57 815 828 Prediction of Fatique Life of Cold Forging Tools by FE Simulation

PREDICTION OF FATIGUE LIFE OF COLD FORGING

TOOLS BY FE SIMULATION AND COMPARISON
OF APPLICABILITY OF DIFFERENT DAMAGE
MODELS

M. Meidert and C. Walter

Thyssen/Krupp Presta AG

Liechtenstein

FL-9492 Eschen

K. P ¨ohlandt

Institut f¨u r Statik und Dynamik der Luft-und Raumfahrtkonstruktionen

Universit¨at Stuttgart

Pfaffenwaldring 27

D-70569 Stuttgart

Abstract

Tools for cold forging mainly fail due to cyclic fatigue. Tool costs can reach
a significant portion of production costs and therefore methods to improve
tool life are of high interest. However, tools are still mainly designed and
optimized by the trial and error method.

The purpose of the work presented is to implement damage models in a FE

code for determination of location of failure and prediction of tool life. Dam-
age models implemented are the uni-axial models of Smith-Watson-Topper
(SWT) and Bergmann and the multi-axial energy based model proposed by
H¨ansel. Tool material was ASP23 for which material data was available.

The FE simulation of the tools is done non-linear with a material model

proposed by Chaboche taking into account kinematic hardening and the
Bauschinger effect. The evaluation of applicability of the damage models
is done for specific cold forging tools made of PM steels.

It is shown that the damage models of SWT and Bergmann give rather

inaccurate results for multiaxial states of stress and strain. The energy based

815

816

6TH INTERNATIONAL TOOLING CONFERENCE

model of H¨ansel shows a good correspondence between computed and actual
failure of tools. Location of failure is predicted correctly and prediction of
tool life is acceptable.

Keywords:

Cold forging, low cycle fatigue, tool life, Finite Element Simulation

INTRODUCTION

Manufacturing costs for a cold forging part mainly consist of costs for

material, forming machine and for tooling. The costs for the tools, dies
and punches, are significantly high. The more complicated the geometry of
the part and the tool is the higher the costs because manufacturing is more
expensive and tool life is shorter.

Today cold forging tools are designed by empiric principles. Loading

by process loads onto the tool is often not exactly known and assumptions
have to be made. Engineering tools like Finite Element simulation offer vast
opportunities for improved process and tool layout. The main parameters
which can be varied in tool design are the prestressing condition and tool
material. The geometry of the cavity can seldom be altered because of given
dimensions of the part to be formed.

The parameters, stress and strain state in prestressing and loading condi-

tion and tool material highly affect the die life. Cold forging tools mainly
fail by cracking due to low-cycle fatigue, seldom due to wear.

In the work presented a software was established to calculate damage pa-

rameters and predict life time from results of non linear FEM die stress anal-
ysis. Uniaxial damage parameters considering mean stress (Smith-Watson-
Topper and version) and multiaxial damage parameters (H¨ansel and modified
version) were investigated for their applicability for specific cases. Com-
puted and practical results were compared. Tool material considered was
ASP23 for which static and cyclic material was available from investigations
carried out at Risœ National Laboratory.

ESTIMATION OF DAMAGE

The method applied in this work for estimation of fatigue life was the

local concept. For the problems studied in this work uniaxial and multiaxial
approaches were taken into account. The following damage models were
implemented and evaluated:

Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...

817

Smith-Watson-Topper (SWT) damage model.

SW T

(σ

+ σ

) · ε

(1)

In the Smith-Watson-Topper model [1] the influence of cyclic mean stress

is integrated. For purely elastic material the mean stress sensitivity is mod-
erate and can be taken into account very well. However in case of highly
strained material with higher mean stress sensitivity the SWT model will not
lead to correct results.

Bergmann damage model.

Berg

(σ

+ a

) · ε

(2)

Based on the difficulty described above Bergmann [2] proposed an im-

proved damage model and introduced the correction factor a. The factor
corrects the damage dependant on the mean stress state (tensile or compres-
sive stress).

H¨ansel damage model.

