Marciniak–Kuczynski type modelling of the effect of Through-Thickness Shear on the forming limits of sheet metal

Abstract The Marciniak–Kuczynski (MK) forming limit model is extended in order to predict localized necking in sheet metal forming operations in which Through-Thickness Shear (TTS), also known as out-of-plane shear, occurs. An example of such a forming operation is Single Point Incremental Forming. The Forming Limit Diagram (FLD) of a purely plastic, isotropic hardening material with von Mises yield locus is discussed, for monotonic deformation paths that include TTS. If TTS is present in the plane containing the critical groove direction in the MK model, it is seen that formability is increased for all in-plane strain modes, except equibiaxial stretching. The increase in formability due to TTS is explained through a detailed study of some selected deformation modes. The underlying mechanism is a change of the stress mode in the groove that results in a delay of the onset of localized necking.

[1]  P. Houtte,et al.  An extended Marciniak-Kuczynski forming limit model to assess the influence of through-thickness shear on formability , 2008 .

[2]  Jian Cao,et al.  Prediction of forming limit curves using an anisotropic yield function with prestrain induced backstress , 2002 .

[3]  K. Inal,et al.  Forming limit comparisons for FCC and BCC sheets , 2005 .

[4]  Kengo Yoshida,et al.  Forming limit stresses predicted by phenomenological plasticity theories with anisotropic work-hardening behavior , 2008 .

[5]  Plastic Flow Properties in Relation to Localized Necking in Sheets , 1978 .

[6]  M. A. Bertinetti,et al.  Predictions of forming limit diagrams using a rate-dependent polycrystal self-consistent plasticity model , 2009 .

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

[8]  Sean R. Agnew,et al.  Crystal plasticity-based forming limit prediction for non-cubic metals: Application to Mg alloy AZ31B , 2009 .

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

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

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

[12]  K. Hashiguchi,et al.  Localized necking analysis by the subloading surface model with tangential-strain rate and anisotropy , 2004 .

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

[14]  Y. Chastel,et al.  Forming limits prediction using rate-independent polycrystalline plasticity , 2002 .

[15]  Albert Van Bael,et al.  Prediction of forming limit strains under strain-path changes: Application of an anisotropic model based on texture and dislocation structure , 1998 .

[16]  Joost Duflou,et al.  Finite element based formability predictions of sheets subjected to the incremental forming process , 2007 .

[17]  D. Lloyd,et al.  Effect of cube texture on sheet metal formability , 2004 .

[18]  Thomas B. Stoughton,et al.  Review of theoretical models of the strain-based FLD and their relevance to the stress-based FLD , 2004 .

[19]  A. Erman Tekkaya,et al.  The Increased Forming Limits of Incremental Sheet Forming Processes , 2007 .

[20]  J. Gelin,et al.  Computational prediction of the localized necking in sheet forming based on microstructural material aspects , 1998 .

[21]  Kengo Yoshida,et al.  Effect of strain hardening behavior on forming limit stresses of steel tube subjected to nonproportional loading paths , 2007 .

[22]  John W. Hutchinson,et al.  Sheet Necking-III. Strain-Rate Effects , 1978 .

[23]  On the role of texture development in the forming limits of sheet metals , 1996 .

[24]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

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

[26]  J. C. Gerdeen,et al.  Effect of strain gradient and curvature on forming limit diagrams for anisotropic sheets , 1991 .

[27]  Yonggang Huang,et al.  Effects of superimposed hydrostatic pressure on sheet metal formability , 2009 .