Size effect on the yield behavior of metal foil under multiaxial stress states: Experimental investigation and modelling

In microforming process, the metal foil is often deformed under complex stress states and meanwhile affected by the scale effect. To explore the size effect on the yield behavior of metal foil under multiaxial stress states, the biaxial tensile tests of the annealed stainless steel SUS304 foils were performed. The experimentally determined yield loci evolve from rough ellipse to Tresca-like yield locus with the decrease of the ratio of foil thickness to grain size. The experimental result indicates that both size and shape of the yield locus are influenced by size effect and stress states. Four conventional yield criteria including von Mises, Hill'48, Barlat'89 and Yld2000-2d were utilized to evaluate their applicabilities at micro scale. It is found that the predicting accuracy of the macro-scaled yield criterion is worsened with the decreasing grain numbers across the thickness direction. According to the evolving trend of the experimental yield locus and the deviation analysis of the theoretical yield locus, a multiscale yield criterion was proposed by modeling the relationship between the exponent, anisotropy parameters and size effect. In the end, the developed criterion was verified by analyzing the earing profile of the cup from deep drawing test and Hall-Petch (HP) relationships under multiaxial stress states.