Path-dependence of the forming limit stresses in a sheet metal

Abstract The effect of changing strain paths on the forming limit stresses of sheet metals is investigated using the Marciniak–Kuczynski model and a phenomenological plasticity model with non-normality effects [Kuroda, M., Tvergaard, V., 2001. A phenomenological plasticity model with non-normality effects representing observations in crystal plasticity. J. Mech. Phys. Solids 49, 1239–1263]. Forming limits are simulated for linear stress paths and two types of combined loading: a combined loading consisting of two linear stress paths in which unloading is included between the first and second loadings (combined loading A), and combined loading in which the strain path is abruptly changed without unloading (combined loading B). The forming limit stresses calculated for combined loading A agree well with those calculated for the linear stress paths, while the forming limit curves in strain space depend strongly on the strain paths. The forming limit stresses calculated for the combined loading B do not, however, coincide with those calculated for the linear stress paths. The strain-path dependence of the forming limit stress is discussed in detail by observing the strain localization process.

[1]  A. H. van den Boogaard,et al.  A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states , 2006 .

[2]  V. Tvergaard,et al.  A phenomenological plasticity model with non-normality effects representing observations in crystal plasticity , 2001 .

[3]  T. Kuwabara,et al.  Yield locus and work hardening behavior of a thin-walled steel tube subjected to combined tension-internal pressure , 2003 .

[4]  Z. Zimniak,et al.  Implementation of the forming limit stress diagram in FEM simulations , 2000 .

[5]  A. Needleman,et al.  A tangent modulus method for rate dependent solids , 1984 .

[6]  Plastic Instability of Sheet Metals under Simple and Complex Strain Paths , 1984 .

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

[8]  E. Giessen,et al.  Effects of strain paths on sheet metal limit strains , 1998 .

[9]  Kenneth W. Neale,et al.  On forming limit stress diagram analysis , 2005 .

[10]  Jeong Whan Yoon,et al.  Sheet metal formability analysis for anisotropic materials under non-proportional loading , 2005 .

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

[12]  Viggo Tvergaard,et al.  Use of abrupt strain path change for determining subsequent yield surface: illustrations of basic idea , 1999 .

[13]  M. Kuroda.  Interpretation of the behavior of metals under large plastic shear deformations: comparison of macroscopic predictions to physically based predictions , 1999 .

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

[15]  Frédéric Barlat,et al.  Linear transfomation-based anisotropic yield functions , 2005 .

[16]  William F. Hosford,et al.  The influence of strain-path changes on forming limit diagrams of A1 6111 T4 , 1994 .

[17]  Chu Chin-Chan.  An investigation of the strain path dependence of the forming limit curve , 1982 .

[18]  C.H. Crawford.  Industrial Standards , 1948, Proceedings of the IRE.

[19]  A class of plastic constitutive equations with vertex effect—IV. Applications to prediction of forming limit strains of metal sheets under nonproportional loadings , 1985 .

[20]  R. Sowerby,et al.  A theoretical and experimental investigation of limit strains in sheet metal forming , 1996 .

[21]  Thomas B. Stoughton,et al.  Stress-Based Forming Limits in Sheet-Metal Forming , 2001 .

[22]  Thomas B. Stoughton,et al.  A general forming limit criterion for sheet metal forming , 2000 .

[23]  René de Borst,et al.  Material Instabilities in Solids , 1998 .

[24]  J. Gronostajski,et al.  Sheet metal forming-limits for complex strain paths , 1984 .

[25]  Frédéric Barlat,et al.  Orthotropic yield criterion for hexagonal closed packed metals , 2006 .

[26]  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 .

[27]  Z. Zimniak.  Application of a system for sheet metal forming design , 2000 .

[28]  Viggo Tvergaard,et al.  Use of abrupt strain path change for determining subsequent yield surface: experimental study with metal sheets , 2000 .

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

[30]  Viggo Tvergaard,et al.  Effect of strain path change on limits to ductility of anisotropic metal sheets , 2000 .

[31]  Kengo Yoshida,et al.  Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure , 2004 .

[32]  W. Hosford,et al.  Effect of changing strain paths on forming limit diagrams of Al 2008-T4 , 1993 .