Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales

Reliable material models are necessary for accurate analysis of micro-forming and micro-manufacturing processes. The grain-to-feature size ratio (d/D_c) in micro-forming processes is predicted to have a critical impact on the material behavior in addition to the well-known effect of the grain size (d) itself as manifested by the Hall-Petch relation. In this study, we investigated the "size effects" on the material flow curve of thin sheet metals under hydraulic bulge testing conditions. The ratio of the sheet thickness to the material grain size (N=t₀/d) was used as a parameter to characterize the interactive effects between the specimen and the grain sizes at the micro-scales, while the ratio of the bulge die diameter to the sheet thickness (M=D_c/t₀) was used to represent the effect of the feature size in the bulge test. Thin sheets of stainless steel 304 (SS304) with an initial thickness (t₀) of 51 μm and three different grain sizes (d) of 9.3, 10.6, and 17 μm were tested using five bulge diameters (D_c) of 2.5, 5, 10, 20, and 100 mm. A systematic approach for determining the flow curve of thin sheet metals in bulge testing was discussed and presented. The results of the bulge tests at different scales showed a decrease in the material flow curve with decreasing N value from 5.5 to 3.0, and with decreasing M value from 1961 to 191. However, as M value was decreased further from 191 to 49, an inversed relation between the flow curve and M value was observed; that is, the flow curve was found to increase with decreasing M value from 191 to 49, a new observed phenomenon that has never been reported in any open literature. New material models, both qualitatively and quantitatively, were developed to explain the size effects on the material flow curve by using the N and M as the characteristic parameters of relative size between the grain, the specimen (i.e., sheet thickness), and the part feature (i.e., bulge diameter). The explanation and prediction of the flow curve behavior based on these models were shown to be in good agreement with the bulge test results in this study and in the literature.