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Sparking new design ideas for electricity generation The traditional economic advantages of near net shape powder metallurgy technology can be combined with mathematical and finite element modelling and deployed to produce satisfactory results in the gritty and down to earth industrial environment of day-to-day power generation, where breakdowns can cost both money and reputation…

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here is demand in power station technology for evermore economic ways of generating electric current. Power system providers draw particular attention to technologically reliable and durable switching systems that can be securely operated under severe conditions. The contact components form the main part of breaking chambers, and high-performance materials have to be specifically developed for the use in vacuum and arcing contact systems. Over the past two decades copper-chromium (CuCr) based mate-rials have become established for use with contactors and circuit breakers in vacuum interrupters for the medium voltage range of 1 kV to 72.5 kV. They 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. The chromium content influences the required high-arc quenching and low current chopping characteristics of the component as well as its erosion resistance and welding behaviour [1].

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Beside the choice for an adequate CuCr grade, the geometric features of the contact component also play a significant role in performance during switching operations. In the classical PM manufacturing approach of die compaction and sintering, shape chip-ping and other types of mechanical treatment cannot be avoided in order to get the desired final shape. Because of an a priori unknown functional relationship between final shape/dimensions of the sintered body, ingoing powder material characteristics and the die compaction/sinter process parameters, an iterative strategy has to be applied in practice covering materials development, process design, and field test performance. Reducing material and manufacturing costs as well as optimising the time-to-market characteristics can be realised by minimising material to be machined off. These economically and technologically challenging tasks are commonly referred to as near net shape manufacturing (NNS) strategies. During the design of a NNS process it is convenient to be able to resort to a mathematical model of the PM process which

allows the prediction of sintering distortions as well as density distributions and the determination of appropriate process parameters. Either the individual particles constituting the powder can be considered in a discrete manner, or the powder can be thought of a continuous domain throughout the entire process-chain. The latter approach – employed in this work

The Authors THIS FEATURE was derived from Finite element-based optimisation of a near net-shape manufacturing process chain for CuCr medium voltage circuit breakers, a paper by Arno Plankensteiner1, Christian Grohs1, Christian Feist 2, Robert Grill 1, August Schwaiger3, Lo-renz S Sigl1 and Heinrich Kestler1. It was given at EuroPM2009 in Copenhagen. 1 Plansee

SE, Innovation Services, Reutte, Austria 2 CENUMERICS, Innsbruck, Austria 3 Plansee Powertech AG, Seon, Switzerland

0026-0657/10 ©2010 Elsevier Ltd. All rights reserved.

– allows the application of the concepts of continuum mechanics. Whereas for discrete approaches constitutive behaviour is based on the description of mechanical and chemical interparticle relation-ships, the idealisation of a continuous powder requires the constitutive response to be described in a homogenised phenomenological manner. The mathematical model also has to take into account the toolset – mostly assumed as rigid – and its interactions with the powder. Since such a mathematical model of powder and toolset behaves in a highly nonlinear manner, even for very simple geometries, it can usually only be solved using a numerical procedure in the domain of time-and-space. The most widely used numerical procedure for continuum mechanical problems is the finite element method (FEM), which is also used in the present work. The model employed aims primarily at predicting the densitydistribution ȡ (x) and deformation-state u (x) of the powder domain at any stage of the process-chain. In addition, its stressstate ı (x) can be assessed in order to detect critical phases during compaction and ejection. The deformation state at the end of sintering defines the final geometry obtained by the process-plan and allows comparison with the required final shape.

Modelling powder compaction The numerical simulation of the PM process consists of two consecutive analysissteps: (i) analysis of powder compaction and ejection of the green-compact and (ii) analysis of sintering of the green-compact. Thus, as a restriction imposed by the continuum idealization of the powder the geometry of the powder-body at fill state and its fill-density have to be explicitly given (in contrast, a discrete approach would allow for the implicit solution of these parameters). 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 ȡ (x)) are imported as an initial state into the second analysis step. One of the crucial aspects of the mathematical model outlined is the proper description of constitutive behaviour. The nonlinear mechanical response of granular materials to predominantly triaxial compressive stress-states can be described in

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Figure 1. Combined Drucker-Prager-cap plasticity model: (a) yield surface in the hydrostaticdeviatoric stress-space, (b) evolution of the yield surface with respect to density.

