Editor’s Announcement

Mater. Trans. 57 (2016) 661–668

Investigation of Interfacial Friction and Inverse Flowing Behavior under the Adhesive State

Weiqi Li and Qingxian Ma

(Received November 26, 2015; Accepted February 18, 2016; Published April 25, 2016)

This paper has been retracted by the Editorial Committee of Mater. Trans. due to substantial overlap with the following paper previously published in another journal.

Int J Adv Manuf Technol (2015) 79:255–263Evaluation of rheological behavior and interfacial friction under the adhesive condition by upsetting

methodW.Q. Li・Q.X. Ma

(Received April 14, 2014; Accepted January 14, 2015; Published February 3, 2015)

And thus, it shall not be regarded as an original paper.

Materials Transactions, Vol. 58, No. 7 (2017) p. 1100 ©2017 The Japan Institute of Metals and Materials

Investigation of Interfacial Friction and Inverse Flowing Behavior under the Adhesive State

Weiqi Li and Qingxian Ma*

Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

For improving the precision of numerical simulations in metal forming, it is critical to accurately evaluate the interfacial friction between die/specimen and material deformed behavior. However, there is a huge challenge to assess interfacial friction and material deformed behavior due to the complex mechanisms of tribology at the interfaces. In this study, a program of experimental work directed by ring upsetting has been carried out to evaluate interfacial friction and material deformed behavior on account of the speci�c adhesive friction state. The behavior of adhesive friction was qualitatively identi�ed with characterized phenomenon and quantitatively identi�ed with friction coef�cient, which was obtained by taking advantage of Boltzmann distribution characteristics between the radial velocity �eld and the relative displacements relevant to metal particles on the meridian plane. Furthermore, simple mathematics methods were applied to analyze inverse �owing behavior under the condition of adhesive friction based on the transients displacement achieved by ring upsetting. And the driven mechanism of inverse �owing behavior was also revealed systematically. Finally, a new theory of bi-directionality theory was proposed to illustrate inverse �owing behavior, and the sustainability of adhesive friction was synthetically analyzed.　[doi:10.2320/matertrans.M2015434]

(Received November 26, 2015; Accepted February 18, 2016; Published April 25, 2016)

Keywords:　 interfacial friction, material deformed behavior, adhesive friction, ring upsetting, inverse �owing behavior, bi-directionality theory

1.　 Introduction

Recently, more and more numerical simulation analysis along with the development of computer technology is used in metal forming processes1). The accurate analysis of numer-ical simulations process not only saves time and energy, but also improves material forming quality in metal forming. However, numerical simulation depends strongly on the inter-facial frictional condition and the accurate expression of ma-terial deformed properties2,3). Therefore, it is very signi�cant to intensively concern interfacial friction and material de-formed behavior in metallography and tribology.

Up to now, large numbers of investigations have been car-ried out in sheet4–8) and bulk9–16) metal forming to evaluate interfacial friction and material deformed behavior. Wang et al. have developed a plane-strain compression tribometer to measure friction and material �ow-stress2). Based on numeri-cal simulation and experimental results, Takahashi has inves-tigated the interfacial deformation and friction behavior be-tween Al ribbon and electric pad during ultrasonic bonding17). Brandstetter et al. have examined the effect of surface rough-ness on friction by means of �bre-bundle pull-out tests18,19). Chan et al. have observed that the size effect on micro-scale plastic deformation and frictional phenomenon by the combi-nation of micro-cylindrical compression test, micro-ring compression test and Finite Element (FE) simulation20). However, interfacial friction and material deformed behavior are always varying owing to the complexity of external in�u-ence factors such as stress, temperature, strain-rate, and lubri-cant. Although some efforts including the above study have been done against the different conditions of friction/lubri-cant, they concentrated up on the investigation at low friction condition21–24).

When friction coef�cient is low, extent models are avail-able to analyze interfacial friction and material deformed be-havior precisely. However, it is practically indicated that al-

most all the methods and models existing for analyzing interfacial friction and material deformed behavior are ad-judged invalid under the conditions of high friction coef�-cient, an extremely particular state of which is the adhesive friction studied in this paper. There are various theoretical or experimental studies in simple upsetting related to the inves-tigation of interfacial friction and material deformed behavior in the area of metal forming. In this study, the most widely used method of ring compression test �rst proposed by Kuno-gi and developed by Male and Cockroft have been ap-plied25–29).

