I have a fracture paradox question. I have a brittle ceramic with a certain fracture toughness and crack depth and I calculate strength based on the equation S = KIc/Yc1/2. I get a strength of 15000 psi. The intrinsic tensile strength of this material 20000 psi so it will not fail if I apply say 12000 psi . But to be safe I remove the crack by drilling a small hole, this rounding it out to avoid the crack tip stress riser. But the stress concentration factor around the hole is 2X. So now my applied stress of 12000 psi is now 24000 psi near the hole which is greater than 20000 psi and I show failure.

My question is how can rounding a crack be worst than the crack itself?