Forming limit criterion for ductile anisotropic sheets as a material property and its deformation path insensitivity. Part I: Deformation path insensitive formula based on theoretical models

In the common industrial thin sheet metal forming process at room temperature, in which in-homogenous deformation under the plane stress condition is typically the case, sheets are so ductile that sheet forming more often fails after abruptly severe strain localization, especially in the thinning mode. In such a case, measuring the fracture property might be impractical and an alternative criterion to measure sheet proneness to abruptly severe strain localization according to deformation modes, often dubbed as the forming limit criterion, replaces the fracture criterion to account for formability of the sheet, assuming that the criterion is applicable as a material property. However, severe strain localization is a mathematical consequence (of the boundary value problem) of the principle of linear momentum and the constitutive law; therefore not a part of material properties in principle, regardless of its sensitivity to deformation path. Nonetheless, the assumed applicability of the forming limit criterion as a material property in approximation for room temperature forming under the plane stress condition was partially validated in Part II in view of regular and modified hemispherical dome stretching and circular cup drawing tests, while its deformation path insensitive formulae were theoretically justified in Part I by examining the isotropic hardening formulation of rigid-plasticity and also theoretical forming limit models including the Considere (1885), Dorn and Thomsen (1947) and Hill (1952) models as well as the M–K (1967) model.

[1]  Dong-Yol Yang,et al.  Finite element method for sheet forming based on an anisotropic strain-rate potential and the convected coordinate system , 1995 .

[2]  Yuanli Bai,et al.  Application of extended Mohr–Coulomb criterion to ductile fracture , 2009 .

[3]  M. Berveiller,et al.  Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model , 2009 .

[4]  K. Chung,et al.  Ideal forming—I. Homogeneous deformation with minimum plastic work , 1992 .

[5]  S. Shima,et al.  Criteria for ductile fracture and their applications , 1980 .

[6]  Tomasz Wierzbicki,et al.  Prediction of shear-induced fracture in sheet metal forming , 2010 .

[7]  Ke-Shi Zhang,et al.  Numerical analysis of the influence of the Lode parameter on void growth , 2001 .

[8]  R. Arrieux,et al.  Determination of the Forming Limit Stress Curve for Anisotropic Sheets , 1987 .

[9]  Robert H. Wagoner,et al.  A rigid-viscoplastic finite element program for sheet metal forming analysis , 1989 .

[10]  G. R. Johnson,et al.  Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures , 1985 .

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

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

[13]  J. Hutchinson,et al.  Modification of the Gurson Model for shear failure , 2008 .

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

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

[16]  Akhtar S. Khan,et al.  A new approach for ductile fracture prediction on Al 2024-T351 alloy , 2012 .

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

[18]  Philip Eyckens,et al.  Marciniak–Kuczynski type modelling of the effect of Through-Thickness Shear on the forming limits of sheet metal , 2009 .

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

[20]  T. Wierzbicki,et al.  A new model of metal plasticity and fracture with pressure and Lode dependence , 2008 .

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

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

[23]  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.

[24]  Joseph Marin,et al.  Plastic stress-strain relations under radial and non-radial combined stress loading , 1953 .

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

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

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

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

[29]  J. D. Embury,et al.  A model of ductile fracture based on the nucleation and growth of voids , 1981 .

[30]  Jinkook Kim,et al.  Modeling of Ductile Fracture: Significance of Void Coalescence , 2006 .

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

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

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

[34]  F. A. McClintock,et al.  A Criterion for Ductile Fracture by the Growth of Holes , 1968 .

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

[36]  M. Berveiller,et al.  Strain localization analysis for single crystals and polycrystals: Towards microstructure-ductility linkage , 2013 .

[37]  Jeong Whan Yoon,et al.  Path independent forming limits in strain and stress spaces , 2012 .

[38]  Kwansoo Chung,et al.  Formability of TWIP (twinning induced plasticity) automotive sheets , 2011 .

[39]  Jinkook Kim,et al.  Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity , 2004 .

[40]  W. Hosford.  A Generalized Isotropic Yield Criterion , 1972 .

[41]  R. H. Van Stone,et al.  Microstructural aspects of fracture by dimpled rupture , 1985 .

[42]  R. H. Wagoner,et al.  The shear fracture of dual-phase steel , 2011 .

[43]  M. Touati,et al.  Determination of the forming limits in planar-isotropic and temperature-sensitive sheet metals , 1985 .

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

[45]  Danielle Zeng,et al.  A Path Independent Forming Limit Criterion for Sheet Metal Forming Simulations , 2008 .

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

[47]  K. Chung,et al.  Ideal forming. II : Sheet forming with optimum deformation , 1992 .

[48]  L. Xue,et al.  Constitutive modeling of void shearing effect in ductile fracture of porous materials , 2008 .

[49]  D. M. Tracey,et al.  On the ductile enlargement of voids in triaxial stress fields , 1969 .

[50]  Robert H. Wagoner,et al.  Invariance of neck formation to material strength and strain rate for power-law materials , 1986 .

[51]  Jyhwen Wang,et al.  MODELING THE LOCALIZED NECKING IN ANISOTROPIC SHEET METALS , 2012 .

[52]  Ning Ma,et al.  A modified damage model for advanced high strength steel sheets , 2011 .

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

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

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

[56]  Haowen Liu,et al.  Strain rate and temperature dependent fracture criteria for isotropic and anisotropic metals , 2012 .

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

[58]  B. Loret,et al.  Anisotropic stiffness degradation triggers onset of strain localization , 1997 .

[59]  M. Considére.  Mémoire sur l'emploi du fer et de l'acier dans les constructions , 1885 .

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

[61]  Imad Barsoum,et al.  Rupture mechanisms in combined tension and shear : Experiments , 2007 .

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

[63]  S. Clift,et al.  Fracture prediction in plastic deformation processes , 1990 .

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

[65]  A. Needleman,et al.  Analysis of the cup-cone fracture in a round tensile bar , 1984 .

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

[67]  Zoran Filipi,et al.  Simulation Study of a Series Hydraulic Hybrid Propulsion System for a Light Truck , 2007 .

[68]  M. Baig,et al.  Anisotropic responses, constitutive modeling and the effects of strain-rate and temperature on the formability of an aluminum alloy , 2011 .

[69]  Philip Eyckens,et al.  An extended Marciniak–Kuczynski model for anisotropic sheet subjected to monotonic strain paths with through-thickness shear , 2011 .

[70]  Hoon Huh,et al.  Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality , 2013 .

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

[72]  Jean Lemaitre,et al.  A Course on Damage Mechanics , 1992 .

[73]  K. Chung,et al.  A deformation theory of plasticity based on minimum work paths , 1993 .

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

[75]  Evaluation of Charpy Impact Test Performance for Advanced High-Strength Steel Sheets Based on a Damage Model , 2010 .

[76]  S. Y. Lee,et al.  Finite element simulation of sheet forming based on a planar anisotropic strain-rate potential , 1996 .

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

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

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

[80]  Davide Bigoni,et al.  Uniqueness and localization—I. Associative and non-associative elastoplasticity , 1991 .

[81]  J. Hancock,et al.  On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states , 1976 .

[82]  John E. Carsley,et al.  Forming limit analysis for two-stage forming of 5182-O aluminum sheet with intermediate annealing , 2013 .

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

[84]  Frank A. McClintock,et al.  PLASTICITY ASPECTS OF FRACTURE , 1971 .

[85]  H. Ishigaki.  Deformation Analysis of Large Sized Panels in the Press Shop , 1978 .

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