Anisotropic Damage Evolution of Tools During Forging Process

7/24/2019 Anisotropic Damage Evolution of Tools During Forging Process

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SIMULATION IN DER UMFORMTECHNIK

ANISOTROPIC DAMAGE EVOLUTION OF TOOLS DURING FORGING

PROCESS

Kunio Hayakawa, Shizuoka University, Hamamatsu

Abstract

In forging analysis, the damage evaluation parameters such as Cockloft and Latham, Oyane

models and so on are very useful for the evaluation of the limitation of the deformation of the

workpiece during the process. For the tool failure, the proper damage parameter has not ever been

proposed yet. The damage to the tool material generally has an anisotropic nature that is related to

the direction of the principal stress, since the tool materials are very hard and brittle.

In the present paper, an anisotropic damage evolution model proposed by the present author is

modified and implemented to the simufact.forming by the user subroutines. Then the evolution of

the anisotropic damage to the cold forging die during the process was calculated using the damage

model. The calculated models are axisymmetric and 3-dimensional ones. The proposed

anisotropic damage model can describe the damage to the tools during the process properly.

1. Introduction

In cold forging, the tools are subjected to cyclic high loadings. As a result, we often experience

premature failure of tool. For example, in cold forward extrusion, the die insert often cause fatigue

cracks, wear and axial cracks due to high loadings [1-3]. Therefore, the exact estimation of the

service life of forging tool is very important for the reduction of total cost of forging operations.

Recently, cemented carbide material such as WC-Co has been often used as the tool material of

cold forging for higher dimensional accuracy of the forgings [4,5]. Therefore, precise constitutive

equation of the cemented carbide material is useful for the more precise calculation of the stress

and service life by finite element method.

In the present paper, the elastic-plastic constitutive equation of cemented carbide material is

proposed with anisotropic damage behavior taken into account. The conventional framework of

thermodynamic theory is employed for the formulation [6-8]. The anisotropic damage is considered

to express the salient stress unilateral behavior of cemented carbide material. Uniaxial behavior

and cold forward extrusion is calculated using the proposed equation for the validation.

2. Constitutive Equations of Tool Materials

In the present paper, the behavior of the WC-Co cemented carbides material is modeled by the

elastic-plastic constitutive equations coupled with anisotropic damage based on the framework of

the irreversible thermodynamics theory for the constitutive equation [6-8].

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In the present study, the strain of the tool material can be decomposed into the elastic and the

plastic parts as follows, as the deformation of the forging tools can be assumed infinitesimal.

= e + p (1)

2.1. Material Damage and Damage Variable

The debonding of the interface between the carbides and the matrix, the fracture of the carbides

and/or matrix as well as the plastic deformation of the matrix will cause the microscopic material

damage of cemented carbides.

The initiation and growth of the material damage depends the direction of the applied stress.

Moreover, the effects of the damage are diminished under compression because of the closure

effect of microcracks. As a result, the strength and toughness under tension are known to be lower

than those under compression.

In the present paper, we employ the second rank symmetric damage tensor D for the description

of the mechanical effect of the three dimensionally distributed microcracks in the material as [7, 8]

D = DIp

I p

I( )I=1

3

(2)

where DI and pI (I= 1, 2 and 3) are the principal value and principal direction of the damage

variable, respectively.

2.2. Description of Unilateral Characteristic of WC-Co Cemented Carbides

Some researchers have proposed descriptions of the unilateral property of material damage. In the

present paper, we introduce the modified Cauchy stress tensor as [7, 8]

= I

I

I( )I=1

3

(3)

where is the Macauley bracket, and I

and I

(I= l, 2 and 3) are the principal values and

principal direction of stress tensor , respectively.

The modified stress tensor can be written in the global Cartesian coordinate system xi(i= l, 2 and

3) as

ij =

Bijkl

kl (4)

Bijkl = h K( )K=1

3

QiKQjKQKkQKl (5)

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where h(K

) is the Heaviside unit function for the principal stress K

, and Q is the direction

cosine between the global Cartesian coordinate system xi and the principal stress coordinate

system.

2.3. Elastic-Damage Constitutive Equation and Thermodynamic Conjugate Forces

According to the conventional procedure of the irreversible thermodynamic formulation [6-8], the

elastic constitutive equation of the damaged material can be obtained as follows:

e = ged( )

=

1+0

E0 +

1 20

E0M + 2

1 trD( )M :

M

+

2 D + D ( ) :

(6)

where E0

and 0 are Youngs modulus and Poissons ratio at the initial undamaged state.

