An Investigation Into the Prediction of Forming Limit Diagrams for Normal Anisotropic Material Based on Bifurcation Analysis

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
A. Jaamialahmadi ◽  
M. Kadkhodayan
Keyword(s):  
Bifurcation Analysis ◽  
Work Hardening ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
Optimization Method ◽  
Forming Limit ◽  
Proportional Loading ◽  
Normal Anisotropy ◽  
Left Hand ◽  
Prediction Limit

In this paper, formula derivation for bifurcation analysis based on a constitutive model including Hill 48 yield criterion with normal anisotropy of a pointed vertex on subsequent yield loci to predict the entire forming limit diagram (FLD) is carried out. Proportional loading, total deformation theory of plasticity, and power law relation are assumed. Predicted limit strains for Hill’s zero and minimum extension of localized neck orientation is derived. The dominancy of zero extension and minimum extension on the left-hand side of FLDs for different work hardening components and r-values are investigated in detail. An implicit four order rational function equation for major strain, which preferred that the orientation of neck correspond to minimum value of limit strain, is found by a developed optimization method. Optimized predicted limit strains for typical work hardening components and different r-values are obtained and discussed. Limit strains vary directly on the left and reversely on the right-hand side of FLD when r-value increases. Comparison between the predicted and experimental results exhibits a better agreement compared with those from the isotropic material. In addition, on the left-hand side, the resulted prediction limit strains represent a full dependency to assumed yield criterion. A comparison between the current work and Chow et al. results are performed and discussed in detail.

Bifurcation Analysis of Forming Limits for an Orthotropic Sheet Metal

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Shuhui Li ◽  
Ji He ◽  
Z. Cedric Xia ◽  
Danielle Zeng ◽  
Bo Hou
Keyword(s):  
Sheet Metal ◽  
Bifurcation Analysis ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
Experimental Result ◽  
Forming Limit ◽  
Forming Limits ◽  
R Value ◽  
Value Effect ◽  
The Hill

A bifurcation analysis of forming limits for an orthotropic sheet metal is presented in this paper. The approach extends Stören and Rice's (S–R) bifurcation analysis for isotropic materials, with materials following a vertex theory of plasticity at the onset of localized necking. The sheet orthotropy is represented by the Hill’48 yield criterion with three r-values in the rolling (r0), the transverse (r90) and the diagonal direction (r45). The emphasis of the study is on the examination of r-value effect on the sheet metal forming limit, expressed as a combination of the average r-value raverage and the planar anisotropy (Δr). Forming limits under both zero extension assumption and minimum extension assumption as well as necking band orientation evolution are investigated in detail. The comparison between the experimental result and predicted forming limit diagram (FLD) is presented to validate the extended bifurcation analysis. The r-value effect is observed under uniaxial and equal-biaxial loadings. However, no difference is found under plane strain condition in strain-based FLD which is consistent with Hill's theory. The force maximum criterion is also used to analyze FLD for verification.

Analysis of Forming Limits Using the Hill 1993 Yield Criterion

1998 ◽  
Vol 120 (3) ◽  
pp. 236-241 ◽  
Author(s):  
Siguang Xu ◽  
Klaus J. Weinmann ◽  
Abhijit Chandra
Keyword(s):  
Bifurcation Analysis ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
Anomalous Behavior ◽  
Forming Limit ◽  
Forming Limits ◽  
Material Parameters ◽  
Localized Necking ◽  
Wide Range ◽  
The Hill

Forming limits of thin sheets are investigated using a yield criterion recently proposed by Hill (1993). This criterion utilizes five independent material parameters, which can be determined from uniaxial and balanced biaxial experiments, to describe a wide range of material properties of sheet metals, including the anomalous behavior of aluminum. In the present work, a bifurcation analysis is pursued to predict the onset of localized necking in strain rate insensitive sheet materials. A detailed parametric study is then conducted to evaluate the effect of various material parameters on the positive minor strain side of the forming limit diagram. It is observed that limit strains are strongly dependent on the shape of the yield locus. Forming limits predicted using Hill’s 1993 yield criterion are compared with those predicted using Hill’s 1948 and 1979 criteria. Results from the bifurcation analysis are also compared with experimental observations, as well as the limit strain predicitons based on the M-K analysis.

