How Strain-Rate Sensitivity Creates Two Forming-Limit Diagrams: Bragard-Type Versus Instability-Strain, Correlation-Coefficient-Based Temporal Curves

Abstract

With digital-image correlation techniques, it is now possible to measure the forming-limit diagram, FLD, of metal sheet using both strains outside (Bragard-type analysis) and inside (temporal, correlation-coefficient calculation) of a necking instability. We performed these measurements using the Marciniak and Kuczynski, MK, specimen geometry on three metals having very different strain-rate sensitivities: Zn20, a Zn-Cu-Ti alloy; a cold-rolled steel; and an AA6061-T4 aluminum alloy. The relationship between the Bragard type and temporal FLDs was very different depending on the metal?s strain-rate sensitivity. For the highly strain-rate sensitive Zn20, m = 0.075, the temporal FLD was well above the Bragard type for all strain states, from uniaxial tension to balanced-biaxial deformation. In the case of the cold-rolled steel, m = 0.015, the two analyses were equivalent in balanced-biaxial deformation, but the temporal results were higher in plane-strain and uniaxial tension, by 25 and 40%, respectively. The two types of FLD curves were equivalent for all strain states for the AA6061-T4 aluminum alloy, m = zero. In addition, we found that the strain paths followed by the three metals were different for the same MK sample geometries. These differences were due to different shapes of the yield/flow loci, as confirmed based on visco-plastic self-consistent simulations. These results indicate that engineers should account for the different FLDs for positive strain-rate sensitive metals, possibly as upper and lower bounds. In addition, it appears that for metals with yield/flow loci like that of the AA6061-T4 aluminum alloy, certain strain paths between plane strain and balanced-biaxial deformation are difficult to attain when using the MK-type sample geometry.