For a component used at a stress equal to its yield stress σy, the largest crack size that still lets it yield before brittle fracture can be estimated as a = (1/π)(K_IC/σy)² (geometry factor Y = 1). For a steel with σy = 800 MPa and K_IC = 120 MPa·√m, which value is closest to this critical crack length?

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.