fracture toughness
Strength tells you how much stress a ceramic survives; fracture toughness tells you something different and just as important: how hard it is to make an existing crack advance. Imagine two sheets, one of glass and one of tough plastic, each already carrying a small cut. Push the crack and the glass runs instantly, while the plastic resists, the crack creeping only reluctantly. That resistance to a crack advancing is toughness, and it is not the same as strength or hardness. It is the property that most sharply separates a fragile ceramic from a forgiving one.
The engineering measure is the critical stress-intensity factor, written K_IC. The intensity of the stress field concentrated at a crack tip is captured by a single quantity K = Y times sigma times sqrt(pi times c), combining the applied stress sigma, the flaw size c, and a geometry factor Y near one. As you load the part, K rises, and the crack lurches forward the instant K reaches the material's critical value K_IC. So K_IC, in units of MPa times sqrt(metre), is the material's built-in resistance to crack advance. Typical values tell the whole brittle story: window glass about 0.7 to 0.9, alumina 3 to 4, silicon nitride 5 to 7, transformation-toughened zirconia 8 to 12, while a structural steel sits near 50 to 100. Toughness links to fracture energy through K_IC = sqrt(E times G_c), where G_c is the energy needed to make new crack surface.
Fracture toughness matters because it sets flaw tolerance. Rearranging the same relation gives strength sigma_f = K_IC / (Y times sqrt(pi times c)): for a fixed worst flaw, doubling the toughness raises the strength, and just as valuably, a tougher ceramic can carry a bigger flaw at the same strength, which makes it more reliable and less sensitive to the odd deep scratch. This is why so much ceramic research chases toughening. Two honest caveats: K_IC is not a single fixed constant in tough ceramics, where it rises as the crack extends (R-curve behaviour), so the value depends on crack length and test method; and toughness is not strength, so a very tough ceramic hiding a huge flaw can still be weak, and a low-toughness one with only tiny flaws can still be strong.
Two ceramics carry the same 30 micron flaw. Alumina at K_IC = 3.5 MPa sqrt(m) fails near 360 MPa; toughened zirconia at K_IC = 10 MPa sqrt(m) survives to over 1000 MPa. The zirconia is not made of stronger bonds; it simply resists the advance of that identical crack far harder.
Higher K_IC means a crack advances only at higher stress, so a tougher ceramic tolerates the same flaw at greater strength.
K_IC is often quoted as if it were one fixed number, but in tough ceramics it rises as the crack grows (R-curve), so the reported value depends on crack length and test method. And never conflate toughness with strength: they are linked through flaw size but measure different things.