A constitutive model for stainless steel 304 sheet considering size effect in micro-scale

The deformation behavior of the material in micro-forming processes is different from macro-scale due to the size effect. The size effect in micro-scale appears due to few grains in the deformation region and causes the material behavior to be affected by the thickness and grain size of the sheet. Because of this, conventional constitutive models are not suitable for predicting the material behavior in micro-forming processes. In this paper, a new constitutive model based on the Swift equation and considering size effect in micro-scale is presented to describe the strain-hardening behavior of the stainless steel 304 foil. Comparison of flow stress curves of specimens with different grain sizes showed that the prediction of material flow stress with the new constitutive model is improved compared to the existing model, especially at high strains, so that the average and maximum error of the new model is less than one-third and less than half of the conventional model error, respectively. Finite element simulation of the micro-tensile test was performed using the new constitutive model to investigate the size effect on the deformation behavior of the specimens. The new constitutive model was verified by comparing the results of experimental tests and finite element simulation of sheets with different grain sizes. Also, the results revealed that the estimation of the forming force using the new constitutive model is done with higher accuracy than the conventional and existing model for sheets with different grain sizes and high strain ranges.