Cup Drawing from an Anisotropic Blank

1969 ◽  
Vol 91 (3) ◽  
pp. 766-771 ◽  
Author(s):  
W. A. Mir ◽  
M. J. Hillier
Keyword(s):  
Hydrostatic Pressure ◽  
Drawing Ratio ◽  
Blank Holder ◽  
Limiting Drawing Ratio ◽  
Cup Drawing ◽  
Good Agreement

Tests on aluminum, copper and brass blanks indicate that, provided proper hold-down methods are used, the limiting drawing ratio that can be obtained is almost independent of type of blank holder. A comparison of theoretical and experimental critical punch loads at failure shows that, for aluminum, good agreement can be obtained when drawing under all-round hydrostatic pressure. This method produces a reduction in die friction and a significant increase in limiting drawing ratio. There is an optimum hydrostatic pressure above which no advantage is to be obtained.

A Simplified Approach to Estimate Limiting Drawing Ratio and Maximum Drawing Load in Cup Drawing

2004 ◽  
Vol 126 (1) ◽  
pp. 116-122 ◽  
Author(s):  
Daw-Kwei Leu ◽  
Jen-Yu Wu
Keyword(s):  
Friction Coefficient ◽  
Strain Hardening ◽  
Sheet Metal ◽  
Elementary Theory ◽  
Strain Hardening Exponent ◽  
Drawing Ratio ◽  
Normal Anisotropy ◽  
Limiting Drawing Ratio ◽  
Special Cases ◽  
Cup Drawing

A new and practically applicable equation, including the normal anisotropy R, the strain hardening exponent n, the friction coefficient μ, and the bending factor t0/rd for estimating the limiting drawing ratio LDR (a measure of drawability of sheet metal) in cup drawing of a cylindrical cup with a flat-nosed punch is derived by an elementary theory of plasticity in an explicit form. Whiteley’s and Leu’s equations for estimating the LDR, and Hill’s upper limit value of LDR, all are the special cases of the derived equation. The estimation of LDR agrees well with the experiment. It is shown that the most important parameters for LDR are the normal anisotropy R and friction coefficient μ, however the strain hardening exponent n has little effect on the LDR. On the other hand, a new and simple equation, incorporating the derived LDR and the critical drawing load Pc, for estimating the maximum drawing load Pd at a certain drawing ratio is derived. It also agrees well with the experiment. It is thereby possible to better understand and control the drawing limit of sheet metal in industry necessity.

scholarly journals Study of Influence of Width to Thickness Ratio in Sheet Metals on Bendability under Ambient and Superimposed Hydrostatic Pressure

2021 ◽  
Vol 2 (3) ◽  
pp. 542-558
Author(s):  
Mohammadmehdi Shahzamanian ◽  
David Lloyd ◽  
Amir Partovi ◽  
Peidong Wu
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Ratio ◽  
Fracture Strain ◽  
Stress Triaxiality ◽  
Volumetric Strain ◽  
Thickness Ratio ◽  
Sheet Metals ◽  
The Finite Element Method ◽  
Bending Strain ◽  
Good Agreement

The effect of the width to thickness ratio on the bendability of sheet metal is investigated using the finite element method (FEM) employing the Gurson–Tvergaard–Needleman (GTN) model. Strain path changes in the sheet with change in the width/thickness ratio. It is shown that bendability and fracture strain increase significantly by decrease in the width/thickness ratio. The stress state is almost uniaxial when the stress ratio (α) is close to zero for narrow sheets. Stress ratio is nothing but the major stress to minor stress ratio. This delays the growth and coalescence of micro-voids as the volumetric strain and stress triaxiality (pressure/effective stress) decrease. On the other hand, ductility decreases with increase in α for wider sheets. Fracture bending strain is calculated and, as expected, it increases with decrease in the width/thickness ratio. Furthermore, a brief study is performed to understand the effect of superimposed hydrostatic pressure on fracture strain for various sheet metals with different width/thickness ratios. It is found that the superimposed hydrostatic pressure increases the ductility, and that the effect of the width/thickness ratio in metals on ductility is as significant as the effect of superimposed hydrostatic pressure. Numerical results are found to be in good agreement with experimental observations.

scholarly journals Optimization of the Countersinking Parameters Based on the Response Surface Method

2021 ◽  
Author(s):  
Hassen Mosbah ◽  
Slimen Attyaoui ◽  
Rachid Nasri
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Sequential Quadratic Programming ◽  
Numerical Optimization ◽  
Element Model ◽  
Poor Quality ◽  
Blank Holder ◽  
Surface Method ◽  
Good Agreement

Abstract The countersinking process is affected by many factors including the tools and the workpiece parameters. Some forming phenomena such as the knife-edge affect the quality of the countersunk hole. Up to now, many kinds of research rely mainly on the experiments which lead to poor quality and difficult control of this process. In this paper, a proposed numerical optimization of the countersinking process is developed to obtain a normalized countersunk hole. This optimisation approach is based on the response surface method (RMS), design of experiments (DOE) and the sequential quadratic programming (SQP). Finite element model is performed with an elasto-plastic behaviour for simulating the process. A configuration with an imposed displacement applied to the blank holder is adopted in this study. The comparison between the results of the numerical model and the experiments showed a good agreement.

Analysis of Uniform Deep Oval Reinforcing Rings

1964 ◽  
Vol 8 (02) ◽  
pp. 21-28 ◽  
Author(s):  
William P. Vafakos
Keyword(s):  
Hydrostatic Pressure ◽  
Cross Section ◽  
Composite Structure ◽  
Reference Line ◽  
Taylor Model ◽  
Test Results ◽  
Local Curvature ◽  
Oval Cross Section ◽  
Ring Shell ◽  
Good Agreement

Equations which are applicable to uniform deep oval rings in which the local curvature of an arbitrary reference line is prescribed are derived and simplified for application to oval ring-shell combinations. Theoretical estimates of the stresses and displacements are obtained for a typical reinforcing ring of a ring-stiffened oval cylinder recently tested under hydrostatic pressure by the David Taylor Model Basin. These results are obtained by appropriately approximating the oval cross section and by assuming that the composite structure responds as an oval ring. The theoretical flange stresses are shown to be in good agreement with available test results.

scholarly journals Development of Two-Dimensional Non-Hydrostatic Wave Model Based on Central-Upwind Scheme

2020 ◽  
Vol 8 (7) ◽  
pp. 505
Author(s):  
Gangfeng Wu ◽  
Ying-Tien Lin ◽  
Ping Dong ◽  
Kefeng Zhang
Keyword(s):  
Hydrostatic Pressure ◽  
Large Scale ◽  
Wave Model ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Practical Engineering ◽  
Hydrostatic Model ◽  
Good Agreement ◽  
Biconjugate Gradient

In this study, a two-dimensional depth-integrated non-hydrostatic wave model is developed. The model solves the governing equations with hydrostatic and non-hydrostatic pressure separately. The velocities under hydrostatic pressure conditions are firstly obtained and then modified using the biconjugate gradient stabilized method. The hydrostatic front approximation (HFA) method is used to deal with the wave breaking issue, and after the wave breaks, the non-hydrostatic model is transformed into the hydrostatic shallow water model, where the non-hydrostatic pressure and vertical velocity are set to zero. Several analytical solutions and laboratory experiments are used to verify the accuracy and robustness of the developed model. In general, the numerical simulations are in good agreement with the theoretical or experimental results, which indicates that the model is able to simulate large-scale wave motions in practical engineering applications.

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