Int. J. Mach. Tool Des. Res. Vol. 26, No. 2~ pp. 157170, 1986. Printed in Great Britain
00207357/8653.(XI~.00 Pergamon Journals Ltd.
AXISYMMETRIC EXTRUSION FORGING: EFFECTS OF M A T E R I A L PROPERTY A N D P R O D U C T G E O M E T R Y M. S. J. HASHMI* and F. B. KLEMZ* (Received for publication
14 October 1985)
AbstractExperiments have been carried out on lead and copper cylindrical billets using simple extrusion forging dies under quasistatic and dynamic conditions to produce boss and flange type components. It was observed that during the initial stages of the deformation process, the flow pattern of the metal is significantly different to what is normally assumed in theoretically analysing the process. The profile of the flange becomes very much tapered and the height of the boss obtainable is dependent on the boss to billet dimensional ratio. A theoretical analysis is presented based on rigidplastic property of the billet material which enabled prediction of the tapered deformation profile of the flange under frictionless conditions. The agreement between the theoretically predicted deformation modes and those observed experimentally is found to be very close.
INTRODUCTION
forging is one of the simplest forms of hot and cold forging processes which involve flow of metal in more than one direction to fill the die cavity. The flow pattern of the metal is very much dependent on the geometrical configuration of the dies and the relative dimensions of the billet. The quality of the forged component is known to be influenced by the flow pattern which also affects the die wear and hence tool life. Considerable experimental and theoretical research efforts have been devoted towards the study of extrusion forging processes [16], a review of some of these works appeared in reference [7] and will not be repeated here. Reasonable success has been made in predicting the forging load with good accuracy, specially when upper bound techniques have been used. Prediction of the flow pattern, however, has been found to be rather less successful even when extensive computational techniques were employed. In the present study extrusion forging experiments have been carried out using cylindrical billets. The diebillet assembly is schematically shown in Fig. 1. A thorough study of the deformation modes during the early stages of simple extrusion forging has been made. Simple analytical equations have been developed to predict the deformation mode during the process of formation of the flange and the boss. EXTRUSION
~
Test
piece
Loadc e ~ J FI6. 1. Schematic diagram showing diebillet configuration.
* Department of Mechanical and Production Engineering Sheffield City Polytechnic, Sheffield, England, U.K.
157
158
M.S.J.
HASHM! and F. B, KLEMZ ANALYSIS
In this paper extrusion forging is analysed by assuming that the energy supplied during deformation is dissipated as the plastic work of direct and shear strain in the billet. The deformation is shown to take place in three stages. In the first stage deformation of the top surface begins when the applied load is just sufficient to cause local yielding of the billet. This yielding causes the top surface to spread radially while the lower portion of the billet retains its original radial dimension. However, the lower portion of the billet begins to expand radially when the applied load becomes large enough to cause yielding in that section. This marks the beginning of the second stage. At the end of the first stage the overall depth at which plastic yielding occurs is shown to be equal to half the boss diameter. From the commencement of the second stage any increase in load causes deformation such that axial compression becomes directly related to a simultaneous increase in the billet diameter. At some point during the deformation according to the mode prescribed in the second stage the billet will require less energy to deform in a mode in which only the outer sleeve is compressed and the central core remains solid. This marks the beginning of the third mode. Under frictionless conditions the deformation will continue in the third mode. Equations have been derived which enabled the top load, total energy absorbed, boss and flange heights and profile of the deformed billet to be calculated.
First stage In formulating the equations it is assumed that the material of the billet is rigid perfectly plastic with a yield stress Y. Referring to Fig. 2(a), DB is the diameter of the billet Dc is the diameter of the die cavity and Lo is the height of the undeformed billet. Let Po be the load which is just sufficient to initiate plastic deformation to the ring area of the billet. Thus Po = "rry (DB2 _ Dc2)" 4
(1)
Let P be the applied load which is greater than Po and is sufficient to just cause plastic yielding to the ring area at a depth Ho. At any other intermediate location the compressive load available to deform the ring area is given by (2)
PH = Po + rrDckH
where H is the distance as shown in Fig. 2(a) and k is the shear yield stress of the material which may be taken as equal to Y/2. Substituting for in equation (2) we have
(3)
PH = Po + W2DcYH. When H P. Thus
=
Ho (denoting the top contact surface), PH is simply given by the applied force
"rr
(4)
P = Po + T D c Y H o which upon substitution for Po becomes "/T
P = ~   Y ( D B 2  Dc 2) + ~ D c Y H o .
