Predictions of forming limit diagrams using a rate-sensitive crystal plasticity model

Abstract A rate-sensitive crystal plasticity model is applied directly in conjunction with the Marciniak-Kuczynski approach to predict forming limit diagrams (FLD's) for annealed FCC sheet metals having various initial textures. Sheets with ideal orientations are first analysed in order to investigate analytically the influence of microstructure and microscopic properties on the FLD. Two ideal orientations of rolling textures, (101) [010] (Goss) and (001) [OTO] (cube), are considered. In the limit of zero material strain-rate senstivity (m → 0), a simple analytic expression for the localized necking strains is obtained. It indicates that localized necking occurs when the total accumulated shear over all slip systems in the band of localized deformation reaches a critical value. The FLD's of annealed sheets having arbitrary initial textures are then determined numerically. Three particular initial textures are considered. Among these, the predicted FLD for the R-type initial texture shows the best agreement with the experimental ones. Finally, the effects of various factors on the forming limit diagrams are discussed such as: slip hardening, strain-rate sensitivity, initial imperfections, initial texture and yield surface shape.

[1]  James R. Rice,et al.  Localized necking in thin sheets , 1975 .

[2]  J. Hutchinson,et al.  Bounds and self-consistent estimates for creep of polycrystalline materials , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  John W. Hutchinson,et al.  Sheet Necking-II. Time-Independent Behavior , 1978 .

[5]  Z. Marciniak,et al.  Limit strains in the processes of stretch-forming sheet metal , 1967 .

[6]  Kwai S. Chan,et al.  Effects of plastic anisotropy and yield surface shape on sheet metal stretchability , 1985 .

[7]  Kenneth W. Neale,et al.  Limit strain predictions for strain-rate sensitive anisotropic sheets , 1980 .

[8]  Frédéric Barlat,et al.  Characterization and modeling of the mechanical behavior and formability of a 2008-T4 sheet sample , 1989 .

[9]  Frédéric Barlat,et al.  Crystallographic texture, anisotropic yield surfaces and forming limits of sheet metals , 1987 .

[10]  Z. Marciniak,et al.  The mechanics of sheet metal forming , 1992 .

[11]  J. L. Duncan,et al.  Failure in sheet metal in biaxial tension , 1971 .

[12]  John L. Bassani,et al.  Yield characterization of metals with transversely isotropic plastic properties , 1977 .

[13]  R. Asaro,et al.  Overview no. 42 Texture development and strain hardening in rate dependent polycrystals , 1985 .

[14]  W. T. Roberts,et al.  Effect of Grain anisotropy on limit strains in biaxial stretching: part i. influence of sheet thickness and grain size in weakly textured sheets , 1981 .

[15]  P. Bate.  The prediction of limit strains in steel sheet using a discrete slip plasticity model , 1984 .

[16]  Z. Marciniak,et al.  Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension , 1973 .

[17]  J. Jonas,et al.  Large strain shear and torsion of rate-sensitive FCC polycrystals , 1990 .

[18]  Kenneth W. Neale,et al.  A modified model for simulating latent hardening during the plastic deformation of rate-dependent FCC polycrystals , 1993 .

[19]  Pierre Coulomb,et al.  Eulerian simulation of deformation textures , 1979 .

[20]  M. Gotoh.  A theory of plastic anisotropy based on a yield function of fourth order (plane stress state)—I , 1977 .

[21]  Horst Lippmann,et al.  Metal Forming Plasticity , 1979 .

[22]  J. Jonas,et al.  Stress response and persistence characteristics of the ideal orientations of shear textures , 1989 .

[23]  Y. Zhou,et al.  Analytical solutions for the ideal orientations of f.c.c. rolling textures , 1991 .

[24]  Frédéric Barlat,et al.  Plastic behaviour and stretchability of sheet metals. Part II: Effect of yield surface shape on sheet forming limit , 1989 .

[25]  D. Koss,et al.  Localized Necking of Sheet at Negative Minor Strains , 1984 .

[26]  R. Hill,et al.  On discontinuous plastic states, with special reference to localized necking in thin sheets , 1952 .