Processing characteristics and parameters in capacitor discharge sintering

Abstract

A powder processing technique is here presented. The process consists in a single short impulse (5–40 ms) of electric current (with current densities greater than 10⁸ A/m²) combined with mechanical pressure and allows for nearly complete to complete densification of powders (>90% of theoretical density) with energy inputs from 1 to 4.5 kJ/g. The fundamental process parameter known as SEI is analyzed and is correlated with other known electro-discharge sintering techniques which present analogous values. An experimental equation correlating SEI and densities is proposed. Theoretical physical considerations on the amplification of mechanical and electrical energies during the process are made to explain the sintering process and the experimental evidence.

Introduction

The basic concept behind electric current assisted sintering techniques is the rapid delivery of energy to the powders through the aid of an electro-magnetic (EM) field with relatively low time frequencies (<500 Hz) (Orrù et al., 2009). These systems compared to traditional furnace sintering methods, based on thermal conduction and convection, offer advantages in materials processing that are connected to short processing time, useful to increase production rates and to control material microstructures hence material properties as explained, for example, by Groza and Zavaliangos (2000).

The physical phenomena behind these processing routes have not yet been fully explained. Plasma has been evoked frequently as promoter of densification (as in spark plasma sintering, SPS) but, as shown by Hulbert et al. (2009) no presence of low frequency plasma can be found in SPS. The acquisition system used by the authors had, though, a cut off filter at 100 MHz thus leaving the question on plasmas partially open: can there be unstable high frequency plasmas?

Atomic diffusion seems to have a predominant role but the interactions between the thermal, electro-magnetic and mechanical field of forces complicates the work of the analysts. Theoretical predictions of densification rates have been attempted by Wang et al. (2007) but have only, at present time, explained the stress distribution and the temperature distribution throughout dense or apparently dense compacts. However, often they have ignored the local heat balances and EM field amplification factors caused by pores inside the powder compact as done for example by Olevsky and Froyen (2006). Furthermore investigators of these techniques such as Mishra and Mukherjee (2000), Newman (2000) and Kodash et al. (2004) have reported plastic phenomena not so easily explainable with simple resistive heating and consequent lower strength and higher ductility of the powders under process. There are strong experimental evidences that diffusivity is enhanced and driven by the EM field as observed by Pierce and Brusius (1997) and Bertolino et al. (2001) and that plasticity is enhanced by the flow of electrical currents through conductors from the electro-plastic effect, EPE, as explained by Troitskii, 1975, Troitskii, 1976, Troitskii, 1977 and Conrad, 2000, Conrad, 2001, Conrad, 2002, Conrad, 2005.

In the big family of electric current aided sintering techniques, electro discharge compaction a less popular method limited to conductive materials because it employs direct flow of the currents through the powders. The technique is based on a single RLC type circuit in which the resistance R is the resistance provided by the powder compact. A capacitor bank is loaded at from a few kV to tens of kV and discharged on a pre-compacted powder column. The method began with Clyens et al. (1976) which have also studied the pulse currents and equations governing the phenomenon. Developments on the method which discharges directly high voltages on the powders compacts have been then carried on by Okazaki, 1992, Okazaki, 2000 aided by his previous works on the electro-plastic effect with Conrad: Okazaki et al., 1979, Okazaki et al., 1980. Capacitor discharge sintering (CDS) was initially approached by Knoess and Schlemmer (1996) as a compaction capable of increasing the density of metal compacts. It was later studied and improved by the present author Fais (2008) to obtain nearly dense to fully dense sintered metals and cermets. It was also researched upon by Egan and Melody (2009) at Element Six calling it simply but a little bit audaciously electric discharge sintering, EDS (Fig. 1).

It is an electric current assisted sintering technique capable of delivering a single pulse of current in less than 30 ms to conductive powders after having applied a mechanical pressures from 50 to 1000 MPa. CDS can be distinguished for the use of two mutually induction coupled power circuits instead of a single RLC. This combination allows for low voltages on the powder compact thus limiting the possibilities of discharges, breakdown and local plasma formation during the process.

With CDS many metals (Fe, Cu, Ti, Mo, Ni, Co) and alloys (high speed steels, previously discussed by Fais and Maizza (2008), bronze, invar) have been sintered to theoretical or nearly theoretical density (>90%) as shown in Table 1. The technique has also showed a limited tendency to anneal the microstructure in the powders employed. The table presents a list of materials with density, fundamental processing parameters and mean grain size of sintered specimens and of the starting powders. These values have been obtained with different X-ray diffraction pattern analysis methods: Williamson–Hall plots and Warren–Averbach by the present author Fais (2008) and whole powder pattern modelling (WPPM) by Scardi and Leoni (2002). Electron backscattering diffraction maps (EBSMs) have been also acquired where possible.