a phenomenological manner using a capmodel formulated in the framework of the theory of elasto-plasticity [2]. Its elliptical cap-shaped yield surface fc is defined in the hydrostatic-deviatoric stress-space p-q (Figure 1a) with p and q denoting the first and second stress-invariant, respectively. As usual in soil- and grain-mechanics the hydrostatic pressure stress p is taken positive for compressive stress-states. The yield surface is considered to be independent of the third stress-invariant, resulting in circular sections in the deviatoric plane. The cap surface – described by the triaxial compressive strength pb and the capeccentricity R – limits compressive stressstates with high values of triaxiality p/q as found especially for compaction processes such as die compaction. However, the cap surface is not suited for describing the response to 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 tool-geometries. Such stress-states might lead to the formation of discontinuities and cracks in the powder-body being

compacted and hence should be avoided. 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 simplest case the well-known linear Drucker-Prager yield-surface can be used (Figure 1a) given by the cohesive strength d and the angle of internal friction ȕ. 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 is related to the inelastic logarithmic volumetric strain İvpl which in turn can be expressed in terms of the current material density ȡ as İvpl ≈ ln(ȡ /ȡ0) with ȡ0 as the reference density of the material (ie the density of the powder in loose packing). Along with the hardening under compressive loading the cap-surface will change its shape, such that the cap-eccentricity parameter R becomes density-dependent. Finally, compaction of a granular material is accompanied by a significant increase

Figure 2. Results obtained from sintering experiments for two types of CuCr alloy – greendensity (ρg ) dependence of (a) sinter density ρs , (b) axial sinter shrinkage εz and (c) radial sinter shrinkage εr .

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Figure 3. Mechanical powder-characterisation: (a) experimental determination of cap- and shear-failure surface parameters, (b) density dependence of cohesive strength d.

in the shear-strength which is accounted for by density-dependent formulations of the shear-failure parameters d and ȕ. Appropriate evolution functions must be chosen and their coefficients adapted in order to fit experimental results for the particular powder. The evolution of the combined Drucker-Prager-cap surface with respect to density is shown for an exemplary powder in Figure 1b.

Modelling sintering Together, the cap-surface fc = 0 and the shear-failure surface fs = 0 confine the elastic domain (Figure 1a). For stressstates within this domain isotropic elastic behaviour expressed by the constants of elasticity E and Ȟ is assumed to be valid. In order to be able to numerically capture the elastic spring-back taking place during the ejection phase of a green compact it is also necessary to describe the densitydependence of the modulus of elasticity E. Sintering is a thermally activated process that causes the powder compact to be consolidated to a bulk material with a residual sintering porosity. It is

consequently accompanied by an increase in density and shrinkage of the material. A constitutive model describing the mechanical behaviour of a solid being sintered for usage in the present context must be able to reproduce the evolution both of density and shrinkage depending on the greendensity as shown for two different CuCralloys by results from sintering experiments in Figure 2. Hence, it is sufficient to make use of a phenomenological model, which however is derived from a micromechanical description of particle interactions [3, 4]. Such a constitutive model can be formulated within the framework of the theory of visco-elasticity. Depending on the type of powder a more or less pronounced anisotropy (more precisely: transversal isotropy) can be observed with respect to the sintering strains. This is shown for two CuCr powders in Figures 2b and 2c, where sintering strains in compaction-axis differ significantly from those in the plane normal to compaction. This effect is accounted for by a general anisotropic formulation of the visco-elastic model [5]. From sintering experiments one can determine the density

Figure 4. Switching contact made of CuCr alloy: (a) preliminary final nominal geometry with main features, (b) finite element model of fill-body and toolset.

