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A macroscopically defined critical frontal process zone (CFPZ) size ahead of a crack tip isestimated for alumina ceramics, alumina-based nanocomposites, and porous aluminaceramics. A three-point flexure test is carried out systematically on alumina using flexuralspecimens with various depths of a sharp V-shaped notch. The relation between the flexuralstrength and the local fracture stress is clarified based on the Griffith criterion and the localfracture criterion, and the formula for the relation between the strength and the notch depth issuccessfully established.