The damage models given above are restricted

to one-dimensional problems. The influence of three dimensional stress
states is described unprecisely. An energy based damage model taking into
account the multi axial stress state and mean stress influence was postulated
by H¨ansel [3]. It is based on an approach which considers the energy brought
in a material element during one cycle. The total work is defined as sum of
elastic and plastic energy:

∆W

= ∆W

+ ∆W

(3)

The elastic energy is defined as:

∆W

1
2

∆σ

∆ε

1
8

∆σ · ∆ε

(4)

The plastic energy is defined as:

∆W

(1 − n′)
(1 + n′)

∆σ · ∆ε

(5)

The factor n′ considers the change of the area of the hysteresis loop during

cyclic loading. For most metals the factor n′ is positive which means that a

818

6TH INTERNATIONAL TOOLING CONFERENCE

Figure 1.

Plastic and elastic deformation energy.

strain hardening behavior exists. The elastic energy is influenced by mean
stress. Mean stress causes a shift of the hysteresis loop. A positive mean
stress results in an increase of elastic deformation energy area, a negative
mean stress results in a decrease of elastic deformation energy area. The
influence of mean stress is considered by an additional term W

1
2

(σ

) − C

(σ

)

(6)

In case of tensile mean stress W

is added to the elastic energy, in case

of compressive mean stress W

is subtracted.

∆W

e++

= ∆W

(7)

With term (3) and (7) and

1 −

(8)

Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...

819

Figure 2.

Mean Stress influence.

the total energy becomes:

∆W

1
8

∆σ · ∆ε

1
2

(σ

) − C

(σ

)

(1 − n′)

(1 + n′) · ∆σ · ∆ε

(9)

Term (8) is valid for one dimensional stress states. Extended to three

dimensional problems the term becomes:

∆W

ef f

1
8

∆σ

′ ·

∆ε

′ ±

1
2

(σ

m,ij

) − C

(σ

m,ij

)

(1 − n′)
(1 + n′)

3
2

∆σ

′ ·

∆σ

′

1
2

2
3

∆ε

p
ij

∆ε

p
ij

1
2

(10)

Modified H¨ansel damage model.

It was shown that for high compressive

mean stress the correction term for the mean stress sensitivity becomes so
dominant that negative damage parameters are calculated. In addition to
negative damage parameters a convergence of the curves for different stress
amplitudes was observed.

820

6TH INTERNATIONAL TOOLING CONFERENCE

Figure 3.

Damage parameters

∆W

over mean stress σ

To correct this phenomenon a factor C was introduced which gives the

equivalent amplitude of fully reversed cycles for cycles with negative or
positive mean stress. The total energy is then

∆W

1
8

∆σ

(1 − n′)
(1 + n′)

∆σ · ∆ε

(11)

Extended to multiaxiality

∆W

ef f

1
8

∆σ

′

(1 − n′)
(1 + n′)

3
2

∆σ

′ ·

∆σ

′

1
2

2
3

∆ε

p
ij

∆ε

p
ij

1
2

(12)

Life time prediction: The stress cycle diagram was described in the low

cycle regime

(N ≤ N

) by Manson, Coffin, Basquin and Morrow [4].

Elastic strain amplitude:

′

(2N )

(13)

Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...

821

plastic strain amplitude:

= ε

′ ·

(2N )

(14)

with total strain:

= ε

+ ε

(15)

the strain cycle diagram is:

′

(2N )

+ ε

′ ·

(2N )

(16)

the stress cycle diagram is:

= σ

′ ·

(2N )

(17)

Equation (16) and (17) put in damage model of Smith-Watson-Topper leads
to

SW T

′ ·

(2N )

′

(2N )

+ ε

′ ·

(2N )

(18)

Equation (18) can be transformed to

SW T

′

(2N )

+ ε

′ ·

E ·

(2N )

b+c

(19)

The number of cycles

2N until failure can be determined by the Newton

iteration method. Equation (16) and (17) put in damage model of H¨ansel
leads to elastic deformation energy.