(5)
Axisymmetric Extrusion Forging
159
I ~H
i= Dc'i (a)
D8
,
D2
IH7 .~"H, (b)
hi
I_
~B
_1
m
hb
E
1 I_
i
0~
FIG. 2. Theoretical deformation modes during (a) primary and (b) secondary stages.
When P reaches a value P1 which is sufficient to cause plastic yielding of the billet as a whole, then
P = P1 = ~DB 2Y.
(6)
Substituting for P in equation (5) we get ~x 4 D BZY =
4 "rr  (DB2  Dc2)y + ~ _ DcYHo
which upon rearrangement and simplification gives the depth, Ho, of the plastically yielded zone before the billet starts to deform as a whole, thus
Ho = Dc/2.
(7)
Hence during the first stage of deformation the plastic zone will extend to a depth equal to half the diameter of the boss. Assuming that the billet deforms under the action of P in the manner shown in Fig. 2(a), let an element at location H before deformation correspond to an element at location h of the deformed billet. PH will thus be the load just sufficient to plastically deform the new element of outer diameter D. Thus
PH = T
'IT
Y ( D2  Dc 2)
(8)
16(1
M.S.J.
HASHMI and F. B. KLEMZ
substituting for PH in equation (3) and noting that Po = ~ r / 4 Y ( D f  D c 2) and k = Y/2,
4 Y( D2  DC2) = ~4 Y( DB2  D('2) "Jr" ~2 Y D c " which upon simplification and rearrangement becomes H = (O 2  DB2)/2Dc .
(9)
Equation (9) gives the relationship between the diameter of the deformed shape and the parameter H which locates the position of the element of the undeformed billet. During this first stage of deformation the total work done may be expressed in terms of the plastic work and shear work done in the billet. The plastic work per unit volume in pure compression may be given by w = ( ¢de
(10)
d 0
Since for a rigid perfectly plastic material = Y (constant) thus w = Ye, which for the small element of original thickness "dH" becomes
(d,,)
(11)
w = Y In cih "
Plastic work done on the element dWp =
4 (D2  Dc2) dhYln
~
.
(12)
Total plastic work done on the outer sleeve is thus given by w
Wp = ~
(D 2  Dc 2) In
Y
dH dh dh.
(13)
0 From volume constancy of the element dH(Df
 D c 2) = dh (D 2 
dH dh
D c 2)
D 2  D c2 DB 2  D c 2
anddh=dH(DB2
(14)
De2)
D 2  D c 2
(15)
so that combining equations (1315)
%

rr
( D B 2 )
( _ . ~  Dac 2lD ) lc 2' D c 2) In \~ozoz
(16)
Axisymmetric Extrusion Forging
161
From equation (9) dH
2D
dD
2D c
(17)
so that D dH = D~ dD.
(18)
Combining equations (18) and (16) we get Wp =
+Y
~Df (DB2  D 2) In ( ~BD B2 2 L Dc2 "~C2 ) D dD
which upon integration and rearrangement becomes
Wp = [(0, 2  0 c 2) {In(D12  Dc 2)  1  ln(Os 2  0c2)} + (OB2  Dc2)] Y ( Da2  Dc 2 ~r4
2Dc
)"
(19)
The shear work done along the interface of the outer sleeve and inner core material gives:
Ws =  ~"rr D ~ Y~ (Ho  Xo)Xo.
(20)
Total work done
W r = W . + Ws. The total work done by the tup load = average tup load x displacement hence
2
" Xo = Wp + Ws.
(21)
When the tup load reaches P1 Pl~"  7 ( O 1 2
 O c 2) Y = + O B
2Y
which gives the diameter D1 of the billet at the tup interface at the end of the first stage of deformation. Thus
01 = "X/DB2 + 0C 2 .
