Structural Engineering & Statics
where the load goes
Concept

Critical crack — where it appears

The crack length at which a member under a given stress fails by fracture, found by setting the crack's stress intensity equal to the material's toughness. Near the yield stress the yielded zone at its tip is as long as the crack, and fracture mechanics alone then puts the critical length too long.

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

The crack length at which the strength stops mattering. Failure stress against crack length for a toughness of 100 MPa√m, with two steel grades drawn. The falling curve is fracture — Kc divided by Y times the root of pi a — and it does not know what the yield stress is. The horizontal lines are the grades. At 275 N/mm² the two cross at a crack 33.5 mm long; At 460 N/mm² the two cross at a crack 12.0 mm long. The stronger grade's transition is the shorter one — raising the yield stress does not raise the strength of a cracked member, it only shortens the crack that takes it away.

The flaw that sets the strength

A member with a crack twenty millimetres long fails at its yield stress. Make the steel stronger and the crack that does it gets shorter, so the same flaw that was harmless in the weaker grade decides the stronger one.

materials · Fracture Between the two lines, a curve below both. The stress at which a plate of grade 355 steel of toughness 100 MPa√m, with an edge-crack factor of 1.12 fails, against the length of the crack in it on a logarithmic scale. Dashed: the fracture-mechanics line, the toughness over Y√(πa), and the yield stress; the usual check takes whichever is lower. Solid: Dugdale's strip-yield model, in which a thin strip ahead of the crack yields and the two mechanisms act together. The two dashed lines cross at the transition length, 20.1 mm, and there the strip-yield stress is 288 N/mm², 0.81 of both: the lower of the two simple answers overstates the plate by 23 per cent. At 20 mm the strip-yield stress is 289 N/mm² against 355 N/mm². Far from the crossing on either side the curve joins the line it approaches.

The crack between the two checks

A cracked plate is checked twice: once for fracture, as if the steel could not yield, and once for yielding, as if the crack could not grow, and whichever answer is lower is taken. Each check is right far from the other. Where they cross — at a crack of twenty millimetres in an ordinary structural steel — the plate fails at four fifths of both, because a strip of yielded steel ahead of the crack is by then two and a half times as long as the crack itself, and neither check has a place for it.

materials · Fracture

Named alongside it

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

Brittle fractureDuctilityFractureFracture toughnessStress intensityGriffithPlastic zoneSize effectStress concentrationTransition temperature

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