INTRODUCTION
The injection forging also termed as radial extrusion, lateral extrusion, sideway
extrusion or radial forging is an important branch of the extrusion process
in which the cylindrical solid or tubular billet contained in the chamber is
pressed by one or two opposite simple punches, causing the radial material flow
through a fixed die cavity. The machine components with complex flange geometry
or segmented protrusions such as gears and splines, which are very difficult
to produce by the conventional forging, can be easily produced by the injection
forging to near or net shaped parts. The injection forging method will allow
reducing the subsequent operations such as machining. Its important characteristics
features of this method in relation to conventional forging are that it consumes
low energy and offers better die filling for complex parts. Qin
and Balendra (1998) and Balendra and Qin (2000, 2004a,
b) have studied effects of process parameters on material flow and load
requirement for complete flanges. They have been defined an aspect ratio of
primary deformation zone (the ratio of gap height to billet initial diameter,
T = s/d) for complete flanged part produced by this method. When T<0.8 acceptable
material flow can be obtained but required force increase since metal flows
into narrow die gap. Lee et al. (2001) and Choi
and Choi (2001) studied the effect of punch diameter and the friction factor
on the forming load by the FEM on the combination of lateral and forward or
backward extrusion. Altinbalik and Can (2006) studied
the barreling profile and effect of aspect ratio on material flow in lateral
extrusion of gearlike forms by using upper bound solution and experimentally.
Du Ko et al. (2001) studied the effect of die
geometry parameters on material flow in this process. They showed a certain
pattern in the material flow in each deformation case and studied the some die
geometry parameters on the material flow into the flange gap by FE simulation
method.
In this study, the forming load and material flow into the flange gap in two
variant injection forgings of a solid cylindrical billet is analyzed by extensive
finite element simulation study. The major process parameters considered in
this work are the relative gap height, die corner radius and friction factor.
The analysis procedure is as follows: first, the results of simulation performed
under the same condition as for experiment are compared with experimental data
that obtained by Pale et al. (1989), and reported by Du
Ko et al. (2001), in terms of forming load. This comparison is to
verify the validity of the rigidplastic finite element method.

Fig. 1: 
The die geometry of injection forging in (a) case I and (b)
case II 
Second, extensive
simulation work for various combinations of parameter value was performed and
then the main characteristics of the forming load and deformation patterns of
each case are observed to define the terms which represent the forming characteristic
of the flange.
MATERIALS AND METHODS
The geometrical parameters in injection forging: This study investigates
two basic variants of injection forging, as shown in Fig. 1.
Figure 1 shows the principle of two processes and the geometrical
parameters utilized in this study. Case I involves forcing of a cylindrical
billet by a punch against a flat die which is stationary. In case II, both upper
and lower punches move together toward the center of the billet. The initial
billet and the final product of two cases are shown in Fig. 2.
The major process parameters are identified as the relative gap height (s/d),
the relative deformation (hst/d) and the die corner radius (r). To investigate
the influence of relative gap height (s/d), die corner radius (r) and friction
coefficient (m) on the material flow and forming load, finite element analysis
is performed for different values of gap height (s), friction coefficient (m)
and die corner radius (r) selected.

Fig. 2: 
(a) The initial billet and final formed parts in, (b) case
I and (c) case II 
Basic equations of rigidplastic FEM: This study performs rigidplastic
finite element simulations using DEFORM^{TM}2D software (DEFORM^{TM}2D
Software User Manual, 2005). The material employed in the simulations is
AISI1006 steel.
The flow stressstrain relationship of this material at room temperature can
be modeled as Eq. 1. The friction coefficient at the diematerial
interface is assumed to be 0.1 in the cold forging of steels, using conventional
phosphatesoap lubricants or oil (Kobayashi and Altan, 1989).
The basic equations of the rigidplastic finite element are as follows:
Equilibrium equation:
Compatibility and incompressibility equations:
Constitutive equations:
Boundary conditions:
where, σ_{ij} and
are the stress and the velocity, respectively,
and
are the effective stress and the effective strain velocity, respectively, F_{j}
is the force on the boundary surface of S_{F} and U_{i} is the
deformation velocity on the boundary surface of S_{U}.
The weak form of rigidplastic FEM can be determined by applying the variation
method to Eq. 14, i.e.,
where, V and S are the volume and the surface area of the material, respectively
and k is the penalty constant. The NewtonRaphson iteration method is applied
to obtain the solution of the equations. The frictional boundary condition is
given by the vector form:
In which m is the friction coefficient, k is the local flow stress in shear and u_{0} is a very small positive number in comparison with V_{s}, where V_{s} is the velocity vector of the work piece relative to the die and t is the unit vector in the direction of V_{s}.
RESULTS AND DISCUSSION
The results obtained from FE simulation are given and analyzed in the following
two sections, showing the influence of some major parameters mentioned above
on the forming load and material flow. The first section consists of validating
the model used in this study. So, the results obtained from simulation in this
study compared with the experiments data were obtained from the reaserch study
perform under the same conditions, exactly. The essential contribution here
consist to high lighting the effectivness of die geometry parameters on the
forming load, that it is not the same in the reaserch study presented by Du
Ko et al. (2001).
The influence of some basic geometric parameters such as s/d, r and m on the forming load and material flow into the flange gap investigated, the results are discussed.
FE model validation: Here, to verify the modeling and simulation work
for injection forging process, the loadstroke relationships obtained by FE
simulation are compared with the experimental data that obtained by Pale et
al. (1989) reported by Du Ko et al. (2001).

