and perhaps break a rib, but these consequences are preferable to the damage caused by a bullet penetrating the body.

Scientists at Southwest Research Institute (SwRI) began working to improve body armors. In particular, the Institute is attempting to reduce body armor weight while retaining its ability to stop bullets.

## Two threats: ball and armor piercing

Regular rifle bullets, used by hunters, are called ball rounds because they are similar to the lead spherical rounds that were fired out of muskets. Today's ball round is filled with lead and usually has an outer metal jacket of copper or gilding metal. However, rifles can also fire armor-piercing rounds, so called because they can pierce metal armor on vehicles. These rounds have a hard steel core, a small amount of lead on the front and back, and a metal jacket of copper or gilding metal.

Armor-piercing rounds are much harder to stop than ball rounds, yet it is necessary to have armors that protect against both. An APM2 armor-piercing round can penetrate 1.5 inches of an aluminum alloy designed for vehicle armor or 0.6 inch of an armor steel.

Given the strength of those materials, people may assume there's an obvious solution -- give police and soldiers a jacket made of aluminum or steel to stop the bullets. This approach seems a good idea until one does the arithmetic: 1.5-inch thickness of aluminum totals 21 pounds per square foot and 0.6-inch thickness of steel totals 25 pounds per square foot. For the two square feet needed to protect the front and back of a person's torso, body armor made of aluminum or steel would weigh up to 50 pounds. This is clearly unacceptable for the people who need to wear the armor.

 This comparison of a large-scale numerical simulation and the results of the analytical model is for a ball round. The upper plot shows the front and back velocities of the projectile. At early times, the front of the projectile is stopped at the ceramic surface while the back of the projectile continues at its same speed. After significant penetration, the front and back velocities become equal, and what is left of the bullet is decelerated until it is brought to rest. The lower plot compares the pressure at the projectile-target interface. The agreement is excellent, showing that the analytical model contains the important physics of the impact.

## The two variables in body armor design: materials and geometry

Advanced materials that weigh less than either steel or aluminum can be combined to stop these ballistic threats. These armors have a two-layer geometric design: a hard material, usually a ceramic, as the outer layer; and a more ductile material, such as aluminum or KevlarTM fabric, as the inner layer. For example, a common combination is a thin alumina ceramic tile backed by Kevlar fabric in a stiffening resin.

Alumina is a very hard ceramic with the composition Al2O3 -- the same chemical composition as sapphire, which is known for its superior hardness. It comes in various grades with different ballistic performances. Kevlar is a poly(para-phenylene terephthalamide), which is a long organic molecule that includes aromatic rings and nitrogen in the chain. The fibers are spun into strands, which are then woven into fabric. In body armors, either the fabrics are used as a weave or they are placed in a hardening resin to give stiffness -- thus the final composite can behave either as a flexible fabric or a stiff plate.

Armors comprised of a hard layer (ceramic) backed by a soft layer (Kevlar) highlight the two key features of armor design: materials and geometry. These are the only variables available to armor designers -- either the material itself is changed or the way the materials are positioned is changed. Current body armor designs have been obtained through years of experimentation to determine the required amounts of materials. Improvements over the past 30 years essentially have been in materials -- the geometry of a hard layer backed by a soft layer has remained the same.

Current state-of-the-art hard layer-soft layer designs can stop an armor-piercing round with materials weighing seven pounds per square foot. Such designs can protect the front and back torso of a person with an armor weight of only 14 pounds -- a considerable reduction over aluminum or steel.

The U.S. Army recently set ambitious goals to further reduce the weight of body armor by 30 to 50 percent. It was clear that traditional "shoot and look" testing programs could not achieve this goal because there are no new wonderful materials to test. Institute scientists therefore proposed a unique approach, one that would identify the needed properties of materials to obtain the goal, determine geometry changes that could lead to lighter weights, or use a combination of both.

## The Institute's unique approach

Institute scientists proposed the same methodology for tackling the problem that has been successfully used in solving previous ballistics challenges (see Technology Today®, September 1993). The approach simultaneously pursues experimentation, large-scale numerical simulations, and analytical modeling.