Application of Barlat Yld-96 Yield Criterion for Predicting Formability of Pre-Strained Dual Phase Steel Sheets

2016 ◽  
Author(s):  
Shamik Basak ◽  
Sushanta Kumar Panda
Keyword(s):  
Dual Phase Steel ◽  
Yield Criterion ◽  
Thin Sheet ◽  
Damage Model ◽  
Forming Limit Diagram ◽  
Plasticity Theory ◽  
Forming Limit ◽  
Dual Phase ◽  
Strain Paths ◽  
Anisotropy Coefficients

The selection of advanced material model considering the anisotropy mechanical properties of the thin sheet is vital in order to estimate stress based forming limit diagram (σ-FLD). In present study associative plasticity theory was applied indulging Barlat Yld-96 anisotropy yield function and the Swift hardening law was implemented for estimating the limiting stresses from the conventional strain FLD (ε-FLD) of an automotive grade dual phase steel DP600. Three different approaches were made to evaluate Yld-96 anisotropy coefficients using experimental results of stack compression and tensile tests. To impose complex strain path, two stage stretch forming processes were simulated in finite element solver LS-DYNA. After biaxial pre-straining, the sample geometries were varied to achieve different strain paths during the second stage of deformation. The results indicated that there was negligible difference in limiting stress estimated by Yld-96 plasticity theory when the anisotropy coefficients were calculated based on plastic strain at ultimate tensile strength compare to that by minimum plastic work method. It was concluded that the dynamic shift of ε-FLD could be restricted by σ-FLD estimated using Yld 96 plasticity theory, and hence it was proposed to be a suitable damage model to evaluate formability of pre-strained DP600 steels.

A Modified Storen-Rice Bifurcation Analysis of Sheet Metal Forming Limit Diagrams

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
A. Jaamialahmadi ◽  
M. Kadkhodayan
Keyword(s):  
Bifurcation Analysis ◽  
Metal Forming ◽  
Optimization Procedure ◽  
Forming Limit ◽  
Forming Limit Diagrams ◽  
Left Hand ◽  
Modified Equations ◽  
Special Cases ◽  
Subsequent Yield Surface ◽  
Prediction Approach

Bifurcation analysis is a theoretical prediction approach to measure the FLD when the localized neck causes development of vertex on subsequent yield surface as was adopted by Storen-Rice. Some analyses lead to solutions for special cases such as zero and minimum extension. They offer an equation which needs to be optimized with respect to the minimum limit strain versus neck orientation for the whole domain of FLD. Moreover, the previous reported results for the left-hand side of FLD are not quite satisfactory. In this paper, a re-investigation into bifurcation analysis adopted by S-R lead to modified equations which significantly improved FLD and could be respected as a more general approach to find FLD theoretically. The derivation and optimization procedure of equations are indicated and discussed in detail. The predicted limit strains are studied for different work hardening coefficients and compared with Storen-Rice, Zhu and some experimental data and the obtained results show more agreement. Furthermore, the present restrictions and the required conditions for validation of the Zhu approach are fully discussed.

Effects of Anisotropic Yield Functions on Prediction of Forming Limit Diagram for AHS Steel

2014 ◽  
Vol 622-623 ◽  
pp. 257-264
Author(s):  
Sansot Panich ◽  
Vitoon Uthaisangsuk
Keyword(s):  
Biaxial Tension ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
High Strength ◽  
Forming Limit ◽  
Bulge Test ◽  
Yield Criteria ◽  
Hardening Law ◽  
Yield Functions ◽  
Work Hardening Coefficient

