Some mechanical properties of some materials

Since one or two of my projects involve building structures, I give here some mechanical properties of materials we might chose to use for such construction. Since the square root of the ratio of ultimate tensile stress to density is a velocity which shows up in the projects given, it is listed here as densile speed (for want of a better name). For the SI-challenged, 100 m/s is 224 miles/hour; 1000 miles/hour is 447 m/s.

Note that real engineers take into account more than just the properties given below and allow for safety margins. In particular, for constructions in space, various of the materials described below would suffer severely from radiation damage. To reinforce the point (and provide some gentle amusement), I include some materials below which would not be suitable for use in space-based construction – notably balsa wood, polystyrene and rubber.

Note, also, that the figures given are only illustrative – particular samples of the materials in question are not guaranteed to exhibit the properties illustrated here. For example, at least one other source has quoted a higher ultimate tensile stress (about 2 GPa) for steel than Kaye & Laby, below; who, in turn, quote a higher value than my Nuffield data book.

The following data are drawn from Kaye & Laby (ISBN 0-582-46354-8).

Densile Speed data via Kay and Laby
Property

Ultimate tensile stressDensitydensile speed
Material S/MPa D.cc/g sqrt(S/D).s/m
Glass 30 to 902.2 to 4.0 86 to 200
Cast Iron 100 to 2307.0 to 7.4 116 to 181
Carbon Steel 430 to 4907.8 230 to 250
Steel 400 to 15007.8 226 to 440
Molybdenum 1100 to 300010.202 114 to 756
Tungsten 1500 to 350019.254 131 to 574
Nylon 66 60 to 801.13 to 1.15 228 to 266
Polystyrene 30 to 1001.04 to 1.09 166 to 310
Hard Rubber 391.13 to 1.18 181 to 186
PVC about 501.3 to 1.4 about 190
Polycarbonates 52 to 621.2 208 to 227
Heavy Polyethylene20 to 36.94 to .965 144 to 196
Polyethylene terephthalate661.37 to 1.38219
Cellulose 80 to 2401.48 to 1.53 228 to 403

The following data are drawn from my A level Nuffield science course's data book (ISBN 0 582 82672 1), which is somewhat old (copyright 1972). I've used chemical symbols of elements to indicate the pure element …

Property

Ultimate tensile stressDensitydensile speed
Material S/MPa D.cc/g sqrt(S/D).s/m
Polyester laminate,
70% woven glass fibre
3501.65461
Steel 250 to 3407.7180 to 210
Fe 2107.86163
Aluminium alloy 240 to 4002.8292 to 378
Al 50 to 1142.7136 to 205
Au 120 to 22019.3279 to 107
Zr 340 to 5606.53228 to 293
Ta 340 to 124016.6143 to 273
W 12019.3579
Mo 16510.22127
Ti 2304.54227
Ni 340 to 9908.9195 to 334
Co 230 to 9108.9161 to 320
Mg 90 to 2201.74227 to 356
Rubber 32.93 to 1.17165 to 185
Oak 21.72171
Western red cedar11.38170
Balsa 25.20353
Hardboard 25 to 55.80 to 1.0158 to 262

For the sake of somewhere to record the data as I find it, the following table lists what I know about some whackier materials that might be fun to contemplate … if you have data on these, or similar, I should be delighted to hear from you.

Property

Ultimate tensile stressDensitydensile speed
Material S/GPa D.cc/g sqrt(S/D).s/km
Kevlar® .338 [=49e3 psi]1.38 [=.050 lb/in**3]0.494
graphite fibre1.17 [=.17e6 psi]1.58 [=.057 lb/in**3]0.86
Titanium .345 to .5524.5080.277 to 0.350
90% Titanium, 10% Vanadium1.1934.666 (interpolated)0.506
vapor-grown carbon fibre2.71.81.22
heat-treated carbon fibre72.11.83
Carbon nanotubesc. 130c. 1.3 c. 10
Diamond ? 3.53 ?
Cubic Zirconium ? ? ?

with thanks to TimM for most of that. See also Paul Hills' pages, though his quoted densities are kg/m/m, i.e. area densities (for laminates; I get the impression he makes armour), so not as much help as I'd like (I need to know thicknesses) … but I've used his S-data for Titanium in the last table, along with Kaye & Laby densities. For more on Kevlar®, see below.

