Size-dependent stress intensity factors in a gradient elastic double cantilever beam with surface effects

Abstract

In this article, the size-dependent stress intensity factors in an elastic double cantilever beam (DCB) are obtained using strain gradient theory. The surface effects are included, while the DCB is assumed to undergo large deformation. Both cracked and uncracked parts (root effect) of the DCB are incorporated in modeling and analyses. The Variational principle is employed to obtain the governing equation and the corresponding boundary conditions. The deflections along the beam axis and stress intensity factors are obtained and plotted. Results exhibit large deformation to be influential for slender beams at small scale. Strain gradient effect tends to increase beam stiffness though reverse holds true for the root effect of the DCB. These effects on structure stiffness are conspicuous when the beam thickness is less than the material characteristic length. Due to positive surface residual stress, beam exhibits less stiff behavior in comparison with the negative surface residual stress. This softening behavior may be credited to the sign of curvature that causes an additional distributed load and alters beam stiffness. It is shown that even with the root effect, negative surface residual stress causes the DCB to display stiffer response by lowering the stress intensity factors and vice versa.