The objective of this investigation is to study interfacial friction and material deformed behavior aimed at the adhe-sive friction state. In order to evaluate interfacial friction be-havior, friction coef�cient was calculated qualitatively based on the Boltzmann distribution characteristics. In the respect of material deformed behavior, a new metal �owing behavior of inverse �owing behavior was found. And then, the driven mechanism of inverse �owing behavior was analyzed system-atically. The bi-directionality theory was proposed to illus-trate and evaluate explicitly inverse �owing behavior. Finally, the sustainability of adhesive friction was analyzed.

2.　 Experiment

This investigation was developed in metallic Lead used to make ring specimens with outer diameter of 60 mm, inner diameter of 30 mm and height of 20 mm. All the ring speci-mens were divided into two groups. The specimens of the �rst group were cut into halves averagely along the meridian sur-face by means of spark cutting. And then the �nite element discretization on the meridian surface of these specimens was carried out and shown in Fig. 1. After that, both correspond-ing halves of the same specimens were welded together with Wood’s metal alloy. For the sake of unifying the experimental condition of interfacial friction, both of the top and end inter-faces of all the specimens were polished with emery cloth made with brown fused alumina, and graved with circular lat-* Corresponding author, E-mail: maqxdme@mail.tsinghua.edu.cn

Materials Transactions, Vol. 57, No. 5 (2016) pp. 661 to 668 ©2016 The Japan Institute of Metals and Materials

Retra

cted

tices shown in Fig. 2.The ring upsetting test was carried out at a constant speed

of approximately 0.005 mm/s by hydraulic universal testing machine at room temperature. For the specimens of the �rst group, ring upsetting tests were implemented at �ve levels of strokes of 10, 20, 30, 40 and 50%. For the specimens of the second group, ring upsetting tests were implemented with the strokes exceeding 50%. The role of the second group is to demonstrate the disappearance of the adhesive friction, and the results of the second group are only used in Section 4.5. Owing to that the elastic deformation is much smaller than the plastic deformation in the bulk metal forming, the effects of elastic deformation on the specimens dimension was neg-ligible and wasn’t considered in this study.

After ring upsetting tests were implemented at each stroke of 10, 20, 30, 40 and 50% for the specimens of the �rst group, the displacements of lattice points on the interface were mea-sured. And then the welded specimens were separated into halves along the welded surface by means of fusing Wood’s metal alloy on the cohesive meridian. After the meridian sur-faces of the specimens were cleaned up, the images of the meridian surface were scanned with HD scanner. The dis-placements of deformation graphics for lattice points on the meridian surfaces were derived by statistics and computing. Further, the displacements on the meridian surfaces were

transferred to raster image in order to analyze material �ow-ing behavior.

3.　 Numerical Analysis Model

3.1　 Numerical method for analyzing inverse �owing be-havior

After the specimens are compressed between both of the �at parallel dies, numerical method of piecewise cubic her-mite polynomial interpolation is implemented to analyze ma-terial �owing behavior for the purpose of improving the com-putation accuracy. The constructed object function of piecewise cubic hermite polynomial interpolation is shown in eq. (1).

H3(x)xk→xk+1

= Mk(xk+1 − x)3

6∆k+ Mk+1

(x − xk)3

6∆k

+

yk −Mk∆

2k

6

xk+1 − x∆k

+

yk+1 −Mk+1∆

2k

6

x − xk

∆k

(1)

Where, k =  0, 1, ···, n −  1, xk and yk are radius and axial dis-placement measured by the repetitive ring upsetting testing, respectively. Unknown parameter Mk can be determined with eq. (2).

2 λ0

µ1 2 λ1

. . .. . .

. . .

µn−1 2 λn−1

µn 2

M0

M1...

Mn−1

Mn

=

l0l1...

ln−1

ln

(2)

Where, the value of the boundary elements λ0 and μn is equal to 1. All the other correlation coef�cients λk+1, μk, k =  0, 1, ···, n −  1 listing in eq. (2) are determined by eq. (3).