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ȡs attainable through sintering (Figure 2a) for which ȡg < ȡs = f(ȡg) < ȡth holds with ȡth as the theoretical density of the (porefree) solid material and the sinter density depending on the green density ȡg. Hence, it is convenient to relate all density measures used in the evolution equations of the viscosities and their respective ratios to the current relative density with respect to the attainable sinter density d = ȡ /ȡs. A prerequisite for application of the mathematical model is the identification of the involved constitutive parameters and their density-dependence. This so called powder-characterisation is usually done on an experimental basis. In order to identify the mechanical response of the powder during die compaction uniaxial compaction tests are conducted using a standard or instrumented die (Figure 3a, (1)). These tests can be used to obtain indirectly the hardening relationship between the triaxial compressive strength pb and the inelastic volumetric strain İvpl or the density ȡg, respectively. For identification of the parameters related to the shear-failure surface fs at least two different types of experiments at different levels of stress triaxiality p/q have to be conducted. In this context those most employed are the Brazilian disc test (Figure 3a, (2)) and the uniaxial compression test (Figure 3a, (3)). They are conducted on 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, the shear-failure parameters can be derived from the maximum applicable loads. In order to determine the densitydependence of the strength parameters, identical sets of experiments must be conducted at various density levels ȡ1, ȡ2 … (Figure 3b) relevant for PM production purposes. For simulation purposes the discrete values obtained d1, d2, … and ȕ1, ȕ2 … are fitted using an appropriate regression-function (see Figure 3b for the case of cohesion d). Application of the described mathematical model for the NNS PM processchain is shown by a switching contact made of a CuCr alloy. The preliminary final nominal geometry of the part under consideration is shown in Figure 4a, where one quarter is cut away for illustration purposes. The part is formed by a circular disc with a diameter and

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Figure 5. Selected results of PM analysis for a switching contact: (a) relative density after compaction, (b) relative density after sintering, (c) geometrical deviation from simplified nominal geometry.

height of approximately 46 mm and 5 mm, respectively. The outer section is slightly inclined 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 half-cylindrical base, establishing a fourfold cyclic-symmetry. For the contact to be placed between adjacent adapter parts sunk holes with depths of 1.5 and 1.0 mm are arranged on both sides. Die-compaction is carried out on a multilevel press. Individual control of the inner and outer punches allows uniform compaction of the distinct sections of the component, reducing green-density gradients. The upper outer punch is inclined in order to form the coneshaped outer cross-section. Formation of the slots is established using four core-punches. For the simulation initial processparameters are estimated using a simplified analytical procedure, based on which a first numerical model of the powderbody in fill state is established. Exploiting the cyclic-symmetric character only one fourth is modelled and appropriate coupling constraints are imposed to the symmetry planes. In order to obtain an almost uniform green-density distribution it is decided to design both sunk-holes with an identical diameter. In addition, for the analysis the geometry is simplified by neglecting all fillets except for the basefillet of the core-punches. The FE-model consisting of the fill body meshed with linear hexahedron elements and the tools modelled as rigid surfaces is depicted in Figure 4b. The model reproduces the fill-body assuming it in a state after a first powder-transfer established by the inner punches forming the initial cavity of the upper sunk-hole. A uniform

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fill-density ȡf (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 die and core-punch are filleted or chamfered in order to allow smooth ejection of the green-compact. All simulations are carried out using the commercial finite element code Abaqus [6]. 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 followed by ejection of the part and final removal of the punches. The model now represents the state of the unloaded green-compact and the initial state of the sintering-process as shown in Fig. 5a. The latter can then be simulated employing the deformed mesh associated with the end of the compaction-simulation. The green-density distribution ȡg(x) serves as additional input to the sintering-simulation for which only the green-compact has to be considered. Results in terms of the relative density measures (with respect to the theoretical density of the alloy) obtained are shown in Figure 5 both for the green-state (a) as well for the sintered state (b). Deviations from the simplified final nominal geometry Δn are given in Figure 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. However, for most of the part maximum deviations of app. 0.1 mm can be observed. The geometrical deviations obtained now serve as a basis for respective adjustments of the relevant process-parameters in order to arrive at the desired final geometry complying with the required tolerances and exhibiting almost uniform density-distributions. To this end, an iterative scheme is applied based on the numerical model until these requirements are met.

References [1] Copper Chromium (CuCr) Contact Materials for Vacuum Interrupters, Technical In-formation, Plansee 7000764TI-E 018 E 09.08, Plansee SE, Reutte, Austria, (2008). [2] O Coube, and H Riedel, Powder Metallurgy 43 [2], 123-131, (2000). [3] H Riedel, Proceedings Ceramic Powder Science III, G.L. Messing et al. Eds., American Ceramic Society, Westerville/OH, pp. 619-630, (1990). [4] 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). [5] 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). [6] Dassault Systèmes, Abaqus Analysis User’s Manual, Version 6.8, (2008).

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