A thermodynamically consistent phase-field regularized cohesive fracture model with strain gradient elasticity and surface stresses

Abstract

Microstructure and surface stresses play a vital role in the micro- and nano-scale. In this paper, a thermodynamically consistent phase-field regularized cohesive fracture model (PF-CZM) is initially proposed to analyze crack propagation in the micro- and nano-scale, where strain gradient elasticity is introduced by higher-order elastic energy, and surface stresses are obtained using geometrical nonlinearity. After that, the higher-order theory is implemented through a mixed-type formulation finite element method. The specimen size effect of Mode I crack propagation is investigated. It is found that both strain gradient elasticity and surface stresses increase the critical load of crack nucleation, which becomes more pronounced as the size of the specimen decreases. The strain gradient elasticity increases the fracture toughness due to the reduction in stress singularity, while the maximum value of stress is still equal to the fracture strength during crack propagation. The surface stresses improve the local-fracture strength at the crack tip. Finally, the strain gradient elasticity further enhances the effect of surface stresses by changing the damage distribution at the crack tip when surface stresses are taken into account along with strain gradient elasticity. The presented framework has shown great potential for modeling crack propagation in the micro- and nano-scale.