µk =∆k−1

∆k−1 + ∆k, λk+1 =

∆k+1

∆k + ∆k+1 (3)

lk, k =  0, 1, ···, n are determined by the interpolation of eq. (4).

Fig. 1　Geometry and nodal discretization on the meridian surface.

Fig. 2　Circular lattice pattern of interfaces for Δc =  cn =  2.5 mm.

662 W. Li and Q. Ma

Retra

cted

l0 =6∆0

y1 − y0)∆0

− f0 ,

lk = 6∆k−1(yk+1 − yk) − ∆k(yk − yk−1)

∆k−1∆k(∆k−1 + ∆k),

ln =6∆n−1

fn −yn − yn−1

∆n−1

(4)

Where, f0 is the boundary quantity of in�nity, and fn is the boundary quantity con�rmed by further compression with the stroke of over 50%. In eq. (1), eq. (3) and eq. (4), Δk is the radial displacement difference of two adjacent strokes, as shown in eq. (5).

∆k = xk+1 − xk, k = 0, 1, · · · , n − 1, x ∈ [xk, xk+1] (5)

3.2　 Theoretical foundation for solving friction coef�-cient

There are three distinct deformation modes accompanying with the location variation of the neutral layer ρ for the com-pressed ring specimen owing to the variation of friction coef-�cient μ. There is a strict one-to-one correlation between the value of friction coef�cient and the location of the neutral layer. The speci�c performances are shown in Fig. 330–32).

When friction coef�cient is low, the radius ρ of the neutral layer is less than inner radius R1 of the specimen, all the met-al particles of which �ow away from the central axis, as shown in Fig. 3(b). With the increase of friction coef�cient, there must be a critical value when the radius ρ of the neutral layer is equal to inner radius R1 of the specimen, metal parti-cles of which on the inner boundary �ow towards the sym-metric plane of the specimen and all the other metal particles of the specimen �ow away from the central axis as shown in Fig. 3(c). Along with the further increase of friction coef�-cient, it is found that the neutral layer of radius ρ appears on the meridian plane and locates between the inner and outer diameter as shown in Fig. 3(d). Under this circumstance, met-al particles outside and inside the neutral layer �ow away from and towards the central axis, respectively. There are three equations shown in Table 1 corresponding to the above

three situations.R0 and R1 are outer radius and inner radius respectively. It

is evident from the expression of friction coef�cient μ that the location of the neutral layer is signi�cant to determine fric-tion coef�cient, and the quantitatively solving problems of friction coef�cient can be translated into the solving problem of the neutral layer ρ. And solving accuracy of plastic friction

Fig. 3　Deformation �owing behaviors with different friction coef�cients: (a) Undeformation, (b) Low friction, (c) Critical friction, (d) High fric-tion.

Table 1　Relationship between COF and NL, COF: friction coef�cient, NL: Neutral layer.

COF NL Expression Diagram

Low ρ < R1 µ = − 1√

3ln

R21

R20

1 + 1 +3R4

0

ρ4

1 + 1 +

3R41

ρ4

/2R0

H1 − R1

R0Fig. 3(b)

Critical value ρ < R1 µ =1

2√

3· H

(R0 − R1)· ln

3R20

R21 + R4

1 + 3R40

Fig. 3(c)

High R1 < ρ < R0 µ = − 1√

3ln

R21

R20

1 + 1 +3R4

0

ρ4

1 + 1 +

3R41

ρ4

/2R0

H1 +

R1

R0− 2 × ρ

R0Fig. 3(d)

663Investigation of Interfacial Friction and Inverse Flowing Behavior under the Adhesive State

Retra

cted

coef�cient depends strongly on the solving accuracy of the radius ρ of the neutral layer.

4.　 Results and Discussion

4.1　 Identi�cation of adhesive friction state4.1.1　 Identi�cation of adhesive friction state based on

deformationAfter ring upsetting tests, the deformation results at the in-

terface between die/specimen for the stroke of 10, 20, 30, 40, 50% are shown in Fig. 4. It is observed from Fig. 4 that, outer diameter is increasing constantly and inner diameter is de-creasing constantly in the wake of the reduction in height. The whole interfacial surfaces are in the condition of increas-ing.