∆W

1
8

2 · σ

′ ·

(2N )

2 ·

′

(2N )

(20)

Equation (20) transformed is

∆W

1
2

′

(2N )

(21)

Plastic deformation energy is

∆W

(1 − n′)
(1 + n′)

′ ·

(2N )

2 · ε

′ ·

(2N )

(22)

822

6TH INTERNATIONAL TOOLING CONFERENCE

Equation (22) transformed is

∆W

= 4 ·

(1 − n′)
(1 + n′)

′ ·

(2N )

b+c

(23)

Total deformation energy is

∆W

1
2

′

(2N )

+ 4 ·

(1 − n′)
(1 + n′)

′ ·

(2N )

b+c

(24)

The number of cycles

2N until failure can also be determined by the

Newton iteration method.

SIMULATION PROCEDURE

The simulations were carried out using the commercial Finite Element

(FE) program systems DEFORM [5] und ANSYS [6] available at the Krupp-
Presta company. The FE-program system DEFORM was utilized for simu-
lation of the forming process. DEFORM includes a solver using an implicit-
iterative procedure which is faster than an explicit one. Remeshing of heav-
ily deformed meshes of the workpiece is possible. ANSYS was utilized
for non-linear calculation of the tooling on which loads from the DEFORM
simulation is applied. Also modeling of the components was carried out in
ANSYS.

Figure 4.

Simulation Flowchart.

Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...

823

Since cold forging tools often have complicated 3D shapes of the cavity

and fatigue life estimation can not be done without finite element simulation,
almost all the models studied in this work were 3D problems. For evaluation
of the results axisymmetric specimens were included but they were also
simulated by 3D models. Some auxiliary programs were written for coupling
the program systems DEFORM and ANSYS. After the DEFORM simulation
the nodal forces were mapped to the ANSYS model for each increment and
a nonlinear static simulation was carried out. The results obtained this way
were evaluated by means of a macro resp. C program for various damage
parameters and finally given back to the ANSYS program for visualization
by the postprocessor.

MATERIAL DATA

The utilized tool steel ASP23 was characterized by Brondsted and Skov-

Hansen at Risœ national laboratory [7] by cyclic material testing and data
was published. Material data is measured by strain controlled cyclic tensile
experiments with mean strain and strain amplitude as parameter. Also step
test were made. For the analytical description of the cyclic stress-strain
curve the formula proposed by Ramsberg and Osgood [7] was applied:

K′

′

(25)

The identification of cyclic material parameters b,c, ε

′

, σ

f 0

′

, σ

f m

′

, σ, n′

and K′ was obtained by curve fitting procedures.

ASP 23 exhibits no well-defined yield point but a continuous transition

from elastic to plastic deformation. Therefore the material law proposed by
Chaboche [9] was applied for simulation in ANSYS:

∆σ

−

tanh(γ

∆ε

)

(26)

RESULTS

FATIGUE TEST SPECIMEN

For evaluating the results, at first a fatigue test specimen was studied

because of its almost uniaxial state of stress.

824

6TH INTERNATIONAL TOOLING CONFERENCE

Figure 5.

Stress-strain material response for tensile specimen (ASP23)

After a large number of experiments the average life was about 4000

cycles but there was a large scatter from 500 to 10000 cycles. The tool
life estimation according to Smith-Watson-Topper (axial component) was
140000 cycles. An explanation for this very high tool life prediction may
be that only one component of damage is considered. Also the compressive
mean stress reduces the damage parameter significantly.

The damage parameter according to Bergmann is about 40 % higher than

that according to SWT for all three directions, resulting into a life of about
600 parts. Both damage parameters defined for uniaxial load were inaccurate
for the state of uniaxial stress.

In the H¨ansel damage parameter Fig. 8 the plastic contribution was only

1/3 of the entire deformation energy density; despite this, the plastic defor-
mation energy determines damage in the range of low cycle fatigue. For the
minimum life 2837 cycles were obtained. The modified damage parameter
was lower, resulting in a minimum number of 6143 load cycles. These re-
sults do not allow a clear distinction between the H¨ansel and the modified
damage parameter.

Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...

825

COLD FORGING DIE

The forming process of a yoke is an example of a three dimensional state

of stress.

Figure 6.

Tensile specimen.

Figure 7.

Damage in axial direction

(SWT)

Figure 8.

Damage (H¨ansel)

826

6TH INTERNATIONAL TOOLING CONFERENCE

Figure 9.

Cold forging part.

Figure 10.

Cold forging die with cracks (cut).

Forming is carried out by combined forward extrusion and backward can

extrusion. In the fillet radius cracks occur after an average of 50000 parts. In
the damage calculation the SWT damage parameter became imaginary due to
the high compressive mean stresses resulting from the prestress condition and
no results could be obtained. The damage parameter according to Bergmann
indicated the location of failure correctly for tangential and axial load but
it predicted a fatigue life of more than 200000 cycles which was by far too
high.

Figure 11.

Damage (H¨ansel).

Figure 12.

Damage (modified H¨ansel).

Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...

827

Again the largest part of the H¨ansel damage parameter is given by the

elastic deformation energy density. This is in agreement with the observed
fatigue life of about 50000 cycles which is in the range of high cycle fatigue.
The life time calculation according to H¨ansel gives a minimum of 7900
cycles at the lower position of the fillet radius and about 85000 cycles for
the true position of failure. Compared with practical results this is rather
inaccurate.

The modified damage parameter, however, indicates the location of fail-

ure correctly and a life of about 34500 cycles is in good agreement with
experiments.

CONCLUSIONS

Both the SWT and the Bergmann damage parameter gave rather inaccurate

results for the examples studied. These uniaxial damage models seem not
to be applicable for 3D problems with high compressive mean stress.

The results obtained with the multiaxial damage parameters according to

H¨ansel were in good correlation with experimental results.

In case of the extrusion die, the modified H¨ansel damage parameter was

even more accurate than the H¨ansel parameter itself. However, this statement
cannot be generalized before more examples have been studied.

ACKNOWLEDGMENTS

The presented work has been performed within the Fifth Framework Pro-

gramme in the scope of G5RD-CT-1999-00067 project COLT, entitled Im-
provement of service Life and Reliability of Cold Forging Tools with Respect
to Fatigue Damage due to Cyclic Plasticity.

Technical support from the consortium and financial contribution from

European Commission are gratefully acknowledged.

REFERENCES

[1] K. N. SMITH, P. WATSON and T. H. TOPPER, A stress-strain function for the fatigue

of materials, J. of Materials 5 (1970), 767–775.

[2] J. W. BERGMANN, Zur Betriebsfestigkeitsbemessung gekerbter Bauteile auf

der Grundlage der 'örtlichen Beanspruchungen, Institut f'ür Stahlbau und Werk-
stoffmechanik, TH Darmstadt 1983.

828

6TH INTERNATIONAL TOOLING CONFERENCE

[3] M. HÄNSEL, Beitrag zur Simulation der Oberfl¨a chenerm'üdung von Umformwerkzeu-

gen (On the simulation of surface fatigue of metal forming tools) Berlin, Springer-Verlag
1993.

[4] B¨a umel, A.: Experimentelle und numerische Untersuchung der Schwingfestigkeit rand-

schichtverfestigter eigenspannungsbehafteter Bauteile, Institut f'ür Stahlbau und Werk-
stoffmechanik, Darmstadt 1991.

[5] Scientific Forming Technologies Corporation (SFTC): DEFORM Users Manual 3D,

Version 3.3, August 2001.

[6] ANSYS 5.6 Theory Reference

[7] P. BROENSTED and P. SKOV-HANSEN, Fatigue properties of high-strength materials

used in cold forging tools, Int. J. Fatigue 20 (1998), 373–381.

[8] S. SURESH, Fatigue of Materials, Cambridge University Press 1998.

[9] J. LEMAITRE and J.-L. CHABOCHE, Mechanics of solid materials, Cambridge, Cam-

bridge University Press 1990.

Wyszukiwarka

Podobne podstrony:

więcej podobnych podstron