Fracture process zone and fracture energy of heterogeneous soft materials

Bio-inspired heterogeneous soft materials are under rapid development due to their superior fracture and fatigue resistance. In the last few years, several kinds of fibrous soft composites in different length scales have been fabricated. However, the fracture behavior and toughening mechanism of this class of materials are still elusive. Here we develop a theoretical model for the crack tip field of fiber reinforced soft composites. The distribution of deformation around the crack tip and released elastic energy during crack propagation are obtained. The fracture process zone and fracture energy are quantified. There is a critical sample height, below which the fracture process zone size and fracture energy are size-dependent, above which they approach material-specific constants: steady-state fracture process zone size and steady-state fracture energy. A formula is derived to relate the steady-state fracture process zone size and parameters of the composite. It is found that both the steady-state fracture process zone size and the critical sample height scale with the fractocohesive length of the composite. The steady-state fracture energy of the composite can be enhanced either by enlarging the fracture process zone size through tuning fiber geometry or by increasing the work to rupture of the fiber through chemical treatment. This work reveals the toughening mechanism of heterogeneous soft materials and paves the way to design soft materials of high fracture energy, high fatigue threshold, and low hysteresis. It also provides a practical guideline for determining the sample size to measure the steady-state fracture energy of heterogeneous soft materials.