Finite Element Simulation on Cross Shear Ratio in Asymmetrical Rolling

www.ijm‐me.org International Journal of Material and Mechanical Engineering (IJMME), Volume 4, 2015 doi: 10.14355/ijmme.2015.04.008

Finite Element Simulation on Cross Shear Ratio in Asymmetrical Rolling *1

D.L.Tang , X.H.Liu2, M.Song3, X.K.Sun4 Northeastern University research academy, Northeastern University, Shenyang, 110819, China *1

tangdelin2014@163.com, 2liuxh@ral.neu.edu.cn, 3sm_162@163.com, 4sxk2010@163.com

Abstract The formula for calculating neutral angles and cross shear ratio in asymmetrical rolling was established in this study. The influences of asymmetrical ratio, friction coefficient, elongation to the value of cross shear ratio were analyzed by calculation and simulation. Finite element simulation on shearing stress state in the deformation region had been done by ABAQUS. The results of simulation showed the variation trend of cross shear ratio along with the three parameters above and proved that the formulae for calculating the cross shear ratio were consistent with the reality.

Key words Asymmetrical Rolling; Finite Element Simulation; Neutral Angle; Cross Shear Ratio

Introduction Asymmetrical rolling is a rolling method which has two work rollers with different linear speed. Compared with symmetrical rolling, asymmetrical rolling can reduce rolling force1,2, break the minimum value of exit thickness in symmetrical rolling3, roll the metals or alloys which are difficult in deformation and obtain special microstructures4. The above advantages are closely associated with deformation region characteristics, which were studied by many researchers.Halloumi5 analyzed the stain‐stress in the deformation region and established the formula to rolling force and torque by entry velocity.Liu6 conducted rolling experiments with different asymmetrical ratio, reduction and rolling temperature and investigated the influence of reduction and rolling temperature on rolling force. With the development of finite element simulation technology, more and more researches about asymmetrical rolling were studied by finite element simulation technology. Hao7 did a finite element simulation on bending phenomenon in asymmetrical rolling process. The simulation result showed that the bending phenomenon is influenced by the stress state of rolling piece. Angella8 did experimental research and finite element simulation on asymmetrical rolling compared with equal channel angular pressing. The result showed that the test specimen by asymmetrical rolling obtained more dislocation density and higher strength than the specimen by ECAP. Unlike symmetrical rolling, asymmetrical rolling has a cross shear region in deformation region. Two frictions in opposite direction on the top and bottom surfaces of rolling specimen can availably reduce the rolling force9,10.

Moreover, the crossshear ratio makes stress state different from symmetrical rolling and breaks the limit of the minimum permission thickness. Under the influence of cross shear ratio, asymmetrical rolling can obtain rolled piece with thinner thickness compared with symmetrical rolling. Because of the importance of the cross shear ratio, it is necessary to study geometric parameters in asymmetrical rolling and find out the determinants of cross shear ratio which is the percentage of cross shear region in the whole plastic deformation.

Geometrical Analysis The deformation region in asymmetrical rolling is generally divided into three parts: forward slip zone, backward slip zone and cross shear zone, as shown in Fig.1. The deformation region can be also divided into three types: three zones (forward slip zone, backward slip zone and cross shear zone), two zones (this deformation type contains two cases: one is made up of forward slip zone and cross shear zone and the other is made up of backward slip zone and cross shear zone) and one zone (cross shear zone). The deformation type can be

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International Journal of Material and Mechanical Engineering (IJMME), Volume 4, 2015 www.ijm‐me.org

determined by certain geometrical parameters and rolling process parameters. In these parameters, three most important ones are asymmetrical ratio, elongation and friction coefficient.

The geometric parameters in asymmetrical are analyzed based on the following assumptions: 1) The metal flow velocitieson the same vertical section are the same.

2) When the rollers are flatted, the flatten contact arc are also supposed to be arc with the equivalent radius of R′. The equivalent radiuses of top and bottom work rollers are the same.

Based on the above assumptions, the cross shear ratio can be defined by the following formula: ´

λ

´

(1)

Whereλ is cross shear ratio, lc is the horizontal projection length of cross shear region, l is contact arc length, R′ is the equivalent radius of flatten contact arc, γ1 and γ2 are the neutral angles of the faster work roller and the slower work roller, α is the nip angle.

