Dog-bone copper specimens prepared by one-step spark plasma sintering

Abstract

Copper dog-bone specimens are prepared by one-step spark plasma sintering (SPS). For the same SPS cycle, the influence of the nature of the die (graphite or WC–Co) on the microstructure, microhardness, and tensile strength is investigated. All samples exhibit a high Vickers microhardness and high ultimate tensile strength. A numerical electro-thermal model is developed, based on experimental data inputs such as simultaneous temperature and electrical measurements at several key locations in the SPS stack, to evaluate the temperature and current distributions for both dies. Microstructural characterizations show that samples prepared using the WC–Co die exhibit a larger grain size, pointing out that it reached a higher temperature during the SPS cycle. This is confirmed by numerical simulations demonstrating that with the WC–Co die, the experimental sample temperature at the beginning of the dwell is higher than the experimental control temperature measured at the outer surface of the die. This difference is mostly ascribed to a high vertical thermal contact resistance and a higher current density flowing through the WC–Co punch/die interface. Indeed, simulations show that current density is maximal just outside the copper sample when using the WC–Co die, whereas by contrast, with the graphite die, current density tends to flow through the copper sample. These results are guidelines for the direct, one-step, preparation of complex-shaped samples by SPS which avoids waste and minimizes machining.

Appendix

The Joule heating model obeys to the heat Eq. (1) and the current Eq. (2):

$$ \nabla \left( { - \lambda \nabla T} \right) + \rho C_{p} \frac{\partial T}{\partial t} = {\text{JE}} $$

(1)

$$ \nabla \vec{J} = \nabla \left( {\sigma \vec{E}} \right) = 0 $$

(2)

with E the electric field, J the current density, λ the thermal conductivity, σ the electric conductivity, Cp the heat capacity, ρ the density, and T the temperature. The relevant physical properties are given in Tables 1 and 2.

The thermal model uses two main boundary conditions. Surface radiation is governed by Eq. (3):

$$ \phi_{\text{r}} = \sigma_{\text{s}} \cdot \varepsilon \cdot \left( {T_{\text{e}}^{4} - T_{\text{a}}^{4} } \right) $$

(3)

with ϕ _r the radiative heat flux, σ _s the Stefan–Boltzmann’s constant (5.6704 × 10⁻⁸ W m⁻² K⁻⁴), ε the emissivity (0.80 for graphite and 0.85 for WC–Co), T _a the chamber wall temperature, and T _e the emission surface temperature. The heat flux at the level of the water cooling system obeys Eq. (4):

$$ \phi_{\text{c}} = h_{\text{c}} \cdot \left( {T_{\text{i}} - T_{\text{w}} } \right) $$

(4)

with ϕ _c the convective heat flux, T _w the water temperature, T _i the Inconel wall surface temperature, and h _c the convective coefficient (200 W m⁻² K⁻¹).

The electric and thermal contacts at the inner interfaces obey Eqs. (5) and (6):

$$ J_{\text{c}} = \sigma_{\text{c}} \left( {U_{1} - U_{2} } \right) $$

(5)

$$ \dot{q}_{\text{c}} = h_{\text{cr}} \left( {T_{ 1} - T_{ 2} } \right) $$

(6)

with: J _c and $\dot{q}_{c}$ the current density and the heat flux across the contact, σ _c the electric contact conductance, h _cr the thermal contact conductance, and U _i and, T _i the electric potential and temperature on each side of the contact interface.