Furthermore, M and are hydrostatic stress tensor and deviatoric stress tensor, respectively.

Moreover, 1 and

2are material constants. The first and second terms of the right side of eq.

(10) correspond to the common linear isotropic elastic constitutive equation. The third and fourth

terms express the effects of the anisotropic damage on the elastic behavior of the material.

The thermodynamic conjugate forces, Y, R, XN and Bof the internal state variables D, r, Nand

on the other hand, can be derived as

Y =1 M M( )+2 ( ) , (7)

R =R

1 exp brr( ){ } , (8)

XN =2

3CNN (N= 1, 2, 3), (9)

B =Kb . (10)

2.4. Plastic-Damage Constitutive Equation

For the cemented carbide material considered in the present paper, the effect of the damage on

plastic deformation is considered by the use of the effective stress that describes the enhanced

stress effect by the existence of the damage.

The plastic potential Fp and yield surface fp is given as follows by use of the effective stress

as

Fp = 3J2

X( )yR +

CN

N mN + 2( )N=1

3

N

CNXeqN

mN+2

, (11)

fp = J2 X( )y R =0 , (12)

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fd = Yeq B ( )+B0{ } = 0 (21)

Then, the evolution of damage can be prescribed as

D = d

fd

Y+

Fd

Y (22)

where d and are the unknown multiplier determined by the consistency condition on the

damage surfacef

d, and magnitude of the damage development related to the fatigue, respectively.

In order to describe the fatigue damage behavior properly, we assume as

=

nd

Kd ep( )

Yeq Y0

Kd ep( )

nd1

Yeq , (23)

Kd ep( ) =

2Kd0

exp bdep( )+ exp bdep( )

, (24)

ep =2

3p:

p

1/2

dt

. (25)

where nd , Kd0 and bd are material constants. The value of Y0is the threshold of the evolution of

damage by fatigue. Therefore, the Y0can be calculated by eqs.(11) and (22) with the fatigue limit

f .

An equivalent damage variable Deq is introduced in the present study as

Deq

= D : D . (26)

The material is assumed to attain to final fracture when the equivalent damage variable Deq

reaches the threshold value Dcr.

3. Uniaxial loading of cemented carbides material

3.1. Cemented Carbides Material

Uniaxial loading behaviors of WC-Co cemented carbide material are calculated by use of the

proposed constitutive equation. In the present case, x3axis is the direction of loading, and x1and x2

axes are on the cross section of the test specimen.

The cemented carbide material G7 (WC: 75%, Co: 25%, San Alloy Industry Company, Japan) was

selected in order to compare the experimental results by Brndsted et. al [4] and Skov-Hansen et.

al [5]. This material was GT55 type hot isostatiscally pressed. From the literatures, Initial Youngs

modulus E0and Poissons ratio n0were selected as

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E0 = 470GPa, 0 = 0.3 . (27)

The material constants in eqs. (7) - (17) were determined so that the proposed constitutive

equation can describe the uniaxial tension and compression of the cemented carbides G7 as

follows:

1 =2.61105,2 =3.0310

5,

y =2.00102 ,R

=0,Kb =0.80, c

p=0.3

C1 =7.20105,C2 =2.20106 ,C3 = 1.00105,

1 = 8.00102 ,2 =2.00103, 3 = 50.0,

m1 =10.0,m2 = 10.0,m3 = 10.0

nd =6.00,Kd0 =3.0,f =6.50102

(28)

3.2 Results and Discussion

Figure 1 shows the experimental and calculated results of stress-strain curves under uniaxial

tension. The development of damage components is also shown. The tensile strength is about

1700MPa. We can observe the good agreement between the experimental and calculated results.

We can also observe the damage component D33is larger than D11= D22.

Figure 2shows the experimental and calculated results of stress-strain and damage components-

strain curves under uniaxial compression. The compressive strength of the material is

approximately 3200MPa. We can observe that the damage components D11= D22is dominant in

the compression case. It can be predicted from the result that microcracks parallel to the loading

direction are predominantly developed and cause the final fracture under the uniaxial compression,

which will occur to most brittle materials.

