CHAPTER - VI

CONCLUSIONS

1. A square billet, when axially deformed by introducing a conical die constraint at

one end of the die results with three geometries namely: a barrelled part,

truncated part and an extruded part irrespective of the lubricating conditions and

aspect ratios.

2. When square and rectangular billets are axially upset under differential

lubricating condition (By applying lubricant at one end of the specimen and

maintaining the other end in dry lubrication) results with two geometries namely:

a barrelled part and a truncated part irrespective of geometries, aspect ratios and

lubricants applied at one end face of the specimen.

3. The curvature of the barrelled part of the specimen, physically measured, follows

the geometry of circular arc for all-the experimented cases.

4. The stresses namely the axial stress, the hoop stress, the effective stress and the

hydrostatic stress, which are calculated using simple theory of plasticity, are

found to increase with increase in the level of deformation. It is observed that for

any strain level, the increase in hoop stress is appreciably lower as compared with

the axial stress for all the experimented cases.

297

5. The relationship between the new hoop strain and the axial strain confirms a

straight-line behaviour irrespective of geometries; aspect ratios and lubricants

used both in square and rectangular billets under all the experimented cases.

6. The calculated value of radius of curvature of the barrel is found to be in close

proximity with the measured value of radius of the barrel. The radius of curvature

of the barrel fits a circular arc for all the experimented cases.

7. New geometrical shape factor is derived for all the upsetting conditions. The In-In

plots between the barrel radius and the new geometrical shape factor shows a

straight-line behaviour in all the cases irrespective of geometries, aspect ratios

and lubricating conditions. This straight-line relation suggests a power law

relationship between them. The power law equation is in the following form:

R=CS-m

where R is the barrel radius, S is the new geometrical shape factor and C and in

are empirically determined constants.

The rate of change of barrel radius with respect to the new geometrical shape

factor does not vary much with different aspect ratios, lubricants and geometries.

8. The stress ratio parameter showed a direct effect on the barrel radius under all the

upsetting conditions. The radius of curvature of the barrel decreases

exponentially with increasing value of the stress ratio parameter irrespective of

geometries, aspect ratios and lubricants used.

9. The In-In plot between the radius of curvature of the barrel and the stress ratio

parameter establishes a straight line relationship with different slopes between

them irrespective of geometries, aspect ratios and lubricants used for all the

298

upsetting conditions. The straight line behaviour between these two parameters

suggests a power law relationship of the following form

R= G 1 [(CYm/&) (h0-hf)] —m0

where R is the barrel radius, m is the hydrostatic stress, a is the representative

stress, h0 is the height before deformation, h f is the height after deformation, G1

and m0 are empirically determined constants.

10.The hydrostatic stress has a direct effect on the radius of curvature of the barrel.

The radius of curvature of the barrel decreases exponentially with increasing

value of the hydrostatic stress irrespective of the geometries, aspect ratios and

lubricants used in all the upsetting cases. The behaviour of the hydrostatic stress

is same as seen in the case of the stress ratio parameter

11.The relationship between the friction factor 'm' and the new geometrical shape

factor is found to be a straight line. This suggests that a power law relationship

exists between the friction factor and the new geometrical shape factor, which is

expressed as follows.

m G2 lnS + G3

where 'm' is the friction factor, 'S' is geometrical shape factor, and G 2 & G 3 are

empirically determined constants.

12. The friction factor 'm' decreases linearly with increasing value of the natural

logarithmic value of the stress ratio parameter. The logarithmic plot shows that

the straight relationship between the friction factor and the logarithmic value of

stress ratio parameter is the manifestation of the following expression

m = G4 In [(cm/)(ho - hf)] + G5

299

where m is the friction factor, cm is the hydrostatic stress, cy is the representative

stress, h0 is the initial height of the billet, h f is the final height of the billet after

deformation and G4 & G5 are empirically determined constants.

300

SUGGESTED TOPICS FOR FURTHER INVESTIGATIONS

From the consideration of results of the present study, several additional areas

may be worth for further investigations:

a) A study on barrelling of square and rectangular billets of ferrous metals can

be studied.

b) A study on barrelling of different polygons can be studied.

c) A study on barrelling of elliptical specimens of non- ferrous metals can be

carried out.

d) A study on the effect of die constraint at both ends on barrelling can be done.

e) Further work on cold work effect (Pre strain) on barrelling can be carried out.

f) A complete slip line solution for the effect of barrelling on various

parameters can be carried out.

g) Research study on the effect of work hardening value and other mechanical

properties on barrelling can also be carried out.

h) Research work on the effect of chemical composition and microstructure of

steels and non-ferrous metals on barrelling can also be carried out.

301

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