Aluminum foil ⁑ Dernocua

Kragen Javier Sitaker, 02021-05-24 (updated 02021-09-11)
(14 minutes)

Kitchen aluminum foil is a remarkable material.

It’s typically 10 μm thick and 400 mm wide, giving it an aspect ratio
of 40000 in that dimension, and rolls are commonly some ten meters in
length, for an aspect ratio of 1 000 000; heavy-duty versions can
reach 30 μm or more. Despite their thinness, foils of 25 μm or
more are impermeable to oxygen, water, and light, though Wikipedia
claims thinner foils typically are plagued with pinholes. It comes in
a fully annealed state, so it rapidly work-hardens when bent, and
because of its thinness can be bent at deep submillimeter scales to
form metamaterials. It’s highly reflective (88% on the bright side
across the visible spectrum and even higher in the infrared) and
conductive, rivaling copper. It resists corrosion for years in
weather, it’s nontoxic, it’s light (2.71 g/cc), and it’s damn cheap,
under 50¢/m².

Robert Lang recommends laminating tissue paper on one or both
sides of kitchen aluminum foil to make “tissue foil”, which for years
he considered the ideal origami material. Notably, he uses a weak
sacrificial adhesive layer to hold the foil in place for the
lamination process.

Typical alloys include especially 1100 and 1200, but also 8111,
8015, and 8006, with 0.06%–0.6% silicon and 0.4%–1.6% iron, and in
some cases also some copper or manganese, under 0.5%. (1100 is
sometimes described as an “unalloyed aluminum grade” but it’s
specified to contain 0.05%–0.20% of copper, and it unavoidably has
other impurities.) Room-temperature yield strengths of these alloys
range from 30–170 MPa, with ultimate tensile strengths of 70–200 MPa,
and of course they all have a Young’s modulus around 70 GPa. Because
its crystal structure is fcc, it remains ductile down to absolute
zero, making it suitable for cryogenic applications; indeed, aluminum
becomes stronger at cryogenic temperatures. And, although it
weakens dramatically at higher temperatures, it doesn’t melt until
almost 650°, enabling it to be used at higher temperatures than
organic materials.

If oxidized (for example, with a soda solution, an arc, or
anodization) it yields amorphous sapphire, which if crystallized is an
excellent insulator, refractory, and abrasive. The oxidation process
produces a great deal of heat, making aluminum a
very-high-energy-density fuel, and, thanks to aluminum’s sternly
trivalent nature, electrical current; aluminum-foil fuel cells are
routinely produced by amateurs, though these typically oxidize the
aluminum to the chloride rather than the hydroxide or the oxide.

50¢/m² is 50¢/kWp in a solar concentrator, or 0.05¢/Wp, which is
noticeably cheaper than photovoltaic cells, currently around 18¢/Wp,
360 times more expensive. (However, the foil number there is sunlight
watts; if you’re making a PV solar concentrator you have to divide by
the efficiency of the solar cells, say 21%, which gives you 0.24¢/Wp
electric.) A large aluminum-foil assembly would be
vulnerable to significant deflections, but many small assemblies could
be placed on a hard, stable surface such as a rock or an adobe wall.

Alternatively, though, it might be possible to stiffen the foil by
making the equivalent of corrugated cardboard out of it, maybe using
aqueous boric acid (US$1.70/kg according to Potential local sources and prices of refractory materials) or
borax as the glue. The surface tension of water is ample to hold
aluminum foil in place until the water dries.

The feature that currently attracts my attention is the possibility of
work-hardening, which suggests the tempting possibility of making
tooling from aluminum foil that can itself work aluminum foil at room
temperature, a possibility reinforced by the immense aspect ratios
routinely available. As a simple example, you can in theory roll some
foil into a cone, and the point of this cone can dent, form a rib in,
or even pierce more of the same foil; but this is much easier in
practice if you first fold the foil 16 layers thick, form ribs
converging to a point on the last-formed fold, then roll the cone
around that point. If the last-formed fold is reversed, the aluminum
along the outer edge of the fold is the aluminum that was most
strained previously, having been bent double with as small a radius as
possible, and so will be the most work-hardened.

I was able to use such a cone to pierce not just aluminum foil but the
skin of an apple. I folded it from some foil which, folded 256 layers
thick, measured 2.57 mm in my shitty digital calipers; the resulting
square measured 27–29 mm on each side and weighed 1.8 g, giving a
density of only 0.8–1.0 g/cc, so it’s probably more than half air,
though it rapidly sinks in water, so probably the density is a
little higher than that.

Using such a cone point to form ribs without piercing foil is tricky,
because it tends to have significant asperities around the tip, which
tend to tear the foil if it is unbacked. These can presumably be
removed, permitting traditional SPIF processing of raw foil by sliding
the point over the foil; a better alternative might be to produce a
sequence of dents in the foil, then add new dents between them,
eventually producing a continuous groove in a way analogous to how
chain drilling cuts through a block of metal. However, when the foil
“workpiece” is backed by something reasonably hard (I’ve used
corrugated cardboard and the above-mentioned packed 256-layer
aluminum-foil square) and I’m using one of the other point types
described below, tears are relatively uncommon; in this situation it
fairly reliably just forms ribs. (I need to test more rigorously to
find out if the point type, the backing, or both is relevant here.)

Because such ribs are work-hardened, they are able to imprint their
shape on fully-annealed foil repeatedly. I wrote a short word in
cursive on foil using a layered aluminum-foil point (“single-point
incremental forming”), with the foil simply backed by the
somewhat-hard 256-layer square, then pressed this master against
another piece of foil in several places, pressing the two foils
between my fingers in each position (“stamping”). This resulted in
very readable copies of the word in several locations, although I’m
guessing there was substantial springback, so repeating this sort of
stamping through multiple generations would make the stamping
shallower at each generation.