In this study, experimental and numerical analyses of Forming Limit Diagram (FLD) for Advanced High Strength (AHS) steel grade 980 were performed. Forming limit curve was first determined by means of the Nakazima stretch-forming test. Then, analytical calculations of the FLD based on the Marciniak-Kuczynski (M-K) model were carried out. Different yield criteria, namely, Hill’48 (r-value and stress-based), Yld89 (r-value and stress-based) and Barlat2000 (Yld2000-2d) were investigated. The strain hardening law according to Swift was applied. To identify parameters of each model, uniaxial tension, balanced bi-axial bulge test and in-plane biaxial tension test were performed. As a result, predicted plastic flow stresses and plastic anisotropies of the AHS steel by various directions were evaluated. In addition, effects of the anisotropic yield functions, strain rate sensitivities, imperfection values and work hardening coefficient on the predicted FLD were studied and discussed. It was found that the FLD based on the Yld2000-2d yield criterion was in better agreement with the experimental curve. Accuracy of the FLD predictions based on the M-K theory, especially in the biaxial state of stress, significantly depended on the applied yield criteria, for which yield stresses and r-values of different loading directions were required.

Effect of Alloy Composition and Pre-Ageing on the Stretch Formability of 6xxx Automotive Sheet Alloys

2018 ◽  
Vol 941 ◽  
pp. 955-960
Author(s):  
Hao Zhong ◽  
Ling Fei Cao
Keyword(s):  
Strain Rate ◽  
Work Hardening ◽  
Tensile Testing ◽  
Alloy Composition ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Cu Content ◽  
Automotive Sheet ◽  
Stretch Formability ◽  
Strain Rate Hardening

In this study, the effect of Mg/Si ratio, Cu content and/or pre-ageing treatment (e.g. 100 °C for 2 h and/or 200 °C for 20 s) on the stretch formability of 6xxx alloys was investigated through their influence on the work hardening and strain-rate hardening behaviour using tensile testing and forming limit diagram tests. The results showed that a high Mg/Si ratio, a low Cu content and/or the employment of pre-ageing could deteriorate the stretch formability due to the decrease in work hardening and/or strain rate hardening capabilities. Moreover, the stretch formability was observed to have an opposite correlation with the paint-bake response of the alloys studied.

Damage Analysis and Prediction of Forming Limits for IF Steel

2009 ◽  
Author(s):  
Jing Huang ◽  
Lijun Li ◽  
Zhida Li
Keyword(s):  
Sheet Metal ◽  
Damage Mechanics ◽  
Yield Criterion ◽  
Density Measurement ◽  
Coupled Model ◽  
Simple Expression ◽  
Forming Limit ◽  
If Steel ◽  
Proportional Loading ◽  
Anisotropic Plasticity

Based on Continuum Damage Mechanics, an isotropic damage model is developed to give a damage-coupled localized necking criterion. Hill’s 1948 quadratic yield criterion and flow theory are employed to describe anisotropic plasticity of sheet metal during forming procedure. Sheet forming experiments in three stress states and density measurement test have been performed on IF steel, and then the damage data obtained are used to validate numerical results based on the damage-coupled model. As for the proportional loading, a simple expression of limit strains has been obtained to predict the forming limit curve. Then the forming limit diagrams predicted by this damage-coupled anisotropic model have been validated with experimental data for two kinds of sheet metal. Also the influences of material properties on forming limit curves are discussed.

Effect of necking types of sheet metal on the left-hand side of forming limit diagram

2010 ◽  
Vol 210 (8) ◽  
pp. 1070-1075 ◽  
Author(s):  
Junying Min ◽  
Jianping Lin ◽  
Ying Cao ◽  
Wenhua Bao ◽  
Zhiguo Lu
Keyword(s):  
Sheet Metal ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Left Hand

scholarly journals Prediction of Forming Limit Diagram (FLD) and Effect of Work Hardening Property on FLD of Sheet Metals

2002 ◽  
Vol 88 (2) ◽  
pp. 88-94 ◽  
Author(s):  
Liwei GU ◽  
Akinori TANAKA ◽  
Kenji TANAKA ◽  
Koe NAKAJIMA
Keyword(s):  
Work Hardening ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Sheet Metals
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