Fracture initiated from corners in brittle soft materials

Abstract

This paper studies a commonly observed phenomenon: the initiation of fracture from corners in a brittle soft material. A rectangular hydrogel is prepared and glued between two plastic films, such that the hydrogel meets the films at 90° corners. When the two plastic films are pulled, the hydrogel undergoes a shear deformation, and the stress-strain curve is recorded until fracture initiates from a corner. We find that the shear modulus is independent of the thickness H of the hydrogel, but the shear strength scales as ∼ H−0.4. A numerical simulation shows a nonlinear elastic zone around the corner, in which the stress field varies slowly. However, when the nonlinear elastic zone is small compared to the thickness, an annulus exists in which a singular field of linear elasticity prevails. In this annulus, the stress field scales with the distance R from the corner as ∼ R−0.41. We call this condition small-scale nonlinear elasticity. Our results indicate that small-scale nonlinear elasticity prevails even when the applied shear strain is as large as 80%. This condition explains the experimentally observed scaling between strength and thickness. The condition of small-scale nonlinear elasticity simplifies the characterization of fracture initiated from corners of brittle soft materials.