E2 Microstructure: Grain Size and Porosity

Topic

Porosity and grain size are the two microstructural state parameters described by this model; each independently determines the ceramic's elastic modulus and mechanical strength—the pair of mechanical properties characterized in detail by another model in this set. Since these two parameters determine that same pair of mechanical properties—despite stemming from distinct aspects of the microstructure—they must be developed separately before their effects are combined. We begin by addressing porosity.

The porosity data used in this model come from another model in the set, which describes the ceramic's porosimetry and density. Because that model experimentally measures the material's total porosity, this total porosity can be broken down into two components: open porosity (consisting of pores connected to one another and to the piece's outer surface) and closed porosity (consisting of pores isolated within the material). Since total porosity is the sum of these two components, any change in one of them is directly reflected in the total porosity.

This total porosity also has a counterpart: the ceramic's relative density. Higher total porosity results in lower relative density, as a larger fraction of the piece's volume is occupied by pores rather than solid material; conversely, lower total porosity results in higher relative density.

Higher total porosity also leads to a lower elastic modulus and reduced mechanical strength: pores disrupt the continuity of the solid material, reduce the effective load-bearing cross-section, and create stress concentrations around them; consequently, the higher the total porosity, the less rigid and strong the piece becomes. We now turn to the model's second parameter: grain size. The grain size of this ceramic is measured using the same linear intercept method already employed—for the same purpose—by the metallurgical grain-size model: a line of known length is drawn across the microstructure to count the number of grain boundaries it intersects, and the average grain size is derived from this count. Because this model reuses that same method, the ceramic's grain size is measured in a manner comparable to that used for metals.

A smaller grain size results in a higher elastic modulus and greater mechanical strength for the ceramic: grain boundaries—which are more numerous when grains are finer—act as obstacles that impede crack propagation through the material; conversely, a larger grain size means fewer such obstacles, resulting in a lower elastic modulus and reduced mechanical strength.

For this reason, the model—starting with the established porosity and grain size values—feeds both microstructural parameters into another model within the suite: the one that describes the ceramic's elastic modulus and mechanical strength in detail. Essentially, the values ​​determined here for total porosity and grain size serve as the inputs for the calculations performed by that other model.

ID:4385