a forming flaw
When a ceramic breaks, it almost never fails because its bonds gave out — it fails because a crack started at some tiny defect and ran. A forming flaw is any such defect that was born during the shaping step: a big pore, a hard agglomerate, a crack or lamination, a trapped air bubble, a fleck of foreign matter, an organic inclusion that burns out to leave a hole, or a density gradient. It is the fingerprint your forming method leaves inside the part, and more often than not it is what decides how strong the fired ceramic will be.
The reason it is so consequential comes straight from Griffith: a brittle ceramic's strength is set by its worst flaw, not by its average quality. Strength scales as K_IC divided by sqrt(pi times c), where c is the flaw size and K_IC is the fracture toughness — so doubling the biggest flaw drops the strength by about 30 percent. A 30 micron pore left by an agglomerate in a material with K_IC = 3 MPa sqrt(m) caps the strength near 300 MPa, far below the theoretical bond strength. And because the worst flaw varies from part to part, a batch of nominally identical ceramics has a spread of strengths, described not by one number but by a Weibull distribution — which is also why a bigger part, holding more flaws, is statistically weaker.
The honest, unifying principle of this whole field is that forming flaws are inherited. Sintering shrinks a green body and closes fine porosity, but it does not heal a large void, a crack, or an inclusion — if anything, firing too hard makes it worse by growing grains that trap the pore inside where it can never leave. So a flaw you press, cast, or print into the green body is very likely to be there in the finished part, sitting as the crack starter that sets the Weibull strength. That is why every forming method is judged, in the end, by the flaws it does or does not leave behind, and why clean powder, good dispersion, and uniform packing are worth so much.
A hard agglomerate in an alumina compact fires into a 30 micron pore. With K_IC = 3 MPa sqrt(m), Griffith puts the strength near sigma = K_IC / sqrt(pi times c), around 300 MPa — even though the same alumina, made flaw-free, could be far stronger. The one flaw, not the material, set the number.
Forming flaws are the crack starters that cap a ceramic's strength; firing shrinks but does not heal them.
Firing does not fix forming flaws — it inherits them, and firing too hard can make a pore permanent by trapping it inside a grown grain. This is why a ceramic's measured strength is a Weibull distribution, not one value, and why bigger parts are statistically weaker.