Structural Engineering & Statics
where the load goes
Concept

Fracture toughness — where it appears

A material's resistance to the growth of a crack, measured as the stress intensity at which a crack extends unstably. It is what separates a structure that leaks before it breaks from one that fails at a flaw nobody could see, and for steel it falls sharply with temperature.

Named by 6 essays across 2 fields — 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 The crack length at which the strength stops mattering. Failure stress against crack length for a toughness of 100 MPa√m, with three 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 355 N/mm² the two cross at a crack 20.1 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. At a working stress of 120 N/mm² the critical crack is 176.0 mm.

Designed to be found in time

A fatigue design that promises a detail will not crack is making a claim about a hundred years of traffic. A damage-tolerant one assumes it will crack, and sets the inspection interval from how long a crack takes to grow from the smallest size anybody can find to the largest the section can survive.

materials · Fatigue 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 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 Between the two counts, and the root's toughness says where. What a 20 mm S355 plate welded from one side to 0.5 of its thickness keeps of a double-sided butt throat, pulled straight across, against the toughness of the metal at its root: assessed as a crack on the strip-yield line (solid), by the toughness alone (dashed), and by the elastic and plastic counts (dotted, 0.25 and 0.41). Below 30 MPa√m the root tears before the elastic count's load; at 46 MPa√m the toughness alone would allow the whole plastic count, but the assessment gives 0.34, and it takes 66 MPa√m to reach 95 per cent of it. At 30, 50 and 100 MPa√m the root keeps 0.25, 0.35 and 0.41.

The land that is already a crack

A partial-penetration weld made from one side leaves the rest of the joint unfused, and pulled across, that unfused land is an edge crack whose tip is the root. Counted as a crack it keeps neither the elastic quarter of a double-sided weld nor the plastic 0.41, but a share between them that the root's toughness chooses — and the toughness of a crack front is the toughness of its length, which for a weld is the whole weld. A long weld in a cold structure can tear below the elastic count, and the same joint drawn twice as large tears sooner, which no count of stresses can see.

connections · Weld strength Where along its front a surface crack starts to cleave. Where along the front of a surface crack 8 mm deep in a 40 mm plate at −60 °C, 22 degrees below the steel's reference temperature cleavage starts, as a probability per millimetre of front, at the stress that gives a 5 per cent chance of cleavage, against the position on the front, for cracks 80 mm long, 40 mm long and 16 mm long at the surface. The middle third of the front, 60° to 120°, holds 76 per cent, 69 per cent and 28 per cent of the chance.

The front that counts for half its length

A ferritic steel's cleavage toughness depends on how much crack front it has to sample, and for a crack through a plate the front is the plate's thickness. The cracks inspections find are not through cracks; they are thumbnails at weld toes, whose curved front sees a stress intensity that varies round it. Weighted by the weakest link, the front counts for a little over half its length — so counting all of it is safe by 8 per cent, and counting none of it, as the 25 mm toughness does, is unsafe by up to a fifth for a long shallow crack.

materials · Fracture

Named alongside it

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

FractureStress intensityBrittle fractureCritical crackSize effectMaster curveDuctilityPlastic zoneTransition temperatureWeakest-linkConstraintCrack growth

All concepts