Special Feature: Kevlar® data from DuPont

DuPont have kindly sent me a PDF with lots of information about Kevlar® (which is a trade-mark of DuPont); as at 2002/Feb, it's priced at between 8 and 50 US $/lb, depending on the type of fibre. They give tensile modulus rather than ultimate tensile stress, so I've called it M and computed a modulus speed from it and the density. They also give tenacity, which their glossary identifies with tensile stress (but not necessarily ultimate tensile stress); so I've called that T and computed a tenacious speed from it and density. How these compare with ultimate tensile stress data, I'm not sure; but at least they give corresponding data for some other materials, so I illustrate those for comparison. Here's a summary of salient data from that (eighth of a gigabyte) report:

Property

Tensile modulusBreaking TenacityDensitymodulus speedtenacious speed
Material M/GPaT/GPaD.cc/gsqrt(M/D).s/kmsqrt(T/D).s/km
Kevlar 29 (Conditioned) 70.52.921.447.001.42
Kevlar 29 (w/ Resin) 833.61.447.591.58
Kevlar 49 (Conditioned) 112.43.001.448.831.44
Kevlar 49 (w/ Resin) 1243.61.449.281.58
S-Glass 85.54.592.495.861.37
E-Glass 72.43.452.555.331.16
Steel Wire 2001.977.755.08.504
Nylon-66 5.52.9861.162.18.921
Polyester 13.81.161.383.16.915
HS Polyethylene 1172.59.9711.01.63
High-Tenacity Carbon2213.101.811.11.31

The Conditioned Yarns (Conditioned) are ASTM D885-85, tested at 1.1 twist multiplier, while the Resin Impregnated Strands (w/ Resin) are Epoxy-impregnated strands, ASTM D2343 (whatever this may mean). Whether the density figure applies to the thus-treated Kevlar, I cannot say; though I suspect it relates to the un-treated raw Kevlar, which would bias the data. The data DuPont gives for other materials is only in customary units – psi for the stresses and pound per cubic inch for the density – so I've given the SI-converted values above (but used the raw data to compute the speeds, rather than computing speeds from the rounded converted data; so there may be minor (apparent) discrepancies in the data given).

DuPont also report on Kevlar's tolerance of adverse physical conditions. Notably: Kevlar shows essentially no embrittlement or degradation at temperatures as low as −196 Centigrade, i.e. down to 77 Kelvin, which is promissing; as is

Electron radiation is not harmful to Kevlar. In fact, filaments of Kevlar 49 exposed to 200 megarads show a very slight increase in tenacity and modulus …

Inconveniently, ghostview fails to display some of the PDF, including the graphs for electron and UV radiation effects, but the text does tell me that:

Kevlar is intrinsically self-screening. External fibers form a protective barrier, which shields interior fibers in a filament bundle or fabric. UV stability increases with size …

[Yes, that is how they spell fibre.] However, they give no information on its endurance in vacuum, which would matter for space-based uses.

For those interested in Kevlar's molecular structure (which is, presumably, subject to a patent): there are two kinds of unit in the tesselation; each is a benzene ring with the usual single Hydrogen hanging off four vertices; the other two vertices are opposite one another and have the same construct hanging off each. In one case, the construct is a Carbon with an Oxygen double-bonded to it, leaving one bond free; in the other case, the construct is a Nitrogen with one Hydrogen hanging off it, leaving one bond free. To tesselate, first form a line alternating these two kinds of unit, binding the stray bond of one's N to that of the other's C. Take a second such line and so position it that each double-bonded O of either chain is in position to form a hydrogen bond with the H hanging off each N of the other chain. Add further chains on either side of these in the corresponding manner. Thus one forms a wiggly ..H-N-C=O..H-N-C=O.. chain running across the primary chains to form a hydrogen-bonded sheet. Such sheets are then stacked together as radial planes to form fibres. No wonder it's so strong ;^)

I've had several enquiries asking me to send the PDF to folk. However, the document is copyright DuPont and I (never asked for, so) don't have their permission to re-distribute it, so I shalln't do that. However, DuPont were most helpful when I enquired about Kevlar: so, if you want such information yourself, I strongly recomment a visit to their web-site. Rummage around for such information as they give about Kevlar and look for a suitable contact page or e-mail address (these links worked last time I checked, 2006/May): I've no doubt they'd be happy to provide you with information.

Special Feature: carbon nano-tubes

In a NASA-sponsored paper (PDF) Bradley C. Edwards, PhD, sets out contemporary (2002) data on a space elevator: engaging reading and very encouraging. In this, he states that

… a fiber made of carbon nanotubes 1/8″ (3mm) in diameter could support 45 tons (41000 kg).

Assuming circular cross-section, US tons, Earth's surface gravity and accuracy in the US-unit figures, this gives an ultimate tensile stress of 12.6 GPa (the SI-unit figures imply 14.2 GPa). Later he cites a density of 1300 kg/m3, i.e. 1.3 g/cc, along with a tensile strengh of 130 GPa, 10 times as strong as the fiber cited earlier. This would indicate a densile speed of 3 or 10 km/s. Regardless of the discrepancy, these figures indicate that carbon nanotubes are a feasible material for a geosynchronous space elevator :^)

Keith Henson says that carbon nanotubes with a density 30% greater than that of water have been measured to handle almost 6 million pounds per square inch, which is about 41 G Pa; that implies a densile speed of 5.6 km/s, which is quite encouraging.

A special issue of the New Journal of Physics was devoted to carbon nano-tubes in 2003.


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