Spark Plasma Sintering of Nanostructured Aluminum: Influence of Tooling Material on Microstructure

Abstract

The influence of tooling material, i.e., graphite and WC-Co, on the microstructure of a spark plasma sintering (SPS) consolidated, nanostructured aluminum alloy is studied in this paper. The results show that tooling selection influences microstructure evolution, independent of process parameters. The influence of tooling on microstructure is rationalized on the basis of the following factors: heating rate, electrical current density, localized heating, and imposed pressure. A theoretic framework, based on the physical properties of graphite and WC-Co, is formulated to explain the observed behavior.

Appendices

Appendix A

See Table AI.

Table AI Values of Physical Parameters at Room Temperature

Appendix B: Calculation of the Localized Pressure P _c

Under the assumptions that the powder particles are solid spheres having uniform radius r _p and they are closely packed in the mold, a section perpendicular to the axis of the mold and passing the center of a sphere is illustrated in Figure B1(a). To render the problem tractable, the section is divided into numerous repeated small rectangles and one sample is highlighted gray in Figure B1(a). The load exerted on the area of a small rectangle is actually supported by the area of the whole center circle and four circular quarters at the corners, or a total of two circles. Thus, one can get

Fig. B1

(a) A schematic diagram showing a section perpendicular to the axis of the mold and passing the center of a sphere. (b) A solid sphere model showing the packing of the spheres. (c) A free-body diagram for the lower semisphere of an arbitrary sphere. (d) A schematic diagram used for the calculation of the P _c

$$ P_{\text{D}} = 2\sqrt 3 r \cdot 2r \cdot P_{\text{a}} /2 $$

(B1)

where P _D is the force exerted on the area of a circle.

Next, a lower semisphere of an arbitrary sphere D (Figure B1(b)) is taken as a free body. To simplify the problem, the force acting on it from the spheres of its layer and its gravity is not considered. Then, its force diagram, which includes the P _D exerted by its upper semisphere and three P _x exerted by the three spheres (A, B, and C) supporting it, is shown in (Figure B1(c)). Application of the Newton’s second law in the z-direction yields the following equation:

$$ 3P_{\text{x}} \cos \alpha - P_{\text{D}} = 0 $$

(B2)

$$ P_{\text{x}} = \frac{{P_{\text{D}} }}{3\cos \alpha } = \frac{{P_{\text{D}} }}{{3 \cdot \frac{\sqrt 6 }{3}}} = \frac{{P_{\text{D}} }}{\sqrt 6 } $$

(B3)

Finally, the pressure exerted on the section perpendicular to the radius connecting the center of the sphere and the contact point between the two spheres (Figure B1(d)), can be estimated by

$$ P_{\text{c}} = \frac{{P_{\text{x}} }}{{\pi [r_{\text{p}}^{2} - (r_{\text{p}} - x)^{2} ]}} $$

(B4)

where x is the distance from the contact point to the section as shown in Figure B1(d). A substitution of Eqs. [B1] and [B3] into Eq. [B4] yields

$$ P_{\text{c}} = \frac{\sqrt 2 }{\pi }P_{\text{a}} \frac{{r_{\text{p}}^{2} }}{{r_{\text{p}}^{2} - (r_{\text{p}} - x)^{2} }} $$

(B5)

It should be noted that Eq. [B5] only applies to the location close to the contact point because the force acting on the location far from the contact point may be different from the P _c estimated by Eq. [B5]