Size-dependent linear elastic fracture of nanobeams

A nonlocal linear elastic fracture formulation is presented based on a discrete layer approach and an interface model to study cracked nanobeams. The formulation uses the stress-driven nonlocal theory of elasticity to account for the size-dependency in the constitutive equations, and the Bernoulli-Euler beam theory to define the kinematic field. Two fundamental mode I and mode II fracture nanospecimens with applications in Engineering Science are studied to reveal principal characteristics of the linear elastic fracture of beams at nanoscale. The domains are discretized both through the transverse and longitudinal directions and the field variables are derived by solving systems of the nonlocal equilibrium equations subjected to the variationally consistent and constitutive boundary and continuity conditions. The energy release rates of the fracture nanospecimens are calculated both from the global energy consideration and from the localized fields at the tip of the crack, i.e. the cohesive forces and the displacement jumps. The results are shown to be the same, proving the capability of the interface model to predict localized fields at the crack tip which are important for the cohesive fracture problems. It is found that the nanospecimens with higher nonlocality have higher fracture resistance and load bearing capacity due to higher energy absorptions and lower energy release rates. The crack propagation in the nanospecimens are also studied and load-displacement curves are presented. The nonlocality considerably increases the stiffness of the initial linear response of the nanospecimens. The fracture model is also able to capture the non-linear post-peak response and the unstable crack propagation, the snap-back instability, which is more intense for nanospecimens with higher nonlocality.