However, it is remarkable that there is no movement for the size of annulus lattice on the interface. That is to say, there is no radius displacement for the primitive metal particles on the interface. For the newborn particles on the increscent area of the interface, they still keep stationary at the moment of enter-ing the interface and have no radius displacement after enter-ing the interface. In a word, there is no radius displacement for all metal particles on the interface and the state of adhe-sive friction exists on the interface all the time.

4.1.2　 Identi�cation of adhesive friction state with fric-tion coef�cient

According to experimental research and plasticity theory, friction calibration curves can be elaborated in Fig. 5 based on the results of �nite element modeling. If the value of fric-tion coef�cient exceeds the critical value of 0.5, the whole interface entirely becomes sticky, and friction pair on the in-terface is in the adhesive state30,33). It is re�ected in Fig. 5 that the relation curve between outer diameter and height along with the variation of stroke will drop into the region of adhe-sive friction once friction coef�cient exceeds the critical val-ue of 0.5.

After ring upsetting tests, the deformation on meridian sur-face for the stroke of 10, 20, 30, 40, 50% are shown in Fig. 6. It is obtained in Fig. 6 that the neutral layer ρ situates between internal boundary and external boundary whatever the stroke is. Therefore, friction coef�cient μ can be calculated with the equation corresponding to Fig. 3(d). And the neutral layer ρ is determined by taking advantage of its own property of zero value in radius velocity �eld and the characteristic of Boltz-mann distribution between the radial velocity �eld and the relative displacement on the equatorial plane owing to that the radial velocity �eld and the relative displacement on the

Fig. 4　Deformation state at the interface.Fig. 5　Calibration curve related to the outer diameter with different friction

coef�cients.

Fig. 6　State of continuous deformation at the meridian plane under the different strokes of (a) original specimen (0%), (b) 10%, (c) 20%, (d) 30%, (e) 40% and (f) 50%.

664 W. Li and Q. Ma

Retra

cted

interface don’t occur in the adhesive state. The processes and �nal results of friction coef�cient are listed in Table 2.

Under the condition of friction coef�cient of 0.57, the rela-tion curve between outer diameter and height along with the stroke’s augment is depicted in Fig. 5 based on the upsetting test. It is observed that the �ow curve lands in the region of adhesive friction, also explaining the state of adhesive friction exists all the time.

4.2　 Identi�cation of inverse �owing behaviorBy taking advantaging of piecewise cubic hermite polyno-

mial interpolation shown in eq. (1), the grid lines graved on the meridian surface are reshaped based on the measured dis-placements of the different strokes, while the speci�c orienta-tion of velocity �eld of metal particles under the different strokes is determined with eq. (6), which can be achieved by inverse tangent function of taking the derivative of piecewise cubic hermite polynomial of eq. (1).

θOR = arctan −Mk(xk+1 − x)2

2∆k+ Mk+1

(x − xk)2

2∆k

+

yk+1 − yk +Mk∆

2k

6−

Mk+1∆2k

6

/∆k

(6)

Here, k =  0, 1, ···, 4, θOR is angle �eld. All the correlation co-ef�cients in eq. (6) are to obtain with eq. (2) to eq. (5).

Figure 7 shows the orientation distribution of velocity �eld on the meridian surface of ring specimens under the condi-tions of each stroke. It is observed in Fig. 7 that all metal particles on the meridian surface �ow towards the equatorial

plane at the initial stage, except that on the equatorial surface which just �ow to both sides along the radial direction. The magnitude of the orientation of velocity �eld for all metal particles inside the neutral layer, on the neutral layer and out-side the neutral layer have greater than 90°, 90° and less than 90°, respectively. Moreover, the magnitude of the orientation of velocity �eld for all metal particles varies with the stroke’s variation, such as Node 8.

