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

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$Refractory metals in furnace construction and engineering$

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-
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