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Materials for Use as Cores in Foam Weapons for Full-Contact Swordfighting Sports by Arrakis
There exist in modern America several organizations dedicated to empowering their constituent members to participate in Medieval-style melee combat as depicted in such popular movies as The Lord of the Rings, 300, Troy, and Braveheart. One such organization is called the “Belegarth Medieval Combat Society” and differs from most of these sundry organizations in that it allows full-contact combat, with no restrictions on hit strength. In order to facilitate such forceful clashes without causing injury to the participants and without requiring large quantities of armor or protective gear (a significant financial barrier to new fighters in certain other organizations; see: the SCA), Belegarth weapons must be well padded and judged safe by the rules of the game. They must also pass simple tests wherein specially trained individuals designated as “weapons checkers” strike each other with the weapons to make sure they won’t harm anyone.
The weapons, by the rules of the game, are required not to have: 1) a metal core, 2) the ability to flex further than 45 degrees in any direction. Additionally, these cores, once padded, will be expected to withstand powerful impact forces from blocking and delivering powered hits to both unarmored human beings, other weapons, plate armor, and padded shields, among other things and to do so over a fairly long lifespan. Thus, they need to be of significant strength, but not brittle and not prone to fatigue failures. Too, it is generally considered a benefit for cores to be lightweight, as this allows total weight reductions and better balance. Thus far, it appears that the following properties are preferred: high yield strength, high elastic modulus, high fracture toughness, high fatigue strength, and low density. Also, to maintain current size profiles, we should try to limit the functional size of any material to between 0.25x0.25 and 1x1 inches.
That's the introduction and general specifications for analysis. This isn't new to any of y'all, or hideously relevant, but I figured I should include it for completeness.
To get a better idea of the characteristics that make an adequate weapon core, it is instructive to analyze what is currently used. This should yield a range or a set of minimums for each parameter. We should also be able to use certain performance indices to characterize the performance of these materials.
The most common current core materials are fiberglass rods (rebar, fenceposts, bars, whatever one can get one’s hands on), PVC pipe, preferably high-psi rated (600psi preferred), graphite or carbon fiber-wrapped golf club shafts, and kitespar (a type of hollow graphite rod used in kite making). PVC is the heaviest and most flexible of these, fiberglass is generally considered to be an all-around good material, kitespar is ultra-light, but is brittle and weak enough that it fails much more often than the other cores and over a lesser period of use. Golf club shafts are a less commonly used material because they’re harder to find in a standard retail/internet order environment, but high quality carbon fiber-wrapped golf club shafts are quite stiff and relatively strong. Finding these materials on a selection chart using the stiff beam performance index of M = (1/ρ)*E^1/2 (1) provides a fair picture of where the current technology lies (See Figure 1).
Figure 1: By examining the general whereabouts of the most commonly used weapons cores, we can determine the approximate properties that we will need to improve upon to find a better core. Here are show PVC, GFRP (Fiberglass), CFRP (Carbon fiber, like a golf club shaft), and bamboo, a decent cheap core alternative used more commonly in the past than nowadays.
Here, M just indicates the Performance index; it doesn't really mean anything. E is the Young's or elastic modulus (the strength of the material against flexure) and ρ is the density of the material.
With the general regime of the current materials in mind, we begin analysis of all of the nonmetallic materials in our database. The first plot built is a plot of the performance index for stiffness vs. weight shown in Equation (1), with a line of slope 1 dividing the plot, with materials above the line being better and below being worse. The second plot shows the price of each class of Nonmetallic materials. The third plot is yield strength vs. fracture toughness, with materials appearing in the upper right hand corner of the chart being box selected for their extraordinary toughness and strength. The fourth plot strangely plots fatigue strength at a billion cycles vs. elongation %, but selecting for high fatigue strength and elongations in the range of .5 to 10% gives a bloc of materials that is both highly fatigue-resistant and very ductile. Stage five of this analysis was simply a chart of the Process Universe Joining by Adhesion process and the sorts of shaping processes useful to the creation of a long, thin beam. Options like deposition and rapid prototyping were removed, essentially, as being not a common or feasible method of preparing the sorts of shapes we are interested in. Stage six was a simple tree stage to select for materials that could be shaped into prismatic axisymmetric shapes, like long thin cylinders or square prisms. With all of these stages of selection combined and the failing options hidden, it appeared that there were still quite a few materials left to discount. Fortunately, it can be easily determined that quite a few of these 139 passing materials are the same as another member thereof with only minor differences. Thus, we are left with relatively few final choices. (See Figures 2, 3, and 4).
Figure 2: The plot of Stiff Beam Performance Index with a minimum limit placed on the M-value of the materials and with materials that failed this or one of Stage 1-4’s test criteria hidden. We see here many fiber-reinforced polymers, a couple of woods, and several composites have made the first cuts. The composites thus far seem to be superior to the other materials.
Figure 3: A plot of yield strength versus fracture toughness allows for an easy selection of strong, tough materials that ought to hold up to the rigors of combat best. We see that the composites continue to prevail over the reinforced polymers in both areas.
Figure 4: A plot showing elongation vs. fatigue strength, allowing a selection of ductile materials (ductile rarely fail in fatigue at low stresses and generally have a higher strain to failure than brittle materials) to be made with relative ease while allowing a material that will stand up to years of impacts to be selected for.
Selecting for various physical properties a weapon core should exhibit: strength, toughness, rigidness, stiffness, and longevity.
Now, we factor in the cost and can discard most of the composites straightaway as being much too costly (some at over 3000USP/kg!). On the high end of density, some of these materials would mass almost half a kilogram for a half-inch cross-section 36” long square prism, so anything over about 100USD is right out. This leaves us with an even smaller group of serious contenders. (See Figures 5 and 6).
Figure 5: A plot of price by material type, used to sort out metal core materials and to select for reasonably priced options. Restricting the price knocks a goodly portion of the otherwise front-running composites out of the race.
Figure 6: The new Stiff Performance Index plot with high cost materials hidden. Fiberglasses of various types and carbon fiber/glass fiber reinforced polymers are now very much contenders.
Now for cost analysis...
The absolute strongest and stiffest materials that made the cuts are, without a doubt, high strength (metal-including) composites like titanium silicon carbide and aluminum boride. These materials, however, are too pricey to manufacture and process and, truth be told, are also probably just too heavy. Their high density is in keeping with their other high properties (strength, stiffness, etc.), but in the sizes most commonly built on in Belegarth, these materials would be strength overkill and weigh too much to be worth using.
Coming in a close second in terms of strength and at a much more reasonable density and price are epoxy/aramid fiber, carbon fiber, and GFRP/CFRPs. Almost any of the variations on these materials listed in the database would be a good match for this type of application. This holds with conventional wisdom that carbon fiber gold club shafts, fiberglass rods, and kitespar rods are the best materials for the job.
If everyone was able to afford them, structural metal foams (if not classed as "metals") and, even better, PEEK/IM Carbon Fiber tubes would be the absolute ideal solution (terrific stiffness, good strength very low density), but these materials are yet too costly, so we must continue on using the lightest, strongest CFRPs we can find, at least for now.
Hope this was at least somewhat helpful! It got me an A that year and confirmed my suspicions regarding core materials and their relative suitabilities, so I consider this paper to have been a success. The paper was written in late 2007, about 7 months into my foamfightng career.