Experimental characterization and theoretical modeling of size-dependent distortional hardening behavior of ultrathin metal sheets under multi-axial loading

The research on distortional hardening (DH) behavior of ultrathin metal sheets under multi-axial proportional loading affected by size effect is still missing and existing constitutive models cannot accurately predict the size-dependent distortional hardening (SDDH) behavior of ultrathin metal sheets. To solve the problem and fill the gap, experimental investigation and theoretical modeling of SDDH behavior of ultrathin SUS304 sheets under biaxial proportional loading is conducted in this paper. Firstly, the experimental yield loci of the ultrathin SUS304 sheets with different thicknesses and grain sizes are characterized through biaxial and uniaxial tensile tests. Experimental results show that DH behavior exists during the micro-scale plastic deformation of the ultrathin SUS304 sheets and that the degree of DH is amplified with the increase of the grain size. Subsequently, a mixed hardening constitutive model considering SDDH is proposed based on the Yld2000-2d yield criterion and its effectiveness to predict the evolving yield behavior of ultrathin SUS304 sheets with different grain sizes is verified. In addition, the capability of the developed model to predict the plastic flow behavior of the ultrathin SUS304 sheets under biaxial loading cases is explored. It is found that the prediction accuracy by the developed model is higher than that by the Yld2000-2d yield criterion. The developed constitutive model has a stronger capability than the Yld2000-2d yield criterion combined with isotropic hardening, extensively implemented in commercial software, to enhance the prediction precision of plastic deformation behavior of the ultrathin sheets in micro forming.