Prediction of Cracks in multistage Cold Forging Operations by
Finite-Element-Simulations with integrated Damage Criteria
Arno Behrens & Hendrik Just & Dirk Landgrebe
Institute for Production engineering, University of the Federal Armed Forces, Hamburg, Germany
ABSTRACT: In order to avoid the formation of cracks during cold metal forging processes the model of effective stresses was modified and implemented into FE simulations of various deformation processes. The
necessary material dependent parameters were identified from tensile and compression tests. Then the model
was verified by FE simulations of a collar specimen compression test at which the arise of cracks will be detected by special ultrasonic techniques. It was found that ductile damage could be accurately predicted using
the given model. After that the theory of damage evolution was applied to different industrial workpieces produced in multistage forming processes at which in practice the appearance of cracks was observed mostly in the
former forging stages. These are a pinion gear shaft and a conical gear wheel blank as examples for two dimensional simulations and a hexagon socket screw for three dimensional simulation. Based on these simulations
modifications could be imposed on the processes to avoid material failure.
1 Introduction
Computer simulations of cold and semi hot forging processes using the finite-element-method (FEM)
have reached a high standard. Thus it is possible to use
FE simulations not only for analyzing material flow or
the stress-strain behavior but also to predict secondary
effects, for example the susceptibility to cracking of
the material at the different forming stages. Several
methods are thinkable to avoid the arise of cracks
like modifications of the forming tool, use of different workpiece material or process-annealing before
the critical stage.
This article will give a suitable model for the prediction of ductile damage evolution during cold forging operations and the applicability of FE simulation to their prediction. The modification of industrial
cold forging processes by the use of damage criteria
can help to reduce costs and scrap and therefore is a
progress in planning and design of tools.
In the first section different models for the prediction of ductile damage are briefly mentioned from
which the model of effective stresses is chosen and
extensively described in the second section. In the
third section an overview on some industrial cold
forging operations is given to proof the applicability
of this model in order to predict cracks by simulations
at two- and three-dimensional realistic forging operations.
2
Different criteria for the prediction of ductile
damage
It is possible to distinguish between two main categories of damage criteria for the prediction of ductile damage in cold forging operations that are the
macromechanical and the micromechanical ones. The
first ones describe the evolution of specific stresses
and strains in combination with material dependent
parameters that reach critical values when failure
arises. This group of damage criteria can roughly be
divided into strain independent and strain dependent,
the latter are also called integral. The strain dependent values have in common that they are integral
functions of the stress , the strain "R and some ma"
terial dependent parameters a as B
0 f ; "; a d".
Thus they invoke not only the current state of the
material involved in cold or semi-hot forging operations but also the previous forming history. This is
the main difference in comparison to the strain independent variables which are mere instantaneous values and are therefore not suitable for large changes of
strain. Integral damage criteria model the distribution
of the forming energy into shaping of the material,
dissipated energy and other terms. The main problem
in FE simulations is the comparability of the critical
values obtained from integral damage criteria as they
have partially been developed for specific materials
or forging operations. Several authors deliver detailed
=
1
(
)
discussions about the applicability of integral damage
criteria like (Groche 1991), (Dahl & Pawelski 1993),
(Seidenfuss 1992).
Micromechanical damage criteria values try to describe the impact of the stresses on the microstructure
of the material when ductile damage occurs. These
processes are characterized by the initiation of microcavities i.e. the decohesion of atomic bonds and inter
crystal linkages, the growth of these defects finally
leads to the failure of the material in the macrostructure by coalescence of the defects. The fundamental
considerations of these criteria are verified by experiments but the integration of mathematical formulations into FE simulation is still complicated due to
numerical instabilities. Moreover the necessary material parameters for these models are difficult to obtain.
