Bullet-Proof Analysis

April 12, 2005

10 Min Read
Bullet-Proof Analysis

DuPont fibers have been used for over 25 years as the main component in bulletproof vests. To further understand the factors that govern the performance of bulletproof vests, we recently developed efficient computational models that can simulate complex, high-energy impacts. Solving these difficult problems is an adventure even for the most experienced engineers. The technology is finally capable of keeping up with analysts who take a creative approach. Our simulations have produced results that are remarkably close to the results of real-life tests.

We analyze our FEA models using ABAQUS/Explicit. For the vest study, the system we have modeled consists of three components: a high-speed deformable bullet made of a lead core and a copper jacket, a protective barrier composed of numerous layers of flexible fabric, and a body simulant made of plastillina clay. An extensive physical testing program run in conjunction with the modeling effort utilizes a variety of novel experimental methods, either to generate data used to drive modeling parameters or to confirm the validity of modeling results.

Gaining insight into the physics of this class of problem requires us to constantly strike a balance in our analysis approach. We have to model the system in enough detail to obtain sufficient accuracy while we also aim for computational practicality. But we had a good reason to feel confident in tackling this thorny problem. Simulation studies we had undertaken previously during the design of a DuPont residential storm shelter advanced our ability to predict the impact performance of fabric-based structures. These studies laid the foundation for our recent work on vest packs.

Storms and stress

Traditional above-ground storm shelters are constructed with steel or poured concrete walls. They must withstand winds of 250 miles per hour and resist impacts from timbers and other windborne debris that fly around like projectiles during a tornado or hurricane. Our team wanted to offer a lightweight alternative to traditional building materials by taking advantage of the outstanding strength and toughness of DuPont fibers. Their question was how to configure a wall panel of woven fabric so the final structure would meet or exceed the stringent performance criteria for storm shelters defined by the Federal Emergency Management Agency (FEMA).

According to FEMA’s National Performance Criteria for Tornado Shelters, the wall system had to resist an impact with standard 2 by 4 framing timbers traveling at a speed of 45 m/s (100 miles per hour). Our engineers had already tested a number of physical prototypes using an air cannon. The test consisted of shooting an 8-foot wooden 2 by 4 end-on at a woven fabric wall panel at 100 miles per hour. They recorded the results with high-speed video for later examination.

The dominant problem revealed in the initial physical tests was that the woven fabric wall panel deflected too much from the impact with the 2 by 4. To address the deflection, the engineers were exploring different ways of fastening the fabric panel to the framing studs in the wall. For each new configuration, they performed several physical tests. Our model showed them that the cause of the deflection was not related to the way the panel was fastened to the studs. It showed them that they had to think about the problem in a different way and gave them ideas for a new design path that was ultimately successful.

Predicting the mechanical response of structures in which fabrics are a dominant load-carrying component is extremely difficult. Woven fabrics are not like homogeneous sheet materials such as steel, which essentially is equally stiff to a load applied in any direction.

In finite element analysis, the penalty for not using the correct modeling approach is large. If your model doesn’t capture the important physical forces involved, the analysis will mislead you about how your product will behave under operating conditions. Of course, if you try to model every possible physical detail involved, the model may take too long to compute, or may be not computationally possible at all. The goal is to devise a model that is complex enough to be representational, and simple enough to be computationally viable.

The storm shelter project is an example of how analysis helps engineers gain insight into product performance when radically new materials are proposed in place of traditional materials. With a material change from steel to woven fabric, the engineers found that the design of the wall panel also had to change. With simulation and physical testing, they discovered a fruitful engineering path faster than they would have if they had used physical testing alone.

(a)

(b)

(c)

(d)

(e)

To analyze the performance of ballistic vests, DuPont engineers simulated the behavior of the entire physical system shown in view (a), including a high-speed deformable bullet, a protective barrier woven fabric, and a clay body simulant. Views (b) and (c) show simulated results of a bullet striking a layer of woven fabric over clay. Views (d) and (e) show physical test results captured with high-speed video. Good correlation between experimental and FEA results demonstrate that the simulation model can be a useful tool in understanding system bahaviors.

Faster than a speeding bullet

Like our study of the storm shelter wall panel, FEA analysis of ballistic vests also involves modeling a projectile threat and a protective barrier. But the comparison ends there. The performance requirements for ballistic vests refer to physical events on an entirely different scale.

Bullets travel at nearly 1000 miles an hour. When a bullet hits the protective barrier, the fabric undergoes dramatic wrinkling, stretching, and partial failure. The bullet itself undergoes incredible amounts of distortion from the impact, which in turn influences the behavior of the fabric layers in the vest.

