The data reffered to in part $($a$)$ is provided as the $2$ graphs below. Also be sure to answer part b as well please:

A sintered $A{l}_2{O}_3$ component must not fail when a tensile stress of $13$ MPa is applied.

$($a$)$ Determine the maximum allowable surface crack length if the surface energy of

$A{l}_2{O}_3$ were $0\mathrm{.}83\frac{J}{m^2}.$ Consider the data in slide $10($of $15),$ shown in class, and assume a porosity of $0\mathrm{.}1.$ Assume no plastic deformation and assume

a stress concentration factor $\frac{{}_m}{{}_0}=2$ at the crack tip.

Figure $7\mathrm{.}21$ The influence of porosity on

the flexural strength of aluminum oxide at

room temperature.

Figure $7\mathrm{.}20$ The influence of porosity on

the modulus of elasticity for aluminum oxide

at room temperature. The curve drawn is

according to Equation $7\mathrm{.}21.$

$($b$)$ In a metallic component with an initial crack, would a contribution from plastic

deformation at the crack tip stabilize or destabilize the material? Consider stress

concentration and the shape of the crack tip in your explanation.