(22)
To determine the shape of the billet profile at the end of the first stage of deformation we have, from equation (15)
dh = dH (DB2  0C2) 
162
M.S.J. HASHMIand F. B. KLEMZ
and from equation (18) DdD = DcdH. Combining these two equations and integrating and noting that when h get h = KIn(D 2  Oc 2)  KIn(DB2  Dc 2)
= 0, D =
DB, we
(23)
where K = (DB 2  Dc2)/(2Dc). Second stage During this stage, any increase in load will cause deformation such that the outer sleeve will be compressed axially with a simultaneous increase in the billet diameter. Let the load P be greater than P1 such that P=
~4 (DB')iY
(24)
where D~' is the expanded billet diameter at the lower end. Equation (5) is equally applicable to this new situation. Thus PH' _
Iv 4 Y(DB2 _ Dc2) + @  D c Y H '
(25)
where H' locates an element of the deformed sleeve as shown in Fig. 2(b). In this case, at H' = H1, PH' = P so that 'iT
P = ~4 Y(DB,2  Dc 2) + ~ D c Y H 1
(26)
by combining equations (25) and (26) it can be seen that
H1
Dc 2
(27)
Thus the shear zone is extended axially by an amount H1 and the lower part of the deforming billet, of height (L~  H1), will deform in a pure compression mode. For an axial compression of xl the shear zone changes from H1 to H2.
(
The axial strain e = In L1
xL
)=
or H2 = ( H 1  H I ~ )
(28)
The mean shear zone is thus given by Hm
HI + H 2 2
_
H1
•
(29)
2L1
The height of the section of the billet under pure compression may be obtained as follows
Axisymmetric Extrusion Forging
•
=
or h2 
In
L1
hi L1
(L1  x1).
163
Xl (30)
Total work done in the second stage Plastic work done on the sleeve
W p s _ ~ 4 (DB2  Dc2) Y In ( ~h i )
(Ha + Xo).
(31)
Shear work done between the sleeve and the inner core, making use of the mean shear zone, given by equation (29) is Ws
~rDcY 2
(
Xl H1
HIX1) 2L~ "
(32)
The shear work done at the junction of the boss and the lower part of the flange which is deforming in a pure compression mode
(Dc I  Dc) W s ,  ~Dc2y 8
(33)
where Dc 1 is the virtual increase in Dc due to an incremental compression Xl. Also the plastic work done on the lower part of the billet is given by
"IT
2
( hi ]
Wpb (Lo  Xo  HI) ~   D B Yln \ h2 j"
(34)
Total work done in the second stage is thus
Wt = { ( + ( D B 2  Dc 2) Yln ( hi ~} (H 1 + Xo) \hE / +~
xl Ha
~rDc2Y 8
(Dc
 Dc).
2L1
+ [(Lo  xo  H1) ~ DBayln
]+
(35)
The tup load at the end of a small axial compression, ~Lx,can be calculated by equating the external work to the internal plastic work done. Thus
( PI + P2 ) Ax = so that
P 2  2Wt Ax
MTDR 26:2F
P1.
(36)
164
M.S.J. HASHMIand F. B. KLEMZ
From Fig. 2(b) the boss height is given by
hb = Xo + [&x  hi +
h2]
(37)
and the flange height is given by hf = H2 + h2
(38)
where H2 and h2 are given by equations (28) and (30) respectively. The radial strain at the top of the sleeve is given by ~r = In[(D2  Dc) (D De) l where D 2 is the diameter at the top end of the flange. Now, ~r is half the axial strain e, hence
D2Dc=(D1
or
 Dc) exp ( + )
D2 = Dc + (D,  Dc) exp ( + ) .
(39)
Similarly, the radial strain at the bottom of the sleeve is given by
(DB'  Dc) er = In [ (DR Dc) ] 
E 2
where DB' is the new diameter at the lower end of the billet. Thus
DB , = Dc + (DB  Dc) exp (  2  ) "
(40)
The diameter at any intermediate point is calculated in the same manner to determine the profile of the final shape of the flange.
Third stage At some point during the deformation according to the mode prescribed in the second stage the billet will require less energy to deform in a mode in which only the outer sleeve is compressed and the central core remains rigid. The energy required is given by the sum of the energy to compress the outer sleeve and the shear energy at the sleevecore interface. Thus, the plastic energy in the sleeve is given by Wpsi
(L1)
"rr4 YLo(DB 2 _ Dc2) In L l   x j
(41)
and the shear energy is given by
W,~i
~rDc ( 2 YxI L1
xl] 2 j"
(42)
Axisymmetric Extrusion Forging
165
The tup load at the end of a small axial compression, Ax, can now be calculated by equating the external work to the internal plastic work done. (P2 + /'3) Ax/2 = Wt = Wmi + Psi.
