M–K Analysis of Forming Limit Diagram Under Stretch-Bending

2012 ◽  
Author(s):  
Ji He ◽  
Z. Cedric Xia ◽  
Shuhui Li ◽  
Danielle Zeng
Keyword(s):  
Sheet Metal ◽  
Deformation Theory ◽  
Plane Deformation ◽  
Forming Limit Diagram ◽  
Flow Theory ◽  
Forming Limit ◽  
Bending Effect ◽  
Stretch Bending ◽  
Right Hand ◽  
Bending Process

Since the Forming limit diagram (FLD) was introduced and developed by Keeler etc. about four decades ago, it has been intensively studied by researchers and engineers. Most work has been focused on the in-plane deformation which is considered as the dominant mode of the most forming processes. However the effect of out-of-plane deformation modes especially bending effect becomes important in accurate prediction of formability when thick sheet metal and smaller forming radii are encountered. Recent work on experiment research of stretch-bending induced FLD (BFLD) shows that it gives higher formability than conventional forming limit. In this paper, bending effect through the sheet metal thickness on right-hand side of FLD is studied. The Marciniak-Kuczynski (M-K) analysis is extended to include bending and models based on both flow theory and deformation theory are proposed. The radial return method is adopted as the frame to calculate the stress states from given strain and deformation history. The effect of bending and unbending process on the Right-Hand-Side FLD is investigated and compared. The obtained results show that the bending process slightly decreases the sheet metal formability on right-hand side in flow theory based model which is a discrepancy with the prediction of deformation theory based BFLD model. The insight gained from new proposed FLD prediction model in this paper provides an understanding of how the bending process effects on the FLD. This is important for the further research to reconsider the problems of how the bending effect evolves in forming process to enhance the conventional FLD and how to get a perfectly true theoretical explanation for this phenomenon.

M–K Analysis of Forming Limit Diagram Under Stretch-Bending

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Ji He ◽  
Z. Cedric Xia ◽  
Shuhui Li ◽  
Danielle Zeng
Keyword(s):  
Deformation Theory ◽  
Plane Deformation ◽  
Forming Limit Diagram ◽  
Flow Theory ◽  
Dominant Mode ◽  
Forming Limit ◽  
Thick Sheet ◽  
Bending Effect ◽  
Stretch Bending ◽  
Bending Process

Since the forming limit diagram (FLD) was introduced by Keeler, etc., five decades ago, it has been intensively studied by researchers and engineers. Most work has focused on the in-plane deformation which is considered as the dominant mode of the majority forming processes. However the effect of out-of-plane deformation becomes important in the accurate prediction of formability when thick sheet metals and/or smaller forming radii are encountered. Recent research on the stretch-bending induced FLD (BFLD) has been inconclusive. Some studies indicated that the bending effect will enhance a sheet metal's formability while others suggested otherwise. In this paper, we present an in-depth study of the through-thickness bending effect on the forming limits. The Marciniak–Kuczynski (M–K) analysis is extended to include bending, and models based on both flow theory and deformation theory of plasticity are proposed. The study is limited to the right-hand-side of FLD where the bending is along the major stretch direction. The radial return method is adopted as the framework to integrate constitutive equations. The results show that the bending process decreases the sheet metal formability with the flow-theory based model, while the opposite is true if the deformation theory based analysis is adopted. A detailed examination of the deformation histories from those two models reveals that the loading–unloading-reverse loading process during stretch-bending holds the key to the understanding of the conflicting results. The insight gained from the proposed FLD prediction model in this paper provides a new understanding of how the bending process affects the FLD, which can be used to predict and explain the localized necking phenomenon under the stretch-bending condition.

