Bridging stresses from R-curves of silicon nitrides
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The increasing crack resistance (R-curve) behaviour of ceramic materials is of high interest for technical applications. The initial value at the onset of crack extension is called the crack-tip toughness KI0. Very often but not in all cases a saturation of KR → KR,max is observed. Whereas silicon nitride ceramics show an increase of KR up to saturation within a few micrometers, alumina exhibits a comparably low initial steepness and shows saturation even after some mm crack extension.
Several reasons can be responsible for this effect. In coarse-grained materials, large grains can transmit tractions between the two crack faces resulting in so-called bridging stresses acting against the crack opening. As the consequence, such bridging effects shield the crack tip partially from the applied loads.
R-curve behaviour is commonly described by a relation KR = f(Δa) in which KR is the stress intensity factor necessary for crack propagation by an amount of Δa. This would be an appropriate...