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

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].