From the upper considerations we suggest in the
following the use of the phenomenological model
of effective stresses first developed by Kachanov
(Kachanov 1986) and later mainly extended by
Lemaitre in (Lemaitre & Chaboche 1990). The main
benefits of this model are in brief its applicability on
complex forging operations, the comparability of the
critical values obtained, the possibility to include thermal effects of damage and the possible modeling of
anisotropic material behavior.
r
n
1
=1
∂Ai
A0
r
F
Macroscale
~
A = ∑ ∂ Ai
i
D = A / A0
Mesoscale
Figure 1: Definition of the RVE and the damage variable D
age as the load must now be transferred through the
reduced cross section A A0 A. This leads to the
definition of the effective stress in the case of tension
as follows:
~
F~
F
:
(1)
~
A
A
D
A0
A0
~
=
~ := =
=1
1
The modification of the stress can be transferred
to other variables like the modulus of elasticity E as
shown in (Lemaitre & Chaboche 1990). In case of
compression the upper model has to be modified because the creation and growth of microcavities is initiated later than in the tension case. Moreover the existing defects close partially and new cavities come up
under much higher stress than in the former case. In
Lem96 this effect is taken into account by defining a
crack closure parameter h as follows:
;
h :
(2)
hD
This parameter is related to the material dependent
critical damage D1c to be defined in eq. 7. In practice
this parameter can be identified by the measurements
of elasticity modulus in tension and compression. The
evolution of the damage variable D can be derived
from tensile tests where uniaxiality in tension is guaranteed (Fig. 2). In the beginning of the test no damages occur thus D
. With increasing plastic deformation measured by the logarithmic plastic strain
"pl the damage variable increases until a critical value
D1c is reached. This value describes the macroscopic
failure of the material in case of one-dimensional state
of stresses. The evolution of D is related to the increase of "pl and the triaxiality :
~=1
~=
0
RVE
x
2.1 Model of effective stresses
For this model the evolution of ductile damage under
large plastic deformations is characterized by three
stages. On the scale of the microstructure of the material decohesion of atomic bonds leads to the creation
of microcavities in the first stage. With increasing
load on the material these cavities will grow further
in the second stage until in the third stage coalescence
occurs that finally leads to rupture when the material’s
plastic instability is reached. In order to describe the
ductile damage mathematically the cavities in the microscale are averaged in the mesoscale thus leading
to the definition of the representative volume element
(RVE). A RVE at any point M in the material, oriented by a plane which is defined by its normal ~n and
its abscissa x along the normal, is shown in Figure 1.
The material is under load F~ which is high enough for
plastic deformation. The cavities resulting from the
plastic deformation intersect the original plane A0 of
P
the RVE thus leading to a damaged area A
i @Ai
which is the sum over all cavity areas. The ratio of
damaged cross section and original plane defines the
damage variable D A=A0 ; D , where D
describes the undamaged RVE and D
the failure
due to rupture. In case of isotropic damage D is considered to be a scalar otherwise it is a tensor of second
order.
Under load F~ the undamaged RVE can endure the
stress which is to be modified in the case of dam-
=~
r
F
0
1
=0
=0
_ = @D f () d":
D
2
@"
(3)
σ
σU
is critically and irreversibly damaged. The relation between D1c and Dc is given by:
2
D1c u
D
:
Dc
(7)
f v
compression test
σf
1
()
1
D
1
D1c
2.2 Determination of material parameters
The parameters necessary to implement the model of
effective stresses into FE simulations for the calculation of ductile damage in cold metal forming have
been defined in the preceding section. According to
Figure 2 the stress at failure u , the slope of the damage variable D and the critical damage D1c can be
derived comparing tensile and compression tests.