Sheet Metal Forming Limit Under Stretch-Bending

2008 ◽  
Author(s):  
Z. Cedric Xia ◽  
Danielle Zeng
Keyword(s):  
Sheet Metal ◽  
Biaxial Loading ◽  
Plane Deformation ◽  
Forming Limit Diagram ◽  
Dominant Mode ◽  
Forming Limit ◽  
Theoretical Formulation ◽  
Limit Model ◽  
Bending Effect ◽  
Bending Radius

The Forming Limit Diagram (FLD) as developed by Keeler etc. has been widely used to assess sheet metal failure during a variety of forming operations. Its theoretical and empirical foundation is based on localized necking under biaxial loading for the sheet metal. While the in-plane deformation is generally the dominant mode for most forming operations, sheet metal bending is inevitably coupled to the deformation process, and the traditional Forming Limit Diagram has to be modified to take into account the bending effect, especially when the bending radius becomes smaller. This paper presents a theoretical formulation for the Bending-Enhanced Forming Limit model. The deformation theory of plasticity is employed for the instability analysis, and the bending is assumed only in the direction along one principal loading. The obtained results show that the forming limit is enhanced by the bending effect, consistent with experimental observations.

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.

Forming Limits Under Stretch-Bending Through Distortionless and Distortional Anisotropic Hardening

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Ji He ◽  
Bin Gu ◽  
Yongfeng Li ◽  
Shuhui Li
Keyword(s):  
Detailed Comparison ◽  
Forming Limit ◽  
Anisotropic Hardening ◽  
Hardening Model ◽  
Stretch Bending ◽  
Bending Process ◽  
Hardening Models ◽  
Out Of Plane ◽  
Forming Limit Curves ◽  
Insight Into

The necking behavior of sheet metals under stretch-bending process is a challenge for the forming limit prediction. State-of-the-art forming limit curves (FLCs) allow the prediction under the in-plane stretching but fall short in the case under out-of-plane loading condition. To account for the bending and straightening deformation when sheet metal enters a die cavity or slide along a radius, anisotropic hardening model is essential to reflect the nonproportional loading effect on stress evolution. This paper aims to revisit the M-K analysis under the stretch-bending condition and extend it to accommodate both distortionless and distortional anisotropic hardening behavior. Furthermore, hardening models are calibrated based on the same material response. Then the detailed comparison is proposed for providing better insight into the numerical prediction and necking behavior. Finally, the evolution of the yield surface and stress transition states is examined. It is found that the forming limit prediction under stretch-bending condition through the M-K analysis strongly depends on the employed anisotropic hardening model.

Incremental Sheet Forming with an Industrial Robot – Forming Limits and Their Effect on Component Design

2005 ◽  
Vol 6-8 ◽  
pp. 457-464 ◽  
Author(s):  
L. Lamminen
Keyword(s):  
Sheet Metal ◽  
Industrial Robot ◽  
Forming Limit Diagram ◽  
Sheet Forming ◽  
Incremental Sheet Forming ◽  
Point Of View ◽  
Forming Limit ◽  
Forming Process ◽  
3D Cad ◽  
Component Design

Incremental sheet forming (ISF) has been a subject of research for many research groups before. However, all of the published results so far have been related to either commercial ISF machines or ISF forming with NC mills or similar. The research reported in this paper concentrates on incremental sheet forming with an industrial robot. The test equipment is based on a strong arm robot and a moving forming table, where a sheet metal blank is attached. The tool slides on the surface of the sheet and forms it incrementally to the desired shape. The robot is capable of 5-axis forming, which enables forming of inwards curved forms. In this paper the forming limit diagram (FLD) for ISF with the robot is presented and it is compared with conventional forming limit diagrams. It will be shown that the conventional FLD does not apply to incremental forming process. Geometrical accuracy of sample pieces is also studied. Cones of different shapes are formed with the robot equipment and their correspondence with the 3D CAD model is evaluated. The results are compared with other results of accuracy of incremental sheet forming, reported earlier by other researchers. The third issue covered in this article is a product development point of view to incremental sheet forming. In addition to fast prototyping and low volume production of sheet metal parts, ISF brings new possibilities to sheet metal component design and manufacturing. These possibilities can only be exploited if design rules, that will take the possibilities and limitations of the method into account are created for ISF.

Finite Element Validation of Forming Limit Diagram of IN-718 Sheet Metal

2015 ◽  
Vol 2 (4-5) ◽  
pp. 2037-2045 ◽  
Author(s):  
K. Sajun Prasad ◽  
T. Kamal ◽  
S.K. Panda ◽  
S. Kar ◽  
S.V.S. Narayana Murty ◽  
...  
Keyword(s):  
Finite Element ◽  
Sheet Metal ◽  
Forming Limit Diagram ◽  
Forming Limit

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.

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