Near Net Shape Manufacturing of CuCr Vacuum Switching Contacts ...

Feist, Oberbreyer et al. 17th Plansee Seminar 2009, Vol. 3 WS 15/1
Near Net Shape Manufacturing of CuCr Vacuum Switching Contacts
Abstract
without Prototyping
C. Feist*, R. Oberbreyer**, A. Plankensteiner***, R. Grill***,
A. Schwaiger****, M. Hochstrasser****, F.E.H. Müller****
* CENUMERICS, Austria
** Plansee Metall GmbH, Austria
*** Plansee SE, Austria
**** Plansee Powertech AG, Switzerland
Within the framework of classical powder metallurgy (PM) industrial parts are formed from metallic powders
in a mainly two-stage process consisting of die-compaction and sintering. Sintering causes the transformation
of porous green compacts into almost fully dense metallic components. The accompanying
shrinkage primarily depends on the green density and thus can lead to considerable distortions if the latter
is significantly inhomogeneous. As a consequence extensive mechanical treatment has to be applied
in order to obtain the desired geometrical shape. In the framework of near net shape (NNS) manufacturing
the classical PM process is designed such that mechanical treatment is minimized or even made obsolete.
The demanding task of designing a NNS process can be efficiently assisted by the tools offered by
numerical simulation allowing to minimize prototyping.
The present paper presents a mathematical model of the combined compaction and sintering process
based on the concepts of continuum mechanics and solved numerically by means of the finite element
method (FEM). To this end, appropriate constitutive models for both process stages are employed. Identification
of the relevant constitutive parameters in the context of powder characterization is outlined. Appropriate
initial guesses for the relevant process parameters are found by means of a simple analytical
procedure based on a strategy stepping-back from the desired final geometry to an approximate required
fill geometry. Application of the presented model in the framework of a true 3D-analysis is shown by means
of the design of a switching contact made of CuCr alloy.
Keywords
near net shape, NNS, finite element method, FEM, powder compaction, sintering, switching contact, CuCr
Introduction
In power station technology demands still exist for even more economical ways of generating electric current.
Power system providers draw particular attention to technologically reliable and durable switching
systems which can be securely operated under severe operational conditions. The contact components

WS 15/2 17th Plansee Seminar 2009, Vol. 3 Feist, Oberbreyer et al.
form the main part of breaking chambers and high performance materials have to be specifically developed
for the use of these components in vacuum and arcing contact systems.
Over the past two decades CuCr based contact materials have become established for use with contactors
and circuit breakers, respectively, in vacuum interrupters for the medium voltage range of 1 kV to
72.5 kV. Generally speaking CuCr contact materials provide a combination of high current breaking capacity,
dielectric strength of the open contact gap and long service life-time of up to 10,000 operations at
the rated current.
Depending on the application field of the CuCr contact component the Cr content typically varies between
about 20 wt.% and 60 wt.% with the lower range applying to operational conditions where high arc quenching
and low current chopping play a significant role and the higher range applying where high erosion resistance
as well as a proper welding behavior come into focus. Beside the choice for an adequate CuCr
grade the geometrical features of the contact component also play a significant role on the performance
during switching operations.
CuCr contact components are manufactured via a powder metallurgical processing route which includes
mixing of the Cu and Cr powders, die compaction of the powder blend to a green body and sintering typically
below the melting point of copper. After sintering CuCr contact materials may exhibit a small amount
of retained porosity. By further reduction of porosity after sintering, i.e. by repressing, the electrical, thermal,
and mechanical properties of the contact material can be improved. A principal description of the
influence of the Cr content on the microstructure of the CuCr material and its implications on the operational
behavior of the contact component can be found in [1].