ϕΒ pl ϕ pl
Figure 2: Evolution of the damage variable D in uniaxial tests
_
The triaxiality is defined as the ratio between the
mean normal stress m and the equivalent von Mises
stress v . Relation (3) takes into account the state of
stresses in form of the triaxiality function f . From
thermodynamic considerations Lemaitre derived in
Lem96 the following function for the triaxiality influence on the damage variable:
()
2
2
m
f ( ) = (1 + ) + 3(1 2 )
:
3
v
r
F
( ) = e ( ):
1
3
2
3
(4)
dB
ρB
ρ
d0
r
F
r
F
Figure 3: Correction function after Bridgman for
necking tensile specimen
The material dependent value of D1c is calculated
from the ratio
of
the yield stresses derived from
pl tenpl
+
sile tests kf "B and compression tests kf "B as
described in (Lemaitre 1996):
kf+ "pl
B
pl :
D1c
(8)
kf "B
Practically the value of kf+ "pl
B is difficult to obtain
as the tensile specimen tend to necking before failure
of the material is reached thus changing from the uniaxial state of stresses to a inhomogeneous one. Bridgman developed in (Bridgman 1952) a correction function for the measured value of stress in case of neck-
(5)
In simulations the sign of can be taken into account making use of the crack closure parameter h
as cracks do not close completely after they are once
initiated:
(
D if D
(6)
hD if < :
_
_
r
F
d
With entering as a quadratic term into (4) no difference is made upon the state of stresses whether it
is tension or compression. This is unfavourable as it
is known from practice that tensile loads have much
more influence on damage than compression. A more
suitable formulation for the triaxiality can be found
in (Hartley & Pillinger 1997) where the sign of is
considered:
_=
)
This equation gives the relation between the onedimensional critical damage D1c , the triaxiality function f , the damage value D and the ratio between
u and v where u is the stress at failure determined
in tensile and compression tests. Equation 7 becomes
valid only if Dc . As the scalar value D1c depends
on the material behavior it has to be determined in
tensile tests which is described in the following section.
ϕ
f (1
= ()
tensile test
σy
=1
0
0
The critical value of damage Dc for the multiaxial
state of stresses is a quantity which describes the occurrence of measurable cracks in the material. When
D reaches this value one can deduce that the material
3
ing. The uniaxial value of stress at the moment of failure is approximated using
kf+ "pl
B
'
d2
4F~ 1 + 4d 1 + 4d
(9)
where F~ is the uniaxial load, d is the smallest diameter of the specimen after necking and is the radius
of a circle adapted to the geometry as shown in Figure
3. The specimen were measured on a profile projector
after the failure thus ignoring the elastic strain which
is imposed on the material during the tensile test, too.
The value kf+ "pl
B in 8 represents the uniaxial stress
the material of the specimen can transmit at the moment of tension failure ("pl
B ) if the material would not
get ruptured. This value can be derived from a compression test using the same charge of material. In order to avoid influence of friction rastegaev specimen
were used. The diameter was identical to the original tensile specimen. The compression specimen must
pl
be compressed up to "pl
B . With kf "B being the corresponding stress the value for D1c can be achieved
from 8 and inserted into equation 7.
For the calculation of the increment of the damage
value D the slope of the damage function from Figure 2 namely @D=@" is approximated. From various
experiments Lemaitre obtained a linear relation between the increase of " and the associated variable D
(Lemaitre & Chaboche 1990). For the following let us
assume that the slope meets:
Figure 4: Prediction of the damage locus in a collar
compression test by the model of effective stresses
( )
Vallen Systems, Germany) as the first appearance and
detection of damages is more complicated than in tensile tests at which visible necking and failure coincides. The data samples obtained were then processed
with statistical classifiers build on base of known ductile damage events from tensile tests. This method is
convenient for the detection not only of the time of
the first damage but also for its locus. During the experiments all the specimen showed first signs of damage on the inner rim of the collar at an average punch
travel of : mm. However the exact location on the
collar itself is indetermined but of no significant influence on the results.
Simulations were carried out using the FE simulation software MSC.AutoFORGE on SGI workstations. After modeling the compression test the damage criterion D , the critical damage Dc and a relative damage Drel D=Dc were implemented in the
numerical simulation. The evolution of D is continuous during the simulation but the calculation of Dc
is done for every increment with values changing for
each run. Thus the relative damage is a convenient
way to describe the damage evolution in critical regions and to make the results comparable for different simulations. Based on the accumulated value of
D the effective stress as defined in eq. 1 and the modified elasticity modulus
( )
27 8
_
@D
@"
' D" = Dpl1c 0
"B
0
=
(10)
which is fulfilled if ductile damage occurs only if the
initial yield stress is exceeded. With equations 3 and 6
it is now possible to include the necessary parameters
into the FE simulation. Thus the distribution of the
critical value of damage Dc within the cross section
of the examined forging process can be established at
every increment of the simulation.
