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

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.

Automated summary

Digital-image correlation techniques can now be used to measure the forming-limit diagram (FLD) of metal sheets, and the relationship between Bragard-type and temporal FLDs varies depending on the metal's strain-rate sensitivity. The strain paths followed by different metals with the same MK sample geometries were found to be different, indicating the need to account for different FLDs for positive strain-rate sensitive metals.