An analytical approach for the prediction of forming limit curves subjected to combined strain paths

Abstract In the present work, an analytical approach for the prediction of forming limit curves is proposed to incorporate the effect of combined strain paths. The effect of combined strain paths (considering the directional dependency of pre-straining and further straining) is addressed by integrating the incremental equivalent strain expression in two stages i.e., pre-strain and subsequent loading. In each stage, the strain path is assumed to be linear and different combinations of pre-strain (uniaxial, plane-strain and equi-biaxial) are considered. Material anisotropy is taken into account in each stage. The predictions of the present model are compared with the experimental results on forming limit curves under combined strain paths for Al6111-T4 [24] and are found to be in good agreement with each other.

[1]  J. Embury,et al.  Effects of superimposed hydrostatic pressure on fracture in sheet metals under tension , 2010 .

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

[3]  C. Chow,et al.  A Unified Damage Approach for Predicting Forming Limit Diagrams , 1997 .

[4]  J. Embury,et al.  Effects of superimposed hydrostatic pressure on fracture in round bars under tension , 2009 .

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

[6]  J. Rice Localization of plastic deformation , 1976 .

[7]  W. Hosford,et al.  Effect of changing strain paths on , 1993, Metallurgical and Materials Transactions A.

[8]  Mehrdad Aghaie-Khafri,et al.  Predicting of plastic instability and forming limit diagrams , 2004 .

[9]  H. Aretz,et al.  An extension of Hill’s localized necking model , 2010 .

[10]  William F. Hosford,et al.  Upper-bound anisotropic yield locus calculations assuming 〈111〉-pencil glide , 1980 .

[11]  C. Chow,et al.  Prediction of Forming Limit Diagram Based on Damage Coupled Kinematic-Isotropic Hardening Model Under Nonproportional Loading , 2002 .

[12]  John A. Williams,et al.  The use of a shear instability criterion to predict local necking in sheet metal deformation , 1983 .

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

[14]  A. P. Karafillis,et al.  A general anisotropic yield criterion using bounds and a transformation weighting tensor , 1993 .

[15]  Abhijit Chandra,et al.  A unified bifurcation analysis of sheet metal forming limits , 2001 .

[16]  Fabrice Morestin,et al.  Experimental and analytical necking studies of anisotropic sheet metals , 2001 .

[17]  D. Lloyd,et al.  Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet , 1999 .

[18]  Effect of stress state on cavitation and hot forming limits of a coarse-grained Al5052 alloy , 2002 .

[19]  M. Jie,et al.  Forming limits of AL 6022 sheets with material damage consideration: theory and experimental validation , 2004 .

[20]  Luen Chow Chan,et al.  Forming limit diagrams of strain-rate-dependent sheet metals , 2009 .

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

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

[23]  K. Chan,et al.  The stress state dependence of cavitation in commercial superplastic Al5083 alloy , 2002 .

[24]  K. K. Chow,et al.  The cavitation behavior of a coarse-grained Al5052 alloy under hot uniaxial and equibiaxial tension , 2001 .

[25]  T. Balan,et al.  Strain localization analysis using a large deformation anisotropic elastic-plastic model coupled with damage , 2009 .

[26]  M. Worswick,et al.  Computational analysis of stress-based forming limit curves , 2007 .

[27]  Jørgen Amdahl,et al.  Analytical and numerical analysis of sheet metal instability using a stress based criterion , 2008 .

[28]  W. Hosford,et al.  Calculations of forming limit diagrams for changing strain paths , 1993 .

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

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

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

[32]  Julian M. Allwood,et al.  Generalised forming limit diagrams showing increased forming limits with non-planar stress states , 2009 .

[33]  Amar Khennane,et al.  Fracture in sheet metal forming: Effect of ductile damage evolution , 2007 .

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

[35]  Payam Matin,et al.  Influence of transverse normal stress on sheet metal formability , 2003 .

[36]  Carpóforo Vallellano,et al.  A Study to Predict Failure in Biaxially Stretched Sheets of Aluminum Alloy 2024-T3 , 2008 .

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

[38]  T. Stoughton The Influence of the Material Model on the Stress-Based Forming Limit Criterion , 2002 .

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

[40]  H. W. Swift Plastic instability under plane stress , 1952 .

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

[42]  Payam H. Matin,et al.  Practical limitations to the influence of through-thickness normal stress on sheet metal formability , 2005 .

[43]  J. Min,et al.  Effect of necking types of sheet metal on the left-hand side of forming limit diagram , 2010 .

[44]  A. Gurson Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

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

[46]  W. Hosford,et al.  Calculations of forming limit , 1993, Metallurgical and Materials Transactions A.

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

[48]  P. Friedman,et al.  Effects of plastic anisotropy and yield criteria on prediction of forming limit curves , 2000 .

[49]  W. Lode,et al.  Versuche über den Einfluß der mittleren Hauptspannung auf das Fließen der Metalle Eisen, Kupfer und Nickel , 1926 .

[50]  Mitsutoshi Kuroda,et al.  Path-dependence of the forming limit stresses in a sheet metal , 2007 .

[51]  R. Arrieux,et al.  Determination and use of the forming limit stress diagrams in sheet metal forming , 1995 .

[52]  Yuanli Bai,et al.  Forming severity concept for predicting sheet necking under complex loading histories , 2008 .

[53]  Carpóforo Vallellano,et al.  Prediction of Ductile Failure in the Stretch‐Forming of AA2024 Sheets , 2007 .

[54]  Tomasz Wierzbicki,et al.  DUCTILE FRACTURE CHARACTERIZATION OF ALUMINUM ALLOY 2024-T351 USING DAMAGE PLASTICITY THEORY , 2009 .

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

[56]  L. Xue,et al.  Localization conditions and diffused necking for damage plastic solids , 2010 .

[57]  Yansheng Zhang,et al.  Mathematical description for flow curves of some stable austenitic steels , 1994 .

[58]  Fahrettin Ozturk,et al.  ANALYSIS OF FORMING LIMITS USING DUCTILE FRACTURE CRITERIA , 2004 .

[59]  Jean Lemaitre,et al.  Coupled elasto-plasticity and damage constitutive equations , 1985 .

[60]  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.

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