~ = E (1
E
2.3 Experimental and FE simulation results
To verify the applicability of the model of effective
stresses practical experiments with tensile and compression test were performed and compared with FE
simulations. The experiments included simple tensile
tests on several steels and compression test with special collar specimen (Fig. 4). The latter ones were designed to produce visible damages on the collar itself
during the experiments which were carried out on a
hydraulic press. In the following only the results from
the compression tests are presented because the tensile tests lead to similar trends.
The identification of damage in a compression test
was done by an ultrasonic material tester (AMSY 4,
D
) = "el
(11)
are calculated in each increment to impose the effect
of damage on the material.
The software used has the capability of automatic
remeshing during the simulation. In the case of distorted or collapsed elements the old mesh is replaced
by a new one transferring the calculated values without user intervention. The benefit of this operation is
obvious as large plastic strains and deformations can
be simulated. Detrimental is that the transferred values are interpolated between the old nodes and integration points to match the new geometry. This influences especially the damage D and more the critical
damage Dc which is known to be highly localized.
4
It could have been observed through all simulations
with a high number of remeshing operations that the
moment of failure is thus predicted slightly too late.
The results of the simulation shown on the right
side of Figure 4 coincide exactly with the experiments
regarding the damage locus on the inner collar rim.
The maximum of the relative damage is located at
the same position where the first visible material failure was observed. At this point the relative damage
Drel has a value of : which corresponds to a punch
travel of : mm. In contrast the calculated value for
coincides with a punch
the critical damage of Drel
travel of : mm.
The exact moment of failure is therefore slightly
underestimated by this model because the theoretical value of failure should have been (Fig. 5). As
mentioned above this happens because of the high
number of 22 remeshing operations in the collar compression test. Moreover the exact value is strongly dependent on the shape of the triaxiality function. The
formulation by Hartley (eq. 5) performs better than
the Lemaitre one (eq. 4) as the exponential function
climbs steeper for higher values of . In Figure 5 the
27 8
28 5
updated Lagrangian approach. MSC.Marc is a leading general purpose program for nonlinear FE analysis. Both programs allow the graphical generation
of the geometrical model and the mesh structure as
well as all other necessary parameters for the simulation. More the evaluation of the simulation results
can easy be done with the graphical post-processor.
MSC.AutoFORGE allows the use of an elastic-plastic
material law with mechanical-thermical coupling. It
is possible to model two-dimensional and threedimensional problems with a variety of element types.
0 85
=1
To show the effectiveness of MSC.AutoFORGE
and the proposed model of effective stresses in the
prediction of material failure two examples are given
for two-dimensional FE simulations and one threedimensional analysis. The model of effective stresses
was integrated in the simulations to predict ductile
damage in the materials used and to improve the processes by varying the production stages. This is done
in a user defined subroutine which is compiled and
linked to the solver program at runtime. At each integration point of the elements chosen the values D ,
Dcrit and Drel are evaluated and transferred to the solution file. The values for D are summed over time
thus the transfer between the computation increments
has to be performed especially in the case of rezoning operations. MSC.AutoFORGE allows the use of
user definable variables called State Variables which
are transferred correctly in a rezoning where element
and nodal relationships are changed to generate a better mesh. It has to be noticed here that the transfer
of the values from on mesh to another one is linked
with problems. The values on the integration points
of the new elements are interpolated from the preceding one thus the regarded values are smoothed in
a non-predictable way. The smoothing operation depends largely on the size of the elements and can
be influenced positively by using a relatively small
grid. Not only with three-dimensional meshes this can
rapidly lead to a large number of elements with the
consequence of highly increasing computational cost.