CDS is based on the storage of high voltage electrical energy in a condenser bank inserted in a freely oscillating system composed of a primary circuit and a mutually coupled secondary circuit (Fig. 3). The secondary circuit is combined with a mechanical press governed by a programmable logic controller (PLC). Once the desired force from the press is reached the switch closes the circuit, the electromagnetic energy is transferred to the secondary circuit by means of the transformer that converts from high voltage and low current (in the primary circuit) to low voltage and high current (in the secondary circuit). In Fig. 2 the variations of pressure along with the shape of a characteristic current impulse for CDS is shown.

The circuit can be solved through Laplace transforms in the (not so real) hypothesis of constant circuit parameters. The current on the secondary circuit used to densify the material will be:

$$I_2(t)=\frac{U_{C0}\cdot M}{a}\cdot \left[\frac{p_1\cdot \exp (p_1\cdot t)}{(p_1-p_2)\cdot (p_1-p_3)}+\frac{p_2\cdot \exp (p_2\cdot t)}{(p_2-p_1)\cdot (p_2-p_3)}+\frac{p_3\cdot \exp (p_3\cdot t)}{(p_3-p_1)\cdot (p_3-p_2)}\right]$$

where U_C0 is the energy stored in the capacitor bank and p_i, i = 1, 2, 3, are the poles of the third order equation: a · p³ + b · p² + c · p + d = (p − p₁) · (p − p₂) · (p − p₃) in which the coefficients a, b, c and d are (in reference to Fig. 3):

$$a=L1\cdot (L2+LS)-M^2$$

$$b=R1\cdot (L2+LS)+L1\cdot (R2+RS)$$

$$c=R1\cdot (R2+R2)+\frac{L2+LS}{C}$$

$$d=\frac{R2+RS}{C}$$

Through an appropriate choice of parameters the circuit can be optimized to obtain the maximum energy transfer from the capacitor bank. The machines used for the present work could obtain a thermodynamic efficiency of energy transfer from the capacitor bank to the sintering apparatus of 0.6–0.9 and operated without a controlled atmosphere. The main advantage of CDS over the most similar technologies such as electro-discharge compaction (EDC) described and used by Clyens et al., 1976, Okazaki, 2000, Rajagopalan et al., 2000, An et al., 2005, An and Lee, 2006 and Cheon et al. (2007) is the reliability of the discharge apparatus that employs power solid state devices instead of ignitrons as switches to close the circuit. This allows for reliable and predictable discharges with a life time for the electronic components of the primary circuit >10⁷ cycles. Furthermore while storing and transferring a high quantity of energy to the powder compact the applied voltages can be kept low with the step down transformers between the two power circuits. In the machines used for this work, adapted from commercial capacitor discharge welding apparatus, typical voltages on the capacitor bank of the primary circuit range from 1.5 to 3.5 kV while the voltages on the powder compacts range from 5 to 30 V.

SEI is the specific energy input as defined by Ervin et al. (1988). It is obtained by the integration in time of the product between the real part of the current and the real part of the applied voltage as shown in Eq. (6):

$$\text{SEI}=\underset{t\to +\infty }{\lim }\frac{E_j(t)}{w}=\underset{t\to +\infty }{\lim }\frac{1}{w}\cdot {\int }_0^{t}i(\tilde{t})\cdot v(\tilde{t})d\tilde{t}\approx \frac{1}{w}\cdot {\int }_0^{t^{*}}i(\tilde{t})\cdot v(\tilde{t})d\tilde{t}$$

where E_j is the energy dissipated by the finite value of electrical resistance (Joule effect), $w$ is the weight of the powders inserted in the mould, t^* is approximately the discharge time, while i(t) and $v(t)$ are the current and the voltage, respectively, measured during the discharge. SEI is expressed as [J/g] or more easely [kJ/g]. As it is possible to see in Fig. 4, $E_j(t)/w$ varies in time in a sigmoid-like behavior. The electrical discharges last from 10 to 40 ms. In a typical discharge, of about 30 ms, 90% of the energy is delivered to the powders in less than 20 ms.

The second important parameter for CDS is pressure seen as the force per unit area applied on the section of the plungers/electrodes. As already shown by Wang et al. (2007) for analogous moulds used in SPS the stress distribution is not properly uniform and it does not correspond to this nominal value of pressure. The value is nonetheless significant because all the experiments here presented have been executed with the same terminal apparatus which is composed of an inner high strength graphite mould with an inner diameter of 10 mm and an outer diameter of 20 mm and an external mould with an inner diameter of 20 mm and an outer of 30 mm while the height of the mould was 40 mm. High strength Cu–1%Co–0.5%Be alloys where used for the electrodes.