An improved analytical approach for determination of forming limit diagrams considering the effects of yield functions

Abstract The purpose of this study is to develop a methodology for prediction of the forming limit diagrams (FLD). The methodology is based on the Marciniak and Kuczynski theory. Two yield functions proposed by “Hosford” and “BBC2000” and two hardening laws one with and the other without strain rate sensitivity have been applied. To solve the nonlinear systems of equations, the modified Newton–Raphson with globally convergence method has been used. In this process, a technique for step length selection in the frame of gradient descent method for unconstrained optimization has been applied. This technique has guaranteed the convergence of the solution with the Newton–Raphson method. Also for the purpose of rapid convergence the so-called “Armijo” condition has been used. The predicted results have been compared with the published experimental data for AK steel and AA5XXX alloys.

[1]  Evânio L. S. Vieira,et al.  Proposing a better forming limit diagram prediction: a comparative study , 2003 .

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

[3]  John W. Hutchinson,et al.  On the Prediction of Necking in Anisotropic Sheets , 1979 .

[4]  E. Spišák,et al.  Comparison of the Forming - Limit Diagram (FLD) Models for Drawing Quality (DQ) Steel Sheets , 2005 .

[5]  Frédéric Barlat,et al.  Prediction of the forming limit diagrams of anisotropic sheets in linear and non-linear loading , 1985 .

[6]  A. P. Karafillis,et al.  Prediction of localized thinning in sheet metal using a general anisotropic yield criterion , 2000 .

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

[8]  C. Chow,et al.  Prediction of forming limit diagrams for AL6111-T4 under non-proportional loading , 2001 .

[9]  Dorel Banabic,et al.  Prediction of the influence of yield locus on the limit strains in sheet metals , 2001 .

[10]  L. Armijo.  Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[11]  D. Blackwell.  An analog of the minimax theorem for vector payoffs. , 1956 .

[12]  A. Barata da Rocha,et al.  A more general model for forming limit diagrams prediction , 2002 .

[13]  P. B. Mellor,et al.  Some comments on the limit strains in sheet metal stretching , 1975 .

[14]  Amit K. Ghosh,et al.  Effects of strain path changes on the formability of sheet metals , 1978 .

[15]  Gorton M. Goodwin,et al.  Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop , 1968 .

[16]  Effect of rounded vertices in the yield surface on localized necking in biaxially stretched sheets , 1982 .

[17]  Frédéric Barlat,et al.  Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions , 1989 .

[18]  W. Chien,et al.  A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions , 2004 .

[19]  Viggo Tvergaard,et al.  Forming limit diagrams for anisotropic metal sheets with different yield criteria , 2000 .

[20]  J. Gracio,et al.  The performance of Yld96 and BBC2000 yield functions in forming limit prediction , 2002 .

[21]  E. Voce,et al.  The relationship between stress and strain for homogeneous deformations , 1948 .

[22]  J. Pan,et al.  FAILURE PREDICTION IN ANISOTROPIC SHEET METALS UNDER FORMING OPERATIONS WITH CONSIDERATION OF ROTATING PRINCIPAL STRETCH DIRECTIONS , 2000 .

[23]  Siguang Xu,et al.  Prediction of forming limit curves of sheet metals using Hill's 1993 user-friendly yield criterion of anisotropic materials , 1998 .

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

[25]  Dorel Banabic,et al.  Application of various FLD modelling approaches , 2005 .