Regarding the location of the values there is another
problem directly combined with the evaluation of the
damage variable D . It is necessary to predict the moment of material failure and the location exactly in
order to make use of the model of effective stresses in
real applications. The interpolation between rezoning
operations also changes the location of the original integration points of the interesting damaged elements.
This is critical in case of large plastic deformation.
1
Figure 5: Evolution of the damage variable D at the
locus of failure on a collar specimen rim
FE-calculated evolution of the damage value D , the
critical damage Dc and the adjoint relative damage
Drel is demonstrated. The critical damage starts with
high values because of f being very low. It decreases within the experiment until the damage on the
inner collar rim occurs. Ensuring the numerical stability of the simulations the maximum value for D is
fixed to : which marks material failure.
()
0 95
3 FE simulations of industrial cold forging processes
FE simulations were carried out using the FE simulation program MSC.AutoFORGE 2.3. The program
is a derivative of MSC.Marc K 7 specially created
for the simulation of forging operations based on an
The two-dimensional simulations given in the subsequent sections 3.1 and 3.2 are similar in the modeling of the problem. As these two processes are axisymmetric a two-dimensional mesh representation is
possible which inherently adds the third dimension
of the model. For the two-dimensional simulations
5
axisymmetrical isoparametrical four node elements
(also called quadrilateral) are taken for the description of the workpiece. The three-dimensional mesh
consists of isoparamtrical eight node hexahedral elements. The use of quadrilateral and hexahedral elements is indicated here as they show better performance regarding stiffness (Kraft & Pfeufer 1997),
number of elements for the definition of a geometric structure and computational cost than tetrahedral
elements do (Lee & Yang 1996). Moreover the localized stress and strain behavior is represented more
precisely (Tekkaya 1997).
The program MSC.AutoFORGE is able to perform
automatic remeshing operations in the case of distorted elements and tool penetration. The newest version of the remeshing tool allows the definition of refining boxes in interesting areas of the mesh thus the
number of elements in whole can be kept small while
critical regions are highly detailed. This was not possible yet but for the three-dimensional remeshing tool
only. In how far the benefit from this feature influences the results of the simulations regarding the damage values must be left for future work.
The necessary tools are assumed rigid with infinite
elasticity modulus, constant heat transfer and a constant temperature of Æ C. The true material flow is
only slightly influenced by this assumption as well as
the material failure itself. It must be taken into account that an elastic formulation of the tool’s behavior is possible but to very high computational cost
especially regarding three-dimensional simulations.
Moreover the model of effective stresses is not influenced by thermal effects which is left to further research. Therefore heat effects play a minor role in the
direct evaluation of the damage.
The material parameters as poisson ratio, heat conductivity and others are taken from literature whereas
the stress strain behavior had to be determined from
bulk compression tests with material of the same
charge. This was necessary as the material data base
of MSC.AutoFORGE is taken from literature and differs to much from the experimental values. This is one
of the greatest problems in FE simulations as slight
modifications of the material values have great influence on the results especially on the damage evaluation.
For all simulations the shear friction model is used
with a shear friction factor of m
: that has shown
good results in the correct representation of the material behavior (Schafstall 1998).
A great advantage of MSC.AutoFORGE is the
predefined database of forging machines like crank
presses, hydraulic stage presses and others. This allows a simple implementation of the machine behavior into the simulations without the necessity of defining complex loadcases. Moreover the different forg-
Figure 6: Two alternative production sequences of a
pinion gear shaft
ing stages as there are workpiece positioning, initial
contact between tools and workpiece, the deformation
sequence and the release procedure are comfortably
influenced.
20
3.1 Surface fissures at a pinion gear shaft
In this section two alternative deformation stages are
investigated for the cold forging of a pinion gear shaft
made of 16MnC5 (AISI 5115) steel in a combined
four stages forging process. The two alternatives are
shown in Figure 6. The upper production sequence
was designed in a more traditional way as each sequence is performed on a separate hydraulic press
whereas the second variant could be carried out on a
modern transfer press. In brief the first sequence consists of the following steps: A combined full forward
cup backward extrusion process in the first stage followed by a reduction of the shaft diameter. In the third
stage a hocker forward extrusion process for wall reduction is applied closed by a lateral extrusion of
the flange for the gear. Due to the high straining of
the material an annealing operation could be thinkable after the end of Stage 3 to avoid material failure.
