21-Mat-A6 Materials Selection and Design for Materials Processing · Dec-12-Mtl-A6 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Die pressing. A ceramic powder — usually first granulated (spray-dried into free-flowing, roughly spherical agglomerates ∼50–200 μm across) with a small amount (2–4 wt%) of a temporary organic binder and a lubricant — is loaded into a rigid steel die and compacted under a uniaxial (or, for less-tapered shapes, isostatic) pressure typically in the 20–200 MPa range. Consolidation proceeds by particle/granule rearrangement first (filling large voids at low pressure), then by elastic and plastic deformation and fragmentation of the granules at higher pressure, which closes the remaining porosity and develops mechanical (and binder-mediated) green strength. The punch is withdrawn and the shaped, rigid "green" compact is ejected intact, ready for binder burnout and sintering.
Slip casting. The ceramic powder is instead dispersed in a liquid (usually water) together with a small amount of a deflocculant, producing a stable, low-viscosity, high-solids-loading suspension (the "slip"). The slip is poured into a porous plaster-of-Paris (or polymeric) mould; capillary suction in the mould's own fine pore network draws the liquid vehicle out of the slip, depositing a consolidated layer of particles against the mould wall. Cast-wall thickness grows approximately as $\sqrt{t}$ (a Darcy-flow-controlled process, resistance increasing as the cast layer itself thickens). Once the desired wall thickness has built up, the excess slip is poured out (drain casting, giving a hollow part) or the mould is left full until solid (solid casting); after further drying and shrinkage away from the mould wall, the green part is removed and fired.
Die pressing advantages. Very short cycle time (seconds, easily automated for high-volume production); tight, repeatable dimensional tolerances (the rigid die constrains the green shape precisely); high, uniform green density achievable along directions perpendicular to pressing, giving predictable, low sintering shrinkage.
Die pressing disadvantages. Density GRADIENTS develop along the pressing direction (die-wall and particle-particle friction attenuate the transmitted pressure with depth), which sinter non-uniformly and can warp or crack the fired piece unless corrected (double-action pressing, lubricants, or isostatic pressing); geometry is limited to relatively simple axisymmetric or prismatic shapes without deep undercuts or very thin walls, since powder must flow and compact uniformly under a single punch stroke; tooling (hardened dies) is expensive and shape-specific, a poor fit for low-volume or highly complex parts.
Slip casting advantages. Can form complex, thin-walled, hollow, or highly non-axisymmetric shapes (sanitaryware, art ware, large technical ceramics) that die pressing cannot produce at all; green density is comparatively UNIFORM throughout the part (built up gradually and isotropically against the mould wall, with no single compaction-direction gradient); mould (plaster) tooling is inexpensive, well suited to short runs and prototyping.
Slip casting disadvantages. Slow cycle time (wall buildup rate falls as $1/\sqrt{t}$, so thick sections take disproportionately long); typically lower, and less tightly controlled, green density than pressing; higher water content in the green part gives more drying shrinkage and a higher cracking risk; dimensional tolerances are looser (mould wear over repeated cycles, batch-to-batch slip rheology variation); the process is labour-intensive (filling, timed draining, careful demoulding) and harder to automate than pressing.
True (total) porosity is the fraction of the specimen's bulk volume occupied by ALL pores, open and closed alike, obtained from the ratio of the measured bulk (envelope) density $\rho_{\text{bulk}}$ to the material's true (pore-free, theoretical) density $\rho_{\text{true}}$:
$$P_{\text{true}} = 1 - \frac{\rho_{\text{bulk}}}{\rho_{\text{true}}}$$Apparent porosity counts only the OPEN, interconnected pores that are accessible to an external fluid, measured directly by liquid-saturation methods (e.g. the Archimedes boiling-water absorption test): the mass of water absorbed into the open pore network, divided by the specimen's bulk volume, gives $P_{\text{apparent}}$ directly — closed (isolated, sealed) pores never fill with water and are simply invisible to this test.
The two are related by $P_{\text{true}} = P_{\text{apparent}} + P_{\text{closed}}$: the difference between them is exactly the closed porosity, so comparing the two measurements on the same specimen is the standard way to quantify how much of a ceramic's total porosity is sealed off (and therefore inaccessible to infiltration, permeation, or further densification by continued sintering) versus open to the surface.