Fig. 3: 
Comparison of the simulated and experimental curve of forming
load for (s/d = 0.25, r = 5, d = 32) 

Fig. 4: 
Effect of s/d on forming load in case I 
The FE model is performed under the same conditions of relative gap height s/d
= 0.25, die corner radius r = 5 mm, billet diameter d = 32 mm, for AISI 1006
steel. The loadstroke curves of simulation and experimental data for two cases are
shown in Fig. 3. There is a significant correlation between
the results in each case and FEM analysis results obtained in this study are
more closely to experimental data in comparison with FEM results that reported
by Du Ko et al. (2001).
Influence of geometric parameters: In these subsections, the influence of parameters such as s/d, r and friction coefficient (m) on material flow and required forming load investigated.
Influence of s/d in case I and case II: The simulation study is performed
exactly at the same condition of those in validation condition, the flange gap
to billet diameter ratio (s/d) is varied between 0.125 and 0.25 in case I and
the loadstroke curves are shown in Fig. 4. In case II, the
(s/d) parameter increases from between 0.125 to 0.5, the friction coefficient
is considered to be 0.1, the results show in Fig. 5.

Fig. 5: 
Effect of s/d on forming load in case I 

Fig. 6: 
Separation height (hG) defect in case I 
The results obtained show the increasing (s/d) cause decreasing the forming
load in each two cases, but in the case II, the required forming load at each
stroke is high for lower gap to billet diameter ratio (s/d = 0.125) in comparison
with forming load due to (s/d = 0.5).
Figure 6 shows the separation height (hG), one of the important
deformation characteristic of injection forging process. The lower hG was obtained
at higher (s/d) values, Fig. 7 shows that in case I the hG
value tend to zero at s/d = 0.5.
Figure 8a shows the flange angle defect in case II, Fig.
8b and c show effect of (s/d) on the flange angle (α_{f}).
It is considerable where, increasing (s/d) from 0.125 to 0.5, cause increasing
α_{f} from 8° to 38°. On the other hand the better material
flow can be obtained with the lower (s/d).
Influence of die corner radius in case I and case II: The simulation
work were performed in each two cases to show the influence of die corner radius,
r. This parameter is important die design item. Figure 9a
and b shows the effect of die corner radius on the required
forming load in case I, II, as shown in these figures, forming load decrease
about 16% with increasing die corner from 1 to 5 mm, when punch stroke is 20
mm.

Fig. 7: 
Effect of s/d on separation height (hG) defect in case I (r
= 5, d = 32, m = 0.1) 

Fig. 8: 
(a) Flange angle defect in case II, (b) s/d = 0.125, a_{f}
= 8°, in case II and (c) s/d = 0.5, a_{f} = 38°, in case
II 

Fig. 9: 
(a) Effect of die corner radius on forming load in case I
(s/d = 0.25, m = 0.1, d = 32) and (b) In case II (s/d = 0.25, m = 0.1, d
= 32) 

Fig. 10: 
Effect of r on separation height (hG) defect in case I 
This could be explained by the fact that at higher die corner radius, there
is lower constraint when material goes to flow. In case II, at the similar conditions,
the forming load approximately decrease 13% such as shown, the forming load
in each stroke in case II is about 7.2% higher than case I.

Fig. 11: 
(a) Effect of friction coefficient on forming load in case
I (s/d = 0.25, r = 5, d = 32) and (b) In case II (s/d = 0.25, r = 5, d =
32) 
According to Fig. 4, 5, 9a
and b and comparison the forming load at similar punch stroke,
between two cases, at different (s/d) it can concluded that effect of (s/d)
is higher than r.
Figure 10 shows that the better material flow (lower hG)
in case I could be obtained for lower r. The result could be explained by effect
of contact surface augmentation at higher die corner radius.
Influence of friction coefficient in case I and case II: In the study
of friction coefficient effect, the forming load obtained from simulations work
when the conditions is similar to other study items (s/d = 0.25, r = 5, d =
32 mm) at different friction coefficient m = 0, 0.1 and 0.2 represented by curves
in Fig. 11a and b. The results show that
the friction coefficient in case I have significant effect in comparison with
required forming load in case II. It can be concluded that lowers material flow
in case I, with higher m, is due to high resistance of lower die surface.

Fig. 12: 
Effect of m on separation height (hG) defect in case I 
Also the friction coefficient has significant effect on separation height hG.
This parameter decrease with increasing m up to 0.2, for m = 0.2, separation
height hG tends to zero. Figure 12 shows that the friction
coefficient has significant effect on material flow in case I. The friction
coefficient hasn’t important effect on material flow in case II.
CONCLUSION
The model validation was performed via comparing the forming load required,
obtained numerically and experimentally. The results obtained from simulation
work were reported in two cases.
Case I 
: 
Forcing a cylindrical billet against a flat die 
Case II 
: 
Forcing the same billet by moving both the upper and the lower dies in
opposite directions 
The following conclusion is obtained:
• 
Load required to deformation for same (s/d), in case I is
lower than that case II 
• 
Increasing (s/d) cause to decreasing the forming load in each two cases 
• 
Thelower separation height (hG) was obtained at higher (s/d) in case I
(hG value tend to zero at s/d = 0.5) 
• 
Flange angle (α_{f}) increase by increasing (s/d) and better
material flow can be obtained with the lower (s/d) 
• 
Forming load decrease by increasing die corner radius (r) in two cases 
• 
Effect of (s/d) on forming load is higher than die corner radius (r) in
two cases 
• 
Better material flow (lower hG) in case I could be obtained for lower
r. The result could be explained by effect of contact surface augmentation
at higher die corner radius 
• 
Forming load increase by increasing friction coefficient (m) but the friction
coefficient in case I have significant effect in comparison with required
forming load in case II 
• 
Separation height defect in case I, (hG) decrease with increasing friction
coefficient (m), but it hasn’t important effect on material flow in
case II 