Analysis of dynamic effects during high-speed forging of sintered preforms

Journal of Materials Processing Technology 112 (2001) 53±62

Analysis of dynamic effects during high-speed forging of sintered preforms Saranjit Singha, A.K. Jhab,* a

Department of Production Engineering, Birla Institute of Technology, Mesra, Ranchi 835215, India b Department of Mechanical Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221005, India

Received 15 September 1999; received in revised form 2 November 2000; accepted 28 November 2000

Abstract This paper discusses the various technological aspects of high-speed forging of sintered preforms. The relationship between the frictional stress at the interface and other process variables is discussed and an analysis has been done for the estimation of die load by energy method taking barrelling into consideration in addition to the inertial forces for axial symmetry and plane strain sinter-forging conditions. Results are discussed critically to illustrate the interaction of various processing parameters involved during high-speed forging of sintered preforms and are presented graphically. # 2001 Published by Elsevier Science B.V. Keywords: High-speed forging; Densi®cation; Barrelling; Velocity ®eld; Die load

1. Introduction During the last few decades, high-speed working of materials has occupied an important position in industry, as it is being used successfully in producing engineering components at competitive rates. The deformation pattern during high-speed sinter-forging process is in¯uenced by several factors, which interact with each other in a complex manner. The decisive factors are the density of the preform, forging temperature, lubrication conditions at the die±workpiece interface, the ¯ow stress of the sintered material and the factors related to the forging equipment such as deformation speed and contact time under load. Many solutions to sinter-forging problems have been reported on the various technological aspects of industrial processing of sintered materials [1±6], not much systematic attempt has been made so far to study the dynamic effects during high-speed sinter-forging process. Since the speed is a very important factor, attention should have also been towards the effect of inertial forces and the variation of frictional stresses at the interface on the deformation mode of sintered preforms. Recently, authors have reported important investigations concerning the dynamic effects during

*

Corresponding author.

0924-0136/01/$ ± see front matter # 2001 Published by Elsevier Science B.V. PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 8 9 8 - 0

high-speed forging of sintered copper powder solid discs, hollow discs and strips [7±9]. This paper is concerned with an energy method analysis taking barrelling into consideration in addition to the inertial forces, constructed for determining the die load during the high-speed cold forging of sintered preforms under axial symmetry and plane strain conditions. In the analysis an appropriate interfacial friction law and yield criterion for porous sintered material have been used. The results so obtained are analysed and discussed to explain the interaction of the various processing parameters involved and presented graphically. It is expected that the work will be useful for the assessment of the deformation load during the high-speed forging of sintered materials. 2. Interfacial friction law [10] In high-speed sinter-forging process, the surface of the workpiece is distorted and takes on an impression of the die surface. Therefore, the actual contact area, as far as the speci®c cohesion of the surface is concerned, is not negligible. Friction conditions in forging are essentially different from sliding friction in machine parts. The relative velocity between the workpiece material and the forging die surface together with high interfacial pressure and/or deformation modes will create the conditions essential for adhesion in addition to sliding [11].

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Nomenclature ai h n p P r; y; z S U U_ Ui V DV x; y; z 2b 2l

associated acceleration field instantaneous thickness of the workpiece constant quantity much greater than unity pressure at the die±workpiece interface die load cylindrical co-ordinates surface area die velocity acceleration displacement rate field volume magnitude of the relative velocity Cartesian co-ordinates diameter of the disc length of the strip

Greek letters b arbitrary parameter which determines the amount of barrelling e strain e_ ij corresponding strain rate tensor field Z constant and a function of relative density r only l flow stress of the sintered material m coefficient of friction x…%† …jp=ljwith dynamic effect jp=ljwithout dynamic effect †= jp=ljwith dynamic effect rp initial density of the sintered preform rr real density of the real contact area r0 dimensionless, rr =r  r apparent density of the apparent area s0 yield stress of the non-workhardening matrix metal t shear stress f0 specific cohesion of the contact surface

3. Analysis of die load In addition to the usual assumptions during high-speed wrought material forging [14], the following assumptions are made in the analysis. 1. Friction due to adhesion is a function of the relative density r. 2. Yielding of sintered material is sensitive to the hydrostatic stresses imposed during forging. For analysis of die load, axial symmetry and plane strain high-speed forging conditions are considered separately here. The following equations may be obtained for the highspeed forging of a sintered preform by two ¯at rigid dies moving with velocity U towards each other (Fig. 2).

