A strain gradient based yield criterion

Abstract

The classical yield criteria do not describe the yield size-dependency that has been observed in micro-scale structures (Fleck, Muller, Ashby, & Hutchinson, 1994; Stolken and Evans 1998; Moreau et al. 2005), and may also significantly underestimate the yield loads of structures at micron and sub-micron scales (Son, Jeong, & Kwon, 2003; Liu et al., 2013). The present paper suggests a specific size-dependent yield criterion based on the strain gradient theory that is aimed at addressing this inadequacy. In order to develop the strain gradient based yield criterion, the deviatoric part of the strain energy is calculated based on this theory and equated to the deviatoric strain energy of a macro-sample under tensile yielding load. For bending of microbeams and torsion of microbars, the yielding loads are derived in closed-forms and compared with the experimental results as well as the results calculated based on the classical von-Mises criterion. It is indicated that when the characteristic size of the structures (e.g., thickness of the microbeams or diameter of the microbars) is comparable to the length scale of the structure material (which are usually on the order of micrometers), there is a considerable gap between the results of the classical von-Mises criterion and the experimental observations while the results of the strain gradient based criterion are in good agreement with the experimental findings. As the size of the structure increases, the results of the new criterion converge to those of the classical von-Mises criterion.