Within the classical powder metallurgical manufacturing approach of die compaction and sintering shape
chipping and other types of mechanical treatment cannot be avoided in order to get the desired final shape
of the contact component. This is mainly due to an inhomogeneous spatial density distribution in the diepressed
green body which governs the spatial gradient in sinter density. This way sinter shrinkage along
with sinter distortions have to be handled properly when defining the design of pressing tools and pressing
kinematics. Because of an a priori unknown functional dependence between final shape/dimensions
of the sintered body, ingoing powder material characteristics and the die compaction/sinter process parameters,
respectively, an iterative strategy has to be applied in practice covering materials development,
design of processing, and performance of field tests. As long as mechanical treatment of the contact
component is chosen for obtaining the final shape of the component empirical knowledge on the interaction
between material characteristics, process parameters, and the quality relevant parameters of the
sintered product is widely being proofed to be sufficient for a successful product development. However,
economically more challenging tasks such as minimization or even complete prevention of material to be
machined off aim at reducing material and manufacturing costs as well as optimizing the time-to-market
characteristics. Commonly such strategies are referred to as near net shape manufacturing (NNS) which
typically make use of advanced tools for numerical simulation of the NNS process chain and advanced
material characterization methods. Whereas the latter are intended for extracting material parameters for
the material laws describing the constitutive behavior of powder materials and sintered materials under
die-pressing and sintering operations, respectively, the numerical simulation tools are intended for performing
efficiently numerical experiments of the NNS process chain aiming at reducing overall costs in
establishing an experimentally and numerically verified prototype for the NNS process chain.

Feist, Oberbreyer et al. 17th Plansee Seminar 2009, Vol. 3 WS 15/3
Finite element modeling of PM process-chain
The numerical simulation of the PM process-chain is based on the finite element method (FEM) and the
concepts of continuum mechanics. To this end all powder-material forming the designed part is modeled
as a continuous domain through the entire process-chain starting from the beginning of powdercompaction
till the end of sintering. Furthermore the simulation relies on a phenomenological description
of the material response (constitutive modeling) with respect both to compaction and sintering.
The simulation primarily aims at predicting the deformation-state u(x) of this domain at any stage as well
as its density-distribution ρ(x). In addition, the stress-state σ(x) found in the powder-domain can be assessed
in order to detect critical states during the compaction and ejection phase.
FE-analyses of the process-chain start with compaction of the powder-domain. This implies that the fillstate
described by the geometry of the fill-body and the fill-density distribution have to be explicitly given
for the analysis. Procedures to implicitly obtain the fill state based on simulation can be found e.g. in the
framework of discrete element method (DEM) [2], which is not covered within the present work.
Numerical modeling of the PM process-chain requires two principal analysis-steps: (i) analysis of powder
compaction and ejection of the green-compact and (ii) analysis of sintering of the green-compact. The
provided basic distinction is necessary since the driving mechanisms are different in both stages. In order
to provide a continuous work-flow, results obtained from the first analysis step (in terms of the deformed
geometry and the corresponding green density distribution ρg(x)) are imported as an initial state for the
second analysis step.
Analysis of powder compaction and ejection also requires a mathematical representation of the employed
tools. The latter are usually considered as rigid surface representations of the tools’ surfaces in contact to
the powder.
Constitutive modeling of powder-compaction
The nonlinear mechanical behavior of granular materials under predominantly triaxial compressive stress
states can be described in a phenomenological manner employing a cap-model formulated in the framework
of theory of plasticity [3]. Its cap-shaped yield surface is formulated in the hydrostatic-deviatoric
stress-space p - q with p = − 1
3
tr(σ) as the hydrostatic stress (i.e. the first invariant of stress tensor σ)
and q = � 3/2 s : s as the VON MISES equivalent stress (i.e. the second invariant of stress tensor σ with
s denoting the deviatoric stress tensor). As usual in mechanics of soils and other granular materials, the
hydrostatic pressure stress is considered as positive for compressive stress states.
