The ability of a cracked material to resist fracture. It is expressed as the critical value of the stress intensity factor, K_IC (in MPa·√m), and fracture is judged by comparing it with K = Yσ√(πa).
Japanese name: 破壊靭性
Fracture toughness appears in 6 practice questions across 4 topics, including Mechanical properties and fracture, Fracture mechanics and fatigue, Ceramics and glasses.
The intensity of stress at a crack tip is expressed by the stress intensity factor K = Yσ√(πa). σ is the remote stress, a is the crack length (the depth for a surface crack, half the length for an internal crack), and Y is a factor determined by the shapes of the crack and component. When K reaches a critical value for the material, the crack propagates suddenly and fracture occurs; this critical value is called the fracture toughness. Its unit is MPa·√m, notable for containing both stress and crack length. It lets you compare numerically not just strength but resistance to cracks.
Fracture toughness values change with plate thickness. Thin plates are close to plane stress with a large plastic zone at the crack tip, so the apparent value is high; thick plates are in plane strain, and the value drops and levels off at a constant minimum. This value is the plane-strain fracture toughness K_IC, where the subscript I denotes loading that opens the crack (mode I). K_IC can be treated as a material constant and is a conservative value for design. Typical values are about 50–150 MPa·√m for structural steels (lower for higher-strength grades), about 20–45 for aluminum alloys, about 3–5 for alumina and below 1 (about 0.7–0.8) for soda-lime glass.
In general, raising strength by heat treatment or other means tends to lower fracture toughness. The higher the strength, the smaller the crack that can be tolerated, and since the critical crack length is proportional to (K_IC/σ)², the effect is large even when the working stress is the same fraction of the strength. Aircraft and pressure vessels therefore select materials for toughness as well as strength. In ceramics, toughness is raised by measures such as transformation toughening in zirconia and crack bridging by fibers or particles. In metals, grain refinement and reducing inclusions improve toughness.
In damage-tolerant design, you assume the largest crack that nondestructive inspection might miss and check that K at the working stress stays below K_IC. Combining this with the Paris law for fatigue crack growth rate, you estimate the number of cycles for the crack to reach its critical length and set the inspection interval. For highly ductile materials with large plastic zones, K is hard to apply, so elastic–plastic fracture mechanics parameters such as the J-integral and the crack-tip opening displacement (CTOD) are used. Which parameter to use is judged from the ductility of the material and the dimensions of the component.
Answer: A. About 20 mm
Setting K = K_IC gives a = (1/π)(K_IC/Yσ)². K_IC/σ = 50/200 = 0.25 √m, so a = 0.25²/π = 0.0625/3.14 ≈ 0.0199 m, about 20 mm. About 62.5 mm forgets to divide by π, and about 80 mm is the mistake of taking 0.25/π without squaring. The critical crack length is inversely proportional to the square of the stress, so halving the stress allows a crack four times as long. Comparing the crack sizes that nondestructive inspection can detect against this critical value is the basis of damage-tolerant design.
Answer: C. It decreases as constraint grows, approaching the plane-strain value K_IC
In a thin plate, constraint through the thickness is weak (close to plane stress), so the plastic zone at the crack tip spreads widely and absorbs much energy, giving a high apparent fracture toughness K_c. As the plate thickens, deformation through the thickness is constrained and the plate approaches plane strain; the plastic zone shrinks and K_c decreases, leveling off above a certain thickness at a nearly constant minimum, K_IC. This is why K_IC can be treated as a material constant and is used in design as a conservative value. Test standards require a thickness, proportional to (K_IC/yield stress)², large enough for plane strain to hold.
Charpy impact energy is the energy needed to break a notched specimen; it is convenient for comparing materials and evaluating the ductile-to-brittle transition, but it is not a value that can be used directly in design. Fracture toughness is a material constant that lets you predict fracture quantitatively from crack size and stress.
In K = Yσ√(πa), σ is in MPa and a in m, giving MPa·√m. Y and π are dimensionless.
About 3–5 MPa·√m for alumina, about 5–8 for silicon nitride and about 6–10 for partially stabilized zirconia, from a few tens of times to a few times lower than metals. Ceramics therefore fracture easily even from small flaws, and their strength scatters widely.
In a thin plate, constraint through the thickness is weak (close to plane stress), so the plastic zone at the crack tip spreads widely and absorbs much energy, giving a high apparent fracture toughness K_c.
When the fracture toughness of plates of the same material …Brittle materials break most easily under Mode I loading, and cracks tend to turn toward the direction that makes them Mode I, so fracture toughness is usually expressed as the critical value for Mode I, K_IC.
Among the modes of crack deformation, which statement corre…In the high region where the maximum stress intensity factor K_max approaches the fracture toughness K_IC, the rate rises sharply and leads to unstable fracture, so the claim that growth stops is backwards.
Which statement correctly describes the curve of fatigue cr…The thermal conductivity of quartz glass is low, about 1.4 W/(m·K), and its fracture toughness of about 0.8 MPa·√m is on par with soda-lime glass, both far below metals.
Red-hot quartz glass (fused silica) rarely cracks when drop…Stress intensity factor Transformation toughening Paris law Thermal stress Coefficient of linear thermal expansion 0.2% offset yield strength Creep Fatigue limit Young's modulus