The magnitude of the orientation of velocity �eld of Node 8 increases persistently with the increasing of the stroke, and it is notable that its magnitude exceeds 180° at the stroke of 30%. In other words, Node 8 has been �owing to the interface rather than the equatorial surface since the �ow angle has ex-ceeded 180° at the stroke of 30%, illustrating that the particle of Node 8 brings about inverse �owing behavior. There is a further remarkable change of the orientation of velocity �eld of Node 8 to a greater value in the wake of the stroke’s aug-ment. With the augment of the stroke, more and more metal particles like Node 8 on the internal boundary transform to �ow towards the interface rather than the equatorial surface. As far as metal particles on the external boundary are con-cerned, they have a remarkable change of the orientation of velocity �eld from 0° to the negative value, the results of which show that metal particles on the external boundary �ow to the interface instead of the equatorial surface. Inverse �owing behavior continuously happens from metal particles approaching to the equatorial surface to metal particles ap-proaching to the interface since the ring upsetting started. Meanwhile inverse �owing behavior on the boundary is bound to cause interior inverse �ow due to the continuity of

Table 2　Solving processes and results of friction coef�cient, COF: friction coef�cient.

Stroke(%)Node and its radius velocity �eld (mm/s) Neutral layer (mm)

COFNo. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 Single Average

10% −0.002 −0.001 7e-4 0.001 0.002 0.002 0.003 19.44

19.39 0.57

20% −0.003 −0.002 0.002 0.002 0.003 0.003 0.004 18.99

30% −0.004 −0.003 0.001 0.003 0.004 0.004 0.004 19.32

40% −0.007 −0.004 4e-4 0.005 0.005 0.005 0.005 19.60

50% −0.01 −0.005 e-4 0.007 0.007 0.007 0.006 19.59

Fig. 7　Orientation distribution of velocity �eld on the meridian plane.

665Investigation of Interfacial Friction and Inverse Flowing Behavior under the Adhesive State

Retra

cted

metal specimen.

4.3　 Driven mechanism of inverse �owing behaviorThe �owing behavior of metal particles of the specimen is

a comprehensive reaction of internal interaction, external pressure, temperature, friction, and some other in�uencing factors. Among all the in�uencing factors, friction is the unique factor to bring about inhomogeneous deformation of upsetting forgings30). The in�uence of friction on metal parti-cles increases gradually from the equatorial surface to the in-terface. With regard to the radius velocity �eld, its magnitude can be obtained by combining the orientation of velocity �eld shown in Fig. 7 and the magnitude of velocity �eld shown in Fig. 8. It can be found that the magnitude of radius velocity �eld decreases gradually from the equatorial surface to the interface under the in�uence of friction.

Figure 8 shows the magnitude of velocity �eld under the condition of different strokes. It is observed in Fig. 8 that the distribution of velocity �eld is varying during the process of the stroke augment. In order to analyze the driven mechanism of inverse �owing behavior exhaustively, Node 1 and its near-by region are taken as characteristic region. It is observed that the magnitude of velocity �eld of Node 1 and its nearby re-gion is pretty small at the beginning of the stroke. However, the magnitude of velocity �eld of Node 1 and its nearby re-gion will be larger and larger, and has already surpassed the stroke speed of 0.005 mm/s at the stroke of 40%. Since the �owing behavior of metal particles is always subservient to the principle of minimum �ow drag30), it is no doubt that Node 1 possessing the fastest radius velocity �eld �ows to-wards coordinate origin on the equatorial surface. Thus, inho-mogeneous deformation of internal surface of ring specimen will become more and more apparent. For other metal parti-cles of internal surface nearby Node 1, they also �ow with obeying the minimum �ow drag principle; however, their free-�owing direction is up-inclined, so they have to �ow up-inclined, indicating inverse �owing behavior inevitably happens. The phenomenon is also suitable for metal particles on the external surface. Inverse �owing behavior is inevitable owing to the existence of friction. However, if friction coef�-cient is small, the region of inverse behavior is also very small

and just happens on the nearby region of Node 1 of the inter-nal surface and of Node 7 of the external surface. The region will increase along with the augment of friction coef�cient. Moreover, the internal surface is earlier to bring out inverse �owing behavior than the external surface.