(43)
The boss height increases by Ax and the flange height decreases by Ax whilst the total height remains constant. The foregoing equations were used in the following sequence in evaluating the theoretical results. (a) Equations (1) and (6) were used to calculate the values of Po and P1, the forces needed to initiate stages one and two respectively. (b) Equation (7) was used to obtain Ho, the amount of plastic deformation at the end of the first stage. (c) Equation (19) was used to calculate Wp, the plastic work done at the end of the first stage. (d) Equation (20) was used to calculate Ws, the amount of shear work done at the end of the first stage. (e) Equations (1921) together with equations (1) and (6) were used to find Xo, the boss height at the end of stage 1. (f) Equation (35) was used to calculate Wt, the total work done at any stage during the second stage, for known values of &r, the incremental axial compression during this stage. (g) Equation (36) was used to calculate P2, the forging load during the second stage. (h) Equations (37) and (38) were used to calculate hb and hf, the boss and flange heights respectively. (i) Equations (39) and (40) were used to calculate D2 and DB' the top and bottom flange diameters respectively, and finally (j) Equation (43) was used to calculate the forging load P3 during the third stage of deformation. EXPERIMENTAL WORK
Cylindrical lead and copper billets of 24 mm dia. and 24 mm height were forged dynamically under a drop hammer and quasistatistically using a compression testing machine. The tool and die arrangement is schematically shown in Fig. 1. Three different die cavities of dia. 18, 12 and 9 mm were used to obtain different billet to cavity diameter ratios. During dynamic extrusion forging the load was recorded using a straingauge load cell incorporated in the anvil unit to the drop hammer, the details of which have previously been described in reference (8) and will not be presented here. During quasistatic compression the load was recorded using the machine's inbuilt recording devices. Quasistatic compression tests were carried out on cylindrical specimens to obtain the stressstrain characteristics of the material used in this study. From these curves it was found reasonable to assume that the lead billets used in this study behaved as rigidperfectly plastic material with a constant yield stress of 17 N mm 2. Under dynamic test conditions, of course, strain rate sensitivity and material inertia effects would render this value inapplicable as far as forging load is concerned. RESULTS AND DISCUSSION
Experimental results were obtained using lead and copper billets. In this paper, however, we shall present experimental results mainly for lead billets and theoretical results entirely concerning the lead billets. In Fig. 3 a number of photographs are shown which depict (a) shapes of lead specimens at different stages of deformation, (b) shapes of copper specimens at different stages of deformation and (c) shapes of lead specimens having different billet to boss diameter ratios. The first two photographs clearly
166
M . S . J . HASHMI and F. B. KLEMZ
(a)
(b)
(c)
FIG. 3. Photograph showing deformation profiles for (a) lead billets, (b) copper billets and (c) lead billets with different billet to boss diameter ratios.
Axisymmetric Extrusion Forging
167
demonstrate the tapering nature of the profile of the flange. The third photograph shows how this tapering effect is influenced by the diameter of the boss. Applying the equations derived in the analysis, the deformation mode of a number of billets were predicted for different billet to boss diameter ratios. Figure 4(a) and (b) shows a series of such predicted deformation profiles of billets when dies of 18 mm and 9 mm dia. cavities were used. The predicted profiles show close similarities with those observed experimentally. Such close arguments were observed with billets deformed both dynamically and statically for different billet to die cavity diameter ratios. The evidence that the flange does not deform in pure cylindrical mode should be noted and taken into account when attempting to analyse the deformation profile and hence to predict the flow pattern in extrusion forging. It became evident from the forged specimens that the tapering of the shape of the flange varied with the ratio of the boss to billet diameters. For larger boss diameters the resulting flange taper was found to be greater whether the billets were forged quasistatically or dynamically. The extent of this taper in the flange is demonstrated in Figs 5 and 6 for boss diameters of 18 and 12 mm respectively, the billet diameter in both cases being 24 mm. Figure 5(a) shows experimental and theoretically predicted variations in the top and bottom diameters of the flange with the axial compression under static lubricated condition. Both the experimental and theoretical results show significant difference between the top and bottom diameters. Similar trend is demonstrated in Fig. 5(b) in which the experimental results were obtained under dynamic forging conditions. Figures 6(a) and (b) demonstrate the tapering effect of the flange profile when the boss diameter was 12 mm and the billet was forged under quasistatic and dynamic conditions respectively. The extent of taper is visibly less than that seen in Fig. 5. Figure 7 shows this tapering effect of the flange in a comprehensive manner in terms of the ratio of the top and bottom diameters for three different boss diameters. It is evident that when the boss diameter is 9 mm negligible tapering occurs over the entire range of axial compression. The height of the boss obtainable for different boss diameters but using same diameter billet is shown in Fig. 8(a) in which experimentally observed results are also plotted for comparison. One of the most informative parameters in extrusion forging is the ratio of the boss to flange height obtainable for different boss diameters. This parameter is shown in Fig. 8(b). It is evident that the greater the boss diameter the larger the boss to flange height ratio for any given axial compression. The variation in forging load with axial compression as predicted theoretically is shown in Fig. 9(a) for three different boss diameters. In Fig. 9(b) the theoretically predicted De:
rT~
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(o1
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F1G. 4. Theoretically calculated d e f o r m a t i o n profiles for lead billet with (a) D c = 18 m m and (b) D c = 9 m m .