Subscripts r radial x lateral y longitudinal z axial y circumferential For such a mechanism of composite friction, which usually occurs in axisymmetric process, the shear equation becomes t ˆ m‰p ‡ r0 f0 Š

During the high-speed sinter-forging process, the compressive force supported by impact gradually increases the relative density and hence, the real area of contact grows and approaches the apparent one as the force increases (Fig. 1). This approach will probably be an asymptotically one [12]. The pattern of metal ¯ow during the forging of a sintered material is such that there exists two zones: an inner zone where no relative movement between workpiece and die occurs (the sticking zone) and an outer zone where sliding occurs. Therefore, the appropriate interfacial friction laws for different deforming conditions are: Axial symmetry h n r r oi m (2) t ˆ m p ‡ r0 f 0 1 nb Plane strain h n x xoi m t ˆ m p ‡ r0 f 0 1 (3) nl where rm and xm denote the sticking zone radius for axial symmetry and plane strain conditions, respectively, which may be approximated by the relation given by Rooks [13], and n  1. Though the contribution of adhesion in Eqs. (2) and (3) is less pronounced, it constitutes a major drawback in production, because it affects the die life, deformation load and the surface ®nish of the forged product appreciably.

(1)

where, the ®rst term on the right side is the sliding friction and the second term is the friction due to adhesion which is due to change of the relative density of the preform. The change in relative density depends upon the processing conditions such as speed and surface conditions.

3.1. Axial symmetry 3.1.1. Velocity ®eld and strain rates Compressibility [7] @Ur …1 2Z† @Uz ‡ ˆ0 2…1 ‡ Z† @z @r

(4)

Because of symmetry, the velocity ®eld with bulge satisfying the compressibility equation (4) is Ur ˆ

…1 2Z†b e bz=h Ur 2…1 ‡ Z†…1 e b=2 †h

(5)

S. Singh, A.K. Jha / Journal of Materials Processing Technology 112 (2001) 53±62

55

Fig. 1. Physical model of a high-speed sinter-forging process.

…1 e bz=h †U …1 e b=2 †

Uz ˆ Uy ˆ 0

(6) (7)

The strain rates are: e_ rr ˆ

@Ur …1 2Z†e bz=h bU ˆ @r 2…1 ‡ Z†…1 e b=2 †h

(8)

e_ yy ˆ

Ur …1 2Z†e bz=h bU ˆ r 2…1 ‡ Z†…1 e b=2 †h

(9)

e_ zz ˆ

@Uz ˆ @z

e_ rz ˆ

…1 e bz=h †U …1 e b=2 †

…1 2Z†b2 Ur e bz=h 4…1 ‡ Z†h2 …1 e b=2 †

e_ ry ˆ e_ yz ˆ 0

(10) (11)

3.1.2. Plastic deformation of a sintered preform For plastic deformation of a sintered preform, the external power J  supplied by the platen is given as Z r Z Z 2s0 1 J  ˆ p e_ ij e_ ij dv ‡ tjDVj ds ‡ rp ai Ui dv (12) 3 V 2 s v The ®rst term on the right-hand side denotes the rate of internal energy dissipation Wi , the second term denotes the frictional shear energy losses Wf , and the last term Wa denotes the energy dissipation due to inertia forces. The external power J  supplied by the press through the platen is J  ˆ Wi ‡ Wf ‡ Wa ˆ 2PU The internal power of deformation, Wi is given by s   2s0 1 2 2 2 Wi ˆ p e_ rr ‡ e_ zz ‡ e_ rz 2pr dr dz 2 3

Fig. 2. Schematic diagram of an axially symmetric sintered disc during the high-speed sinter-forging process.

(13)

(14)

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S. Singh, A.K. Jha / Journal of Materials Processing Technology 112 (2001) 53±62

Now putting Eqs. (8), (10) and (11) in Eq. (14) and solving one gets 2( 3   )3=2  0 2 3=2 2ps0 bUb3 4 4h2 a0 1 2Z 2 4a h 5 p Wi ˆ ‡ 1‡Z b 2 b2 b2 b 2 3 3h

where Wi , Wf and Wa are given by Eqs. (15), (17) and (19), respectively, and the barrelling parameter b depends upon interfacial lubrication condition.

