Friction Determination During Bulk Plastic Deformation of Metals N. A. Abdul
S
m
 Submitted by J. M. Alexander ( 1 )
Y
The process economy of metalforming operations largely depends on the mechanism of friction vhich must be controlled appropriately to avoid pickup, galling and scoring which are principally responsible for premature failure of tool. In spite of the fact that there are numerous metalforming lubricants on the market, the main problem confronting production engineers is an optimum choice of a lubricant for a specific operation. However, a reasonably accurate and reproducible method of determining friction during bulk plastic deformation of metals will eliminate this prohlem. This work enables easy experimental means of assessing lubricants without involving the user in any theoretical or computational exercise by providing a calibration chart for the determination of friction factor. All that is required ring testpiece at appropriate temperature. is a measured deformation geometry of a6:3:2
WMENCLATURE
*
Effective forming stress Direct basic yield stress
r.
=
Current internal radius
Ro
=
a '

Y
J
R.

lnitial internal radius Initial outside radius
K

Current outside radius
T

Initial Thickness Current thickness Frictional shear stress Friction factor Neutral radius
t

.
A

m

K

IXTRODUCTION A plastically deforming ring between two rigid compressing platens has a property of deforming in relation to the amount of the frictional resistance at the ringlplaten interface. The deformation is such that the material of the ring can flow either entirely outward when the interface friction is lov or partly outward and inward vhen the interface friction is high
enough as illustrated in Figure 1. In flow of material is dependent upon the present at the ringlplaten interface. o f the ring under compression offers a assessing friction.
either case the rate of amount of friction This peculiar property sensitive means of
Kunogi El] first applied the property of the ring under compression in the aSsessment of lubrica ts for the cold extrusion of steel. Hale and Cockcroft 721 later adapted the technique for direct determination of friction by publishing calibration curves based on both experimental and indirect theoretical considerations of the deformation of a ring under compression. They observed the major disadvantage of the technique a8 nonavailability of satisfactory theoretical method of cnnverting measured deformation pattern of a ring testpiece into actual coefficient of friction. However, entirely theoretical analyses describing the deformation pattern of a ring under canpression vith any amount of friction a t the ringlplaten interface had been made b Kunogi [3]. Kudo [ L ! , Avitzur [ 5 ] , Hawkyard and Johnson t6] etc. While Havkyard and Johnson [ 6 ! used the 'Stress Analyses' method in their theoretical analyses of the deformation of a ring under compression with any amount of friction, Avitzur [5] used the minimum 'Upper Bound' method. Somehow, both methods gave similar results and the relevant working equations of Avitzur's analyses vere applied in this work.
RING COMPRESSION ANALYSES Avitzur'a 'Upper Bound' analyses of a ring under compression between t v o rigid platens with interfacial friction assumed that: (1)
The deformation of a ring testpiece is uniform throughout its thickness thus implying that the frictional shear stress is uniformly distributed throughout the thickness of the ring.
(2)
The ring is made of a perfectly plastic incompressible material which obeys von Yises yield criterion.
r l
n=O Frictionless Condition
Low Friction CondRlan
The outcome of the analyses differentiated between the two possible types of material flow pattern for a ring under compression with interfacial friction. Hence two separate expressions were obtained for the rate of frictional work done depending on the type of flow pattern, Figure 1. Flow Pattern When r
< I.
n
1
The ratio of the forming stress to the basic yield stress othervise known as the reduced stress is given by:
Medium
And High Friction Condltlon 'I
C rn
d
ro
(b)
MODE OF RING DEFORMATION SHOmNG POSITIONS OF NEUTRAL SURFACE AT VARIOUS LEVELS OF FRICTION FIG 1
Annals of the CIRP Vol. 30/1/1981
and r
is obtained from:
r
(?
2
r1 J3
J
( 3 4
21
.. .. ..
(2)
143
vhere: tr
2

(r
n
r 2 
i
Equations (1). (2) and (3) are valid at any instant of compression only when:
Flow Pattern When r: z r  < rn In this case the corresponding reduced stress is given by:
2
 R.~)T 1
f
..
.. ..
(9)
The possibility also exists of the whole material of the ring flowing radially outward. this corresponds to the neutral radius being less than the inside radius. In the limit. the neutral radius becomes zero and the ring will deform as if it is an annular part of a solid disc. Equation (9) remains valid for all positions of the neutral radius between the geometric centre and the outside radius. After ensuring that the condition of equation (4) had been satisfied for a given value of friction factor then equation (3) was evaluated and used in (9) to solve equation (2). Similarly when the condition of equation (7) had been satisfied for a given value of friction factor then equation ( 9 ) was used to solve (6) by successive approximation. The ratios of neutral radius to outside radius obtained by solving equations ( 2 ) and (6) could be substituted in equations (1) and ( 5 ) respectively to obtain the reduced stress value for the given Friction factor at the current strain. The elution vas made using electronic digital compu:er for a ring geometry whose ratio of external diameter to internal diameter to thlckness is 6:3:2. PZSiiT AND DISCUSSION Some of the experimentally derived curves by Male and Corkcroft [Z] were compared with those derived theoretically. The correllaiion hcswern thrm is show, in ?igvre 2.
L and r
0
The theoretical frictionless curve agrees quite well with the popular opinion thet under frictionless condition a ring would deform ss if it is an anrular part of a solid disc. There is also a good agreement between theoretic91 and experimental curves of m 1.0 and 0.35. However there is some difference between theoretical and experimental CUNVCS at low intermediate level of friction, i.e., m 0.05 and m 0.1. The disparity is very much llkely to be due to the indirect vsy of determining experimental friction.
i s obtained from:


