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.

A New Approach to the Evaluation of Forming Limits in Sheet Metal Forming

2015 ◽  
Vol 639 ◽  
pp. 333-338 ◽  
Author(s):  
Marion Merklein ◽  
Andreas Maier ◽  
Daniel Kinnstätter ◽  
Christian Jaremenko ◽  
Emanuela Affronti
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Strain History ◽  
Failure Behavior ◽  
Forming Limits ◽  
Optical Strain Measurement ◽  
Optical Strain

The forming limit diagram (FLD) is at the moment the most important method for the prediction of failure within sheet metal forming operations. Key idea is the detection of the onset of necking in dependency of different sample geometry. Whereas the standardized evaluation methods provides very robust and reliable results for conventional materials like deep drawing steels, the determined forming limits for modern light materials are often too conservative due to the different failure behavior. Therefore, within this contribution a new and innovative approach for the identification of the onset of necking will be presented. By using a pattern recognition-based approach in combination with an optical strain measurement system the complete strain history during the test can be evaluated. The principal procedure as well as the first promising results are presented and discussed.

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.

Effect of Yield Criterion on Numerical Simulation Results Using a Stress-Based Failure Criterion

2006 ◽  
Vol 128 (3) ◽  
pp. 436-444 ◽  
Author(s):  
Aaron Sakash ◽  
Sumit Moondra ◽  
Brad L. Kinsey
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Sheet Metal ◽  
Failure Criterion ◽  
Path Dependence ◽  
Yield Criterion ◽  
Forming Limit Diagram ◽  
Dome Height ◽  
Forming Limit ◽  
Simulation Results

Determining tearing concerns in numerical simulations of sheet metal components is difficult since the traditional failure criterion, which is strain-based, exhibits a strain path dependence. A stress-based, as opposed to a strain-based, failure criterion has been proposed and demonstrated analytically, experimentally in tube forming, and through numerical simulations. The next step in this progression to the acceptance of a stress-based forming limit diagram is to demonstrate how this failure criterion can be used to predict failure of sheet metal parts in numerical simulations. In this paper, numerical simulation results for dome height specimens are presented and compared to experimental data. This procedure was repeated for various yield criteria to examine the effect of this parameter on the ability to predict failure in the numerical simulations. Reasonable agreement was obtained comparing the failure predicted from numerical simulations and those found experimentally, in particular for the yield criterion which has been shown to best characterize the material used in this study.

Optimization of Sheet Metal Process Parameters of a Shield Case Piece Using Computer Simulation

2006 ◽  
Vol 510-511 ◽  
pp. 330-333
Author(s):  
M.C. Curiel ◽  
Ho Sung Aum ◽  
Joaquín Lira-Olivares
Keyword(s):  
Sheet Metal ◽  
Thickness Distribution ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Physical Processes ◽  
Forming Process ◽  
Element Analysis ◽  
One Step ◽  
Range Of Values ◽  
Principal Strains

Numerical simulations based on Finite Element Analysis (FEA) are widely used to predict and evaluate the forming parameters before performing the physical processes. In the sheet metal industry, there are basically two types of FE programs: the inverse (one-step) programs and the incremental programs. In the present paper, the forming process of the shield case piece (LTA260W1-L05) was optimized by performing simulations with both types of software. The main analyzed parameter was the blankholding force while the rest of the parameters were kept constant. The criteria used to determine the optimum value was based on the Forming Limit Diagram (FLD), fracture and wrinkling of the material, thickness distribution, and the principal strains obtained. It was found that the holding force during the forming process deeply affects the results, and a range of values was established in which the process is assumed to give a good quality piece.

Experimental and Numerical Analysis of Forming Limits in CNC Incremental Sheet Forming

2007 ◽  
Vol 344 ◽  
pp. 511-518 ◽  
Author(s):  
Markus Bambach ◽  
M. Todorova ◽  
Gerhard Hirt
Keyword(s):  
Sheet Metal ◽  
Sheet Forming ◽  
Incremental Sheet Forming ◽  
Negative Slope ◽  
Evaluation Procedure ◽  
Forming Limit ◽  
Limit Curve ◽  
Forming Limit Curve ◽  
Forming Limits ◽  
Straight Line

