The bridging tractions developed behind a crack tipare considered for a stationary crack under cyclic loadingconditions at elevated temperatures in high-toughness,monolithic ceramics. Assuming a temperature range where thegrain-boundary phases are sufficiently soft such that bridgingcan occur due to a viscous layer in the boundary, a viscoelasticmodel is developed in which bridging forces associated with theshear resistance of the grain-boundary phase are transmittedacross the surfaces of a crack. Throughout the work, cyclic andstatic damage mechanisms which may be operating ahead of the cracktip (e.g. creep cavitation) are ignored in order to focusexclusively on the role of viscous grain bridging. A primary goalis to incorporate microstructural details like grain shape,grain-boundary thickness, and glass viscosity, as well as theeffects of external variables such as loading rate andtemperature. A fully self-consistent numerical approach isadopted, which does not require any prescribed assumptions as tothe shape of the crack-opening profile. The self-consistentsolution is compared to an analytical solution for a simplifiedparabolic approximation of the crack-flank opening displacements.The model is applicable to a wide range of ceramic materials atelevated temperatures, and rationalizes the frequency andtemperature sensitivity not generally observed in ceramics atroom temperature. Solutions identify a non-dimensional groupassociated with microstructure and external loading conditions,and solutions are presented over a range of this parameter.
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