True strain distribution profile on sheet metal using different punch geometries
Changes are often necessary during the tryout of stamping tools. These changes may range from adjustments on die and punch designs to the selection of a new material with better formability characteristics. All these actions, however, require time and money creating the need for better initial sheet metal evaluation. Hence, increasing attention has focused on the development of laboratory tests that enable stamping companies to know more about the sheet metal stampability or that can, at least in part, ensure that their stamped products are produced without major problems. Identification of high stress region on stamping may allow for better tool stamping adjustment during tests, rendering a more uniform materials deformation and leading to the production of higher quality parts. Increasing attention has focused on the material evaluation based on the tool geometries in order to calculate the strain distribution. This study deals with an evaluation of four punch models with varied geometries in addition to the traditional Nakazima test tool. An evaluation was also made of the major true strain distribution profile at points distributed linearly from the region close to the die shoulder to the punch center.
Prediction of forming limit curves using an anisotropic yield function with prestrain induced backstress
Abstract The Forming Limit Diagram (FLD), a plot of the maximum major principal strains that can be sustained by sheet materials prior to the onset of localized necking, is a useful concept for characterizing the formability of sheet metal. Both experimental and numerical results in the literature have shown that the level of the FLD is strongly strain path dependent and the prediction of FLD depends on the shape of the initial yield function and its evolution. In this work, to improve the accuracy of FLD prediction under nonlinear strain paths for a given material, the evolution of the yield function is proposed in terms of the changes of its center and its curvature. The center of the subsequent yield surface after preloading and unloading will be determined via a backstress tensor, and the curvature change will be reflected by changing the exponent in the yield function. Both parameters are functions of the effective plastic strain and will be determined using the forming limit strains obtained from two nonlinear tests. Using this approach, a combination of Marciniak–Kuczynski (M–K) analysis (Marciniak, Z., Kuczynski, K. 1967. Limit strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9, 609.) and a general anisotropic yield criterion developed by Karafillis and Boyce (Karafillis, A.P., Boyce, M.C. 1993. A general anisotropic yield criterion using bounds and transformation weighting tensor, J. Mech. Phys. Solids, 41, 1859) is used to predict nonlinear FLDs of both Al2008-T4 and Al6111-T4. Excellent agreements were obtained between computed FLDs with the experimental data of Graf and Hosford (Graf, A., Hosford, W.F. 1993a. Calculations of forming limit diagrams for changing strain paths. Metall. Trans. A. 24, 2497; Graf, A., Hosford, W.F. 1993b. Effect of changing strain paths on forming limit diagrams of Al 2008-T4. Metall. Trans. A. 24, 2503; Graf, A., Hosford, W.F. 1994. The influence of strain path changes on forming limit diagrams of Al 6111-T4. Int. J. Mech. Sci. 36, 897). This prediction capability provides a powerful tool in the design and optimization process of 3D sheet metal forming where strain path changes are inevitable.
Influence of pressure and fluidization velocity on the hydrodynamics of a fluidized bed containing horizontal tubes
Abstract An experimental investigation of the influence of horizontal tubes on the bubble behaviour and through-flow velocity of gas inside bubbles was carried out and the influence of pressure and fluidization velocity was studied. The visible bubble flow rate and the gas velocity through the bubbles were measured simultaneously in a pressurized fluidized bed, using capacitance and Pitot-static pressures probes respectively. Silica sand with a mean particle diameter of 0.7 mm was fluidized at pressures between 01. and 1.6 MPa, in a bed of 0.2 × 0.3 m cross-section. Six different horizontal tube configurations were used and comparisons were made with results obtained in the same bed operated without tubes. The results from the bed with tubes show that the influence of pressure and fluidization velocity is basically the same as in the bed without tubes; an increase in pressure and fluidization velocity increases the bubble activity. At low excess gas velocities, the influence of immersed tubes on the bubble behaviour is less pronounced than at high excess gas velocities. Measurements and visual observations show that a small tube pitch gives a more uniform distribution of the visible bubble flow over the bed cross-section. At a combination of high pressure, high excess gas velocity and a large tube pitch, a preferred bubble path was observed in the centre of the bed cross-section. The pressure probe measurements show that the through-flow velocity of gas inside the bubbles is in most cases higher when tubes are present in the bed. The through-flow velocity consistently decreases with increasing pressure in the bed without tubes. The tendency is largely the same at a low excess gas velocity when tubes are present, but at a high excess gas velocity the through-flow velocity first decreases and then increases as the pressure is increased.