The elliptical cap-surface fc (Fig. 1a) is formally given as
fc = � (p − pa) 2 + (R q) 2 − R qa
where pa and qa denote the hydrostatic pressure and the VON MISES equivalent stress, respectively, associated
to the center and the apex of the elliptical cap and R defines the eccentricity of the cap. The intercept
of the cap-surface with the hydrostatic pressure axis is then given as
(1)
pb = pa + R qa. (2)
The cap surface limits compressive stress-states with high values of triaxiality p/q as found especially for

WS 15/4 17th Plansee Seminar 2009, Vol. 3 Feist, Oberbreyer et al.
q
Drucker-Prager
shear-failure surface
d
1
tan β
elastic domain (E, )
p a
elliptical cap-surface
p b
R (d + p a tan ß)
p
q a = d + p a tanß
(a) (b)
Figure 1: Combined DRUCKER-PRAGER-cap plasticity model: (a) yield surface in the hydrostatic-deviatoric stress-space, (b) evolution
of the yield surface with respect to density.
compaction processes as die compaction. However, the cap surface is not suited for describing the response
under stress-states with lower values of triaxiality. Such stress states take place in the green compact
especially during the ejection phase but might occur also during compaction with more complex toolgeometries.
Such stress states might lead to the formation of discontinuities and cracks in the powderbody
being compacted and hence should be avoided. Thus, for the simulation of the compaction process
it is desirable to be able to assess such stress-states in order to identify critical regions or process stages.
To account for respective stress states the cap-surface is combined with a shear-failure surface fs. In the
most simple case the well-known cone-shaped DRUCKER-PRAGER yield-surface (Fig. 1a) given as
q
¡0
p ¡ ¡
fs = q − p tanβ − d (3)
can be used with d and β as the cohesive strength and the angle of internal friction of the material, respectively.
With fc and fs considered to intersect at pa, ellipse-axis qa in (1) can be expressed as
qa = d + pa tanβ. (4)
It has to be noted that the employed shear-failure surface represents a valid representation of the mechanical
response only for stress states with positive triaxiality values. However, it does not properly account
for three-dimensional tensile stress states which is out of scope of the employed model in the context
of powder compaction.
With respect to the hardening law it is assumed that the cap-surface fc exhibits hardening representing
the behavior of the metallic powder under hydrostatic compression. To this end, the cap-apex value pb (2)
is related to the logarithmic volumetric strain
εv = ε el
v + ε pl
v
consisting of a (reversible) elastic part ε el
v and a (irreversible) plastic part ε pl
v . The total volumetric strain εv
in turn can be expressed in terms of the current material density ρ as
� �
ρ
εv = ln
ρ0
(5)
(6)
¡th

Feist, Oberbreyer et al. 17th Plansee Seminar 2009, Vol. 3 WS 15/5
with ρ0 as the reference density of the material (i.e. the density of the powder in loose packing). Since the
contribution of the elastic part in (5) is of a few orders less than the one from the plastic part, in general it
can be neglected, such that
Hardening of the cap-surface can then be formally defined as
� �
ρ
εv = ln ≈ ε
ρ0
pl
v . (7)
pb = fh (εv) (8)
where fh represents a C 1 -continuous, monotonously increasing hardening function appropriate for describing
the compaction behavior of the powder under consideration. In general, power or exponential
type functions can be successfully employed.
It can be seen from experiments that the cap-surface will not keep its shape under compressive loading,
such that the cap-eccentricity parameter R in (1) also has to be made dependent on the volumetric strain.
Furthermore, compaction of granular material is accompanied by a significant increase in the strength of
the material defined by the shear-failure parameters d and β in (3). Hence, parameters R, d and β are
formally related to the volumetric strain and the density of the material as
R = fR (εv)
d = fd (εv)
β = fβ (εv). (9)
Appropriate evolution functions must be chosen and their coefficients adapted in order to fit experimental
results for the particular powder under consideration. The evolution of the combined DRUCKER-PRAGERcap
surface based on evolution-equations (8) and (9) are shown for an exemplary powder in Fig. 1b.
Together, the convex cap-surface fc = 0 and the shear-failure surface fs = 0 confine the elastic domain
(Fig. 1a). For stress-states within this domain isotropic elastic behavior expressed by the constants
of elasticity E and ν is assumed to be valid. In order to be able to numerically capture the elastic springback
taking place during the ejection phase of a green compact it is also necessary to describe the densitydependence
of the modulus of elasticity E again formally expressed in terms of the volumetric strain as
Constitutive modeling of sintering
E = fE (εv). (10)
Sintering is a heat-treatment process conducted at high-temperatures that causes the powder-particles
within the porous green compact to be bonded together. Since the volume of the pores between the powder-particles
is reduced during this process, the material shrinks and consequently its density is increased.
