IndexVärme och entropiTee

Cryo Fault

Ductile-to-Brittle Transition Physics

\[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\]
$29.99 USD
$29.99 USD
Rea Slutsåld
Color
Size

Size guide S–5XL · inches

Meet Cryo Fault. Some steels bend when warm but snap in hard cold: below a transition temperature their crystals crack before they can flow, the ductile-to-brittle transition. Some wartime Liberty ships broke this way; metals like aluminium stay tough in the cold. Cryo Fault wears it in pixel art on a unisex tee. The physics panel below has the equation, every symbol and the sources.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

För skalans skull: storlek M är 20 in (50.80 cm) bred, ungefär 3.143 × 1034 Plancklängder (lP = 1.616255 × 10−35 m). Ett måttband går snabbare.

Measurements in inches, ±1.5 in tolerance.

ShippingBy destination

Shipping calculated at checkout by destination. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Griffith showed that a crack grows when the elastic energy it releases is enough to pay for the new surface it creates. That makes the breaking stress fall as the crack gets longer, and cold, brittle steel can fail suddenly at stresses well below its normal strength.

Cryo Fault does not bend. That was the problem with the ships.

Most metal parts fail politely: overload a steel bar at room temperature and it stretches and tears, soaking up energy. Cool some steels far enough and that changes. Below a transition temperature the same alloy can crack straight across with almost no warning, like glass. Face-centred cubic metals such as copper and aluminium have no such transition. Ordinary structural steels, whose iron sits in a body-centred cubic lattice, do.

In 1921 Alan Arnold Griffith explained why brittle materials break at a small fraction of their theoretical strength: they contain cracks. A crack grows when the elastic energy it releases by lengthening exceeds the energy needed to create the two new surfaces. The first formula on this page is his result: the stress needed to break falls as one over the square root of the crack length. The second is the engineering form still used today. Each material has a fracture toughness, and when the stress concentrated at a crack tip exceeds it, the crack runs.

In the Second World War the United States built thousands of welded ships, Liberty ships among them, because welding was fast. More than a thousand cases of brittle fracture were reported, mostly in cold weather. On 16 January 1943 the new tanker Schenectady, moored in calm water at its Portland, Oregon, fitting-out dock, cracked almost in half, with a report heard a mile away. Later analysis blamed mainly steel that lost its toughness in the cold. Welding rarely started cracks, but it made each hull one continuous piece, so a crack that began at a sharp hatch corner had no seam to stop it. The investigations helped found fracture mechanics.

Cryo Fault stands still. Each step tests a number they'd rather not know.

Equations

\[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\]
\[K_I = Y\sigma\sqrt{\pi a} \ \ge\ K_{Ic} \;\Rightarrow\; \text{fracture}\]
SymbolMeaningUnit
\(\sigma_f\) Griffith fracture stress \(\mathrm{Pa}\)
\(E\) Young’s modulus \(\mathrm{Pa}\)
\(\gamma_s\) surface energy per unit area \(\mathrm{J/m²}\)
\(a\) crack (half-)length \(\mathrm{m}\)
\(K_I\) mode-I stress-intensity factor \(\mathrm{Pa·m^{1/2}}\)
\(Y\) geometry factor \(\mathrm{1}\)
\(\sigma\) applied stress \(\mathrm{Pa}\)
\(K_{Ic}\) fracture toughness \(\mathrm{Pa·m^{1/2}}\)

Sources

  1. Griffith (1921) The phenomena of rupture and flow in solids, Phil. Trans. R. Soc. A 221, 163
  2. Harris et al. (2015) Revisiting (Some of) the Lasting Impacts of the Liberty Ships via a Metallurgical Analysis of Rivets from the SS John W. Brown, JOM 67, 2965
  3. Failure Knowledge Database (shippai.org) — Brittle fracture of Liberty Ships
  4. TWI — Schenectady T2 tanker (16 Jan 1943 fracture)

Source Griffith, A. A. (1921). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 221, 163–198.doi.org/10.1098/rsta.1921.0006

Field notes

Visa alla
1 3
Visa alla