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

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