A study of microbend test by strain gradient plasticity

Abstract

Metallic materials display strong size effect when the characteristic length associated with plastic deformation is on the order of microns. This size effect cannot be explained by classical plasticity theories since their constitutive relations do not have an intrinsic material length. Strain gradient plasticity has been developed to extend continuum plasticity to the micron or submicron regime. One major issue in strain gradient plasticity is the determination of the intrinsic material length that scales with strain gradients, and several microbend test specimens have been designed for this purpose. We have studied different microbend test specimens using the theory of strain gradient plasticity. The pure bending specimen, cantilever beam, and the microbend test specimen developed by Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale Acta Mater. 46, 5109–5115) are found suitable for the determination of intrinsic material length in strain gradient plasticity. However, the double cantilever beam (both ends clamped) is unsuitable since its deformation is dominated by axial stretching. The strain gradient effects significantly increase the bending stiffness of a microbend test specimen. The deflection of a 10-μm thick beam is only a few percent of that estimated by classical plasticity.