A size-dependent yield criterion

In this paper, a size-dependent non-classical yield criterion is introduced on the basis of the modified couple stress theory in order to capture the size-dependency of the micro-scale structure yielding loads where the attempts of the classical yield criteria such as the von-Mises have been in vain. In order to develop the new yield criterion, the deviatoric part of the micro-scale structure strain energy density, including both classical and non-classical parts, is equated to the deviatoric strain energy density of a macro-size tensile-test sample at the yielding point. For bending of microbeams and torsion of microbars, the size-dependent yielding moments have been determined based on the new criterion. The results of the present criterion are compared to the experimental data and the von-Mises based classical results. A good agreement is observed between the present and the experimental results while the error of using the classical von-Mises criterion is considerable. In addition, it is observed that unlike the von-Mises criterion, the new criterion successfully predicts the size-dependency of the experimental data. It is noted that the results of the new criterion approach the von-Mises results as the size of the structure increases.