A constitutive model describing the mechanical behavior of a solid being sintered for usage in the context
of simulations of the PM process-chain must be able to reproduce both evolution of density and shrinkage
as shown for two different CuCr-alloys by results from sintering experiments in Fig. 2. Hence, it is
sufficient to again resort to a purely phenomenological model, which however is derived from a micromechanical
description of inter-particle interactions [4, 5].

WS 15/6 17th Plansee Seminar 2009, Vol. 3 Feist, Oberbreyer et al.
sinter density £s [g/cm³]
8.5
8.0
7.5
7.0
6.5
6.0
5.5
¢th CuCr alloy 1
¢th CuCr alloy 2
CuCr alloy 1
CuCr alloy 2
lin. regr. CuCr alloy 1
lin. regr. CuCr alloy 2
5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
¢g green density [g/cm³]
axial shrinkage ¤z [%]
5.0
4.0
3.0
2.0
1.0
0.0
5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
¢g green density [g/cm³]
5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
¢g green density [g/cm³]
(a) (b) (c)
Figure 2: Results obtained from sintering experiments for two types of CuCr alloy – green-density (ρg) dependence of (a) sinter
density ρs, (b) axial sinter shrinkage εz and (c) radial sinter shrinkage εr.
An appropriate constitutive model can be found in the framework of the theory of visco-elasticity formulated
for the sintering behavior as
˙ε = S (σ − Iσs), (11)
where the strain-rate tensor ˙ε is related to the stress tensor σ and the sintering stress σs using the inverse
viscosity tensor S.
In the general form of (11) the inverse viscosity tensor can represent isotropic as well as general anisotropic
behavior. For isotropic behavior the inverse viscosity tensor can be formulated in terms of the bulk
and shear viscosities K = f(ρ) and G = f(ρ), for which micro-mechanical relationships have been
derived [4]. For the CuCr powders under consideration in the present work, a more or less significant
anisotropy (transversal isotropy to be more precise) can be observed (Fig. 2b and c): isotropic behavior
can be found within the plane normal to the compaction-axis, whereas sintering strains in the compactionaxis
are significantly different. In the general case of anisotropic behavior the components of the viscosity
– as found from the micro-mechanically derived bulk
and shear viscosities K and G – using the viscosity ratio [6]
tensor Sij can be related to the isotropic term S iso
ij
ϕij = Sij
radial shrinkage ¤r [%]
5.0
4.0
3.0
2.0
1.0
0.0
Siso. (12)
The viscosity ratios in general will evolve during the sintering process [6]. As observed from sintering experiments
the ratio of anisotropy obviously depends on the green density (i.e. the initial density of the sintering
process). Hence, the viscosity ratios depend both on the initial density (i.e. green density) ρ0 = ρg
and the current density ρ and formally are given as
ij
ϕij = fϕ (ρ0, ρ). (13)
From sintering experiments one can determine the density ρs attainable through sintering for which
ρg < ρs = f(ρg) < ρth
(14)

Feist, Oberbreyer et al. 17th Plansee Seminar 2009, Vol. 3 WS 15/7
holds with ρth as the theoretical density of the (pore-free) solid material and the sinter density depending
on the green density ρg. Hence, it is convenient to relate all density measures used in the evolution
equations of the viscosities and viscosity ratios to the current relative density with respect to the attainable
sinter density d = ρ/ρs.
The evolution equations both of the isotropic components of the inverse viscosity tensor S iso
ij (expressed
in terms of the bulk and shear viscosities K and G) and the viscosity ratios are now formulated in terms of
the relative density serving as an internal variable for the model. Under the assumption of mass-conser-
vation its evolution is given as
˙
d = −d tr (˙ε). (15)
with d = 1 indicating a fully sintered state (equivalent to reaching the attainable sinter density ρs).