168
M.S.J. HASHMIand F. B. KI.EMZ
4C
40
(a)
(b)
x 351
3~
~3C
~
E 5C
x ×
zX
~
D
Z~Zl
o 2E c o
s.L3
8
S
~ 2C
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Top diem De (theory) IC Top diem D2 (exp)
I~
..... x
( static  lubricated )
0
I
I
2
I
.....
(dynamicLubricated)
Bottom clio. DB. (theory)
Bottom die. De, (theory) _Bottom die DB.(exp) ~
Top d i o m D2 (theory) Top diam. D2 (exp)
_ Bottom die. D a, (exp)
(staticlubricated)
I
I
l
4 6 8 I0 12 Total, displ,acement xo+ x~ ( m m )
I
14
0
I
2
1
I
(dynamicLubricated)
I
t
I
I
4 6 8 I0 12 Tote[ displacement xo+ x~ ( m e )
14
FiG. 5. Axial compression vs top and bottom diameters of the flange for D c = 18 mm under (a) static and (b) dynamic forging conditions.
4C
(o)
35
x ~
~
3C'
a
(b)
35
D j.
s~
o
30
~
~x~°~ E
25
v
20
25
o 20
E .9
"~
~
15 
Top d i e m De(theory) . . . . . r o _ T o p d i o m . D2(exp)
r5
Top d i a m D 2 (theory) . . . . . .
o
x (staticlubricated)
;0  T o p diam. D2 (exp) u
Bottom dia. D 8, (theory) 5  Bottom dia. De, (exp) z~ ( static  Lubricated)
I 2
I J I I 4 6 8 I0 Tote( displ`ocement Xo+ x~ (mm)
(dynamiclubricated)
Bottom dia Dd(theory)
J 12
5 _ B o t t o m die. DB,(exp) •
I
14
0
I
2
I
I
(dynamiclubricated)
[
I
4 6 8 iO Total displacement Xo+ x, (mm)
I
i2
I
14
FIG. 6. Axial compression vs top and bottom diameters of the flange for D c = 12 mm under (a) static and (b) dynamic forging conditions.
loaddeformation curve for a billet of boss diameter 18 m m is c o m p a r e d with those obtained experimentally from static and dynamic forging tests. It is evident that the load recorded from the quasistatic forging test agree reasonably well in terms of the magnitude with that predicted theoretically. The s a m e could not be, h o w e v e r , said for the load recorded from the dynamic forging test. The dynamic forging load was f o u n d to be generally m u c h higher than both the static load and that predicted theoretically. L e a d is k n o w n to be strain rate sensitive and h e n c e under dynamic forging conditions w o u l d require higher load to be d e f o r m e d . The inertia effect may also have contributed to such differences in magnitudes of the dynamic and static forging loads. N o such effects w e r e incorporated in the analysis presented in this study and h e n c e the predicted load is closer to the static forging load. The total energy requirement predicted theoretically and m e a s u r e d from static and dynamic forging tests are s h o w n in Figs 10(a) and (b) for boss dia. of 12 and 18 m m respectively. Again it is clearly evident that close a g r e e m e n t is d e m o n s t r a t e d b e t w e e n
Axisymmetric
Extrusion Forging
169
Z~
[]
12
[3
~..._~.
