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Previously-reported draw-bend tests showed large discrepancies in springback angles from those predicted by two-dimensional finite element modeling (FEM). In some cases, the predicted angle was several times the measured angle. With more careful 3-D simulation taking into account anticlastic curvature, a significant discrepancy persisted. In order to evaluate the role of the Bauschinger Effect in springback, a transient hardening model was constructed based on novel tension-compression tests for for three sheet materials: drawing-quality steel (baseline material), high-strength low-alloy steel, and 6022-T4 aluminum alloy. This model reproduces the main features of hardening following a strain reversal: low yield stress, rapid strain hardening, and, optionally, permanent softening or hardening relative to the monotonic hardening law. The hardening law was implemented and 3-D FEM was carried out for comparison with the draw-bend springback results.

The influence of die corner geometry on the attainable draw depth of rectangular parts was investigated using 3-D FEM and optimum rectangular blanks. Axisymmetric cup analysis was not adequate because a corner assist effect promotes corner draw. Guidelines for selecting corner radius were developed and the sensitivities of the maximum part depth to other process variables, such as drawbead restraint force; die clearance gap; friction coefficient; strain rate sensitivity; material anisotropy; and strain hardening exponent, were simulated. The results are much more conservative than handbook rules, which to not to take into account the details of blank size, drawbead restraint, die geometry, material properties, and friction.

Square punch/open die experiments were conducted to study the stretch forming of full-width blanks and plane strain strips. In order to measure bending effects, strains on both surfaces of the sheets were measured for three punch profile radii, using circle grids with 1.27 mm diameter. Two rigid-viscoplastic finite element programs, SHEET-S and SHEET-3, were used to predict plane-strain and 3-D strain distributions. The numerical results were compared with experimental data and good agreement was observed. It was found that the section analysis approach may be valid for a wide range of applications not strictly meeting the plane strain conditions, such as the biaxial stretch case. The bending effect is studied and a geometrical correction of the membrane FEM predictions, through t/2r, was introduced. The membrane section analysis program agreed well with measurements for r/t ( radius of curvature/sheet thickness ) values greater than 3 and when compound curvature was not present.

Plane strain, deep drawing experiments were performed to obtain precise strain information for comparison with membrane section-analysis finite element modeling (FEM) results obtained using a FEM program, SHEET-S. Strains on both outer and inner specimen surfaces and draw-in displacements were carefully measured at various punch heights, for varying blank holder loads, and for three square-punch edge radii representing r/t ratio (radius/sheet thickness) of 3, 6, and 9. SHEET-S, a rigid-viscoplastic section analysis finite element program, for plane strain stretching and deep drawing with general tooling shape, has developed and tested by plane strain deep drawing of strips. Simulations and experiments are in good agreement for the large r/t ratios, but deteriorate for r/t ≈ 3, especially for low blank holder loads. Bending and unbending at these locations appear to dominate the deformation modes, causing significant differences from the strains predicted by the membrane FEM.