Powder-characterization, tests and calibration
A prerequisite for successful FE analyses of PM processes based on the described mathematical model
is the identification of the involved constitutive parameters and their dependence on the density of the
powder. This identification – termed as powder-characterization – is usually done on an experimental
basis and will be outlined in the following by means of the constitutive parameters required for the compaction
analysis.
For the mechanical description of die-compaction it is most important to have reliable experimental data
describing the relationship between the uniaxial compaction stress σz and the green density ρg or the
volumetric plastic strain εv, respectively. These data can be obtained from rather simple die-compaction
experiments on small cylindrical samples (Fig. 3a, (1)). The stress state during die-compaction exhibits
high triaxialities, and hence will lie on the cap-surface, however considerably off the p-axis. From the obtained
relationship together with the imposed geometrical requirement that the cap- and the shear-failure
surface (to be determined later) will intersect at pa (Fig. 1a) one can determine the associated relationship
between the cap-apex pb and the volumetric plastic strain εv (i.e. the hardening relationship of the
cap-surface) as (8). A more accurate alternative for compaction processes with triaxialities p/q → ∞ can
be found by conducting triaxial compaction tests (Fig. 3a, (2)) with p/q = ∞, which directly provide the
hardening relationship (8).
For reliable results of the ejection-phase and stress-states at critical regions in the powder-domain during
compaction it is crucial to be able to predict the onset of failure by means of the shear-failure surface
fs (3). For a certain density state it is described by the cohesive strength d and the angle of internal friction
β (Fig. 3a). In order to identify these parameters at least two types of experiments at different levels
of triaxiality have to be conducted [3]: to this end, most often the brazilian disc test (Fig. 3a, (3)) and the
uniaxial compression test (Fig. 3a, (4)) are employed. These tests are conducted again on small cylindrical
samples previously compacted to approximately the same density. The stress states found in the
specimens can be calculated analytically from the applied load. Hence, from the maximum applicable
load at incipient failure of the samples one can easily determine the stress-invariants pf and qf associated
to the failure-state. Consequently, the stress-point pf, qf is located on the shear-failure surface fs
(Fig. 3a) (Remarks: It is assumed that no significant strain-hardening precedes failure of the sample and
that only detection of incipient failure but not resolution of its propagation is to be covered which in turn
justifies the assumption of perfect plasticity for the shear-failure surface.). From the failure stress-states
obtained from the employed tests one can derive the shear-failure surface as a linear regression defined
by the cohesive strength d and the angle of internal friction β. If an additional type of experiment at a dif-

WS 15/8 17th Plansee Seminar 2009, Vol. 3 Feist, Oberbreyer et al.
(5)
q
(3)
d
(4)
tan β
1
p a
ferent level of triaxiality is used (e.g. a four-point bending test, Fig. 3a, (5)) determination of the strength
parameters becomes over-determine which can help reducing potential errors by means of least-squareroot
minimization. Alternatively, a higher order shear-failure surface could be determined from these test.
¥
p b
(1)
p
(2)
d
d 2
d 3
d1 ¥0
¥2
¥3¥th
(a) (b)
Figure 3: Mechanical powder-characterization: (a) experimental determination of cap- and shear-failure surface parameters,
(b) density dependence of cohesive strength d.
The obtained shear-failure surface (in terms of d and β) is only valid for the given density-level ρ1 (Fig. 3).
In order to determine the density-dependence of the strength parameters similar tests must be conducted
at various other density levels ρ2, ρ3 . . . (Fig. 3b) relevant for PM production purposes. The obtained discrete
values d1, d2 . . . and β1, β2 . . . for simulation purposes will be fitted using an appropriate regressionfunction
(9b, c) (see Fig. 3b in case of cohesion d), which will be used to interpolate or extrapolate the
strength parameters at any density ρ.
Analytical assessment of PM-processed parts
When designing the process-plan for a component to be produced on the PM manufacturing route the
designer is mainly confronted with the question on how to arrive at the final nominal geometry. In particular
he has to determine all relevant process-parameters like the geometry of the die, the fill-height of
the powder-body, the required powder mass, the tools, their travel during compaction, the remaining axial
force during ejection etc. This in most of the cases is done on a combined basis of experience and trialand-error
approaches.