(15)

The platens are considered as rigid bodies, the surface in contact with the strip being parallel and moving towards each other with velocity U normal to the surface. The length l of the strip is assumed to be much greater than the width w, so that the plane strain conditions exist during forging (i.e. Uy ˆ 0 and e_ y ˆ 0).

2

0

where a ˆ 2 ‡ ‰…1 2Z†=…1 ‡ Z†Š . The rate of energy dissipation due to friction Wf is given by Z b h n r i r oih m Wf ˆ 4p m p ‡ r0 f0 1 jUr jzˆh=2 r dr nb 0 (16) Pressure distribution between platen and workpiece is required for the computation of the friction losses. If the pressure is assumed constant and equal to average pressure …pav †, then the computed frictional losses are reasonably accurate for practical purposes. Therefore, integrating and simplifying Eq. (16)    2pm…1 2Z†Ub3 3 rm pav ‡ r0 f0 1 ‡ Wf ˆ 4n nb 3…1 ‡ Z†h b e b=2  …1 e b=2 †

(17)

The energy dissipation due to inertia forces is Z b Z h=2 rp …ar Ur ‡ az Uz †2pr dr dz Wa ˆ 2 0

0

(18)

@Ur @Ur @Ur ‡ Uz ‡ ; @r @z @t

az ˆ Uz

@Uz @Uz ‡ @z @t

External power supplied is (20)

The forging load is given as P ˆ …2U† 1 …Wi ‡ Wf ‡ Wa †

(21)

(22)

The velocity ®eld with barrelling satisfying the compressibility equation (22) is given as Ux ˆ

abU e bx=h x h…1 e b=2 †

(23)

Uy ˆ 0

(24) …1 e bz=h †U …1 e b=2 †

Uz ˆ

e_ xx ˆ

Using velocity ®eld equations (5) and (6), integrating and simplifying Eq. (18)    …1 2Z†2 U 3 b4 b2 1 2Z Wa ˆ 4prp 1‡Z 96…1 ‡ Z†2 …1 e b=2 †3 h2    1 2Z 3b=2 3b=2 b ‡ 2e 3e ‡ 1 e 1‡Z _ 4 …1 e b † …1 2Z†2 bU Ub ‡ 2 32…1 ‡ Z† h…1 e b=2 †2   U 3 b2 …e 3b=2 1† b=2 b ‡ e e ‡ 3 2…1 e b=2 †3   _ 2 hU Ub b e b 3 b=2 ‡ 2 e ‡ (19) 2 2 2b…1 e b=2 †2 2

J  ˆ 2PU ˆ 2pb2 Upav

3.2.1. Velocity ®eld and strain rates Compressibility [8] " p# …1 ‡ 2Z2 † 2Z 3…1 Z2 † dex ˆ dez …1 4Z2 †

where a ˆ ‰…1 ‡ 2Z2 † 2Z The strain rates are:

where ar ˆ Ur

3.2. Plane strain

(25) p 3…1 Z2 †Š=…1

@Ux abU e bz=h ˆ @x h…1 e b=2 †

e_ yy ˆ 0 @Uz bU e bz=h ˆ @z h…1 e b=2 †   1 @Ux @Uz ab2 Ux e bz=h ‡ ˆ e_ xz ˆ 2 @z @x 2h2 …1 e b=2 †

e_ zz ˆ

4Z2 †

(26) (27) (28) (29)

3.2.2. Plastic deformation of a sintered strip preform For plastic deformation of a sintered strip preform, the internal power of deformation Wi is given by s p 2 p 2 2s0 U …1 ‡ a2 † 4 a2 b2 w2 p Wi ˆ w‡ 1‡ 2 2h …1 ‡ a2 † 3 p p 2h …1 ‡ a2 † abw log p p ‡ b 2h …1 ‡ a2 † 13 v !2 u u abw C7 (30) ‡t1 ‡ p p A5 2 2h …1 ‡ a †

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The rate of energy dissipation due to friction Wf during forging of a strip is given by:    2mw2 Uab e b=2 2 x ‡ ‡ r f 1 ‡ Wf ˆ (31) p av 0 0 3n nl h…1 e b=2 † The rate of energy dissipation due to inertia forces, Wa during forging of a sintered strip preform is given as: Z w Z h=2 …ax Ux ‡ az Uz † dx dz (32) Wa ˆ 4rp 0