4.4　 Bi-directionality theory for elucidating inverse �ow-ing behavior

Bi-directionality theory, also called the chasing & meet theory, is taken advantage to illustrate inverse �owing behav-ior of metal particles under the condition of adhesive friction. The whole theory consists of the three following parts:

(1) Chasing theory considers that the relatively moving up of metal particles on the free surface brings about the inter-face extension. It is known that the interface area is constant-ly extending with the augment of the stroke. It is observed in Fig. 8 that the downward axial velocity of metal particles on the interface is absolutely faster than that on the internal & external surface at the beginning of stroke. Thus, metal parti-cles on the internal & external surface must enter into the in-terface compulsorily owing to the disadvantage of its axial velocity. Combined with Fig. 4, it is obtained that metal par-ticles lose the radial velocity and �ow towards the equatorial surface once accessing the interface in the way of chasing theory.

Taken metal particle of Node 21 in Fig. 1 as an example, its axial velocity can be obtained by combining the orientation of velocity �eld shown in Fig. 7 with the magnitude of veloc-ity �eld shown in Fig. 8. The ordinate of Node 21 is separated from the Coordinate System, shown in Fig. 9(a). It is no doubt that both the distance between interface and equatorial sur-face (line-1) and the distance to the equatorial surface (line-2) of Node 21 are decreasing constantly with the augment of the stroke. However, it is found that the decreasing rate of line-1 is faster than that of line-2, indicating there must be an inter-section point of line-1 and line-2 at certain stroke, where met-al particle of Node 21 enters into the interface and settles into the adhesive state. After the time corresponding to the inter-section point, metal particle of Node 21 �ows towards the equatorial surface like other metal particle on the interface. With the augment of the stroke, more and more newborn ad-

Fig. 8　The magnitude of velocity �eld on the meridian plane.

666 W. Li and Q. Ma

Retra

cted

hesive particles come forth like Node 21.(2) Meet theory considers that the absolutely moving up of

metal particles on the free surface brings about the interface extension. It is seen in Fig. 7 that the orientation of velocity �eld of metal particles approaching to the equatorial surface has more than 180° for internal boundary and less than 0° for external boundary. Metal particles transform the movement direction towards the interface instead of the equatorial sur-face at certain stroke. Inverse �owing behavior comes forth. Thus metal particles on the internal & external surface have a moving upward direction which is in contrast with that of metal particles on the interface such as Node 8 in Fig. 9(b).

(3) Actually, the closer metal particles on the internal & external surface approach to the interface, the easier they en-ter the interface in the way of chasing theory, and there is no inverse �owing behavior appearing for metal particles of this kind. However, as for metal particles on the internal & exter-nal surface, the closer they approach to the equatorial surface, the easier they enter the interface in the way of meeting theo-ry, and inverse �owing behavior will appear for metal parti-cles of this kind. With the augment of the stroke, more and more metal particles generate inverse �owing behavior and gradually spread from the equatorial surface to the interface accompanied with the phenomenon of inverse �owing behav-ior.

The essence of inverse �owing behavior is the meeting phenomenon of bi-directionality of metal deformed �ow. With the stroke’s augment, all metal particles on the free boundary except those on the equatorial plane enter into the interface in the two methods of bi-directionality theory ulti-mately, rather than �ow in the way of the traditionally hyper-bolic �ow theory20,31). Owing to the integrity and continuity of the specimen, all metal particles inside the specimen also must �ow like metal particles on the free boundary.

Now, it can’t be identi�ed that the bi-directionality of metal deformed �ow is a speci�c phenomenon under the condition of adhesive friction or a common phenomenon of all the state with the in�uence of friction. However, the functions of the bi-directionality theory on conducting the forging process are very effective. For instance, the location of metal particles can be predicted accurately under the certain stroke on the basis of the theory, which can be considered as the basis for controlling the specimen quality and designing the shape and speci�c detail of the mold. In addition, the bi-directionality

theory also offers us a re-cognition of the variety of metal deformed �ow behavior.

