Question 10.5: Design of a Composite Material One method to improve the fra......

Since the composite will operate at high temperatures for a substantial period of time, the two phases—the $Cr_{2}O_{3}$ fibers and the $Al_{2}O_{3}$ matrix—must not react with one another. In addition, the composite must remain solid to at least 2000 °C. The phase diagram in Figure 10-9 permits us to consider this choice for a composite.
Pure $Cr_{2}O_{3}$, pure $Al_{2}O_{3}$, and $Al_{2}O_{3}$-25% $Cr_{2}O_{3}$ have solidus temperatures above 2000 °C; consequently, there is no danger of melting any of the constituents; however, $Cr_{2}O_{3}$ and $Al_{2}O_{3}$ display unlimited solid solubility. At the high service temperature, 2000 °C, $Al^{3+}$ ions will diffuse from the matrix into the fibers, replacing $Cr^{3+}$ ions in the fibers. Simultaneously, $Cr^{3+}$ ions will replace $Al^{3+}$ ions in the matrix. Long before several months have elapsed, these diffusion processes will cause the fibers to completely dissolve into the matrix. With no fibers remaining, the fracture toughness will again be poor.