A micromechanical basis for partitioning the evolution of grain bridging in brittle materials

A micromechanical model is developed for grain bridging in monolithic ceramics. Specifically, bridge formation of a single, non-equiaxed grain spanning adjacent grains is addressed. A cohesive zone framework enables crack initiation and propagation along grain boundaries. The evolution of the bridge is investigated through a variance in both grain angle and aspect ratio. We propose that the bridging process can be partitioned into five distinct regimes of resistance: propagate, kink, arrest, stall, and bridge. Although crack propagation and kinking are well understood, crack arrest and subsequent ‘‘stall’’ have been largely overlooked. Resistance during the stall regime exposes large volumes of microstructure to stresses well in excess of the grain boundary strength. Bridging can occur through continued propagation or reinitiation ahead of the stalled crack tip. The driving force required to reinitiate is substantially greater than the driving force required to kink. In addition, the critical driving force to reinitiate is sensitive to grain aspect ratio but relatively insensitive to grain angle. The marked increase in crack resistance occurs prior to bridge formation and provides an ARTICLE IN PRESS www.elsevier.com/locate/jmps 0022-5096/$ see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2006.10.009 Corresponding author. Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA. Tel.: +1 510 486 5798; fax: +1 510 643 5792. E-mail address: [email protected] (R.O. Ritchie). Deceased. Au th or 's pe rs on al co py interpretation for the rapidly rising resistance curves which govern the strength of many brittle materials at realistically small flaw sizes. r 2006 Elsevier Ltd. All rights reserved.