### Experimentation

Traditional ballistic testing examines the end state: how deep the projectile penetrated thick targets, or whether the projectile was able to perforate thin targets. With modern diagnostics, scientists can gather more information during the actual penetration event. The location of the front end of the projectile as it penetrates a target can be determined with X-rays. The deformation of thin targets can be studied using a moirŽ fringe technique -- in which different relative movements give rise to contours of light and shadow on the straining surface -- photographed by extremely fast electronic cameras.

Experiments are the final arbitrators in ballistics. In the end, the question always remains: Did the armor stop the projectile?

Even with today's diagnostics, there is much information scientists cannot obtain, such as how the material moves within the target, the role of various material properties in the penetration process, and the state of stress within the target.

### Large-scale numerical simulations

Large-scale computer codes for ballistics problems are based on the conservation of mass, momentum, and energy. Space is divided into small cells or elements, and the material is modeled with detailed equations of state and constitutive models to fully represent stress in terms of current deformed shape and deformation history. The smaller the cells or elements the space is divided into, the more accurate the simulation, but also the more time it takes to do a calculation.

Metals are modeled quite well. Modeling of ceramics is still at a research stage, with new mathematical models being studied to examine fracture and failure and post-failure behavior of ceramics. The large-scale numerical simulations agree well with experiments for the thin ceramic tile combination previously described (see sidebar for simulations). The simulations allow examination of the stress states and material motion within the target and projectile. Simulations also allow simple changes in materials and material properties for "what if" scenarios: What if a material were twice as strong? What if it had 20 percent less density or if cracks ran 10 percent faster? Regardless of the data generated, such simulations must be compared to experiments to show that the results are plausible.

### Analytical modeling

In analytical modeling, many detailed mechanical assumptions are made, which reduce the problem to a small number of unknowns. By careful examination of the large-scale numerical simulations, a picture emerges of how the projectile travels through the armor. The material motion of both the target and projectile is written in terms of assumed velocity fields and material strength. Institute scientists use an integrated momentum balance along the centerline to produce analytical models for penetration. The unknowns are the front and back location of the projectile, as functions of time. These unknowns are solved using simultaneous ordinary differential equations. By simplifying the problem in a realistic manner, scientists can reduce the impact event to something that can be quickly analyzed.

The most important features of a problem stand out in analytical models. Many armor designs can be examined by adjusting the parameters, such as the type and amount of material. Calculations can be run quickly, leading to much insight regarding the physical problems.

When combined, experimentation, large-scale numerical simulations, and analytical modeling explain how projectiles penetrate armor. With that knowledge in hand, scientists can look for an armor design that can increase the area and reduce the velocity of a bullet, thereby mitigating the impact and ensuring protection of the individual.

 An analytical model allows rapid calculations of penetrations, and so can be used for optimization studies. The figure above shows penetration by a ball round versus the thickness percentage of the ceramic for four areal densities (which is the armor weight per area). On the left half, there is less ceramic and on the right half the armor is more ceramic. At either extreme, the armor does not stop the round. The minimum penetration (the optimum) is in the center of the graph. For the lightest armor, with an allowed penetration of 4 to 5 cm, the optimal ceramic thickness fraction is 0.51. Adding a fabric model that is currently under development allows three-material optimizations. The figure below shows depth of penetration for a 4.5 g/cm2 armor comprised of silicon carbide, aluminum, and Kevlar when impacted by a ball round, in terms of thickness percentage of each of the components -- each corner corresponds to 100 percent of the material named. The center of the triangle represents equal portions of the three materials.

## What is known

Numerical simulations and experiments have shown that the projectile, either ball or armor piercing, begins to deform when it first hits the hard ceramic. Virtually no penetration occurs for a length of time called the "fracture time." For ball rounds, this is on the order of 10 microseconds. During this time, the ceramic tile maintains its shape and the projectile nose is flattened. At the same time, the ceramic begins to fracture.

