Reduced stress concentration and enhanced fracture toughness by yielding-rehardening combination

A range of tough materials (e.g., metals and polymer solids) exhibit a characteristic mechanical behavior, that is, a combination of yielding and subsequent rehardening. We numerically investigate how the combination of these mechanical behaviors enhances resistance to crack propagation.Our system has a 2-dimensional square lattice structure where pairs of adjacent lattice points are connected by "special" bonds. An isolated bond behaves as a linear spring for small deformations, but yields at a threshold force to produce a plateau in its force-deformation curve, and then shows rehardening on further loading up to a critical force of bond-breaking; on unloading from above the yielding point, the force rapidly decreases with deformation (hysteresis). We simulate crack propagation in the entire system (the square lattice structure) from an initial crack driven by boundary loading. The threshold force for bond-yielding is varied as a simulation parameter, while the critical force for bond-breaking in the rehardening regime is fixed to 1. In other words, the substantial simulation parameter is the ratio between the yielding and breaking forces. We find that the fracture behavior drastically changes depending on the ratio: when the ratio is low, the bond-breaking energy (of a single bond) is low, but more work is required to fracture the entire system via the crack propagation. The opposite tendency between the bond-breaking energy and the fracture work is due to formation of a well-developed yielding zone around the crack tip.