Deformation of crack-bridging ductile reinforcements in toughened brittle materials

The addition of a dispersed ductile phase to a brittle material can lead to significant increases in fracture resistance compared to the untoughened matrix material. Often the important mechanism appears to be bridging by intact ductile ligaments behind the advancing crack tip. Although a framework for predicting toughness enhancements from bridging mechanisms exists, the required detailed model of ligament deformation which would provide the load-extension relation for a typical ligament has not been available. In this paper, numerical modeling of a plastically deforming ligament constrained by surrounding elastic matrix material is performed and the relevant toughness enhancement information extracted. Comparison is made to model experiments as needed to investigate such deformation processes as well as to toughnesses measured for technologically important composites. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.