% E3
A
.....
._% . . . . .
.c...o__ ...L.
o £ $ E o
0J
OE
Theoretical curves Dc = 18 Dc = 12 De= 9 0 4  E x p e r i m e n t a l results ( s t a t i c Lubricated) Dc = 18 n Dc = 12 zx 0 2 Dc " 9 o
I
0
2
I
I
I
I
4 6 8 I0 Total, displacement Xo+ x~ (mm)
I
12
FIG. 7. Axial compression vs diameter ratio of the flange for different boss diameters. D~ = 18 / / (b)
09
I I
iI
[a)
08
Theoretical values ~
i
Experimental, results static Lubricated Dc : 18 ~ "'= . . . . . D~ = 9    = ....
IC
~ Theoretical results Experimental results . . . . .
?
07I
I
/
 E x p e r i m e n t a l results dynamic Lubricated ~'¢/ Dc = 18 ~   o     ill. De:9 zx L/"
o6
I /d
/
Oc= 9
E
~6 L
.
i
o 83 4 
0
°~F
13
L
2
~
[
4
~.,,.
I
6
L
8
e
I
I0
02
I
12
[
14
0
Total displacement Xo+ x~ (mm)
t
I
2
I
l
I
I
I
4 6 8 I0 12 Total displacement Xo+ x= (ram)
I
14
FIG. 8. Axial compression vs (a) boss height and (b) boss to flange height ratio.
statically measured and theoretically predicted results only. Dynamically forged results show much greater energy requirement for the same amount of axial deformation. It should be possible to obtain a much better prediction for the dynamic forging energy requirement provided that the effects of material inertia and strain rate sensitivity could be incorporated in the analysis. CONCLUSION A simple analytical technique has been developed to predict the deformation profiles during extrusion forging of a cylindrical billet. Theoretically predicted deformation profiles show remarkable correspondence with those observed from experiments conducted both dynamically and quasistatically. Reasonable agreement is also found between the theoretically predicted loads and the ones recorded from quasistatic forging tests.
170
M . S . J . IIASHMIand F. B. KLEMZ
16
(b)
/.~;.
Iol

~
Experimental dynamic lubricated static Lubricated Theereticot (static)
32  E x p e r i m e n t a t
~
14
/
 T h e o r e t i c a l (dynamic) . . . . . .
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t /
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Dc : 9 m m Dc " 12rnm . . . .
4
Dc = 18ram . . . . .
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4 6 8 I0 T o t a l displacement Xo+ x, ( mm )
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Fie. 9. Axial compression vs (a) theoretical forging load and (b) theoretical and experimental forging loads for Dc = 18 mm. (a) 40C
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Experimental results (drop h e m m e r ) .......
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E x p e r i m e n t a l resutts (quasistatic) e(static) Theoretical resutts T h e o r e t i c a l r e s u l t s (dynami__c)
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Experimental resutts (drop h a m m e r ) .......
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Total displacement
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x o + x r (ram)
FI6. 10. Axial compression vs total energy absorbed for (a) Dc = 12 mm and (b) Dc = 18 ram.
REFERENCES [1] [2] [3] [4] [5]
H. Kuoo, Int. J. Mech. Sci. 1, 5783 (1960). T. ALTAN, In Metal Forming (ed. A. L. Hoffmanner), pp. 325347. Plenum Press, New York (1971). C. H. LEE and S. KOBAVASm,J. Engng. Ind. Trans. A S M E 95,865870 (1973). S. N. SHAH and S. KOBAYASm,Proc. 15th Int. MTDR Conf., pp. 603610 (1974). R. P. MCDERmOTrand A. N. BeAMLEV,Forging analysisa new approach, Proc. 2nd N. Amer. Metalwkg. Res. Conf., pp. 3547 (1974). [6] J. A. NEWr,IAN and G. W. ROWE (1973) An analysis of compound flow of metal in a simple extrusion/ forging process, J. Inst Metals 101, 19. [7] R. P. MCDEaMOI"r and A. N. BRAMLEVProc. 15th Int. MTDR Conf., pp. 437443 (1974). [8] F. B. KLEMZ and M. S. J. HASIaMI, Proc. 18th Int. MTDR Conf., pp. 323329 (1977).
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