FIG.1 THE DEFROMATION REGION IN ASYMMETRICAL ROLLING

Three stress states of three micro units respectively from backward slip zone, cross shear zone and forward slip zone are analyzed and the horizontal force balance equations are established as follow: In the forward slip zone:

  xF  0  2sin  px R   2 cos  t x R  d 2

(2)

In the cross shear zone:   xC   21 2sin  p x R d

(3)

In the backward slip zone:   xB   1  2 sin  px R -2 cos  t x R  d

(4)

According to the Coulombʹs friction law, the force balance equation of the whole deformation region can be described by following equation:  x   xF   xC   xB  t f h  tb H  0

(5)

Where h and H are the entry thickness and exit thickness, tf and tb are the forward pull and backward pull.The sum of two neutral angles can be expressed by

γ

1

(6)

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According to mass flow equation and the above formula, γ1 and γ2 can be described as following:

γ

(7)

γ

(8)

When the geometric parameters and friction coefficient are fixed, the A in above formula is a constant which can be expressed as

A

α 1

(9)

The cross shear ratio (λ) can also be expressed as



 1 - 2 i 1 -2 A  i 1

iA2

 i  1

2



h i  1,  1   2 R

(10)

Modeling In order to analyze the influential factors of cross shear ratio, finite element simulations were done by ABAQUS. The asymmetrical rolling model was established as shown in Fig 2. The finite element simulations were based on the parameters set as following: the initial thickness of rolled pieces was 50μm; the linear speed of slower work roller was 26 mm/s; the diameter of work rollers was 50mm.

FIG.2 ASYMMETRICAL ROLLING MODEL

Results and Discussion Four shearing stress distributions of rolled piece with asymmetrical ratio of i=1.0, i=1.1, i=1.2 and i=1.5are shown in Fig.3. Specifically,the rolling type is symmetrical rolling when i=0 as shown in Fig. 3(a). The directions of shearing stress along up and down surface of the rolled piece are the same. Both of them point toward neutral face. When i>1, the shearing stress state changes and there is a region with a couple of shearing stress in opposite direction.

The length of cross shear region increases along with the increase of asymmetrical ratio. The results shown in Figs.

3(b), 3(c) and 3(d) indicate the cross shear ratio increases from 0.15 to 0.65 while the asymmetrical ratio increases from 1.1 to 1.5.That is because the neutral angle by the side of slower roller increases while neutral angle by the side of faster roller decreases along the increase of the asymmetrical ratio. The change results in the decreases of the length of backward slip zone and forward slip zone and the cross shear ratio increases. With the same value range of asymmetrical ratio, the cross shear ratio increases from 0.1 to 0.69 by formula above in this study.

Two shearing stress distributions of rolled piece with elongations of 20% and 40%are shown in Fig.4. As can be seen in Fig. 4(a),the rolled piece rolled from 50μm to 40μm got 0.55 cross shear ratio;the rolled piece rolled from 50μm to 30μm got 0.15 cross shear ratio as shown in Fig. 4(b).According to formula (10), the cross shear ratio decreases from 0.53 to 0.11 along with the increase of elongation from 20% to 40%.

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Two shearing stress distributions of rolled piece with friction coefficient of 0.1 and 0.15 are shown in Fig.5. From the result of simulation, the cross shear ratio decreases along with the increase of friction coefficient. The cross shear decreases by 50% while the friction coefficient increases by 50%, which is consistent with above theoretical analysis.

FIG.3 SHEARING STRESS DISTRIBUTION: A I=1.0, B I=1.1; C I= 1.2; D I=1.5

FIG.4 SHEARING STRESS DISTRIBUTION WITH DIFFERENT ELONGATION: A20%, B 40%

FIG.5 SHEARING STRESS DISTRIBUTION WITH DIFFERENT FRICTION: A0.1, B0.15

Conclusions The formulas for calculating the neutral angles and cross shear ratio were established in this study. Finite element simulations on cross shear ratio by ABAQUS were also done. Finally, conclusions were drawn out on the basis of results from theoretical analysis and finite element simulation as following: The cross shear ratio increases along with the increase of the asymmetrical ratio. And the result of FEM shows the cross shear ratio increases from 0.15 to 0.65 while the asymmetrical ratio increases from 1.1 to 1.5.The cross shear ratio decreases along with the increase of the elongation. The rolled piece rolled from 50μm to 40μm got 0.55 cross shear ratio while the rolled piece rolled from 50μm to 30μm got 0.15 cross shear ratio by simulations; The cross shear ratio decreases along with the increase of thefriction coefficient. The cross shear decreases by 50% while the friction coefficient increases by 50%. The theoretical analysis and the finite element simulationwith the parameters set in this study are well matched.

ACKNOWLEDGEMENT

This work was financially supported by the National Natural Science Foundation of China (NSFC) under Grant nos 51374069 and U1460107. Prof. X.H. Liu is grateful for these supports.

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