Microstructure‐Strength Properties in Ceramics: I, Effect of Crack Size on Toughness

A systematic study of the inert‐strength characteristics of ceramics as a function of crack size relative to grain size has been made using controlled indentation flaws. The focus of the test program is on aluminas, with barium titanates and glass‐ceramics providing support data in confirmation of general trends. On progressively diminishing the indentation load, the strengths first show a steady increase, but subsequently tend to a plateau, as the contact size begins to approach the characteristic grain size. A simple extension of conventional indentation fracture mechanics theory (incorporating residual contact stresses) is developed to describe this scale transition. The basis of the analysis is the postulated existence of a “microstructural driving force,” grain‐localized at the center of the pennylike radial crack, in direct analogy to the indentation driving force. This description provides closed‐form solutions to the fracture mechanics equations, such that the data are interpretable in terms of an apparent R‐curve function. Only two quantities are required to specify the function completely, one relating to the macroscopic toughness determined from large‐scale crack specimens and the other to a microstructure‐associated stress intensity factor. These quantities are advocated as useful reliability parameters. It is found that the second quantity can vary widely from material to material, even within a given class, to the extent that materials which show superior strength characteristics at large indentation loads may be dramatically weaker at low loads. The indications are that, at least for aluminas, the key to such weakening effects is to be found in the grain‐boundary structures. The study emphasizes the need for extreme caution in extrapolating macroscopic‐crack data unconditionally into the microscopic‐flaw region, and for more fundamental investigations into the underlying physical processes actually responsible for the microstructural driving forces.