Experimental investigation and numerical simulation of plastic flow behavior during forward backward radial extrusion process

Experimental investigation and numerical simulation of plastic flow behavior during forward backward radial extrusion process H O S T E D B Y Contents lists available at ScienceDirect Progress in Natu[.]

H O S T E D B Y Contents lists available atScienceDirect

Progress in Natural Science: Materials International

journal homepage:www.elsevier.com/locate/pnsmi Original Research

A Farhoumand⁎, R Ebrahimi

Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran

A R T I C L E I N F O

Keywords:

Finite element analysis

Extrusion

Forming

Plastic deformation

Strain heterogeneity

A B S T R A C T Finite element method was employed to investigate the effect of process parameters of plastic deformation behavior in Forward-Backward-Radial Extrusion (FBRE) process The result of an axisymmetric model shows that the friction between die components and the sample has a substantial effect on the material flow behavior Although strain heterogeneity index (SHI) slightly decreases with an increase in friction, large portion of the sample experiences significant strain heterogeneity Increasing the friction factor also localizes the strain heterogeneity effect in the backward section, and spread the effect in the forward section Decreasing the friction

in the FBRE process can reduce the amount of the strain heterogeneity in the product while decreases the required punch force substantially Furthermore, an increase in gap thickness increases the deformation in the area close to the lower punch at the expense of the area in the vicinity of the upper punch The numerical simulation has a good agreement with the experimental results which confirms the accuracy of the proposed finite element model

1 Introduction

Extrusion in comparison to other manufacturing methods used in

industrial application has many advantages such as: minimum material

waste, high dimensional accuracy, reduction or complete elimination of

machining, good surfacefinish, better mechanical properties of

pro-ducts than those of the parent material The basic processes involving

cold extrusion are classified based on their forming direction as

forward, backward and radial/lateral extrusion[1] Radial extrusion

process can be used to manufacture complex parts such as collar

flanges, spur gears, splines with shafts and tube fittings[1–3]

Besides, combinations of extrusion processes in which a billet is

extruded simultaneously in forward, backward and radial directions

can also facilitate to eliminate the need for multistep forming of

relatively complex shaped parts [4] For instance backward-forward

extrusion[5], radial forward extrusion[6,7], radial backward extrusion

[4]and double backward extrusion[8]are some of these processes

Since most of the components are produced on the basis of

experience and trial-and-error [5], it is imperative to eliminate the

unnecessary production cost by modeling the process and optimizing

the parameters The significance of an analysis for a forming process

lies in the determination of required punch force,flow behavior as well

as stress-strain state during the process[9]

In a study by Kim et al.[10], the effect of friction on the material deformation during equal channel angular pressing process was investigated using a 2Dfinite element model It was found that friction intensifies the shear deformation for the surface elements This is due

to substantial effect of friction acting on the opposite direction of the moving surfaces during the process Thus, the friction can decrease the extent of the less-deformed shared zones in the process

Altan et al utilized finite element analysis of an axisymmetric model for a deep cup drawing process to investigate the effect of friction [11] It was concluded that the variation in the friction coefficient over a small range, in which the coefficients are close to the actual values, does not significantly affect the deformation, as long

as the material is not within the instability limit[11] In contrary where material instability is likely to occur due to the large tensile stresses associated with a great punch force or a large blank diameter or small sheet thickness the sensitivity of the process to changes in the conditions of friction becomes significant Farhoumand et al employed

a 3Dfinite element analysis of a novel extrusion process for quantita-tive assessment of strain accumulation in relation to the process parameters [12,13] More recently, in an effort to increase the accumulated plastic strain and obtain a more uniform distribution, a modified backwards extrusion was proposed by Shatermashhadi et al [14]and, Finite Element (FE) analysis results confirmed the successful

http://dx.doi.org/10.1016/j.pnsc.2016.12.005

Received 20 September 2015; Received in revised form 5 November 2016; Accepted 13 December 2016

Peer review under responsibility of Chinese Materials Research Society.

⁎ Corresponding author.

E-mail address: alireza.farhoumand@outlook.com (A Farhoumand).

