Structural Engineering & Statics
where the load goes
Concept

Master curve — where it appears

A single curve giving a ferritic steel's fracture toughness against temperature through the ductile-to-brittle transition, located by one reference temperature. It is fitted from a few tests, corrects for crack-front length by a weakest-link rule, and gives a toughness at any probability.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The same steel, brittle in January. Fracture toughness against temperature for a 25 mm ferritic plate, from Wallin's master curve — 30 + 70·exp(0.019(T − T₀)) in MPa√m, whose shape is the same for every ferritic steel and whose only free parameter is the reference temperature T₀ = -60 °C. Beside it, and on its own scale, is the crack length that toughness will tolerate at 200 N/mm², which goes as the square of it. At +20 °C this plate carries a 764 mm flaw and at -20 °C it carries 199 mm — a factor of 3.8 for a forty-degree change in the weather, in a steel that met its specification on both days. Thickness moves the curve as well, and the wrong way: constraint at a crack tip suppresses the yielding that would have blunted it, so a 100 mm plate of this steel tolerates 27% of the flaw a 10 mm plate does. Loading it in a millisecond shifts the whole curve another forty degrees.

The same steel, brittle in January

Every other material property in this collection is a number. Toughness is a curve, and the axis it runs along is temperature. Between twenty degrees and minus twenty a structural steel does not get gradually weaker — it changes the mechanism by which it fails, and the flaw it will tolerate falls by a factor of four.

materials · Transition temperature One steel, one crack, three plates. The strip-yield failure stress of plates with an edge crack, at −20 °C in a grade 355 steel whose master-curve reference temperature is −38 °C, against the crack length on a logarithmic scale, for plates 12, 25 and 60 mm thick, each with the toughness of its own crack front at the 5 per cent level: 88, 77 and 66 MPa√m. At a 20 mm crack the 12 mm plate fails at 267 N/mm², the 25 mm plate at 242 and the 60 mm plate at 214. Dashed, the simple check with the 25 mm toughness, the lower of fracture and yield: 274 N/mm² at the same crack, for every thickness.

The toughness that belongs to the plate

A steel's cleavage toughness is measured on a specimen 25 mm thick, and a crack through a plate starts at the weakest spot its front passes through — so a crack through a 60 mm flange samples more weak spots than the test did, and is less tough, and one through a 12 mm web samples fewer. Put each plate's own toughness into the strip-yield assessment and the simple check, which overstates a cracked plate by 23 per cent at the specimen's thickness, overstates a 60 mm flange by 36 per cent and a 100 mm plate by 45, while a thin web pays much of the strip-yield debt back.

materials · Fracture

Named alongside it

The objects these essays reach for when they reach for this one.

Brittle failureBrittle fractureCharpyConstraintCrack growthCritical crackDuctilityFatigueFlawFractureFracture toughnessPlastic zone

All concepts