The condition in which, even with a crack present, the whole component yields first and sudden brittle fracture does not occur. The allowable crack size is proportional to (K_IC/σy)², so K_IC/σy serves as the performance index.
Japanese name: 破壊前降伏
Yield before fracture appears in 1 practice question across 1 topic, including Materials selection and design.
When a cracked component is loaded, one of two things happens first: the stress intensity factor K at the crack tip reaches the fracture toughness K_IC and the component fails suddenly, or the stress in the whole component reaches the yield stress σy and it deforms plastically. Yield before fracture is the design approach of ensuring that the latter always comes first. A component that yields deforms visibly, so the abnormality can be noticed before sudden brittle fracture. Solving K = Yσ√(πa) for the crack length at which K = K_IC when σ = σy gives a = (1/π)(K_IC/(Yσy))², and for cracks smaller than this, yielding comes first.
Because the critical crack length is proportional to (K_IC/σy)², raising the yield stress while K_IC stays the same shrinks the allowable crack with the square. For example, a material with K_IC = 40 MPa·√m and σy = 400 MPa (Y = 1) has a limit of about 3.2 mm, but raising σy to 600 MPa at the same K_IC gives about 1.4 mm. In practice, raising strength by heat treatment and similar means often lowers toughness as well, so the allowable crack becomes smaller still. Stronger materials are not necessarily safer, and materials must be chosen by comparison with the crack sizes that inspection can find.
The ratio K_IC/σy appears elsewhere in fracture mechanics too. The size of the plastic zone at a crack tip is proportional to (K/σy)², and in plane stress it is about (1/2π)(K/σy)². To obtain a valid plane-strain K_IC in a fracture toughness test, the specimen thickness and crack length must be at least 2.5(K_IC/σy)² (ASTM E399). For K_IC = 40 MPa·√m and σy = 400 MPa this is 25 mm. A material with a large K_IC/σy can deform plastically to a large extent at a crack tip and, in components of ordinary thickness, is unlikely to fail in a brittle manner.
The yield-before-fracture approach is often used in choosing materials for pressure vessels and piping. When yield before fracture is the objective, the performance index is K_IC/σy, and on Ashby charts K_IC and σy are plotted on logarithmic axes and compared using lines of slope 1. Under the leak-before-break approach, which ensures that even when a crack penetrates the wall and the contents leak out, sudden fracture does not yet occur, the index becomes K_IC²/σy. For steels, whose K_IC drops as temperature falls, it is important in both cases to judge using values at the lowest service temperature.
Answer: A. About 7.2 mm
K_IC/σy = 120/800 = 0.15 √m, so a = (0.15)²/π = 0.0225/π ≈ 7.2×10⁻³ m, about 7.2 mm. With cracks shorter than this, the whole component yields before fracturing from the crack, so it deforms visibly before it breaks and the problem can be noticed. About 23 mm forgets to divide by π (0.0225 m). About 0.35 mm is what a different high-strength steel (σy = 1500 MPa, K_IC = 50 MPa·√m) would give; in high-strength, low-toughness materials, even small cracks that are hard to find by inspection lead to fracture before yielding. So when fracture must be avoided, materials are selected not by strength alone but with K_IC/σy as the performance index, compared against the crack sizes that inspection can detect.
Yield before fracture is the approach of making the whole component yield before it fails from a crack, with the performance index K_IC/σy. Leak before break ensures that even when a crack penetrates the wall and a leak occurs, a crack of that length still does not cause sudden fracture; for pressure vessels the index is K_IC²/σy.
Yielding first means that sudden brittle fracture is avoided, not that failure cannot occur. If the load increases further, ductile fracture occurs after large deformation. Also, if a crack grows by fatigue or stress corrosion cracking, it can exceed the critical length so that the condition no longer holds.
It is a dimensionless factor expressing how the stress intensity factor depends on the shape and position of the crack and the dimensions of the component, written as K = Yσ√(πa). For a central through crack in an infinitely wide plate Y = 1, and it departs from 1 for surface cracks or plates of limited width. The larger Y is, the smaller the critical crack length.
Material index (performance index) Ashby chart (materials selection chart) Life cycle assessment Pareto optimality Specific stiffness Tramp elements