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Cryo Fault

Ductile-to-Brittle Transition Physics

\[K_I = Y\sigma\sqrt{\pi a} \ge K_{Ic} \;\Rightarrow\; \text{fracture}\]
$21.99 USD
$21.99 USD
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Meet Cryo Fault. Some steels bend when warm but snap in hard cold: below a transition temperature their crystals crack before they can flow. Some wartime Liberty ships broke in two this way. On the mug: K_I = Yσ√(πa) ≥ K_Ic ⇒ fracture. Pixel-art full-wrap black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

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Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

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

A crack runs when K_I = Yσ√(πa) reaches the toughness K_Ic. Below the ductile-to-brittle transition, many steels lose toughness, so a small crack can split them at ordinary stress.

Cryo Fault waits for the cold, then finds the crack.

Many steels have a body-centred cubic crystal structure. Warm, they bend and stretch before they break: ductile. Below a ductile-to-brittle transition temperature their crystals split along planes before they can flow, and they snap with little warning. Metals such as aluminium and copper, with face-centred cubic crystals, stay tough in the cold.

Fracture mechanics says when a crack wins. A crack of depth a in a part under stress σ concentrates stress at its tip, measured by the stress intensity factor K_I = Yσ√(πa). If K_I reaches the material's fracture toughness K_Ic, the crack runs: the condition on this mug. A. A. Griffith laid the foundations in 1921. Below the transition, K_Ic falls, so the same flaw becomes dangerous.

A worked number: for a steel with K_Ic = 50 MPa·√m, a 1 mm surface crack (Y ≈ 1.12) fails at about 800 MPa. Halve the toughness in the cold and it fails at half the stress. Some Second World War Liberty ships, in cold water, broke in two this way.

“Stay warm,” says Cryo Fault. “I only need one crack and one cold night.”

Equations

\[K_I = Y\sigma\sqrt{\pi a} \ge K_{Ic} \;\Rightarrow\; \text{fracture}\]
\[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\quad\text{(Griffith, plane stress)}\]
SymbolMeaningUnit
\(K_I\) mode-I (opening) stress intensity factor \(\mathrm{Pa·m^{1/2}}\)
\(Y\) geometry factor of the crack and part \(\mathrm{dimensionless}\)
\(\sigma\) applied tensile stress \(\mathrm{Pa}\)
\(a\) crack length (depth of a surface crack) \(\mathrm{m}\)
\(K_{Ic}\) fracture toughness of the material \(\mathrm{Pa·m^{1/2}}\)
\(\sigma_f\) fracture stress \(\mathrm{Pa}\)
\(E\) Young's modulus \(\mathrm{Pa}\)
\(\gamma_s\) surface energy per unit area \(\mathrm{J/m²}\)

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

Source Griffith, A. A. (1921). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society A 221, 163–198.doi.org/10.1098/rsta.1921.0006

Field notes

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