In this respect, finite element analyses based on the described mathematical model can only help in accelerating
the iterative trial-and-error procedure by virtually conducting the required experiments. However,
also for the numerical simulations the process-parameters as given above have to be explicitly estimated
or prescribed, respectively. This follows from the fact that the described mathematical model exactly
represents the manufacturing process and follows the direction of its work-flow.
In this context it is desirable to obtain appropriate initial estimates for the process-parameters serving as
a valid initial guess for numerically simulated or experimentally conducted process-experiments. These
initial estimates in principle should be obtained by starting from the nominal geometry of the component
and stepping the entire process-chain right back to the fill-state. Through the irreversible character of the
mathematical relationships employed for describing the constitutive state both in the compaction and sintering
step, this however is only possible for very simple geometries based on analytical solutions under
some assumptions:

Feist, Oberbreyer et al. 17th Plansee Seminar 2009, Vol. 3 WS 15/9
To this end, it is assumed that the density is homogeneous across the entire domain at any process-time.
Since any friction taking place between the tools and the powder will preclude this assumption to hold, a
frictionless state µ = 0 is assumed. Furthermore, it is assumed that the considered part will not change
its topology during the entire process – however, it can change its size and its proportions (e.g. a cylindrical
part will remain cylindrical, however, with changing diameter d and height h and changing ratio d/h).
Under this assumption one can easily derive a step-back procedure as outlined below for geometric primitives
as cubes, cones or cylinders. More complex geometries can be assembled from these primitives
allowing the determination of initial guesses for process-parameters also for industrial components.
For the sake of simplicity, the further outline is done by means of a single cylindrical part. The procedure
starts by defining the nominal geometry of the part at the end of sintering given by its diameter ds and
height hs, hence determining its volume Vs. In addition an approximate fill density ρf and a desired green
density ρg have to be assumed – on the basis of the chosen green density the required axial compactionload
Fz can be determined later and compared to the specifications of the press available for production.
Hence, the chosen green density will become an adaptable parameter for the design. On basis of the selected
green density the attainable sinter density ρs can be computed together with the radial and axial
sinter strains εr and εz (cf. Fig. 2). Using the computed sinter density ρs and the given volume Vs one can
determine the total mass m of the part. By reversely applying the sinter strains to the final geometry the
geometrical parameters at the start of the sintering phase (i.e. the green state) dg and hg can be found.
For the given green density ρg and the associated volumetric plastic strain εv (5) all constitutive parameters
of the cap-plasticity model can be computed employing their evolution equations (8), (9) and (10).
Hence, the constitutive state at the end of the compaction phase is fully given and the associated stress
state in terms of the axial and radial stress σz and σr can be computed. Using the diameter of the green
compact dg the maximum axial load Fz required for compaction can be found and compared to the load
available with the press used within the later production.
Using this stress state the radial and axial elastic deformations during the ejection-phase can be esti-
mated in terms of the radial and axial elastic strains ε el
r and ε el
z using the density-dependent Young’s modulus
(10). By reversely applying these strains on the green-compact geometry one arrives at the height hp
and diameter dp of the powder-domain in the compacted state associated to the maximum compactionload.
Diameter dp now must equal the diameter of the used die and consequently the diameter of the fillbody
df .
Postulating conservation of powder-mass m the fill volume Vf can be computed using fill-body diameter
df and consequently its fill-height hf .
Summarizing the outlined procedure it allows to determine appropriate initial estimates for the relevant
process-parameters in the following principle
given : ds, hs
estimate : ρf, ρg
determine : ρs, m, dg, hg, df, hf, Fz
One of the most critical phases of the process-chain is certainly the ejection stage, where the compact radially
constrained by the die is gradually turned to an unconstrained state. It is a common procedure to either
keep a fixed residual axial load on the punches during ejection (load-control) or to keep the distance
between the lower and upper punches fixed (displacement-control). Selecting an appropriate level of the
associated process-parameters is a crucial feature for successful ejection: the application of a residual
(16)

WS 15/10 17th Plansee Seminar 2009, Vol. 3 Feist, Oberbreyer et al.
load will move the stress-state from the regime of high triaxialities to low ones, hence risking possible
failure with stress states moving towards the shear-failure surface (3). In this context the given analytical
procedure can also help to give estimates for the maximum applicable residual load based on the stress
state due to the residual load and the density-dependent strength parameters d and β (3).