Equations (5) and ( 6 ) are valid at any instant of compression only when:
I
AI)Z II '? F
mr .
0
\
Solution Of Ring Deformation Equations The frictional condition at the ring/platen interface is defined by the friction factor, m, as:
It is to be noted that neither the basic yield stress nor the.frictiona1 shear stress appears in the final equations as independent terms. They appear only as ratios. i.e.. reduced stress and friction factor respectively. From the basic assumption of the analyses the ratios remain constant for the material and the condition of deformation. DePiere and Male [7] stated that when the analyses are carried out for a small increment of deformation the basic direct stress and the frictional shear stress (consequently friction factor) are approximately constant and hence the solution is valid for constant friction factor. It is therefore justifiable to solve the relevant equations in a series of small deformation increments using the final ring geometry from one increment as the initial geometry for the subsequent increment and so on. The relative rates of inward and outward flow of material are determined by assuming the concept of incanpressibility of material with a neutral surface separating the two regions of flow, Figure 1. By considering a small increment of deformation during which the neutral radius is assumed constan5 the geometry of the ring at the end of an incremental compression can be defined. Thus. an imposed small reduction in thickness from T to t will cause the inside radius of the using volume constancy ring to change from R. to r. defined of the material betwein the'neutral and internal radius of as: the ring


144

The semiexperimental calibration technique of Male and Cockcroft is more likeiy to br lesa accurate than the entirely thevetical result in view of the three independent methods adoprcd by Hale an0 CockcroEt for the frictionless, intermediate friction and fpll stirking friction. Tbe result over the full range of metalforming friction is presented in the form of a calibration chart shown in Figure 3. The chart shows constant friction factor ?inre and ccnstanc height reduction lines ngainst graduated axis of In this Eom of 'percentage change in internal diaeter'. presentation the chart is very easy to apply and it facilitates extrapolation which is inevitable with experimental results. For example. at an arbitrary and convenient stage during cmpression of a 6:3:2 ring vith constant friction. experimentally determined deformation of the ring can be fed into the set of curves to establish the operating friction factor during compression. The ring analytical solution is based on constant frictional shear stress at the ringlplaten interface throughout the compression process whereas in practical terms frictional condition fluctuates during a compression process. Therefore, the calibration chart,Figure 3, is strictly for use vhen interfacial friction between the ring testpiece and the platens is constant. However, the chart can still be applied when there is fluctuation in friction by matching the slope of the experimental curve vith that of the calibration curve at the same strain value as suggested by Hawkyard and Johnson [fi]. Suitability Of The Ring Technique The ring technique of assessing friction during bulk plastic deformation of metals ia widely favoured for the following reasons: (1)
The mode of deformation of a ring under compression is primarily determined by the amount of friction present at the ringlplaten interface.
(2)
The application of the technique requires only deformation characteristics unlike most other methods requiring mechanical properties as well as the forming load.
(3)
The state of friction during bulk plastic deformation of a ring between rigid platens is very much similar to that encountered in most metalforming operations between the workpiece and rigid dies.
1"
145
Choice Of Homogeneous Deformation Analyses The choice of analyses based on uniform frhtional effect throughout the thickness of a ring testpiece under compression is made in this work. This is because the assumption is true to a large extent if the ring testpiece is made as thin as possible. A further justification for the choice is the apparent inability of existing theoretical analyses to account adequately for all possible forms of inhomogeneity for a ring under compression.
1 I
c//////3
I
(a) I
v/////a
CONCLUSION Working calibration chart has been prepared to facilitate the application of the ring technique in the assessment of friction during bulk plastic deformation of metals. The chart will greatly ease the choice of metalforming lubricants for industrial application. ACKNOWLEDGEMENT The author would like to thank Dr. A. N. Bramley for his useful discussion, Dr. Susan Bloor for her assistance during computation and Professor B. Y . Cole for providing the facilities for this work.
He would also like to acknowledge the efforts of Professor J. M. Alexander for sponsoring his CIRP membership. REFERENCES 1.
( b)
'M. KUNOGI, Journal Of Science Research Institute (Tokyo), 1956. Vol. 5 0 , p. 215.
I
1 I
Y//h
(C)
(d)
td I
I
V//A
2.
A. T. MALE and M. C. COCKCROFT, Journal Of The Institute Of Metals, 196465, Vol. 93. p. 38.
3.
M. KUNOGI. Rep. Science Research Institute (Tokyo), 1954, Vol. 30, p. 63.
4.
8. Kuw. Proceedings 5th Japan National Congress Applied Mechanics, 1955.
5.
8 . AVITZUR. Israel Journal Of Technology. 1965. Vol. 2. p. 295.
6.
J. B. HAVKYABD and W. JOHNSON, International Journal Of Mechanical Science, 1967, Vol. 9. p. 163.
7.
V. DePIERE and A. T. HALE, Technical Report AFMLTR6928, October 1967 Part 1.
8.
N. A. ABDITL. Proceedings of the twenty first International Machine Tool Design and Research Conference, 1980. p. 389.
I
(1)
DEFORMATION MODES OF 6:3:2 MILD STEEL RINGS OBSERVEDAT VARIOUS LEVELS OF FRICTION FIG 4
An examination of the ring estpieces used for the assessment of various lubricants [a] revealed five possible forms of inhomogeneous deformation for a ring, Figure 4. Out of the five forms only two, Figure 4(a) and 4(c) were accounted for in the analyses made by Avitzur and other researchers recently in an attempt to incorporate inhomogeneous deformation of a ring. Therefore, it appears premature to use the analyses since they are limited in scope as at now.
146