Asymmetric incremental sheet forming (AISF) is a relatively new manufacturing process for the production of low volumes of sheet metal parts. Forming is accomplished by the CNC controlled movements of a simple ball-headed tool that follows a 3D trajectory to gradually shape the sheet metal blank. Due to the local plastic deformation under the tool, there is almost no draw-in from the flange region to avoid thinning in the forming zone. As a consequence, sheet thinning limits the amount of bearable deformation, and thus the range of possible applications. Much attention has been given to the maximum strains that can be attained in AISF. Several authors have found that the forming limits are considerably higher than those obtained using a Nakazima test and that the forming limit curve is approximately a straight line (mostly having a slope of -1) in the stretching region of the FLD. Based on these findings they conclude that the “conventional” forming limit curves cannot be used for AISF and propose dedicated tests to record forming limit diagrams for AISF. Up to now, there is no standardised test and no evaluation procedure for the determination of FLCs for AISF. In the present paper, we start with an analysis of the range of strain states and strain paths that are covered by the various tests that can be found in the literature. This is accomplished by means of on-line deformation measurements using a stereovision system. From these measurements, necking and fracture limits are derived. It is found that the fracture limits can be described consistently by a straight line with negative slope. The necking limits seem to be highly dependent on the test shapes and forming parameters. It is concluded that standardisation in both testing conditions and the evaluation procedures is necessary, and that a forming limit curve does not seem to be an appropriate tool to predict the feasibility of a given part design.

Effect of the Constitutive Law on the Accuracy of Prediction of the Forming Limit Curves

2012 ◽  
Vol 504-506 ◽  
pp. 77-82 ◽  
Author(s):  
Liana Paraianu ◽  
Dan Sorin Comsa ◽  
Ioan Pavel Nicodim ◽  
Ioan Ciobanu ◽  
Dorel Banabic
Keyword(s):  
Sheet Metal ◽  
Mechanical Response ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Equivalent Stress ◽  
Point Of View ◽  
Constitutive Law ◽  
Forming Limit ◽  
Accuracy Of Prediction ◽  
Forming Limit Curves

The accuracy of the forming limit curves predicted by the Marciniak-Kuczynski model depends on the type and flexibility of the constitutive equations used to describe the mechanical response of the sheet metal. From this point of view, the yield criterion has the most significant influence. The paper presents a comparative analysis referring to the quality of the forming limit curves predicted by the Marciniak-Kuczynski model for the case when the plastic anisotropy of a DC04 sheet metal is described by the BBC2005 yield criterion. The coefficients included in the expression of the BBC2005 equivalent stress are evaluated using different identification strategies (with 4, 6, 7, and 8 mechanical parameters). The forming limit curves predicted by the Marciniak-Kuczynski model in each of the cases previously mentioned are compared with experimental data.

Influence of Different Pre-Stretching Modes on the Forming Limit Diagram of AA6014

2012 ◽  
Vol 504-506 ◽  
pp. 71-76 ◽  
Author(s):  
Alexandra Werber ◽  
Mathias Liewald ◽  
Winfried Nester ◽  
Martin Grünbaum ◽  
Klaus Wiegand ◽  
...  
Keyword(s):  
Plane Strain ◽  
Biaxial Loading ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Linear Strain ◽  
Forming Limits ◽  
Systematic Analysis ◽  
Measurement Systems ◽  
Non Linear ◽  
Strain Paths

In order to evaluate the formability of sheet materials forming limit diagrams (FLD) are recorded which represent the values of major and minor strain when necking occurs. FLDs are recorded based on the assumption that exclusively linear strain paths occur. In real forming parts, however, particularly in those with complex shapes, predominantly non-linear strain paths occur which reduce the accuracy of the failure prediction according to a conventional FLD. For this reason forming limits after loading with non-linear strain paths have to be investigated. In this contribution a systematic analysis of the forming limits of a conventional AA6014 alloy after loading with non-linear strain paths is presented. This material is pre-stretched in uniaxial, plane strain and biaxial direction up to several levels before performing Nakajima experiments in order to determine FLDs. During the pre-stretching process as well as during the Nakajima experiment the strain distribution can be measured online very precisely with the optical deformation measurement systems GOM Aramis or VIALUX. The gained curves are compared to the FLD of the as-received material. The results prove a significant influence of the pre-stretching condition on the forming limits of the used aluminum alloy. For a low pre-stretching in uniaxial as well as in biaxial direction the FLDs show a slightly reduced formability while after higher pre-stretching levels the forming limit can be improved such as for biaxial loading after uniaxial pre-stretching. The formability after pre-stretching in plane strain direction was changed. Also, a shift of the FLD depending on the direction of pre-stretching can be observed.

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