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Technical Paper

Formability Predictions of Hydroformed AKDQ Steel Tubes by Various Burst Criteria

The accurate prediction of burst of hydroformed tubes is a research area of considerable importance in order to evaluate a design before prototyping. This report applies the presently available criteria (forming limit diagram, stress-based forming limit diagram, extended stress based forming limit curve and the plastic strain criterion) to some of the benchmark examples carried out by the Auto/Steel partnership. It was found that the formability predictions are lowest if the plastic strain criterion is used and highest if either the stress-based criteria are used. Predicted and measured results were also compared.
Technical Paper

A Bursting Failure Criterion for Tube Hydroforming

Fundamental differences exist between sheet metal forming and hydroforming processes. Sheet metal forming is basically a one step metal fabrication process. Almost all plastic deformation of an originally flat blank is introduced when the punch is moved normal to a clamped sheet metal. Hydroforming, however, consists of multiple steps of tube making, pre-bending, crushing, pressurization, etc. Each of the above mentioned steps can introduce permanent plastic deformations. The forming limit diagram obtained for sheet metal forming may or may not be used in hydroforming evaluations. A failure criterion is proposed for predicting bursting failures in tube hydroforming. The tube material's stress-strain curve, obtainable from uniaxial tensile test and subjected to some postulations under large stress/strain states, is used in judging the failure.
Technical Paper

The Effects of Friction on Bursting of Tubes in Corner Filling

Corner filling is a benchmark experiment in tube hydroforming. It was designed to gain knowledge pertinent of this new fabrication process. The corner filling benchmark has been widely used in the automotive and steel industries. Common sense as well as physical tests suggests that friction is an important parameter that affects the deformation of the tube and the bursting of the tubes. However, numerical simulations have yet to verify this fact. In this paper, the stress/strain states in the tube were computed using a finite element model. The dependence of bursting on friction for corner filling was estimated by using the forming limit diagram and a tensile-based failure criterion.
Technical Paper

The Bulge of Tubes and a Failure Criterion for Tube Hydroforming

The bulge test in hydroforming is a simple fundamental experiment used to obtain basic knowledge in tube expansion. The results can be used to assist design and manufacturing of hydroformed automotive parts. It also can be used to develop a failure criterion for tubes in hydroforming. For these purposes, a section of a long unsupported tube with fixed ends was simulated numerically to obtain the mechanical states of the tube subjected to internal pressure. Steel and aluminum tubes are used. For the bulge tests, the internal pressure reaches a maximum and then decreases in value without failure while the stress, strain and volume of the tube keep increasing. A failure criterion for the bursting of a tube is proposed based on the stress-strain curve of the material.
Technical Paper

Deformation, Strain and Stress in Expansion of Tubes in Hydroforming

A simple problem of tube expansion to fill the die corners in the hydroforming process is studied. Based on a two-dimensional plane stress model the tube is simulated numerically using a static implicit finite element analysis, particularly, the commercial finite element code ABAQUS. Similar to the development and application of two-dimensional finite element codes for sheet metal forming, this two-dimensional model provides insight of the detailed deformation and stress/strain development otherwise lost in a more complex three-dimensional model. To facilitate discussions, high friction is assumed such that the tube does not slide on the die surface after contact. The calculated results predict the requirement to form sharp corners and demonstrate the development of the deformation, strain and stress states in the tube.
Technical Paper

A Mathematical Model for Calculating the Dent Initiation Loads at the Door Centers

A computational procedure is presented to evaluate the static dent resistance at the center of a steel door panel. Using the design parameters of geometric shape, thickness and the stress-strain relations of the steel, the static dent initiation load can be calculated. The method is based on the concept of plastic work which is the non-recoverable energy dissipated in the panel by the applied load. A threshold value of plastic work of 0.02 joule is used to signal the dent initiation. A comparison of the computed and measured dent initiation loads of ten experimental panels shows the maximum deviation is less than 20 newtons.
Technical Paper

Predicting Creasing Failures of Automobile Door Panels

This paper presents a numerical method for calculating the maximum force a steel automobile door panel can support at its upper character line without creasing failures. The method is based on the concept of plastic work, that is, the non-recoverable energy dissipated in the panel by the applied force and plastic deformation. By relating the calculated plastic works and the measured creasing forces of twelve experimental panels, a threshold value of plastic work of 0.03 joule has been obtained for signaling the onset of creasing. This critical value was used to calculate the creasing forces of these panels. The results so obtained are accurate. They have an average error of less than six percent from their corresponding measured data. The correlation coefficient between the calculated and measured creasing forces is 0.97.
Technical Paper

