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

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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.

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Acknowledgments

The authors are grateful for the financial support provided by ANPCyT PICT-A 2017-2970. We also acknowledge the invaluable support of Fernando Ugo in performing the forming-limit and tension experiments.

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Authors and Affiliations

  1. Instituto de Física Rosario (CONICET/UNR), Ocampo y Esmeralda, 2000, Santa Fe, Rosario, Argentina

    M. A. Bertinetti, A. Roatta, E. Nicoletti, M. Leonard, M. Stout & J. W. Signorelli

  2. Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario Av. Pellegrini 250, 2000, Santa Fe, Rosario, Argentina

    M. A. Bertinetti, A. Roatta, M. Leonard & J. W. Signorelli

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  1. M. A. Bertinetti
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  2. A. Roatta
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  3. E. Nicoletti
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  4. M. Leonard
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  5. M. Stout
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  6. J. W. Signorelli
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Correspondence to J. W. Signorelli.

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Bertinetti, M.A., Roatta, A., Nicoletti, E. et al. How Strain-Rate Sensitivity Creates Two Forming-Limit Diagrams: Bragard-Type Versus Instability-Strain, Correlation-Coefficient-Based Temporal Curves. J. of Materi Eng and Perform 30, 4183–4193 (2021). https://doi.org/10.1007/s11665-021-05745-w

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