Application of numerical model to CuCr switching contacts
Application of the mathematical model for the NNS PM process-chain as described in the previous sections
will be shown in the following by means of a switching contact made of a CuCr alloy.
The preliminary final nominal geometry of the part under consideration is shown in Fig. 4a, where for illustration
purposes one quarter is cut away. The part is formed by a circular disc with a diameter and
height of app. 46 mm and 5 mm, respectively. The outer section is slightly tapered with an angle of app.
3.5 ◦ and all edges are rounded. In view of the application requirements the part contains four non-radial,
straight slots of 5 mm width each with a cylindrical base, imposing a fourfold cyclic-symmetry. For the
contact to be placed between adjacent adapter parts sunk holes with a depth of 1.5 and 1.0 mm are arranged
on both sides.
Die-compaction is done on a press with multilevel lower and upper punches. Hence, ring-shaped, outer
punches are used for forming the cross-sectional contour of the part, whereas circularly shaped, inner
punches can be used to form the sunk holes. Separate control of the inner and outer punches allows to
uniformly compact the distinct sections of the contact, thus reducing green-density gradients. The upper
outer punch is inclined in order to form the cone-shaped outer cross-section. Compaction is done using
an unseparated die and formation of the slots is established using four slot-punches.
The process-plan is pre-designed using the analytical procedure as given in the previous section. Based
on its results a numerical model of the powder-body in fill state is established. Exploiting the cyclic-symmetric
character only one fourth has to be modeled and appropriate coupling constraints have to be imposed
to the symmetry planes. The latter can be chosen quite arbitrarily as long as reproduction of the
full part is ensured: in order to prevent numerical difficulties during the later analysis it is convenient to
select planes that do not intersect the slot-punches. In order to obtain an almost uniform green-density
upper sunk hole
lower sunk hole
slot
upper outer punch
upper inner punch
(a) (b)
die
lower outer punch
slot-punch
lower inner punch
fill-body
Figure 4: Switching contact made of CuCr alloy: (a) preliminary final nominal geometry with main features, (b) finite element
model of fill-body and tools.

Feist, Oberbreyer et al. 17th Plansee Seminar 2009, Vol. 3 WS 15/11
distribution it is decided to design both sunk-holes with identical diameter. In addition, for the analysis the
geometry is simplified by neglecting all fillets except for the base-fillet of the slot-punches. The FE-model
consisting of the fill body meshed with linear hexahedron elements and the tools modeled as rigid surfaces
is depicted in Fig. 4b. The model reproduces the fill-body assuming it in a state after a first powdertransfer
established by the inner punches forming the initial cavity of the upper sunk-hole (the powdertransfer
itself could be numerically resolved only with a high numerical effort using adaptive procedures
which is out of scope of the present work). A uniform fill-density ρf(x) = const is prescribed for the entire
fill-body. Contact interactions are imposed between the surfaces of the powder-body and the tools. The
upper edges of the dies are filleted or chamfered, respectively, in order to allow smooth ejection of the
green-compact. All simulations are carried out using the commercial finite element code Abaqus [7].
As a first step the inclined upper outer punch is brought into full contact with the powder leading to slightly
higher densities at the outer perimeter of the part. Afterwards both outer punches are driven against each
other ensuring most minimal effects related to friction against the die. Simultaneously, the inner punches
move against one another, however, with a reduced height of travel, thus preventing powder-transfer between
the inner and outer section and ensuring an almost uniform density-distribution. After full compaction
the upper punches are slightly released before the part is ejected and the punches are finally removed.
The model now represents the state of the unloaded green-compact and the initial state of the sinteringprocess
as shown in Fig. 5a. The latter can then be simulated employing the deformed mesh associated
to the end of the compaction-simulation. Besides, the green-density distribution ρg(x) serves as additional
input to the sintering-simulation. For the sintering-simulation only appropriate statically determine
and constraint-free support-conditions have to be provided, however, no additional parts or tools have to
be considered.
