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Crack‐Interface Grain Bridging as a Fracture Resistance Mechanism in Ceramics: II, Theoretical Fracture Mechanics Model
Author(s) -
MAI YIUWING,
LAWN BRIAN R.
Publication year - 1987
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.1987.tb04983.x
Subject(s) - fracture mechanics , fracture toughness , materials science , classification of discontinuities , bridging (networking) , crack growth resistance curve , crack closure , toughening , toughness , mechanics , ceramic , composite material , structural engineering , mathematics , computer science , physics , mathematical analysis , engineering , computer network
A fracture mechanics model is developed for nontransforming ceramics that show an increasing toughness with crack extension ( R ‐curve, or T ‐curve, behavior). The model derives from the observations in Part I, treating the increased crack resistance as the cumulative effect of grain bridging restraints operating behind the advancing tip. An element of discreteness is incorporated into the formal distribution function for the crack‐plane restraining stresses, to account for the primary discontinuities in the observed crack growth. A trial forceseparation function for the local bridge microrupture process is adopted, such that an expression for the microstructureassociated crack driving (or rather, crack closing) force may be obtained in analytical form. The description can be made to fit the main trends in the measured toughness curve for a coarse‐grained alumina. Parametric evaluations from such fits conveniently quantify the degree and spatial extent of the toughening due to the bridging. These parameters could be useful in materials characterization and design. It is suggested that the mechanics formulation should be especially applicable to configurations with short cracks or flaws, as required in strength analysis.