Punch Height Research Articles

Optimum Process Design for Sheet Forming Using the Finite-Element Method and Mathematical Programing. 2nd Report. Proposal of Sweeping Simplex method.

Recently, the development of an optimum forming process design system based on computer-aided technology has been required to reduce both time consumption and cost. The authors have developed an optimum forming process design system based on a concept which integrates the FEA and the numerical optimization method. In this design, an objective function has several local optimum points, and it is necessary to find the global optimum point. Therefore, in this paper, the sweeping simplex method is proposed, which finds the global optimum point efficiently. The proposed method was applied to a drawing process design. In order to obtain products with uniform thickness, two-stage drawing was employed. Two values of punch heights which characterize the first-stage punch shape were chosen as the design variables, and deviation of thickness from the average thickness was chosen as an objective function. It was demonstrated that the system could find the optimum condition efficiently. Furthermore, the optimum condition evaluated by the proposed system was verified to be in good agreement with the experimental results.

A plane strain punch stretching test for evaluating stamping formability of steel sheets

A simple simulative test was developed to evaluate the stamping formability of steel sheets in plane strain stretching deformation. The stamping formability was evaluated by the limiting punch height (LPH) value in the plane strain punch stretching (PSS) test compared to the minimum of the limiting dome height (LDHo) value in the hemispherical punch stretching test, the standard LDH test. The PSS test shows a stable plane strain deformation and a good reproducibility with less scattering data. Moreover, the LPH value in the PSS test ranks well the stamping formability of various sheet materials and shows good correlations with press performance.

Square-punch forming: Experiments and simulations in two and three dimensions

Square punch/open-die forming experiments and finite-element modeling were conducted to study the stretch forming of full-width blanks and the stretch/draw forming of plane-strain strips. Strains on both the outer and inner specimen surfaces and draw-in displacements were measured carefully at various punch heights, for varying blank-holder forces, and for three square-punch edge radii representing r/t (tool radius/sheet thickness) ratios of 3, 6, and 9. Two rigid-viscoplastic finite-element programs, SHEET-S (plane-strain) and SHEET-3 (3-D), were used to predict strain distributions. Simulations and measurements were in good agreement for fairly large r/t ratios (> 5). It was found that section analysis was accurate for some applications not strictly meeting the plane-strain conditions. The main limitation for sectional analysis is the absence of compound curvature along the chosen scan line. The section FEM program was nearly 600 times faster in computation than the 3-D FEM code, making it practical to analyze complex die geometries that are otherwise too time-consuming with today's computers. In plane-strain deep drawing with small die radii, bending and unbending at the punch and die shoulders can dominate the local deformation modes, causing significant differences from the strains predicted by the membrane approach used here.

Nonisothermal punch stretching: Measurements and finite element modeling simulations

In order to investigate the role of thermal effects in punch stretching, a simple nonisothermal forming operation was carried out and was simulated using finite element modeling (FEM). A heated hemispherical punch deformed a steel sheet which was fully clamped between room-temperature circular dies. Strains were measured at standard punch heights for comparison with FEM-simulated ones. The strain distributions were in reasonable agreement, and the qualitative changes in the distributions with punch temperature were predicted very well by the simulations. The form of the nonisothermal FEM formulation was verified by these agreements. Increased punch temperature improves formability by lowering the peak strain in the punch-sheet contact region. Nonisothermality can play a significant role in distributing strains throughout a deforming sheet under conditions similar to these.

A theoretical sensitivity analysis for full- dome formability tests: parameter study forn, m, r, and μ

Sheet material formability has been assessed by many kinds of tests and analyses presented in the literature; the most popular ones are based on hemispherical punch stretching geometry. An axisymmetric version of such a test was analyzed using SHEET-3 [a three-dimensional (3-D) finite element method (FEM) program] to determine the sensitivity of the test to parametersn,m, r, and μ. A realistic and self-consistent failure criterion was established to predict the limiting cup height at failure (LDHf) in sheet specimens from calculated strain distribution data. A 2k factorial experiment was conducted for variations in the four variables (k = 4). The sensitivity of LDHf to variations inn andm is constant, while its sensitivity to variations in μ. is decreased as μ, is increased. The significance of the influence of normal anisotropy on LDHf is unclear, being dependent upon the choice of yield theory. Direct interactions between material properties and friction were, for the most part, not found to strongly influence test results at the parameter levels examined. Materials with different properties will typically not fail under the same strain conditions in full-dome cup tests. Cup test results are influenced by a number of parameters, including some not considered here,e.g., sheet thickness and test temperature. The FEM model for the full-dome cup test, including a prediction of forming limits, provides a useful technique for sorting out important effects that individual parameters have on the strain state in the sheet at failure and the predicted final punch height at failure.

A tensile model analysis of punch stretch tests: The effects of friction and strain hardening on measurement sensitivity

A theoretical model is presented to predict punch height as a function of sample strain and friction at the sheet-punch interface for punch-stretch forming of narrow strips in a Limiting Dome Height (LDH) test. Examination of the strain distribution in narrow punch strips reveals the following trends in LDH test sensitivity when punch height at failure is the measure of formability. First, the sensitivity of out-of-plane punch tests to material deformation behavior decreases with punch travel. Second, the LDH test is more sensitive to variations in friction in lubricated tests than in dry tests, and thus, dry tests may appear as more reproducible than lubricated tests. Third, strain hardening differences between sheet materials are directly manifest through variations in the distribution of strain in the strip. This effect of strain hardening, coupled with the geometry of the LDH test, leads to an almost linear relation between sample strain at instability (or failure) and punch height as experimentally observed. Finally, the sensitivity of punch height measurements to variations in n decreases as n increases.

On the strain distribution during the stretch-forming of low- and high-strength sheet steels

Strain distributions during stretch-forming with a hemispherical punch have been studied for six steels in cold-rolled gauges: a deep-drawing quality steel, a re-phosphorized steel, three dual-phase steels and a HSLA steel. Strain distributions are presented for radial strain, tangential strain and thickness strain. A number of different characteristics of the strain distributions have been evaluated such as the pole-to-peak distance, the width of the strain distributions and the peak- and polar-strains. Significant differences have been observed between, on one hand, the deep-drawing quality steel and, on the other hand, the dual-phase steels. The deep-drawing quality steel gives widely separated strain peaks and thus wide strain distributions, with the state of strain at the peaks being close to plane strain, whilst the dual-phase steels have rather closely situated strain peaks and thus narrow strain distributions, with the state of strain at the peaks being close to equi-biaxial straining. The influence of material parameters such as the work-hardening exponent n and the plastic anisotropy index r on the different characteristics of the strain distribution has been explored. Differences in punch heights to failure between the six materials have been investigated: it has been found that the dual-phase steels have a favourable combination of punch height at failure and tensile strength. Previously it had been thought that this is due to there being wide smooth strain distributions for dual-phase steels but the dual-phase steels do not, however, produce wider strain distributions than, for example, HSLA steels of comparable strength. Instead, the dual-phase steels have the ability to generate a state of strain close to equi-biaxial straining over a large proportion of the cup which, combined with a high forming-limit diagram close to equi-biaxial straining, produces a large punch height at failure.