Sheet-forming Operations Research Articles

Hardening of A6111-T4 Aluminum Alloy at Large Strains and Its Effect on Sheet Forming Operations

In a number of sheet metal stamping and joining processes, the material undergoes large plastic deformation exceeding the range of plastic strain achievable in a standard tensile test prior to material plastic instability. In order to extend the range of effective strains, the multistep rolling process was employed which enabled prestraining of aluminum sheet above 2.0 of true strain. Tensile testing of rolled samples was used to identify the flow stress corresponding to the level of prestrain: By varying the prestrain level, several data points were obtained for the studied flow curve. The numerical simulation using Abaqus software for the cold rolling process of aluminum strips confirmed that majority of the strip is deformed in plane strain compression condition. Performed simulation of the LDH test determined that earlier fracture might occur if the curve obtained via rolling–tensile testing approach is used versus traditional power law approximation and Voce law approximation. The results of simulation for the multistep drawing of a cylindrical cup revealed possible wrinkling in the die entry area during redrawing stage of the process if the rolling–tensile testing flow curve is employed.

Stress Recovery Based h-Adaptive Finite Element Simulation of Sheet Forming Operations

In the present work, stress recovery techniques based adaptive finite element analysis of sheet forming operations is presented. An adaptive two dimensional finite element computer code allows the analysis of sheet forming operations and results in distribution of adaptively refined mesh, effective strain, and punch load, stress and strain rate tensor in the domain that has been developed. The recovery scheme for determining more accurate stress field is based on the least squares fitting of the computed stresses in an element patch surrounding and including a particular node. The solution error is estimated on the basis of an energy norm. It is shown with the help of an illustrative example of axi-symmetric stretching of a metal blank by a hemispherical punch that the adaptive analysis may be usefully employed to predict accurately deformation process, the seats of large deformations and locations of possible instability.

Evaluation of Biaxial Forming Limits by Bulge Testing

Finite element modelling of sheet-forming operations, such as pressure-ram-forming, (PRF™) requires knowledge of forming limits under biaxial strain conditions. In this work, elliptical bulge tests have been used to evaluate the forming limits of an aluminum bodystock alloy, X309, that is used for PRF™ applications. Limiting dome heights have been determined as a function of pressure-rate and temperature. All tests have been done with the rolling direction, RD, of the sheet aligned with the major axis of the bulge.

Plastic anisotropy and the geometry of yield surfaces in stress space

In the context of classical anisotropic plasticity a general theorem is proved in relation to the pure geometry of convex yield surfaces in a six-dimensional Cauchy stress-space. The analysis subsequently focuses on particular yieldpoints where the local radius vector and surface normal represent coaxial tensors. Further detail is presented for a standard family of yield functions associated with states of generalized plane stress produced in sheet-forming operations. The overall objective is a comprehensive theoretical framework for the improved modelling of anisotropic plastic behaviour.

An algorithm for improved convergence in forming analysis

Implicit finite element analysis of sheet-forming operations depends on the ability to find a converged solution, which is frequently difficult because of changing contact and friction conditions at arbitrarily shaped interfaces. This sensitivity is aggravated when draw-in is significant, when the well angle is large, and when the contact region or character changes rapidly (during re-draw, for example). A new algorithm has been developed based on the mesh normal and using a consistent full set (N-CFS) of equations, including equilibrium and contact conditions in the non-linear set. The “N-CFS” algorithm exhibits remarkable stability and strong convergence. In fact, we have not found a well-posed problem, i.e. one which is physically stable within the discrete numerical framework, which exhibits numerical instability. The N-CFS algorithm is presented and several challenging example problems are solved, illustrating the robustness of the new method relative to standard implicit formulations. A series of smaller improvements for implicit methods are also outlined.

Development and application of sheet-forming simulation

Finite-element modeling (FEM) programs for analyzing sheet-forming operations have been developed at The Ohio State University for many years now and have been tested against experiments and various benchmarks. Recent algorithm developments have extended the applicability of the membrane method to arbitrary, 3-D draw-type operations and have improved both the stability and the speed of the original method, even when the wall angle approaches vertical. The usefulness of the newest algorithm is demonstrated by simulations of 2-D and 3-D forming operations, including 1991 VDI Benchmark and 1993 NUMISHEET Benchmark geometrics. Preliminary results and discussion are presented for a new method for introducing bending stiffness into the membrane model without adding degrees of freedom, and for using this approach to compute the springback response in two dimensions.

Verification of an explicit finite-element code for the simulation of the press forming of rectangular boxes of coated sheet steels

The industrial aim for shorter lead times in the development process for new products has encouraged a fast development of finite-element procedures for the simulation of sheet-metal forming. These procedures can shorten the design stage for new sheet-forming tools and the try-out period. In order to reach these goals robust calculation procedures and extensive verification of results are required. This paper presents a detailed validation of one promising type of finite-element code, namely the explicit code DYNA3D. Experiments for verification were performed on a zinc-coated sheet steel with a hot-dip galvanized coating. Stretch forming and deep drawing of cylindrical cups were performed. Rectangular boxes were formed from rectangular blanks and blanks with cut corners. Dies both with and without draw beads were used. Punch forces, flange draw-in and strain distributions were measured. The pressings with cylindrical shape were used to determine coefficients of friction with a fitting procedure based on comparison of data from pressings and from the DYNA3D calculations. These tribological data and constitutive data of the steels were used in the simulation of pressings of rectangular boxes. The calculations with DYNA3D gave a good description of flange draw-in and the strain distributions in the pressings. In most of the cases studied the punch-force curves were well reproduced. It is concluded that the present code is well suited for the simulation of sheet-forming operations.

Strain-rate sensitivity and effects of strain rate in sheet forming

The strain-rate dependencies of flow strength and strain-hardening behaviour are particularly important in sheet-forming operations because they influence strain distribution and necking resistance. Measurements made in uniaxial and biaxial tensile tests on low-carbon steels have shown that strain-rate sensitivity is a function of both strain and strain rate, and that it varies with dissolved interstitial solute content. It is concluded that some simple constitutive equations which are commonly used to describe flow-strength–strain-rate relationships do not provide generally reliable bases for predictions of limit strains in sheet-forming operations. Variations in the plastic behaviour of the workpiece material which resultfrom changes in the speed of pressing can have important influences on performance in practical forming operations, but pressing speed–formability relationships are usually complicated by simultaneous changes in process variables such as lubricant behaviour and the extent of deformation heating. Evidence provided by small-scale stretch-forming and deep-drawing tests show that, while some of the more important effects of interaction between speed-dependent material and process variables can be rationalized in qualitative terms, there is a needfor more searching analysis of the interacting system as a whole under conditions which are representative of industrial sheet-forming processes.