1002-0071/ © 2016 Chinese Materials Research Society Published by Elsevier B.V.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

Please cite this article as: Farhoumand, A., Progress in Natural Science: Materials International (2016),

was performed to investigate the effect of process parameters on the

final dimensions of the product But, the effect of process parameters

on the materialflow behavior, strain distribution and thus the strain

heterogeneity within thefinal product has not been investigated It is

imperative to have a clear understanding of the strain distribution

within thefinal product which can affect the mechanical properties and

microstructure of the product

Hence, in this study, the effect of processing parameters on strain

heterogeneity within the product processed by FBRE was investigated

by implementation of FE method Quantitative analysis of strain

heterogeneity was performed by utilizing an axisymmetric FE model

A number of numerical simulations were performed and the results

were compared with experimental work to verify the accuracy of the FE

model

2 Finite element analysis

An Axisymmetric FBRE model was analyzed in ABAQUS FE

soft-ware[18]using explicit algorithm Punches and dies were assumed to

be rigid due to negligible elastic deformation whereas the sample

material (commercially pure aluminum) was considered as deformable

in the model The kinematic relation of the sample was obtained from a

compression test,Fig 1, which represented by a power law equation as

σ=133ε0.3(MPa)

The kinematic behavior in FE model was incorporated with the von

Misses yield criterion and isotropic hardening The contact condition

between sample and surfaces of die and punches were assumed to

follow coulomb friction law Barrel compression test[19]was utilized

to measure the experimental friction factor (m) The experimental

friction factor (m) was found 0.13 However, it should be noted that the

acquired value is only pertinent to the performed FBRE process, used

lubricant and the existing surface condition of the FBRE die

compo-nents and sample Due to the limitations in ABAQUS software input

variables, Eq.(1)was used to convert the measured friction factor (m)

to coefficient of friction (μ) for numerical simulations,

m

=

2.72(1 − )

0.9

Although Eq.(1)has been derived for double cup extrusion process

[20], this equation is considered to be applicable to FBRE process due

its axi-symmetrical nature similar to that of the double cup extrusion process Several parameters in FBRE can influence the material deformation behavior Friction as a process parameter along with geometrical parameters such gap thickness and die cornerfillet can influence the material deformation behavior in FBRE.Fig 2illustrates the aforementioned parameters schematically

Several simulations were performed to analyze the effect of friction and geometrical parameters on the FBRE deformation behavior and the corresponding punch force

3 Experimental procedures

To perform the FBRE process experimentally, a proper die set was designed and manufactured The punches and dies were machined from cold-worked alloy steel (Grade: X210Cr12 No 1.2080) while the other die components were manufactured from medium carbon steel (Grade: CK45 No 1.1191) The heat treatment of alloy steel parts was performed at 970 °C followed by an oil quenching and subsequent tempering at 250 °C The assembly of the die setup under a screw press

is shown in Fig 3(a) The die was designed with an adjustable gap thickness that eliminates the need for additional die sets The gap thickness has been shown by the arrow inFig 3(b)

Cylindrical samples with 24 mm diameter and 20 mm in length

Fig 1 Before and after a compression test of a commercially pure aluminum sample,

utilized to obtain the kinematic of the material.

Fig 2 The schematic of the die assembly used in FBRE process and the geometrical parameters (gap and wall thickness and die corner fillet).

Fig 3 FBRE setup under a screw press in (a) and the gap between upper and lower dies

in (b).

were machined from commercially pure aluminum (grade 1100) FBRE

process was performed in a 200 kN capacity screw press machine with

the crosshead speed of 0.2 mm/sec at ambient temperature

The die corner fillet and the wall thickness in the experimental

setup were 1 mm and 2 mm, respectively, while samples with two

different gap thicknesses of 2 mm and 4 mm, were processed The cross

sections of the processed samples are shown inFig 4

4 Results and discussion

Variation of frictional conditions during forming processes can

significantly alter the rate of strain hardening and subsequently the

mechanical properties of different sections within the product

Considering the application of the product, these variations of

mechan-ical properties within the product shall be thoroughly examined to

assure its compliance with the engineered design limits

Hence, in case of FBRE product and considering the presence of

three different sections, namely forward, backward and radial, this

frictional variation needs more in depth investigation Therefore,

analysis of plastic strain distribution in different sections of FBRE

product was performed in several frictional conditions The

quantita-tive assessment was fulfilled by defining Strain Heterogeneity Index,

SHI as below,

ε

ave

max min

(2)

where εmax, εmin and ε ave denote the maximum, minimum and

average effective plastic strain over a path, respectively

Different paths in cross section of the FBRE sample were defined

and mapped in the deformed mesh as shown in Fig 5 For the

backward section, paths were defined along the wall thickness of the

simulated deformed mesh with 1 mm spacing As shown inFig 5, a

typical path in backward section is from point aito biwhile the range of

i was chosen according to the extent of this section from point A to B

For each frictional condition, SHI was calculated along each path by

using the FE simulation results as per Eq.(2)

