Recently I bought some Dyneema (UHMWPE) fishing line, a 0.5 mm diameter four-strand braid rated for 50kg; there are thinner grades down to about 0.2mm. Among the first things I did with it were to cut my hands a bit (accidentally) and neatly cut some sandwiches (on purpose).
This Saturday I visited the Mini Maker Faire Buenos Aires and talked with a designer who makes cardboard furniture. She gave me a little laser-cut and laser-engraved heart magnet made from cardboard.
I’m interested in self-replicating machinery fed from cheap materials, and in particular fabrication by planar cutting. It occurred to me that you could almost certainly cut cardboard with this string, although I haven't tried yet.
In particular, I think that you can make a kind of string bandsaw out of this string that will cut cardboard with a precision of about a third of its diameter, which would be about 60μm with the 200μm braid. Laser cutters typically manage about 100μm, but cannot be made out of cardboard themselves.
The pressure of the string along the edge of the cardboard needs to be high enough to cut into it rather than just drag over the edge. But the crucial feature here is the pressure, not the force; the pressure is determined by the force and the string’s bending radius. In the other parts of the machine where cutting is not desired, the string can be run around a large-radius pulley made from the same cardboard without cutting it, because the larger radius reduces the pressure on the pulley proportionally.
Thinner strings at the same stress will produce less pressure on the edge at a given bend radius, directly proportional to the diameter ratio; if their bend radius is proportionally smaller, they will produce the same pressure. This suggests that using thicker string will provide a larger margin between the pressure needed to cut into the cardboard and the tension the string can withstand, at the cost of less precise cuts and larger radii. Laser cutters are typically capable of 100μm-wide kerfs, which will be difficult to achieve with off-the-shelf Dyneema.
(A 490-newton force reaches the rated stress of 2.4 GPa in this 500μm braid; such a string wrapped around a 3mm-radius half turn will be exerting 980N net on it, spread over 6mm diameter and 500μm diameter, for a final pressure of 330 MPa. By contrast, a 200μm-diameter braid stressed at 2.4 GPa bears only 79 N; wrapped around the same 3mm-radius half turn, it exerts 130 MPa. But if instead it is wrapped around a proportionally smaller half turn with a 1.2mm radius — the thickness of a sheet of cardboard — it exerts 330 MPa again.)
However, the cardboard, too, is experiencing bend radii that depend on the string used to cut it. I don’t know enough to know whether this will matter in practice.
The 500μm-diameter braid is comprised of four tows braided together, each of some hundreds of fibers, so each fiber might be 10μm or 20μm across. Rebraiding the braid into smaller braids should make it possible to get sub-100μm kerfs, at least if the resulting string is still capable of cutting cardboard — the analysis above suggests it may not be.
The same kind of string bandsaw could melt through PVC pipe and perhaps plastic sheets, but it may be better not to use UHMWPE for this. UHMWPE is commonly listed as having a softening point or maximum service temperature of about 82° to 90°, barely above PVC's temperature of 54° to 80°. Spun nylon is the standard string used for friction-melting through PVC in construction; I find different sources giving its softening temperature as 75° or 180° (for nylon 6, polycaprolactam, which is not polycaprolactone) and as 76°, 110°, or 230° (for nylon 6,6), so I don’t really have any idea.
Tying knots in the string might help to provide enough irregularity to ensure cutting rather than just sliding.
It should be possible to achieve tight radius turns by rotating the workpiece around the place where the string runs through it.
With the addition of abrasive, this bandsaw could also cut other materials, like metal and glass, but the string won’t last long.
Typical lightweight cardboard box material can withstand an edge crush test of 32 pounds per inch (“32ECT”); over 500 microns, that would be only 2.8 N, while this string is capable of withstanding 490 N on each side, almost 400 times as much. This bodes well for the ability to cut cardboard cleanly by this method. Note that by this measure, thicker string is better in proportion to its diameter; halving the diameter halves the force needed to crush the edge, but cuts the strength of the string by four. The longitudinal motion of the string should reduce the effective strength of the paper further.