stress concentration

Try to tear open a sealed plastic bag by pulling on it and it stubbornly stretches. But nick the edge first with a scissor snip and it rips apart at once, the tear running straight from that little cut. The nick did not weaken the whole bag; it concentrated all your pull onto one tiny spot. That crowding of force at a sharp feature is stress concentration, and it is the root cause of why ceramics break at stresses far below what their bonds could in principle withstand.

Stress flows through a loaded solid rather like water flowing past a rock in a stream: the flow lines bunch up and speed up where they must squeeze around an obstacle, and the sharper the obstacle the tighter the crowd. Inglis worked out the result for an elliptical hole in a stressed plate: the stress right at the tip is roughly the applied stress multiplied by (1 + 2a/b), where a is the half-length across the load and b the half-width along it, or about 2 times sigma times sqrt(a/rho), where rho is the radius of the tip. A crack is an ellipse squashed almost flat, so rho shrinks toward atomic size and the multiplier becomes huge, often ten to a hundred times or more. A modest average stress can therefore reach the full bond strength at the tip of a sharp flaw while the rest of the material feels almost nothing.

This is why brittleness and flaws are such a lethal combination. A ductile metal blunts a sharp tip by yielding, spreading the peak stress out and taming it; a ceramic cannot yield, so the concentration stays savage and the tip stress climbs until a bond snaps and the crack advances. Designers fight it by banishing sharp corners: generous fillets and rounded edges, polished surfaces free of machining scratches, and chamfers instead of square shoulders. The key lesson is that a ceramic's strength is governed not by its average bonds but by the sharpest, worst-placed flaw, because that is where the stress secretly piles up.