FEA Analysis of Butted Rings

As any butted maille maker knows, there is a direct relationship between how big a ring is (it's inner diameter) and how strong it is.  Likewise, there is a direct relationship between how thick the wire is and how strong the ring is.  So at first glance this might seem like a trivial experiment.  But I found it very enjoyable to do, because it puts concrete values and comparisons on the table, and the fact that the simulation behaves as we would expect gives us confidence in the results.

Finite Element Analysis (FEA) is a way to simulate the deformation of bodies.  With today's computing power, it is now easier than ever to simulate the loading of virtual models to see how they will respond to different forces.

For this simulation, I modeled a butted maille ring of different inner diameters (IDs) and different wire thicknesses.   I modeled rings with IDs of 1/4", 5/16", 3/8", 7/16", and 1/2".  Each of these rings was further modeled with the following wire thicknesses: 12GA (.1040"), 14GA (.0800"), 16GA (.0625"), 18GA (.0475"), 20GA (.0348") and 22GA (.0286")

To load the rings, I simulated a force directly on one of the butted ring ends, vectored so as to open the ring.  The other butted ring end was used as a fixed surface, as shown here:

Using the FEA software, I changed the force exerted on the ring end until the simulation determined that the ring had opened an amount equal to 1/2 of the ID.  So for a 1/2" ID ring, the force was found that would open the ring .25" for the various wire thicknesses.

Here is an example of the deformations for a 1/2" ID ring through the range of wire gages.

12ga_ring.jpg (97780 bytes) 14ga_ring.jpg (94726 bytes) 16ga_ring.jpg (94022 bytes) 18ga_ring.jpg (94757 bytes) 20ga_ring.jpg (93199 bytes) 22ga_ring.jpg (92415 bytes)
12 GA
.1040"
[2.64mm]
14GA
.0800"
[2.03mm]
16GA
.0625"
[1.59mm]
18GA
.0475"
[1.21mm]
20GA
.0348"
[.88mm]
22GA
.0286"
[.73mm]

I instructed the computer to use "Structural Steel" as the material for the ring.  I will provide the actual technical specifications as I update this page.  Below is a table showing the results.

LOAD TO ONE HALF OF ID DEFLECTION

Gage (U.S. Steel Wire Gage) Wire Thickness 0.5"
(1/2" ID)
0.4375
(7/16" ID)
0.375
(3/8" ID)
0.3125
(5/16" ID)
0.25
(1/4" ID)
12 0.1040 143.84 172.46 210.44 261.92 332.04
14 0.0800 58.14 70.97 88.12 112.45 148.15
16 0.0625 24.15 30.13 37.68 49.16 66.56
18 0.0475 8.90 11.29 14.53 19.00 26.38
20 0.0348 2.78 3.60 4.66 6.32 8.97
22 0.0286 1.36 1.72 2.25 3.08 4.46

Graphing the data provides expected, but nonetheless interesting, results.

The first graph, "Ring Deformation Forces", shows how rings of various IDs perform against each other.  The graph clearly shows that for a given ring diameter, the thicker the wire it is made of the more force it takes to open it.  Again "failure" is determined by the ring opening to a distance equal to 1/2 of the ID.

The ring also allows us to compare rings of one ID against rings of another ID of the same wire thickness.  For example, we can see that a 1/2" ID ring made of 12GA wire requires less than 150 pounds of force to fail, but a 1/4" ID ring of the same material requires over 300 pounds of force to make it fail!  So ID obviously makes a difference in the strength of the ring.

But we can also see that wire thickness makes a big difference.  The graph below shows us, for example, that a 1/2" ID ring made of 12GA wire requires nearly 150 pounds to fail, but making it out of 14GA wire  requires only about 60 pounds.  The 12GA ring is over twice as strong as the 14GA ring.

 

The next series of graphs are also interesting.  They clearly show what happens to the strength of the ring as the ID changes but the wire thickness is held constant. 

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