4.5　 Sustainability analysis about adhesive frictionIt’s observed that the region of inverse �owing becomes

bigger and bigger from Fig. 7 (a) to (f). There is a timestamp inevitably when metal particles on the intersection of the in-terface and free boundary have a 180° for the internal free boundary or 0° for the external free boundary. Once the time-stamp turns up, metal particles on the intersection of the inter-face and free boundary possess tangential velocity and don’t simply �ow towards the interface inversely. Correspondingly, tangential slip on the interfaces blows up; meanwhile adhe-sive friction disappears. It is notable that the disappearance of adhesive friction comes out earlier for the intersection of the interface and internal free boundary than that for the intersec-tion of the interface and external free boundary. Experimental results of the second group have con�rmed that adhesive fric-tion will disappear when the stroke reaches a �xed value. Fig-ure 10 shows the phenomenon of the disappearance of adhe-sive friction and the phenomenon of turbulence �owing of metal particles on the interface. The disappearance of adhe-sive friction on the interface also means all metal particles on the free boundary surface �ow inversely to the interface rath-er than the equatorial surface.

It is shown in Fig. 5 that the neutral layer remains un-changed with the augment of the stroke and accordingly fric-tion coef�cient, which is 0.57 calculated in the present exper-iment, is also identical. Friction coef�cient of 0.57 is a typical adhesive friction state according to the previous experiment research and the plasticity theory30). Consequently, the disap-pearance of adhesive friction violates the conclusion that the interface is in the adhesive friction state once interfacial fric-tion coef�cient exceeds 0.5, which indicates there is a con�ict

Fig. 9　Bi-directionality theory for analyzing inverse �owing behavior with axis velocity �eld.

Fig. 10　Disappearance of adhesive friction ST: stroke.

667Investigation of Interfacial Friction and Inverse Flowing Behavior under the Adhesive State

Retra

cted

of the existence of adhesive friction between the experimental results and tradition theory. Maybe the reason that internal shear stress will be superior to interfacial friction stress at certain stroke although friction coef�cient keeps invariant with the augment of the stroke leads to the disappearance of adhesive friction. However, the real reason why the con�ict happens is unknown. Therefore, more profound study on plastic tribology, especially high friction coef�cient, is abso-lutely necessary.

5.　 Conclusions

The interfacial friction and metal deformed �owing behav-ior under the condition of adhesive friction were investigated by ring upsetting test. The conclusions which can be drawn from this study show the following: (1) In order to evaluate the behavior of interfacial friction,

characterized phenomenon at the interface is analyzed qualitatively, and friction coef�cient is quantitatively ob-tained by taking advantage of Boltzmann distribution characteristics between the radial velocity �eld and the relative displacements. The friction performances at the interface and the calculated friction coef�cient are in agreement with the adhesive state strictly. Compared with the previous results, there is a huge difference of metal deformed �ow under the condition of adhesive fric-tion. Once accessing the interface, all metal particles lose radial strain and �ow towards the equatorial plane straightly.

(2) The second part of this work focuses on the identi�cation of inverse �owing behavior. A new phenomenon of in-verse �owing behavior with respect to backward transfer of metal particles under the condition of adhesive friction is found. Metal particles �ow to the interface rather than the equatorial plane in the state of inverse �owing behav-ior. For the sake of evaluating inverse �owing behavior accurately, the orientation of velocity �eld is elaborated with the mathematical method of piecewise cubic her-mite polynomial interpolation based on the displace-ments measured after the experiments of ring upsetting. Combining the orientation and magnitude of velocity �eld, the driven mechanism of inverse �owing behavior is evaluated qualitatively.

(3) A new theory called Bi-directionality theory is proposed to illustrate metal inverse �owing behavior. Sustainability analysis about adhesive friction has been done in this study. It is illustrated that adhesive friction is unable to sustain constantly. The disappearance of adhesive friction is explained by analyzing the orientation variation of ve-locity �eld. The con�ict of the disappearance of adhesive friction brings about a huge challenge between the exper-iment results and tradition theory.

Acknowledgments

This paper has been supported by the Major State Basic Research Development Program of China (973 Program, No. 2011CB012903). The authors would like to express our sin-cere appreciation for the funds support.

REFERENCES

1) Y.T. Im, S.H. Kang and J.S. Cheon: J. Eng. Manuf. 220 (2006) 81–90. 2) S.L. Wang and J.A.H. Ramaekers: J. Mater. Process. Technol. 57

(1996) 345–350. 3) Ö.N. Cora, M. Akkök and H. Darendeliler: Proc. Inst. Mech. Eng.

