Let's talk Kevlar or Dyneema!

"cernunnos"Dyneema doesn't seem like a good bet. It is a gel spun uhmw hdpe (ultra high molecular weight high density polyethylene). Very high tensile strength, but low melting point. Heat generated on impact seems likely to do it in. I'd try multiple sheets of unbonded kevlar hung like a curtain.
You could push your finger through a sheet of Kevlar fabric before it's cured in resin. They are called "reinforcements" because they don't have any strength on their own. They just add strength to the resin. On their own, the woven fabrics are just a bunch of threads with nothing holding them together apart from a loose weave. If you even hold them wrong then you accidentally disturb the weave and pull threads out. They are very delicate until cured and totally unsuitable for stopping anything. Not even a stiff breeze.


 
The Vest is made from layers of Kevlar fabric most now have a chest and spine plate that provides further protection. A single sheet of fabric will not stop a bullet it is layered, the number of layers determines the rating of the vest.
The plates are made of Kevlar or in some cases Ceramic, This is due to the fact that higher K.E rounds can still Kill or damage Vital organs without penetration (cave in the chest cavity) The plate is designed to absorb some the impact energy and spread it out.
 
It doesn't matter how a bullet proof vest is made because it's not suitable for a backstop project. They aren't designed to survive repeated impacts on the same spot. They are designed to stop a bullet once. The bullet gets embedded in the vest - it doesn't bounce off.

I honestly don't know what they do to the Kevlar in a vest but I am positive it isn't a plain piece of woven fabric with nothing to hold it together. It will definately be layered (they look quite thick) and there will definitely be a binding agent of some kind. 

Not all resins are rigid. Some are specifically designed to be flexible or semi-flexible. To survive an impact, this is a desirable quality. Usually, the more rigid something is, the more brittle it will be. 

The impact resistant resins I have seen are all "semi flexible". This means they can be bent without breaking if enough force is applied but they still feel relatively hard. They are meant to retain dimensional stability but not crack when force is applied. I just ordered some for a difficult mold I am making so it won't crack when I pull the part.

When I made a Kevlar backstop, I added some layers of fiberglass as well as multiple Kevlar layers to give it the flexibility I wanted. It worked fairly well and lasted longer than any wood backstop I have tried but it still had a shelf life. 

If I was doing it again, I would use a thick front section of kevlar (7-15 layers) sandwiched in Kevlar and fiberglass reinforced task 12 urethane resin.

Task 12 can be bought from Smooth-on and that is the semi-rigid urethane. It comes as a 2 part liquid like epoxy except urethane usually sets faster. I think that, if reinforced with Kevlar and fiberglass strands that are a minimum of 3" in length, there is a good chance it will survive repeated impacts (for at least a while). 

To reduce the noise, I would add a thin layer of thixotropic urethane rubber - painted on the front and back. The front layer of rubber would get ripped to shreds after a while but it's cheap enough and quick-setting enough to re-apply without too much hassle (as long as you don't use too much each time). Unlike silicone, urethane rubber sticks to everything so it won't come off.

It should be a fairly easy concept to test as all the necessary materials are available in small or test quantities. 

I would want some fairly heavy weights to hold the backstop down too. A wooden frame or stand would be the weakest link and would definitely splinter or crack after repeated impacts from anything that powerful. A 50fpe 25 cal made mincemeat of some very strong ironwood I tried a while back. 

I stuck my kevlar backstop to a brick wall and the repeated impact was not kind to the brick at all. The wife was very mad at me for a week....

If the gun puts out 100 fpe, you want at least 100lb of weight to stop it getting knocked over on every shot. I would put it in front of a strong tree for support..
 
In case anyone is interested in how bullet proof vests are made, this explains the process at a high level:

http://dynamicdust.blogspot.com/2015/11/technology-behind-light-weight-bullet.html

They name "Kraton" as one of the impact resistant resins used to wet out the Kevlar for a bullet resistant vest (the new name for bullet proof vests). 

I've never used it but given what they use it for, I would guess it is stronger than the Task 12 I ordered.... Not sure I'm ready to trust a piece of that to keep me safe from a .338 just yet..
 
Did a quick test on some 1050 denier ballistic nylon. Two layers stopped a .177 JSB Exact 7.33g out of my Airwolf. The second layer did have a bulge in it, but the pellet did not pass through. I'll likely add another layer or two, or maybe try a layer of Dyneema to see how that works.

I think with another layer or two it will work for my application. This will be a curtain behind my target/pellet trap to catch any strays and keep them from hitting my fence.
 
I had a couple old Kevlar vest that I shot with different firearms. I would say it isn't going to work as they are not designed to be shot at repeatedly in the same spot. Look up bulletbunker.com they use shredded rubber stops 50 cal in 2ft depth. I take strips of carpet remnants and sandwich them with 2x10 and all thread. extremely quiet and at 12 inch thick stops all airguns I have shot at it up to 45 cal.
 
I'd think that being loose, the pellet would separate the fibers of the Kevlar cloth. Without laminating the sheets in resin, the cloth fibers move around and after a shot or two, I'd imagine the pellet would push the fibers on the sheet around easily. I have some kevlar and CF sheets in my garage, I'll take a look and see how tight the weave is.

Another option is perhaps some kind of pad with non-Newtonian fluid packed into it. Kind of like a trauma pad you add behind the plate of AR500 body armor. Maybe something like that could catch the pellet relatively silently. The kinetic impact energy is dispersed throughout the non-Newtonian sheet effectively. Like others have pointed out, repeated impacts at the same poi would likely reduce the longevity. Maybe a combination of your kevlar sheet to take the initial sting of the pellet. The sheet would be a replaceable component when it's taken enough hits.

Just a thought...
 
I bought some of that Ballistic rubber from Precision airguns and that stuff is garbage. At 50 yards my .22 Cal Cricket at 21 FPE is going straight thru it and punching holes in my plywood. At 75 yards its still going thru it but stopping in the plywood, but my 25 Cal is punching holes in it at 75 yards. At 95 yards its stopping both my .22 and .25 whoop -pee.
 
Here's an idea, I have no experience with but might work. Tires cut the side walls leaving just the tread. now a 3/4" plywood back stop, add 1" foam board, cut the tires into 10-12" sections screw them onto board flattening them out. Continue screwing them like cedar shakes. That board laid at a 45 degree angle. Truck or car tubes cut in strips hung like those energy savers on refridgerator doors. It's all recycled material. .02 cents worth from a wood be MacGiver
 
I was using a similar idea to the above using an automotive tire mat that you wipe your feet on at the front door. I purchased a mat that had 3/4 cut tires linked with steel rods. I placed it on a 45 degree angle just as the above photo and placed a pan of rubber mulch at the base to catch the deflected pellets. It worked fine in stopping and deflecting the pellets even up to my 45 cal air gun. It however was not silent during use. It did lower the resonance of the striking pellet significantly and the deformed pellets were in the trap below. The problem was it was taken from my property. Lots of foot prints and ATV tracks but no backstop remained. Apparently the ATV was used to pull the entire backstop assembled out of the ground and disappeared into the woods with the perpetrators. So I went back to portable backstops that I retrieve when my shooting sessions end. I do not think these were kids and I do not think they realized that I also shoot my high powered rifles on this property in my pit trap of 600 yards. I have had intruders in the past that got educated and have not returned. So the idea is sound and will work but not silent in capturing and stopping the projectiles.