Similar approach was applied for the forward section as paths were

annotated as cjto djfrom point C to D as shown inFig 5

For the center section, only one path was considered on the

axisymmetric axis of the sample from the upper punch (point E)

towards the lower punch (point F) as indicated inFig 5

4.1 Effect of friction between sample and the surfaces of die and

punches in FBRE process

The effect of different frictional conditions on the heterogeneity of

the accumulated strain in backward and forward sections of FBRE

sample is depicted inFig 6(a) and (b), respectively

In frictionless case SHI is the maximum in the vicinity of point A

which rapidly declines towards point B This strain heterogeneity

adjacent to point A is due to intense deformation at the corner of the

punch which causes localized strain heterogeneity As the friction factor

increases from 0 to 0.13, the location of the maximum SHI inFig 6(a) shifts towards point B With further increase of friction factor, m=0.8, the maximum SHI for backward section increases significantly which shows the significant effect of friction on deformation behavior in backward section of FBRE sample Furthermore, not only the SHI increases with increase of frictional conditions, but also the height of the material in backward section decreases Therefore, not only an increase in friction factor in backward section intensifies the strain heterogeneity but also it restricts the material progress into backward section In frictionless condition, the SHI in forward section,Fig 6(b),

is much more intense in the vicinity of the lower punch, (point C in Fig 5) However, as the friction factor increases, the SHI decreases slightly, but wider section of the sample experiences significant strain heterogeneity It was also observed that an increase in friction factor promotes the material progress into forward section which is in contrast to that of backward section, as previously discussed Therefore, an increase in friction in FBRE process has opposing effects for backward and forward sections Increasing the friction factor will promote the material progress into forward section at the expense of the backward one Besides, increasing the friction factor narrows the strain heterogeneity curve in backward section while increasing its maximum which is in contrary for that of forward section

For the center section, the equivalent plastic strain for various frictional conditions has been depicted inFig 7 When the frictionless conditions prevails (m=0), the accumulated strain is higher in the vicinity of the upper and lower punches (point E and F) in comparison

to that of middle section (normalized distance 0.4–0.8 inFig 7) As the

Fig 4 Cross section view of FBRE processed aluminum samples for gap thicknesses of

2 mm (a) and 4 mm (b).

Fig 5 Meshed model with defined paths for various sections for the strain heterogeneity analysis (Un-deformed and Deformed Mesh geometry on the left and right of Axisymmetric axis, respectively.).

friction factor increases, the plastic strain in the vicinity of the punches

decreases significantly which give rise to substantial plastic strain accumulation in the middle of the center section This shows a shift in materialflow preferences as the friction factor increases In frictionless

Fig 6 E ffect of friction on strain heterogeneity, (a) in backward section and (b) in forward section of a FBRE sample.

Fig 7 Effect of friction on the equivalent plastic strain at center region of a FBRE

processed sample.

Fig 8 Equivalent plastic strain contours (PEEQ) and dead zones in a FBRE sample Cross section views of the sample for a friction factor of (a) m=0, (b) m=0.13, (c) m=0.38 and (d) m=0.8.

Fig 9 Effect of friction factor on the FBRE punch force.

condition, the material plasticflow occurs in two discrete regions in the

vicinity of upper and lower punches As friction increases, these two

discrete regions form separate dead-zones with no further material

flow while one central region in the material becomes responsible for

further plasticflow of the material during FBRE

The extent of dead-zones adjacent to the upper and lower punches

for various frictional conditions is shown inFig 8(a)–(d) Regardless of

the friction factor, the extent of the dead zone adjacent to the upper

punch is much more noticeable than that of the lower punch But, as

the friction factor increases this difference abates

It can be established fromFig 8that as the friction factor increases,

the extent of the dead zone adjacent to the upper punch extends which

limits the materialflow into the backward section Consequently, the

restriction of material flow into backward section, promotes the

material flows into forward section and therefore, the difference

between the height of forward and backward sections decreases as

the friction factor increases

The effect of friction on the required FBRE punch force is also investigated as shown inFig 9 The difference in punch force between friction less condition and m=0.13 case is not significant This is due to similarity of the deformation behavior in the aforementioned frictional conditions As the friction increases further to m=0.38, the material plasticflow localizes in central areas, which in turn increases the FBRE required load as can be seen inFig 9

Further increase of the friction from m=0.38 to m=0.8 has a significant effect on the increase of punch force This increase could

be solely due to redundant frictional losses along die/sample interface since there is no significant change in material flow behavior between m=0.38 and 0.8

Hence, increase of FBRE punch force with an increase in friction

Fig 10 Equivalent plastic strain (PEEQ) contours in different stages of a sample formation during frictionless (m=0) FBRE at different punch strokes (in mm) of (a) 0, (b) 1, (c) 1.5, (d) 2.5, (e) 6 and (f) 15.