Results in terms of the obtained relative density measures (with respect to the theoretical density of the
alloy) are shown in Fig. 5 both for the green-state (a) as well for the fully sintered state (b). Deviations
from the simplified final nominal geometry ∆n are given in Fig. 5c in terms of oversize (+) and undersize
(-). It can be seen that the maximum geometrical deviations are about 0.8 mm taking place at the
finger-like acute-angled piece along the slot. This can be explained by the slight over-compaction taking
place in this region as a consequence of a dead-water-effect during compaction (i.e. the powder is not
allowed to flow in circumferential direction). However, for most of the part maximum deviations of app.
0.1 mm can be observed. The obtained geometrical deviations now serve as a basis for respective adjustments
of the relevant process-parameters in order to obtain the desired final geometry complying
to the required tolerances and exhibiting almost uniform density-distributions. To this end, an iterative
scheme is applied based on the numerical model until the geometrical requirements are met.
d g [-] d s [-] ¦n [mm]
1.0
0.8
(a)
1.0
0.9
+0.8
-0.2
(b) (c)
Figure 5: Selected results of PM analysis for a switching contact: (a) relative density after compaction, (b) relative density after
sintering, (b) geometrical deviation from simplified nominal geometry.

WS 15/12 17th Plansee Seminar 2009, Vol. 3 Feist, Oberbreyer et al.
Summary
A mathematical model dedicated to numerically resolve the traditional PM process-chain – consisting of
die-compaction and sintering – by means of the finite element method (FEM) was presented. The model
relies on the concepts of continuum mechanics and describes the constitutive response using a combined
DRUCKER-PRAGER-cap plasticity model and an anisotropic visco-elastic model for the compaction- and
sintering-stage, respectively. Development and application of the model is motivated by the demands for
near net shape (NNS) manufacturing of parts reducing or making subsequent mechanical treatment almost
obsolete. The numerical model allows for fast and relatively cheap evaluation of different processplans
and optimization to achieve the demands of NNS-products.
The mathematical model was outlined with an emphasis on the employed constitutive models. Determination
of the relevant constitutive properties in the framework of powder-characterization was covered
subsequently. In order to determine appropriate initial guesses for the relevant process-parameters based
on the identified material behavior an analytical procedure was presented. Its results can be used both for
subsequent experimental as well as virtually conducted compaction-tests.
Application of the numerical model and the analytical procedure was finally given by means of a switching
contact part made of CuCr-alloy as used in the power-generation industry. For the sake of simplicity,
application of the model was restricted to a first step within an iterative numerical procedure with the objective
both to obtain almost uniform density-distributions and to minimize geometrical deviations from the
desired final geometry.
References
1. Copper Chromium (CuCr) Contact Materials for Vacuum Interrupters, Technical Information,
Plansee 7000764 - TI-E 018 E 09.08, Plansee SE, Reutte, Austria, (2008).
2. O.T. Gillia, L. Dihoru, and A.C.F. Cocks, Proceedings Process Modelling in Powder Metallurgy &
Particulate Materials, MPIF, A. Lawley et al. Eds., Princeton/NJ, pp. 161-165, (2002).
3. O. Coube, and H. Riedel, Powder Metallurgy 43 [2], 123-131, (2000).
4. H. Riedel, Proceedings Ceramic Powder Science III, G.L. Messing et al. Eds., American Ceramic
Society, Westerville/OH, pp. 619-630, (1990).
5. H. Riedel, and D.-Z. Sun, Numerical Methods in Industrial Forming Processes, Numiform 92, J.-L.
Chenot et al. Eds., Balkema, Rotterdam, pp. 883-886, (1992).
6. K. Korn, T. Kraft, and H. Riedel, Proceedings 4th International Conference on Science, Technology
and Applications of Sintering, D. Bouvard Ed., Grenoble, pp. 260-263, (2005).
7. Dassault Systèmes, Abaqus Analysis User’s Manual, Version 6.8, (2008).