When the fracture toughness of plates of the same material but different thickness is measured, what happens to the apparent fracture toughness K_c as the thickness increases?

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.