Figure 1: Stress Strain relation of WC-Co Figure 2: Stress Strain relation of WC-Co

material under uniaxial tension. material under uniaxial compression.

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4. AXISYMMETRIC FINITE ELEMENT ANALYSIS ON COLD FORGING DIE DURING COLD

FORWARD EXTRUTION PROCESS

4.1 Finite Element Model and Material Properties of Workpiece and Shrink Ring

Mechanical and damage behavior of the cemented carbide used as a die-insert of cold forward

extrusion die set is evaluated by FEM in the present paper.

Figure 3 shows the schematic example of typical fatigue, fracture and wear of cold forward

extrusion die (Engel, 1994). From the figure, the different anisotropic damage components can be

expected to describe the different fracture behaviors; forced rupture (axial crack) and fatigue

fracture (radial crack), as the directions of the crack propagation are different.

Figure 3: Typical failure of cold forward extrusion die-insert [1].

In the present chapter, therefore, the proposed constitutive equation will be applied to the

calculation of the damage state of cold forward extrusion die made of WC-Co cemented carbide.

A commercial FE code MSC. Marc 2005 was used for the calculation. The constitutive anddamage evolution equations of the die material are implemented by the user subroutines provided

in the code, HYPELA2, ELEVAR and so on (MSC Software, 2005).

Figure 4shows the geometries and discretization of the die set and workpiece used in the present

calculation. In the finite element analysis, axisymmetric model was used. The x1, x2and x3axes of

Cartesian coordinate system correspond to the axial, radial, and circumferential directions of the

die-insert, respectively. This figure shows the case of the die-angle = 120. In the present

calculations, both the die-angle of = 90 and 120 were performed in order to examine the effect

of the die-angle on the damage behavior of the die-insert. Punch and knockout-pin were modeled

as rigid boundaries

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For materials of die insert and shrink ring, WC-Co G7 and SKD61 (in JIS) were selected. Only

elastic property is used in the SKD61, Youngs modulus and Poissons ratio are set to 206GPa and

0.3.

Figure 4: Geometry and discretization of analyzed model of cold forward extrusion (in case of

die-angle = 120).

As the workpiece material, SS400 (in JIS) was used. The elastic and plastic properties of thematerial are given as follows;

E =206GPa, =0.29 , (29)

=285.0+ 461.0 ep 1.38104( )0.286

(30)

where ep is the equivalent plastic strain of the workpiece material calculated by Equation (25).

The usage of the shrink ring is effective avoiding the onset of forced rupture (axial cracking). The

interference of shrink fit between the die-insert and shrink ring was set to 0.1mm.

The axisymmetric triangular and quadrilateral elements were employed for the extrusion die set

and the workpiece, respectively. The numbers of elements of the die-insert, shrink ring and

workpiece are 3093, 114 and 2739, respectively. The numbers of nodes of the die insert, shrink

ring and workpiece are 1606, 72 and 4442, respectively.

4.2 Results of Development of Damage Components and Discussion

Figure 5shows the distribution of damage components D11, D22, D12 and D33 in case of the die-

angle = 120when the length of the extruded region attains 5.3mm; the corresponding punch

stroke is S= 2.1mm. Although the D11, D22and D12show almost same values, their distributions are

slightly different. This means that one principal damage value is in the plane of x1-x2, and the

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principal direction is around 45from x1axis. The D33is another principal damage value, and it can

describe the possibility of the forced rupture (axial cracking) in Figure 6. In this case, the D33 is

dominant damage component. Therefore, the axial cracking may occur in spite of the shrink fitting.

Table 1shows the principal damage value D1, D

2and D

3(= D

33), and the angle of D

1from thex

1-

axis at each and S. In case of die-angle = 90, the damage component D33is very small value of

6.01310-5 at even the punch stroke of S = 2.95mm. This means the possibility of the forced

rupture (axial cracking) can hardly be encountered. It can be also observed that the principal

damageD1, which stands for the fatigue damage in the region of die radius, is 0.368 and 0.324 in

each a. Therefore, the residual life to the onset of the fatigue damage will be similar in each die-

insert. Furthermore, the angle of principal axis 1 from x1axis, which stands for the direction of the

propagation of fatigue crack, can be found almost same in each case.