0

where ax ˆ Ux

@U @Ux @U ‡ Uz ; ‡ @x @t @z

a z ˆ Uz

@Uz @Uz ‡ @z @t

Using velocity ®eld equations (23)±(25) and solving one gets:  wU 3 …1 e b † w3 U 3 b2 a2 …1 e b † Wa ˆ 4rp ‡ …1 e b=2 †3 6…1 e b=2 †3 h2 _ _ 3 a2 b2 h…1 e b † U Uwh…1 e b † U Uw ‡ ‡ 2b…1 e b=2 †2 6h2 b…1 e b=2 †2 _ U3w 2U Uwh wU 3 …e 3b=2 1† ‡ 2 b…1 e b=2 † …1 e b=2 † 3…1 e b=2 †3  _ U Uwh a2 b2 U 3 w3 …1 a†…e 3b=2 1† ‡ ‡ 2…1 e b=2 † 9h2 …1 e b=2 †3 (33)

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The external power J  supplied by the press is given as: 2PU ˆ Wi ‡ Wf ‡ Wa

(34)

or P ˆ …2U† 1 …Wi ‡ Wf ‡ Wa † pav ˆ

P Wi ‡ Wf ‡ Wa ˆ 2wl 4wlU

(35) (36)

In which Wi , Wf and Wa are given by Eqs. (30), (31) and (33), respectively, and the barrelling parameter b depends on the lubrication conditions at the interface. 4. Results and discussion In an investigation of the plastic deformation of sintered preform during forging it is evident that the cylindrical free surface barrels when friction exists at the interface and cracks gradually appear at the barrelled surface. The amount of barrelling mainly depends on the initial density of the preform and the degree of frictional constraints. Fig. 3(a) and (b) shows the barrelling graphically for various reductions during dry and lubricated high-speed sinter-forging of copper powder disc preform, respectively [7]. Now, to illustrate the order of magnitude of dynamic effects, a typical case of high-speed sinter-forging of a disc is considered for which: b ˆ 0:483, b ˆ 1:1 cm, h ˆ 1:0 cm,

Fig. 3. Development of barrelling during high-speed forging of an electrolytic copper powder disc. (a) Dry forging condition. (b) Lubricated forging condition (vaseline) [7].

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S. Singh, A.K. Jha / Journal of Materials Processing Technology 112 (2001) 53±62

Fig. 4. (a) Theoretical forging load versus percentage reduction curves for high-speed forging of sintered copper powder disc under axial symmetry condition. (b) Theoretical forging load versus percentage reduction curves for high-speed forging of sintered copper powder strip under plane strain condition.

S. Singh, A.K. Jha / Journal of Materials Processing Technology 112 (2001) 53±62

m ˆ 0:30, r0 f0 ˆ 0:4p, n ˆ 3, l ˆ 812 kg cm 2 , rp ˆ 0:007616 kg cm 3 and g ˆ 981 cm s 2 . For simplicity, considering the effects of velocity only and disregarding the die acceleration terms in Eqs. (21) and (35) the theoretical forging load is calculated for the above case.

59

Fig. 4(a) and (b) shows the theoretical forging load versus percentage reduction curves for high-speed forging of sintered copper powder preforms under axial symmetry and plane strain sinter-forging conditions, respectively. The curves express the results for a particular value of the

Fig. 5. (a) Effect of the die velocity U and barrelling parameter b and x under axial symmetry sinter-forging condition. (b) Effect of the die velocity U and barrelling parameter b and x under plane strain sinter-forging condition.

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S. Singh, A.K. Jha / Journal of Materials Processing Technology 112 (2001) 53±62

coef®cient of friction m and the initial relative density r of the sintered preform for different values of the deformation speed U. Fig. 5(a) and (b) shows the effect of the die velocity U and barrelling parameter b and x during high-speed sinter-forging under axial symmetry and plane strain conditions,

respectively. It is noted that an increase in b increases the value of x, for a constant value of U. Also, for a particular value of b, an increase in U results in an increase in x as here. Therefore, it may be concluded that such dynamic effects are important for even moderate to high speed and must be considered.

Fig. 6. Relative density variation with percentage reduction in height during high-speed sinter-forging process. (a) Axial symmetry condition. (b) Plane strain condition [7,8].

