Remarks on crack-bridging concepts

The article draws upon recent work by us and our colleagues on metal and ceramic matrixcomposites for high temperature engines. The central theme here is to deduce mechanicalproperties, such as toughness, strength and notch-ductility, from bridging laws that characterizeinelastic processes associated with fracture. A particular set of normalization is introduced topresent the design charts, segregating the roles played by the shape, and the scale, of a bridginglaw. A single material length, δ₀E/σ₀, emerges, where δ₀is the limiting-separation, σ₀ thebridging-strength, and E the Young’s modulus of the solid. It is the huge variation of thislength-from a few nanometers for atomic bond, to a meter for cross-over fibers-that underliesthe richness in material behaviors. Under small-scale bridging conditions, δ₀E/σ₀ is the onlybasic length scale in the mechanics problem and represents, with a pre-factor about 0.4, thebridging zone size. A catalog of small-scale bridging solutions is compiled for idealized bridginglaws. Large-scale bridging introduces a dimensionless group, a/(δ₀E/σ₀), where a is a lengthcharacterizing the component (e.g., hole radius). The group plays a major role in all phenomenaassociated with bridging, and provides a focus of discussion in this article. For example, itquantifies the bridging scale when a is the unbridged crack length, and notch-sensitivity when ais hole radius. The difference and the connection between Irwin’s fracture mechanics and crackbridging concepts are discussed. It is demonstrated that fracture toughness and resistance curve aremeaningful only when small-scale bridging conditions prevail, and therefore of limited use indesign with composites. Many other mechanical properties of composites, such as strength andnotch-sensitivity, can be simulated by invoking large-scale bridging concepts.