The notion of fracture time brings up an interesting point. An armor is effective if it maximizes the time the projectile interacts with the armor. Over longer interaction times, more projectile momentum transfers to the armor. Ceramics do well in this regard. Initially there is the fracture time, and all the projectile momentum for the shortened length of the projectile is transferred to the ceramic tile. Next, while the projectile penetrates broken ceramic, the projectile continues to erode, so the time spent in the armor is longer than it would be if the projectile were rigid and the front velocity of the projectile were the same as the back velocity, thus transferring more momentum from the projectile to the target.

Fracture begins at the impact site and microseconds later fracture initiates on the opposite side of the ceramic as it bends away from the impact site. The region of fractured material initially has a conical shape, similar to the pattern seen when a BB hits a window. The projectile then penetrates the fractured ceramic, which is much softer than the intact ceramic.

The failed material under the projectile then begins to load the backing material, which can be a ductile metal, a composite based on glass fibers, Kevlar, or some other fabric. The projectile always pushes the crushed ceramic before it, loading the backing material over a larger area, and decreasing the velocity of the projectile.

Either the backing material holds or it breaks, tears, or plugs. When failure occurs, the projectile travels through the armor, carrying pieces of it, and hits the person the armor tried to protect. Even when it holds, the deformation can be large enough to bruise the wearer. The backing material is what the wearer feels. If the area is large enough and the velocity low enough, the impact will feel more like that of a baseball than that of a bullet.

## What has been learned

So far, the most important feature identified is the time it takes the ceramic to initially fracture. Institute scientists are conducting experimental work to investigate this important variable. The longer the ceramic holds together, completely resisting penetration, the more the projectile length is reduced and the lower the velocity of what remains of the projectile. The remaining, slower projectile can more easily be captured by substrates or backing materials.

Currently, the three SwRI procedures are focusing on one of the least understood components of light armors: fabrics. Institute researchers are testing fabric response at low and high strain rates, determining how to accurately model fabrics -- including those embedded in a plastic or resin stiffener. Scientists are also searching for accurate yield and failure surfaces and post-failure models to model fabrics and resin-fabric composite systems in large-scale numerical codes. Once these models are numerically simulated and the results compared against experiments, better fabric models can be developed for the analytical models.

The analytical models have shown that, for very light armor, the amount of ceramic versus the amount of aluminum substrate material is important. Somewhat mitigating this is the role of fabrics. For a ceramic tile backed by a substrate, then backed by fabric, the exact ratios of materials are not as critical. Though still important, there is some leeway because the fabric is more forgiving. This is desirable because the armor should be able to protect against projectiles of slightly different designs and velocities.

Other important parameters are the post-failed, pressure-dependent strength of the ceramic, the strength of the substrate, and the modulus and breaking strain of the fabric. These factors are included in the analytical model and affect the penetration of the projectile. As more comprehensive models are developed, more of these parameters will be examined in the move toward a better armor.

Institute scientists plan to extend these models beyond the traditional hard layer-soft layer designs to find better design geometries. Such designs may include multiple layers of material, spacing between layers, or other geometric innovations. Current models allow arbitrary adjustment of the material parameters to identify good material properties for armor. There has been some work on varying the properties from hard to soft, continuously, throughout a material. Institute scientists will also use models to evaluate a number of other fabrics, such as SpectraTM -- a fiber based on polyethylene, which shows considerable promise as a backing to certain ceramics.

In the end, the use of models can tell scientists that to reach a certain armor weight, a material with x property is needed. Such information will show materials scientists where their efforts should be focused or show armor designers when they have reached diminishing returns.

## Conclusion

Stopping a bullet is a more complex process than most people realize. To do it with lightweight materials and little space requires a clear understanding of the relevant physics and mechanics. The Institute's three-fold approach of experimentation, large-scale numerical simulations, and analytical modeling provides a basis for understanding how projectiles penetrate body armors. This knowledge will ultimately pave the way for the design of better armors and result in increased safety for soldiers and law enforcement personnel.

These lighter-weight armor designs may, in the end, turn bullets into baseballs, giving the wearer another chance for a turn at bat.

### Comparison of Simulation and Photographic Test Data

Published in the Spring 1998 issue of Technology Today, published by Southwest Research Institute. For more information, contact Joe Fohn.

Technics Spring 1998 Technology Today
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