6.2 MECHANICS OF DEEP DRAWING
Deep drawing is the metal forming process by which
a flat sheet of metal is cold drawn or formed by a mechanical or hydraulic
press into a seamless shell. As the material is drawn into the die by the
punch, it flows into a three-dimensional shape. The blank is held in place with
a blank holder using a certain force. High compressive stresses act upon the metal,
which, without the offsetting effect of a blank holder, would result in a
severely wrinkled workpiece.
Wrinkling is one of the major defects in deep
drawing; it can damage the dies and adversely affect part assembly and
function. The prediction and prevention of wrinkling are very important. There
are a number of different analytical and experimental approaches that can help
to predict and prevent flange wrinkling. One of them is the finite element
method (FEM). However, an explanation of this method falls outside the scope of
this book, so it is not explained here.
There are many important variables in the deep
drawing process and they can be classified as:
• material and friction
factors,
• tooling and equipment
factors.
Important material properties such as the strain
hardening coefficient (
n
) and normal anisotropy (
R
) affect the deep drawing operation.
Friction and lubrication at the punch, die, and workpiece interfaces are very important
to obtain a successful deep drawing process. A schematic illustration of the
significant variables in the deep drawing process is shown in Fig. 6.2.
Unlike bending operations, in which metal is
plastically deformed in a relatively small area, drawing operations impose
plastic deformation over large areas. Not only are large areas of the forming
workpiece
Fig. 6.2
Significant variables in deep drawing.
being deformed, but the stress states are
different in different regions of the part. As a starting point, consider what appear
to be three zones undergoing different types of deformation:
• the flat portion of the
blank that has not yet entered the die cavity (the flange),
• the portion of the
blank being drawn into the die cavity (the wall),
• the zone of contact
between the punch and the blank (bottom).
The radial tensile stress is due to the blank
being pulled into the female die, and the compressive stress, normal in the
blank sheet, is due to the blank holder pressure. The punch transmits force
F
to the bottom of the cup,
so the part of the blank that is formed into the bottom of the vessel is
subjected to radial and tangential tensile stresses. From the bottom, the punch
transmits the force through the walls of the cup to the flange. In this
stressed state, the walls tend to elongate in the longitudinal direction.
Elongation causes the cup wall to thin, which if it is excessive, can cause the
workpiece to tear. Fig. 6.3a illustrates the
Fig. 6.3
Fracture of a cup in deep drawing: Caused
a) by too small a die radius, and b) by too small a punch radius.
fracture of a cup in deep drawing caused by too
small a die radius
R
d
, and Fig. 6.3b shows the
fracture caused by too small a punch corner radius
R
i
. Fracture can also result
from high longitudinal tensile stresses in the cup due to a high ratio of blank
diameter to punch diameter.
The tensile hoop stress on the wall indicates that
the cup may be tight on the punch because of its contraction due to the tensile
stresses in the cup wall. If drawing is done without blank holder pressure, the
radial tensile stresses can lead to compressive hoop stress on the flange. It
is these hoop stresses that tend to cause the flange to wrinkle during drawing.
Also note that, in pure drawing, the flange tends to increase in thickness as
it moves toward the die cavity because its diameter is being reduced. Parts
made by deep drawing usually require several successive draws. One or more
annealing operations may be required to reduce work hardening by restoring the
ductile grain structure. The number of successive draws required is a function
of the ratio of the part height
h
to the part diameter
d
, and is given by this
formula:
(6.1)
where:
n =
number of draws,
h
= part height, and
d
= part diameter.
The value of
n
for the cylindrical cup
draw is given in Table 6.1.
6.2.1 Deep Drawability
In deep drawing, deformation may be expressed in
four ways, thus:
(6.2)
The relationship between these equations is:
(6.2a)
The ratio of the mean diameter
ds
of the drawn cup to the
blank diameter
D
is known
as the drawing ratio
m
,
and is
given by:
(6.2b)
Very often, deep deformability is expressed as the
reciprocal of the drawing ratio
m
. This value
K
is known as the limit of the drawing ratio:
(6.2c)
where:
D
= the blank diameter
d
s
= the mean diameter of the
drawn cup
m
= the drawing ratio
K = the limit of the
drawing ratio.
The values of the drawing ratio for the first and
succeeding operations is given by:
(6.3)
The magnitude of these ratios determines the
following parameters:
• the stresses and forces
of the deep drawing process,
• the number of
successive draws
• the blank holder force
• the quality of the
final drawn parts.
In view of the complex interaction of factors,
certain guidelines have been established for a minimum value of the drawing
ratio. The relative thickness of material is the most important and may be
calculated from:
(6.4)
As the relative thickness of the material
T
r
becomes greater, the
drawing ratio
m
becomes
more favorable. In Table 6.2 is given an optimal drawing ratio for a
cylindrical cup without a flange.
Table 6.2 Optimal
ratio
m
for
drawing a cylindrical cup without flange.