The assumption for the simulation then was setting
all stresses and strains equal to zero. The sequence
has been moderated in order to reduce material failure due to ductile damage which showed mainly at the
bottom of the cup caused by the limited formability of
16MnCr5 at room temperature. The second stage begins with a full forward extrusion process followed
by a lateral extrusion of the head and goes on with a
cup backward extrusion and calibration of the flange
in stages three and four. The results of the simulations are shown in Figure 7 for both processes. Here
the value of the relative damage from section 2.1 is
= 0 15
6
Figure 7: Damage evolution in the alternative production sequences of a pinion gear shaft
plotted in the range from 0 to 1. The value of Dc is
exceeded in the first sequence at the locus of real damage. However the damage is very localized here which
is due to several remeshing operations. Normally the
transition between adjacent elements is smoother.
The relative damage evolution for the second sequence proofs the suitability of the modifications of
the process itself as the accumulated damage is much
lower than for the first alternative. Thus even without the suggested inter annealing operation the probability of material failure due to ductile damage is reduced. This is also confirmed by the industrial experiences.
Figure 8: Chevron evolution due to exceeded critical
damage Dc in a conical gear wheel
with the real appearance of chevrons. Drel does not
reach the desired value of which is for two reasons:
the remeshing operation of the simulation software
has a smoothing effect to these values and in real production sequences only
of the wheels are scrap.
Yet this demands an extensively
control.
1
5%
100%
3.3 Rupture at the periphery of a screw head
The last example describes the prediction of ductile
damage with the model of effective stresses in case of
three dimensional material flow and the corresponding three dimensional simulation. The finished unit
here is a hexagon socket screw cold formed in a two
stage process consisting of a full forward extrusion in
the first stage and a combined full forward / transverse
impact followed by a cup backward extrusion process in the second stage (Fig. 10). The first stage can
be simulated like the two former examples as an axisymmetrical model reducing time and computational
cost. The construction of the hexahedral grid, necessary for the three dimensional simulation of penetration of the non axisymmetric die at the second stage,
will be performed by a step-wise rotational propagation of the original four node grid structure after a preceding remeshing operation. After that the mesh values will be transformed to the hexahedral grid. The
socket’s symmetry lies on a cutout of each Æ in sequence with respect to the horizontal axis shown in
below of Figure 10. For reasons of numerical stability
the simulation is based on a Æ cutout as with lower
angles the hexahedral elements at the inner symmetry
tend to rapid distortion.
In Figure 9 the evolution of the relative damage
3.2 Detection of chevrons at a conical gear wheel
A special category of ductile damage are chevrons
which can appear during multiple full forward extrusion or drawing processes. Chevrons are characterized by gaps in the material flow in the middle
of the workpiece thus leading to cavities in form of
arrows. This kind of damage therefore is critical because it cannot be detected only by full ultrasonic testing which leads to high production costs. In Figure 8
the evolution of the relative damage Drel is shown for
the cold forming operation of a conical gear wheel
made of 20MnCr5 steel. In the first stage a full forward extrusion process forms the first shaft of the
wheel which is reduced twice in the second stage. The
third stage again is a full forward extrusion process
for the further reduction of the shaft combined with
the forming of the gear wheel. The fourth stage consists of calibration of the head and reduction of the
end of the shaft.
Ductile damage could appear already in the third
stage as the relative damage value Dc is nearby : .
This grows in the fourth stage up to a value of : .
The locus and time of the damage variable coincides
30
60
07
0 81
7
pression tests in combination with ultrasonic testing.
The experimental and simulation results of a collar
specimen compression test were demonstrated in this
article proofing the applicability of the model of effective stresses for the prediction of material failure.