I’ve tried smoking and annealing this foil with candle flames and
butane lighter flames, but so far I’ve only managed to melt it (in
under a second, usually) without ever smoking it. Maybe if I put
water in it I could get it to smoke up so I could tell when it was on
the point of overheating, but probably a different method of
temperature control would be more practical to anneal such a thin
material, such as a temperature-controlled heat gun.

A more reproducible point construction with a sharper, lower-volume
point was able to pierce the foil and apple even more easily. I
folded the foil three times to get 8 layers with a right-angle corner;
bisected the corner twice to get a 22½° angle; formed a rib bisecting
that angle with thumbnail pressure; then opened the final fold to
about 30° so that the two sides of the point would stiffen one
another.

By laying the foil into a form with a 90° valley in it and dragging
such a point over it, I was able to get a bend into the foil. When
there were ribs running perpendicular to the bend, this required
multiple passes in one case; a second attempt resulted in neatly
cutting through the foil at the intended bend location.

Another way to look at the 40 000:1 aspect ratio is to consider making
a tight cylindrical roll from a strip of the foil, 400 mm long and,
say, 10 mm wide, comprising 40 mm³, a cylinder whose ends are 4 mm³.
The cylinder thus has radius 1.13 mm and diameter 2.26 mm, so a
section through the center of it will go through 226 10-μm layers of
foil. That is, instead of being 40 000 as you’d expect, it’s about
√(40000) · 4/π.

The significance of ribs for folding is not that the ribs themselves
become more flexible — the material in the rib is work-hardened and
thus less flexible in plastic deformation, though its elastic
properties remain unchanged — but that they prevent curvature of the
material around them in any other direction, so if it’s going to
bend, the bend will be parallel to the ribs.

By making many parallel slits in the foil (with a steel box-cutter
blade, backing the foil with cardboard), I was able to make expanded
sheet metal, expanding a bit of foil by more than a factor of 2.

I was also able to fold a rather ugly origami crane by hand from the
foil, about 700 mg and 70 mm wingspan.

This assemblage of techniques seems promising for matter compiler
bootstrapping, although it’s clearly just a beginning. Many of the
problematic aspects of kitchen aluminum foil result from trying to
work with it at the 10-mm scale rather than the 10-μm scale.
Wrinkles, rips, and so on are going to happen unintentionally when
trying to manipulate 10-μm foil with 10-mm human fingers.

(Also, the natural frequencies of such macroscopic objects made by
folding such foil rarely exceed 100 Hz. The wing of the foil crane
resonates at around 100 Hz.)

As a test of alternatives, I also folded an origami crane from a
square cut from an aluminum Monster can, which is normally expected to
be about 100 μm thick. The square was about 125 mm on a side, and the
crane weighs about 3.8 g. One layer of the square measured 0.12 mm;
two layers 0.33 mm; three layers 0.38 mm; and four layers 0.52 mm. We
can conclude from this that (a) my caliper technique is shitty,
(b) the can (including paint) is about 120 μm thick, and (c) the
actual aluminum part of the can is more like 90 μm thick (3.8 g /
125 mm / 125 mm / 2.71 (g/cc)).

It’s a fucking miracle that I didn’t cut myself on the damn crane. It
was all knife edges and burrs, and every time I folded the damn thing
it cracked and ripped more, exposing new cutting edges. Aluminum-can
bodies are typically aluminum 3004, hardened with manganese and
magnesium, and work-hardened from the deep-drawing process rather than
annealed, so it’s not a perfect analogy, but it seems at least
suggestive.

Aluminum flashing for roofing is 0.024 inches, or in modern
units, 610 μm, but I think it’s annealed; aluminum is sold as sheet
metal down to 0.004 inches, 100 μm in modern units.

If we figure that the foil can meaningfully change direction every
20 μm, then we might think of an aluminum-foil machine as being made
of “moving parts” on the order of 1000 μm² (50 μm × 20 μm), 1000
“parts” per square millimeter of foil; a roll of kitchen aluminum foil
is enough to fabricate some 4 billion “parts”. A bootstrapping
compiler might require 100 000 parts and thus a square centimeter of
aluminum foil, cut and folded around into a shape a couple of
millimeters in diameter. If it were doing only one thing at a time,
and needed 10 seconds to construct/assemble each moving part, it would
take about 12 days to recompile itself. This is probably adequately
fast, barely, but probably not adequately robust against errors. It
would probably be better to design it to have more parts and do many
things at once, enabling it to be faster and correct errors.

It would be astonishing if no other materials were needed: you can’t
build anything electrical out of aluminum, at least at sub-microwave
frequencies, because the whole device is at the same electrical
potential. Similarly with getting mechanical power from thermal
expansion and contraction: it would just expand isotropically rather
than bending or sliding to do useful work. It might be possible to
use just aluminum foil coated on one side with something else, such as
glass or a few microns of aluminum oxide.

An interesting way to think of the density of aluminum foil is that
10 μm of 2.71-g/cc aluminum foil is 27.1 g/m², which is the same areal
density as a 23-mm-high column of air.

Other processes that may be very interesting to apply to aluminum foil
include electrolytic machining, electric discharge machining, scanning
probe microscopy, and anodization. Electrolytic machining might make
it possible to use an aluminum-foil tool to cut arbitrary shapes into
metals such as steel, invar, brass, inconel, monel, or tungsten, and
also to transform a scrap of aluminum foil (either flat or of a known
geometry) into a white-light hologram of an arbitrary optical system,
Fresnel-reflector-style.