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Effect of strain gradient and curvature on forming limit diagrams for anisotropic sheets

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Journal of Materials Shaping Technology

Abstract

Recent work on sheet metal formability had shown that the position of forming limit diagrams (FLDs) in punch stretching is higher than that in in-plane stretching because of a strain gradient effect resulting from bending a flat sheet into a curved sheet by punch stretching. To our knowledge, none of the developed theoretical models in the study of localized necking can be used to predict this phenomenon accurately so far. In this study, a new model, using Barlat and Lian’s new nonquadratic anisotropic yield criterion, is proposed by introducing a strain gradient term in the constitutive equation to consider the effect of the first order strain gradient (curvature), in the thickness direction resulting from bending, on the localized necking in anisotropic sheets. The developed model is used to study the effects of curvature on FLDs and to predict FLDs in punch stretching and inplane stretching for various materials. It is found that the theoretical predicted results are in good agreement with experimental data.

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Authors and Affiliations

  1. National Steel Corporation, Product Application Center, 12261 Market Street, 48150, Livonia, MI

    M. F. Shi

  2. Mechanical Engineering Department, University of Colorado at Denver, 1200 Larimer Street, Box 112, 80204, Denver, CO

    J. C. Gerdeen

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  1. M. F. Shi
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  2. J. C. Gerdeen
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Shi, M.F., Gerdeen, J.C. Effect of strain gradient and curvature on forming limit diagrams for anisotropic sheets. J. Materials Shaping Technology 9, 253–268 (1991). https://doi.org/10.1007/BF02833650

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