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During the high-speed sinter-forging process the compressive forces will gradually close the pores and thus the relative density of the sintered material will increase with an increase in the percentage reduction in height. Fig. 6(a) and (b) shows this variation in graphical form for axial symmetry and plane strain deformation, respectively [7,8]. The relative density changes gradually with an increase in percentage height reduction. Lubricated specimens exhibit relatively better densi®cation than unlubricated ones. The relationship between an external pressure p and a relative density r is given by the following expression [15]: p ˆ l

2 loge …1 3

r†

(37)

Solving Eq. (37) results in rˆ1

e

1:5p=l

(38)

For an electrolytic copper powder disc preform with an initial relative density of 0.75, forged at high speed (100 m s 1 ) to a 10% height reduction, the theoretical value of the relative density (against average pressure pav ) is found to be 0.794. The experimentally measured relative density of the sintered copper disc after being forged to a 10% height reduction agrees satisfactorily with the above theoretical value (Fig. 6). As an illustration, Fig. 7(a) shows photomicrograph of pores in an electrolytic copper powder disc sintered at 900 C

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and high speed forged to 30% reduction without lubricant, whereas Fig. 7(b) shows photomicrograph of pores in an electrolytic copper powder disc sintered at 900 C and high speed forged to 30% reduction with vaseline acting as lubricant. 5. Conclusions The deformation pattern during the sinter-forging process is in¯uenced by several factors, which interact with each other in a complex manner. The main controlling factors are the density of the preform, lubrication conditions at the die± workpiece interface, the ¯ow stress of the sintered preform and the factors related to forging equipment, such as deformation speed and contact time under load. The dynamic effects during high-speed sinter-forging process have been analysed using energy method and discussed critically. The following important conclusions have been made:  During high-speed sinter-forging process, the interfacial friction between workpiece and die is quite different from sliding friction in machine parts, and is a function of both pressure and adhesion.  The contribution of adhesion friction is small but it affects the final density and surface finish of the forged product considerably and, therefore, must be considered while dealing with high-speed sinter-forging processes.  The die speed U, the coefficient of friction m and the barrelling parameter b affect the deformation pressure and forging load to a great extent.  The effect of inertia forces on die load is not negligible during high-speed sinter-forging and must be considered while calculating the die loads. The inertia forces encountered are functions of both processing parameters and deformation characteristics. The work was found to be effective for the assessment of the pressure distribution and die load during high-speed forging of sintered materials. It is expected that the present high-speed sinter-forging analysis using energy method will be useful in expanding the research and development work in industrial processing of sintered preforms.

References

Fig. 7. (a) Photomicrograph of pores in an electrolytic copper powder disc sintered at 900 C and high-speed forged to 30% reduction without a lubricant. (b) Photomicrograph of pores in an electrolytic copper powder disc sintered at 900 and high-speed forged to 30% reduction with lubricant (vaseline).

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[5] A.K. Jha, S. Kumar, Forging of metal powder preforms, Int. J. Mach. Tool Des. Res. 23 (4) (1983) 201. [6] T. Tabata, S. Masaki, K. Hosokawa, A compression test to determine the coef®cient of friction in forging P/M performs, Int. J. Powder Metall. Powder Technol. 16 (2) (1980) 149. [7] A.K. Jha, S. Kumar, Dynamic effects during high-speed sinterforging process, Int. J. Mach. Tools Manuf. 36 (1996) 1109. [8] A.K. Jha, S. Kumar, Investigations into the high-speed forgings of sintered copper powder strips, J. Mater. Process. Technol. 71 (1997) 394. [9] M. Agrawal, A.K. Jha, S. Kumar, High-speed forging of hollow metal powder preforms, Inst. Engrs. (I) J. Ð PR 80 (1999) 8. [10] A.K. Jha, S. Kumar, Interfacial friction during cold processing of metal powder preforms, in: Proceedings of the International

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Tribology Conference, The Institution of Engineers, Australia, 1987, p. 346. B.V. Deryagin, Izd. Akad. Nauk. USSR (1952). T. Wanhein, Friction at high normal pressures, in: Proceedings of the First WCIT, Paper No. F-7, New Delhi, 1972. B.W. Rooks, The effect of die temperature on metal ¯ow and die wear during high speed hot forging, in: Proceedings of the 15th International MTDR Conference, Birmingham, 1974, p. 487. S. Kumar, Principles of Metal Working, Oxford/IBH, New Delhi, 1976. S. Shima, J.M. Alexander, The interrelation of density and hardness in the isostatic compaction of powders, in: Proceedings of the 13th International MTDR Conference, Birmingham, September 1972, Macmillan, London, 1973, p. 471.