A Unified Bifurcation Analysis of Sheet Metal Forming Limits

2001 ◽  
Vol 123 (3) ◽  
pp. 329-333 ◽  
Author(s):  
Xinhai Zhu ◽  
Klaus Weinmann ◽  
Abhijit Chandra
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Yield Criterion ◽  
Strain Ratio ◽  
Thin Sheets ◽  
Dimensional Problem ◽  
Localized Necking ◽  
Extension Direction ◽  
Zero Extension

The purpose of this study is to determine analytically the orientations of localized necks occurring in sheet metal forming processes, and obtain the corresponding forming limit diagrams (FLDs). In addition to the force equilibrium condition as adopted by other researchers, we include the moment equilibrium in this study. The shear terms due to the perturbation are found to vanish inside the localized neck of a region of deformation. This simplifies the two-dimensional problem to a one-dimensional problem. Furthermore, it is found that there are only three possible orientations for the initiation of a localized neck, i.e., two principal directions and one zero extension direction (which applies only to negative strain ratio deformations). A special case study using the von Mises yield criterion is also presented in this paper. Predictions from our unified analysis matches with the results of Hill, R., 1952, “On Discontinuous Plastic States, With Special Reference to Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 1, pp. 19–30. For the negative strain ratio regime (left-hand side of the FLDs), and with the results of Storen, S., and Rice, R., 1975, “Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 23, pp. 421–441. For the positive strain ratio regime (right hand-side of the FLD). When the localized neck is assumed to be in the zero extension direction for the negative strain ratio deformation, deformation theory and flow theory of plasticity give the same limit strains, and a unified solution to the limit strain is obtained. This solution is independent of the specific yield criterion used.

A Generalized Mixed Kinematic-Isotropic Hardening Plastic Model Coupled With Anisotropic Damage for Sheet Metal Forming

2002 ◽  
Author(s):  
C. L. Chow ◽  
X. J. Yang
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Kinematic Hardening ◽  
Isotropic Hardening ◽  
Strain History ◽  
Anisotropic Damage ◽  
Plastic Model ◽  
Localized Necking ◽  
Element Simulation

The paper presents a generalized mixed isotropic-kinematic hardening plastic model coupled with anisotropic damage for sheet metal forming. A nonlinear anisotropic kinematic hardening is developed. For the predication of limit strains at localized necking in stamping under complex strain history, the model and its associated damage criterion for localized necking are established and implemented into LS-DYNA3D by compiling it as a user subroutine. The finite element simulation of LS-DYNA3D based on the present model is carried out. The location of localized necking for sheet metal forming has been successfully identified.

Bending and Stamping Processes of FSWed Thin Sheets in AA1050 Alloy

2014 ◽  
Vol 622-623 ◽  
pp. 459-466 ◽  
Author(s):  
Michela Simoncini ◽  
Lorenzo Panaccio ◽  
Archimede Forcellese
Keyword(s):  
Mechanical Properties ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Preliminary Investigation ◽  
Thin Sheets ◽  
Microstructural Investigation ◽  
Bending Tests ◽  
Friction Stir ◽  
Hemispherical Punch

The present investigation aims at studying post-welding forming operations of friction stir welded AA1050 aluminium thin sheets. A preliminary investigation has allowed to define the rotational and welding speed values leading to friction stir welded joints with high mechanical properties. Then, formability and elastic springback were evaluated using the hemispherical punch and bending tests, respectively. A microstructural investigation has allowed to relate the mechanical properties of joints to microstructure. Finally, the friction stir welded assemblies were subjected to air bending and stamping experiments in order to evaluate their attitude to undergo to sheet metal forming operations.

Modelling of Forming Limit Strains of AA5083 Aluminium Sheets at Room and High Temperatures

2016 ◽  
Vol 1135 ◽  
pp. 202-217 ◽  
Author(s):  
José Divo Bressan ◽  
Luciano Pessanha Moreira ◽  
Maria Carolina dos Santos Freitas ◽  
Stefania Bruschi ◽  
Andrea Ghiotti ◽  
...  
Keyword(s):  
Shear Stress ◽  
High Temperature ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Stress Rupture ◽  
Forming Limit ◽  
Limit Curve ◽  
Local Necking ◽  
Localized Necking

Present work analyses mathematical modelling to predict the onset of localized necking and rupture by shear in industrial processes of sheet metal forming of aluminium alloy 5083 such as biaxial stretching and deep drawing. Whereas the AA5083 sheet formability at room temperature is moderate, it increases significantly at high temperature. The Forming Limit Curve, FLC, which is an essential material parameter necessary to numerical simulations by FEM, of AA 5083 sheet was assessed experimentally by tensile and Nakajima testing performed at room and 400°C temperatures. Tensile test specimens at 0o, 45o and 90o to the direction of rolling (RD) and Nakazima type specimens at 0o RD of aluminium AA5083 were fabricated. Simple tensile tests at room and 400°C temperatures were performed to obtain the coefficients of plastic anisotropy and material strain and strain rate hardening behavior at different temperatures. Nakazima biaxial tests at room and high temperature, employing spherical punch were carried out to plot the limit strains in the negative and positive quadrant of the Map of Principal Surface Limit Strains, MPLS, of aluminium AA5083 sheet. The “Forming Map of Principal Surface Limit Strains”, MPLS, shows the experimental FLC which is the plot of principal true strains in the sheet metal surface (ε1,ε2), occurring at critical points obtained in laboratory formability tests or in the fabrication process of parts. Two types of undesirable rupture mechanisms can occur in sheet metal forming products: localized necking and rupture by induced shear stress. Therefore, two kinds of limit strain curves can be plotted in the forming map: the local necking limit curve FLC-N and the shear stress rupture limit curve FLC-S. Localized necking is theoretically anticipated to occur by two mathematical models: Marciniak-Kuczynski modelling, hereafter M-K approach, and D-Bressan modeling. Prediction of limit strains are presented and compared with the experimental FLC. The shear stress rupture criterion modeling by Bressan and Williams and M-K models are employed to predict the forming limit strain curves of AA5083 aluminium sheet at room and 400°C temperatures. As a result of analysis, a new concept of ductile rupture by shear stress and local necking are proposed. M-K model has good agreement with both D-Bressan models.

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