Applications of a Binder Wrap Calculation Model to Layout of Sheet Steel Forming Dies

This paper presents applications of a binder wrap calculation model to several experimental sheet steel forming dies. In one application of a doubly curved die, the calculated binder wrap agrees with physical tests and calculations reported elsewhere. In another door inner panel die, the designer's intent of having more material in certain part of the die cavity was verified. In the third case, the calculated binder wrap agrees quantitatively with measured data for a decklid stretch-draw die. The later result was used in guiding the modifications of the layout.
Technical Paper

A Finite Element Method for Calculating Binder Wrap Surface and Its Applications

This paper describes a robust and user-friendly finite element analysis program, WRAPFORM, and its applications in sheet metal formability analysis for autobody panels. In a sheet metal forming die, a blank undergoes two distinct deformation processes: the forming of a binder wrap and the forming of the part. WRAPFORM is used to analyze binder wrap forming by calculating the surface shape of the formed binder wrap. It was developed using a "black box" approach. The mechanics of the problem, solution procedure and finite element methodology needed in the calculation model were made transparent to the user. A designer with little computer experience can use the program to obtain the binder wrap surface in one computer run. Applications of WRAPFORM have yielded useful results. In one application, the designers' intent was verified. In another, the calculated binder wrap surface shape was used in guiding the modification of the layout of a sheet metal forming die
Technical Paper

Bifurcation in Binder Wrap Forming

Binder wrap forming for automobile body panels can be evaluated by finite element analysis. Sometimes, however, numerical instabilities occur in the implicit nonlinear solution process. While this instability may be an artifact of the numerical model, it may also signal the onset of a real physical phenomenon, such as bifurcation. This paper presents a numerical experiment to examine bifurcation in binder wrap forming, using an experimental decklid die. Numerical instability occurred early in the deformation process. Two stable solutions for the binder wrap surface were obtained, demonstrating that the instability resulted from bifurcation. One of the deformation modes is saddle like, and the other is cylindrical. In practice, the blank will deform to one of the above modes under the clamping actions generated by the closing of the binders. If the deformation takes the other mode, substantially different strains will result in the subsequent punch forming.
Technical Paper

Using a Geometric Toolkit to Link Finite Element Calculations in Sheet Metal Forming Analysis

Sheet metal forming of automobile body panel consists of two processes performed in series: binder forming and punch forming. Due to differences in deformation characteristics of the two forming processes, their analysis methods are different. The binder wrap surface shape and formed part shape are calculated using different mathematical models and different finite element codes, e.g., WRAPFORM and PANELFORM, respectively. The output of the binder forming analysis may not be directly applicable to the subsequent punch forming analysis. Interpolation, or approximation, of the calculated binder wrap surface geometry is needed. This surface representation requirement is carried out using computer aided geometric design tools. This paper discusses the use of such a tool, SURFPLAN, to link WRAPFORM and PANELFORM calculations.
Technical Paper

Evaluation of a Dynamic Explicit Finite Element Code for Binder Forming Calculations

In order to develop a binder forming analysis model based on contact principle of mechanics and to search for an accurate finite element computer code to analyze the model, ABAQUS/Explicit was evaluated using a benchmark example of a step-die. Because the step-die is a quasi-static problem and ABAQUS/Explicit is a dynamic finite element code, we are particularly interested in avoiding oscillations of the blank in the die cavity after the binder is closed. The study reveals that the oscillations can be eliminated and an asymptotic solution obtained if the die close speed is not too high. The optimum die close time for the benchmark is obtained based on the efficiency of computing and accuracy of the solution. The issues of oscillations and asymptotic solutions related to analyzing a quasi-static binder forming problem by a dynamic finite element code are settled in this paper.
Technical Paper

Free Expansion Bulge Testing of Tubes For Automotive Hydroform Applications

Free expansion of straight tubes is the simplest test to evaluate tube properties for hydroforming applications and to provide basic understanding of the mechanics of tube hydroforming. A circular cylindrical tube is sealed at both ends and fluid, usually water, is pumped into the tube to increase its internal pressure to bulge and burst the tube. Previous numerical simulations of the free expansion tube test were limited to modeling the midsection of the tube under various assumptions of deformation path. The simulation results obtained deviated from the experimental results under all simulation conditions considered. A new model is developed in this paper in which the whole tube is simulated instead of considering only its mid-section. Judged by the pressure-expansion relations, the model accurately predicted free expansion hydroforming tests results.