PART J., J. Eng. Tribol. 222 (2008) 899–908. 4) S. Coppieters, P. Lava, H. Sol, A. Van Bael, P. Van Houtte and D. De-

bruyne: J. Mater. Process. Technol. 210 (2010) 1290–1296. 5) D.K. Leu: J. Mater. Sci. Technol. 25 (2011) 1509–1517. 6) L. Figueiredo, A. Ramalho, M.C. Oliveira and L.F. Menezes: Wear 271

(2011) 1651–1657. 7) B.H. Lee, Y.T. Keum and R.H. Wagoner: J. Mater. Process. Technol.

130–131 (2002) 60–63. 8) J. Kondratiuk and P. Kuhn: Wear 270 (2011) 839–849. 9) W. Zheng, G.C. Wang, G.Q. Zhao, D.B. Wei and Z.Y. Jiang: Tribol. Int.

57 (2013) 202–209. 10) Z.H. Yao, D.Q. Mei, H. Shen and Z.C. Chen: Tribol. Lett. 32 (2011)

1376–1389. 11) K. Manisekar, R. Narayanasamy and S. Malayappan: Mater. Des. 27

(2006) 147–155. 12) X.H. Han and L. Hua: Tribol. Int. 55 (2012) 29–39. 13) M. Sahin, C.S. Çetinarslan and H. Erol Akata: Mater. Des. 28 (2007)

633–640. 14) J. Appa Rao, J. Babu Rao, S. Kamaluddin, M.M.M. Sarcar and

N.R.M.R. Bhargava: Mater. Des. 30 (2009) 2143–2151. 15) R. Ebrahimi and A. Naja�zadeh: J. Mater. Process. Technol. 152 (2004)

136–143. 16) N. Kim and H. Choi: J. Mater. Process. Technol. 208 (2008) 211–221. 17) Y. Takahashi, M. Maeda, M. Ando and E. Yamaguchi: Mater. Sci. Eng.

61 (2014) 12004–12011. 18) J. Brandstetter, K. Kromp, H. Peterlik and R. Weiss: Compos. Sci.

Technol. 65 (2005) 981–988. 19) M. Sahin, C.S. Çetinarslan and H.E. Akata: Mater. Des. 28 (2007) 633–

640. 20) W.L. Chan, M.W. Fu and J. Lu: Mater. Des. 32 (2011) 198–206. 21) X. Tan, N. Bay and W.Q. Zhang: Scand. J. Metall. 27 (1998) 246–252. 22) R. Paukert and K. Lange: Cirp. Ann-Manuf. Techn. 32 (1983) 211–214. 23) T. Takemasu, V. Vazquez, B. Painter and T. Altan: J. Mater. Process.

Technol. 59 (1996) 95–105. 24) H.B. Pan, D. Tang, S.P. Hu: J. Univ. Sci. Technol. B 30 (2008) 1266–

1269+1281. 25) A.T. Male, M.G. Cockroft: J. Ins. Met. 93 (1964/1965) 38–46. 26) C.S. Çetinarslan: Mater. Des. 28 (2007) 1907–1913. 27) Y. Sagisaka, T. Nakamurac, I. Ishibashib and K. Hayakawa: J. Mater.

Process. Technol. 212 (2012) 1869–1874. 28) P. Groche, C. Muller, J. Stahlmann and S. Zang: Tribol. Int. 62 (2013)

223–231. 29) G. Shen, A. Vedhanayagam, E. Kropp and T. Altan: J. Mater. Process.

Technol. 33 (1992) 109–123. 30) D.N. WANG: Principles of metal plastic forming. Beijing: China Ma-

chine Press 1982. 31) D.V. Pierre, F. Gruney, A.T. Male: TECHNICAL REPORT AFML-

TR-72-37 1972. 32) B. Avitzur: Metal forming: processes and analysis. New York: Mc-

Graw-Hill 1968. 33) W.Q. Li, Q.X. Ma: Forg. Stamp. Technol. 39(2014):9–19+23.

668 W. Li and Q. Ma

Retra

cted