the size effect
A curious and important fact about ceramics is that a bigger part is weaker. Take the same glass and draw it into a fine fibre and it can be astonishingly strong, yet cast it into a thick rod and its strength drops. Nothing about the glass itself changed; what changed is how much material there is to hide a bad flaw. A longer chain is more likely to contain a weak link, and a larger ceramic body is more likely to contain a large, strength-limiting flaw somewhere in its greater volume. The size effect is this statistical penalty for bigness, and it is a direct consequence of the weakest-link nature of brittle fracture.
It follows straight from Weibull statistics. Comparing two parts of the same material but different stressed volumes V_1 and V_2, their strengths scale as sigma_1 / sigma_2 = (V_2 / V_1)^(1/m), where m is the Weibull modulus. A worked case makes it concrete: with m = 10 and a part ten times larger in volume, the strength ratio is 10^(1/10) = 10^0.1, about 1.26, so the big part is roughly 21 percent weaker. The exponent 1/m is the key: a low modulus makes the size penalty severe, while a high modulus softens it. The same reasoning explains why bend tests read higher than tensile tests, since bending puts only a thin surface layer in high tension, exposing a much smaller effective volume of flaws than uniform tension does.
The size effect is a practical trap for the unwary. You cannot simply measure the strength of a small laboratory test bar and assume a large component made of the same material will be as strong; the component, with its far greater stressed volume, will statistically be weaker, and you must scale the lab value down using the Weibull relation. It is also why ceramic fibres are so remarkably strong and why fine-scale ceramics outperform bulk ones. One honest limit: the clean volume scaling assumes a single random flaw population uniformly distributed, so if flaws are concentrated at surfaces or come in two distinct types, the simple exponent must be replaced by a more careful surface-area or bimodal analysis.
A ceramic tested as a small bend bar shows 500 MPa. Scaled up to a component with a stressed volume 1000 times larger, at m = 10 the predicted strength is 500 divided by 1000^(1/10), that is 500 / 2.0, about 250 MPa. Trusting the lab number would overestimate the real part twofold.
Strength scales as volume to the power minus one over m, so bigger parts test weaker and lab bars flatter the truth.
The size effect means small test coupons systematically overstate the strength of large parts. The scaling exponent is 1/m, so a low Weibull modulus makes the penalty severe. It weakens or breaks down when flaws are not a single uniformly distributed population.