To capture all this behavior in a simulation, we have to be able to refine the mesh in the small, localized area affected by the impact.

The modeling technique that fit the problem is a feature in ABAQUS called Rebar Layers. In a model, the function of a Rebar Layer is to reinforce a structure in a defined uniaxial direction – in the same manner that metal rebar reinforces concrete. Woven fabrics exhibit a similar reinforcement behavior, since the yarns act with unidirectional stiffness. Our experiments showed that this behavior is especially true of orthogonally woven fabrics used in ballistic vests. The yarn directions govern the primary fabric stiffness.

ABAQUS developed Rebar Layers to model the behavior of concrete reinforcement bars and tire cords but devised the algorithms so they would apply to very general nonlinear mechanics problems. Our decision to apply the rebar concept to model the yarns in a fabric was a novel solution made possible by the flexibility built into the software.

With the Rebar Layers approach, mesh refinement allowed us to use smaller, more detailed elements to represent the area of the model most affected by the impact. First, we modeled a single layer of fabric and ran an analysis to predict displacement for different loading forces and boundary conditions, well into the nonlinear region. The results of the analysis closely matched the results of physical tests of the fabric. This validated our model for the fabric structure at quasi-static loading speeds and gave us assurance that we could likely use it to predict the dynamic loading behavior of woven fabric layers in the vest.

But that was just one layer of the fabric barrier! To represent the entire vest pack, we still had to be able to put twenty or more such layers together with general contact defined between each layer. We also had to model the other two components of the system: the bullet threat and the clay body simulant. Both of these components presented their own special problems.

What happens to a bullet upon impact with a ballistic vest is astonishing. Over the course of the event, which occurs in less than a millisecond, the tip of the bullet flattens and peels back. The bullet is shredded, ripped apart, and turned almost inside-out by the force of the impact. Determining how to simulate this physical reality brought us face to face with the fundamental limitations of modern nonlinear analysis. The distortion is so severe that the elements in the meshed bullet can lose their mathematical consistency and appear to have negative volume. If the software detects that any of the elements are distorting to such an extent, the analysis will die before it reaches a complete solution.

One way to address this problem is to automatically remesh the model as the simulation proceeds. Remeshing is a method of redefining the elements as they deform, in order to make sure of obtaining a credible solution. The ABAQUS remeshing technique we used is called adaptive meshing, based on the Arbitrary Lagrangian Eulerian formulation.

After selecting adaptive meshing and solving a few other technical issues, we had a model that would simulate the distortion the bullet undergoes upon impact. We checked the validity of the model by correlating analysis results with physical test results. The first physical tests were quasi-static, whereby we crushed copper jacketed lead bullets between two steel plates and measured the relationship between load and displacement. This physical data helped us “tune” the material laws in our bullet model for greater accuracy. We then shot actual bullets at a few different speeds into vests and compared the resulting deformed shapes of the bullet to those predicted by our system models. The results were impressive. Our model was able to capture the behavior of a bullet turning nearly inside-out upon impact.

We also relied on adaptive meshing to model the clay body simulant. First, we used quasi-static experiments on real clay blocks to make a deep, narrow indent in the clay using an indenter in the shape of a “mushroomed” bullet that we pulled out of a vest. Again, the load/displacement results from these tests helped us tune our plasticity-based material model for the clay. Our model replicated the extremely deep and narrow indent in the clay. To keep the modeling task within scope and budget, we used a clay model that did not include rate effects for the speed of the bullet at impact. Later, when we shot actual bullets at the vest system, our prediction of clay deformation was sufficiently accurate to give our team important guidance about the influence of different vest parameters on body simulant deformation.

So far, our research has demonstrated a viable modeling technique for simulating woven fabric barriers and body simulants subjected to a nonpentrating impact threat. Future studies will investigate ways to model partial penetration of the impact threat and other relevant issues.

To protect and defend

The overall intent of our research is to understand the important trends in the performance of ballistic vests. Modeling the vest mechanics gives us insight into what is happening in the physical system. Where is the energy of the bullet being transferred to, and by how much? If we change the material configuration, will the vest perform better or worse, and by how much? This modeling study has given us additional insight sufficient to estimate certain characteristics of vest performance before actually making a vest and shooting it with a bullet. Research continues to improve our knowledge intensity of how vest mechanics work.

The FEA model that we developed predicts the behavior of the bullet threat, protective vest, and body simulant with enough accuracy to provide significant guidance and insight to the design team, all within a manageable computational effort. Computer simulation is enabling DuPont to better understand the performance issues of advanced fiber systems in less time than if only physical tests are performed. And the more we know about the end-use performance of systems using our materials, the more likely it is that both DuPont and our customers will develop product innovations faster than ever before.

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