Model for Toughness Curves in Two‐Phase Ceramics: I, Basic Fracture Mechanics

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Abstract
A fracture mechanics model is presented for the toughening of ceramics by bridging from second‐phase particles, resulting in toughness curve (T ‐curve) behavior. It is assumed that the second‐phase particles are in a state of residual thermal expansion dilatational mismatch relative to the matrix. In the long‐crack region, these stresses augment frictional sliding stresses at the interphase boundaries, enhancing the crack resistance; in the short‐crack region, the same stresses drive the crack, diminishing the crack resistance. The principal manifestation of these countervailing influences is a reduced sensitivity of strength to initial flaw size, i.e., an increased flaw tolerance. In seeking to incorporate these key physical elements, our model opts for mathematical simplicity by assuming uniformly distributed stresses in two bridging domains: in the first, at small crack‐wall separations, a constant opening stress; in the second, at larger separations, a constant closing stress. The uniform crack‐plane distributions allow for simple closed‐form solutions of the crack K‐field equations, and thence an analytical formulation for the T‐curve. Indentation‐strength data on a “reference” Al2O3/Al2TiO5 ceramic composite are used to demonstrate the main theoretical predictions and to calibrate essential parameters in the T‐curve formulation. The utility of the model as a route to microstructural design is addressed in Part II.