Size-dependent fracture and higher order J-integral for solids characterized by strain gradient elasticity

摘要

Elastic fracture is governed by the material's strain energy released rate and depends on the applied loads and the stiffness of the structure. The effect of stiffness on fracture as a function of structural size is typically modeled using strain-based elastic fracture mechanics, but recent experimental evidence indicated that when the size of the structure is on the order of the higher order material length scale parameters, elastic strain gradients would stiffen the structure. In this paper, the higher order J-integral and energy-released rate for the analysis of fracture of strain gradient stiffened structures are developed. The effects of beam size on the fracture behaviors of strain gradient stiffened cantilevers on a substrate were analyzed using the higher order J-integral and the energy-released rate. Analyses revealed that the fracture load is elevated to more than 1.4 times of the un-stiffened case when the bending stiffness is doubled by strain gradient stiffening. Elastic fracture is shown to have an added dependence on the size of the structure when strain gradient stiffening is non-negligible.