Fig 11 Effect of gap thickness on the FBRE punch force, simulation and experimental

0 0.5 1 1.5 2 2.5

3

Gap Thickness = 1 mm Gap Thickness = 2 mm Gap Thickness = 4 mm

Fig 12 Effect of gap thickness on the equivalent plastic strain in the center section of FBRE processed samples.

factor can be the contribution of two factors Firstly, increasing the

friction is increasing the required redundant work to overcome the

frictional force between the die surfaces and the material Secondly,

increasing the friction in FBRE causes a shift in material flow to be

restricted in the central regions which also limits the deformation

hence giving rise to an increase of required punch force It can be

deducted that the effect of the former is much more pronounced than

that of the latter on FBRE punch force requirements

Equivalent plastic strain contours of the sample in frictionless

conditions are shown inFig 10in six different stages of FBRE It could

be seen that the highest values of strains occur where the maximum

deformation exists The plastic equivalent effective strain is higher in

the areas where the sample is in contact with the punch corners than

anywhere else In addition, at the initial stage of the process, contours

of strains are distributed in extensive areas which gradually decrease

towards the end of the process

4.2 Effect of gap thickness in punch force and equivalent plastic

strain in FBRE process

Another geometrical parameter that was considered to influence the

material deformation behavior in FBRE is gap thickness The effect of

gap thickness on the accumulated effective plastic strain in center

section is shown inFig 11

During the FBRE, similar to conventional extrusion, the punch

force increases significantly with punch stroke at the start of the

process while after certain punch stroke, the required extrusion force

reaches a steady state As can be seen fromFig 11, regardless of the

gap thickness, the location of this transition in punch force is somehow

constant which occurs at point of about 8 mm of punch stroke Besides,

as the gap thickness decreases the punch force increase, which is due to

the restriction of the materialflow into the gap between the upper and

lower dies Reasonable agreement between the simulations results and

the experimental data confirms the validity of the finite element model

and the accuracy of the simulation results

The proposed grid size in the axisymmetric model gave a

con-vergent and stable solution while minimizing the computational cost

To solve the problem, the punch displacement is typically divided into a

large number of infinitesimal time steps each corresponding to a small

stroke increment An incremental displacement field solution was

obtained for each time step while the total strain corresponding at a

given time was calculated by integrating the strain rate along the

normalized distance 0 and 1, respectively, experiences less deforma-tion As the gap thickness increases to 2 mm, an obvious change in material flow behavior can be seen from Fig 12 A narrow gap thickness, for instance 1 mm, restricts the materialflow into the radial section Hence, the material tends to flow more into backward and forward sections As the gap thickness increases, the material tends to progress more into radial section due to an easierflow Hence, the area closer to the lower punch,flows in both forward and radial directions and therefore accumulates more plastic strain inside the material This

on the other hand, causes the restriction of the materialflow in the vicinity of the upper punch hence causing lower strain accumulation in backward section Therefore, as the gap thickness increases, the area in the vicinity of lower punch experiences more deformation at the expense of the area in the vicinity of the upper punch which corresponds to point F and E inFig 11, respectively

4.3 Effect of die corner fillet in equivalent plastic strain in FBRE process

The effect of die corner fillet on the equivalent plastic strain in the center section is not as significant as that of the gap thickness As illustrated inFig 13, a change in die cornerfillet from 1 to 5 mm does not change the materialflow behavior significantly

5 Conclusion

A reliable axisymmetric FE model was developed to investigate the

effect of process parameters on the material flow behavior in FBRE, and the results of which were verified experimentally It is found that the friction between the die components namely punches and dies, and sample has a significant effect on the material flow in FBRE The strain heterogeneity index, SHI, was defined for quantitative analysis of frictional effect on plastic deformation An increase in friction factor increases the SHI for both backward and forward sections But, intense friction confines the extent of strain heterogeneity in backward section, while it has an opposite effect for that of forward section Besides, the minimization of friction in the FBRE process reduces the required punch force significantly As the gap thickness increases, the area in the vicinity of lower punch accumulates more plastic strain in comparison

to that of the upper punch Hence, more uniform deformation is achieved with smaller gap thickness The presented FE model can be used to predict the plastic deformation behavior within the process parameters which in turn can dictate the mechanical properties of the FBRE process products

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