(a) (b)

(c) (d)

Figure 5: Distribution of damage component during extrusion in case of punch stroke S =

2.1mm: (a) Damage D11, (b) Damage D22, (c) Damage D12, (d) Damage D33.

Table 1: Principal damage values of die-insert.

Die-angle( )

PunchstrokeS(mm)

Principal damage componets Angle of principalaxis 1 from x1( )

D1 D2 D3( = D33)

90 2.95 0.368 0.001 6.01310-5 44.1

120 2.10 0.324 0.024 0.338 44.0

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5. THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS ON ANISOTROPIC DAMAGE OF

FORGING DIE DURING COLD FORWARD EXTRUTION PROCESS

The anisotropic damage model proposed in the present paper was applied to the calculation of

damage of forging die of cold forward extrusion process.

Figure 6shows the one-sixth model of cold forward extrusion dies. The material of die-insert was

WC-Co (25%) same as used in Chapter 4. The cylindrical workpiece was extruded to the

hexagonal cylinder. The die angle was 90.

In the present calculation, only the damage evolution was calculated. The plastic property and

coupled elastic-damage effect was neglected since they were not significant in the present case.

The FE software simufact-forming 10 (GP version) was used for calculation. The user subroutines

were also accompanied. The punch strokeS

was set to 20mm.

(a) (b)

Figure 6: Three-dimensional finite element extrusion model for analysis of die damage (one-

sixth model. Punch and shrink ring are not displayed): (a) discretized workpiece and die, (b)

dicretized die.

Figure. 7shows the distribution of equivalent plastic strain of workpiece and maximal principal

stress of die-insert at S= 20mm. Large maximal principal stress is observed at the region of vertex

of hexagonal inlet of die-insert, from which the fatigue fracture is supposed to start.

Figure. 8 shows the distribution of components of damage. The D11, D22 and D33 imply the

possibility of onset of cracks perpendicular to radial, circumferential and axial direction of die-insert,

respectively. From the figure, the D22 is largest among these components. Therefore, fatigue

fracture by the cracks perpendicular circumferential direction at the region around the vertex of

hexagonal inlet of the die-insert is supposed to be most possible. This prediction is consistent to

the prediction of fracture by the maximal principal stress of the conventional method for prediction

of tool fracture. The damage component proposed in the present paper, however, can indicate the

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damaged region in more concentrated manner than the use of maximal principal stress, which is

more useful for the prediction.

(a) (b)

Figure 7: Results of calculation: (a) distribution of equivalent plastic strain of workpiece at S=

20mm, (b) distribution of maximal principal stress of die-insert at S = 20mm.

(a) (b) (c)

Figure 8: Results of components of damage at S= 20mm: (a) distribution of D11, damage to

radial direction, (b) distribution ofD

22, damage to circumferential direction, (c) distribution ofD

33,damage to axial direction.

6. CONCLUSIONS

The elastic-plastic-damage constitutive equations of WC-Co material for cold forging tools were

proposed. The constitutive equation can predict the uniaxial tension, compression and cyclic

loading behaviors with good accordance. From the result of the finite element analysis of cold

forward extrusion with the die insert made of WC-Co using the proposed equations, we can specify

the possible fracture behavior of the die insert. In three dimensional calculation, the proposed

damage model can be useful for the prediction of fatigue fracture of forging tools.


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REFERENCES

[1] Reiss, W.,Annals. CIRP 36, 155-160 (1987).

[2] Geiger, M.,Annals. CIRP 40, 303-305 (1991).

[3] L. Cser, L., Geiger, M., Lange, K., Kals, J. A. G. and Hnsel, M., Proc. Instn. Mech. Engrs.

207, 223-239 (1993).

[4] Brndsted, P., and Skov-Hansen, P., Int. J. Fatigue20, 373-381 (1998).

[5] Skov-Hansen, P., and Brndsted, P., J. Mat. Procces. Technol95, 40-48 (1999).

[6] Lemaitre, J. and Chaboche, J. L., Mechanics of Solid Materials, New York: Cambridge

University Press, 1990, pp. 161-449.

[7] Hayakawa, K. and Murakami, S., Int. J. Damage Mech.6, 333-363 (1997).

[8] Hayakawa, K., Nakamura, T. and Tanaka, S., Materials Transactions45, 461-468 (2004).

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Anisotropic Damage Evolution of Tools During Forging Process

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