Finite Element Analysis of Deep Drawing.
Advisor: Prof.Dr.Ir. J. Huétink.
University of Twente, March 1997.
The deep drawing process is a process to manufacture a product from sheet metal. During the deep drawing
process an initially flat blank is clamped between the die and the blank holder after which the punch moves down to
deform the clamped blank into the desired shape. The final shape of the product depends on the geometry of the
tools, the material behaviour of the blank and the process parameters. Useful tools to study the influence of these
parameters are numerical models like the finite element method. A program based on the finite element method is
DIEKA which has been developed at the University of Twente in close co-operation with Hoogovens Research &
The goal of the research at hand was to develop the existing finite element program DIEKA in order to better
satisfy the requirement for industrial applications of the deep drawing process. This goal is achieved by improving
and extending the existing models and by developing new models for both coated and uncoated sheet metal.
Because the thickness of the blank is very small compared to its other dimensions, the deep drawing process is
analysed with help of a sheet model. The membrane element is a commonly used and rather simple element based
on sheet model. It only incorporates the stretching stresses. When the curvature of the blank becomes sharp, this
description fails. For this reason a Kirchhoff element has been implemented which also incorporates the bending
stresses. Besides, a Mindlin element has been implemented which incorporates the bending-stresses and the
transverse shear stresses as well.
During the deep drawing process the blank is deformed by a set of tools. The contact between the blank and
the tools is the driving force of the deformation process. For this reason contact is of major importance in the
numerical simulations. The existing contact search, i.e. the nodal search, showed a few pitfalls. In order to obtain a
more effective contact search a pinball search has been developed. The pinball search proved to be more robust. A
block search algorithm has been developed to speed up the contact search.
In the contact description a new friction model has been implemented. In contrast with the standard friction
model with a constant coefficient of friction the new friction model has a coefficient of friction which depends on the
local contact conditions. This Stribeck friction model depends on the normal pressure, the combined surface
roughness of the contact, the viscosity of the lubricant and the relative velocity of the contact surfaces. These
parameters may change during the deformation process depending on for example the strain hardening, process
conditions and coatings.
Further a new material description has been developed based on multi-axial stress states. This Vegter yield
function is based on the equi-biaxial state, the uni-axial state, the plane strain state and the pure shear state. The
material anisotropy caused by the rolling process has also been incorporated. The Vegter yield function proved to
give a more accurate description than the classical Hill yield function which is based on the uni-axial stress state
In the die/blank holder area, drawbeads are used to locally control the material flow. The drawbead forces the
blank to bend and unbend several times while it is pulled through the bead. An extensive 2D numerical analysis has
been performed to achieve more insight in the drawbead behaviour. In 3D simulations the drawbead geometry is
replaced by an equivalent drawbead model which incorporates the main characteristics of a real drawbead.
A number of deep drawing products has been analysed with the finite element program DIEKA. These
applications show the possibility of the program and the performance of the different models.
The square cup has been used to analyse the influence of mesh refinement, of different element types and of
different friction models in combination with varying punch velocities.
The S-Rail has been treated to examine the phenomena of wrinkling and springback. For this application the
strip model is used to perform a preliminary study of the springback behaviour of the Kirchhoff element.
The Limiting Dome Height has been treated to study the different material models and to examine the
prediction of failure. In this example the Forming Limit Diagram proved to accurately determine the failure.
The Bracket Headlight has been used to analyse the equivalent drawbead model. Three simulations have been
performed including different drawbead models. The equivalent drawbead effectively replaces the real drawbead
when both the restraining force and the strain changes are considered.
The Mini Bonnet is a product out of sandwich laminate. A sandwich laminate element has been developed
based on the Mindlin element. With this element the Mini Bonnet has been analysed. An advantage of the finite
element method is the possibility of looking in the material. This is demonstrated with an analysis of the shear
stresses in the core of the sandwich laminate.
Three industrial products complete the applications. The cushion seat, the fender and the heat exchanger part
show the possibility of analysing industrial applications with the finite element program DIEKA.