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

Abstract

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

On the toughening of brittle materials by grain bridging: Promoting intergranular fracture through grain angle, strength, and toughness

“…Although the finite element framework does admit distributions of material properties for both the grains and grain boundaries, initial studies on homogeneous systems provide the requisite baseline for future work. Properties for the model system, akin to silicon nitride, mirror our prior study on intergranular fracture (Foulk III et al, 2007 A typical mesh used for this study is illustrated in Figure 3. The radius of the disk is 50 μm and the cohesive surface element size h is 0.5 nm.…”

“…Prior work by the current authors (Foulk III et al, 2007) focused on predicting the evolution of grain bridging in this short-crack regime. To simplify matters, crack propagation was constrained to the grain boundaries (Zavattieri et al, 2001;Espinosa and Zavattieri, 2003a,b;Maiti et al, 2005).…”

“…To simplify matters, crack propagation was constrained to the grain boundaries (Zavattieri et al, 2001;Espinosa and Zavattieri, 2003a,b;Maiti et al, 2005). This work (Foulk III et al, 2007) showed that the grain bridging process, resulting from intergranular fracture of an inclined grain spanning two adjacent grains, can be generally partitioned into five regimes of resistance, namely crack propagation, kinking, arrest, stalling, and bridging with most toughening occurring during the stall regime and prior to actual bridge formation. These findings contrast previous analyses that did not consider bridge formation (Chantikul et al, 1990;Kovalev et al, 2000); moreover, they provides a feasible mechanism for the sharply rising R-curve behavior seen in many structural ceramics (Kruzic et al, 2005) and for the occurrence of crack reinitiation ahead of the stalled crack tip.…”

“…In previous work, we proposed that the grain bridging process, illustrated in Figure 1, can be partitioned into five regimes: propagate J → J p , kink J p → J k , arrest J k → J a , stall J a → J s , and bridge J s → J b (Foulk III et al, 2007). These findings were based on an idealized model of an inclined grain bridging * Although observed experimentally in many ceramics, e.g., Yuan et al (2003), the notion of crack initiation ahead of a main crack tip is at first sight unexpected in a brittle material where, with the absence of plasticity, the local stresses peak essentially at the crack tip.…”

“…The normalized driving force J/J 0,gb is plotted against a direct projection of the crack tip a pp . Endpoints of the loading regimes are illustrated with σ 22 varying from 0 to the grain boundary strength, σ gb (Foulk III et al, 2007).…”