Three industrial cold forging sequences are given then
as examples for the suitability of this model in real
application. Two sequences were modeled as axisymmetrical processes while the third example showed
the three dimensional capability of the model of effective stresses as well.
Future work will focus on the implementation of
anisotropic material behavior and the thermal effects
resulting from ductile damage in cold metal forming.
60
Figure 9: Damage evolution on a Æ cutout of a
hexagon socket screw in the second forming stage
REFERENCES
Bridgman, P. W. 1952. Studies in Large Plastic Flow and
Fracture. McGraw-Hill Book Company, Inc.
Dahl, W., R. K. & Pawelski, O. 1993. Umformtechnik
Plastomechanik und Werkstoffkunde. Duesseldorf: Verlag Stahleisen mbH.
Groche, P. 1991. Bruchkriterien fuer die Blechumformung.
Diss. Dr.-Ing. Universitaet Hannover, Volume 229 of
Fortschr.-Ber. VDI Reihe 2. VDI-Verlag Duesseldorf.
Hartley, P., F. R. H. & Pillinger, I. 1997. Elastic-Plastic
Finite-Element Modelling of Metal Forming with Damage Evolution. Advanced Methods in Materials Processing Defects, p.135-142. Predeleanu M. and Gilormini,
P., Elsevier Press.
Kachanov, L. M. 1986. Introduction to Continuum Damage Mechanics. Dordrecht, Boston, Lancaster: Martinus
Nijhoff Publishers.
Kraft, P. & Pfeufer, P. 1997. Juengste Entwicklungen im
Bereich Hexaeder-Vernetzer fr den vollautomatischen
Einsatz in der Simulationspraxis. XXIV. FEM-Kongress
in Baden-Baden 17.-18. Nov., S. 19 - 28.
Lee, Y. K. & Yang, D. 1996. A New Automatic Mesh Generation Technique and its Application to the Finite Element Analysis of Practical Forging Processes. Proceedings of the 5th ICTP. Columbus, Ohio, USA.
Lemaitre, J. 1996. A Course on Damage Mechanics (2nd
ed.). Berlin, Heidelberg, New York: Springer Verlag.
Lemaitre, J. & Chaboche, J.-L. 1990. Mechanics of Solid
Materials. New York, New Rochelle, Melbourne: Cambridge University Press.
Schafstall, H. 1998. Verbesserung der Simulationsgenauigkeit ausgewaehlter Massivumformverfahren durch
eine adaptive Reibwertvorgabe. Universitaet der Bundeswehr Hamburg.
Seidenfuss, M. 1992. Untersuchungen zur Beschreibung des Versagensverhaltens mit Hilfe von Schaedigungsmodellen am Beispiel des Werkstoffes 20 MnMoNi 5. Techn.-wiss. Ber. MPA Stuttgart. Universitaet
Stuttgart.
Tekkaya, A. E. 1997, Juni. Dreidimensionale Simulation von Massivumformvorgngen. Symposium: Neuere
Entwicklungen in der Massivumformung, S. 389-411.
Stuttgart.
Figure 10: Production sequence of a hexagon socket
screw
on the periphery of the screw head is clearly visible. The exact locus on the periphery is indetermined
what was to be expected due to the isotropic material
model. The relative damage Drel reaches a value of
only : . This is caused on one hand by the smoothing effect of the remeshing operations. On the other
hand the real scrap of this workpiece is below
so
that this value of Drel could be the permissible border in case of crack prediction by FE simulation concerning three dimensional workpieces. Yet this border value depends much on the workpiece shape and
the ductility of the elected material. Nevertheless the
tools shape and the workpiece itself was slightly reconstructed due to these simulation results in order to
inspection.
avoid
0 75
1%
100%
4 Conclusion
In this article the model of effective stresses by
Kachanov et.al. was chosen from various criteria for
the prediction of ductile damage failure of materials
in cold forging operations to be implemented in FE
simulations with MSC.AutoFORGE. The model was
first described and verified by simple tensile and com8