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2. Given that a quality-control inspection can ensure that a structural ceramic part will have no flaws greater than 100 µm (10010-6 m)in size, calculate the maximum service stress available with SiC (KIC = 3 MPa m1/2) and partially stabilized zirconia (PSZ) (KIC = 9 MPa m1/2). (See Example 8.3)

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Answer:

SiC=169.26 Mpa

Partially stabilized zirconia=507.77 Mpa

Explanation:

SiC

Stress intensity, K is given by

[tex]K=\sigma Y\sqrt{\pi a}[/tex] hence making [tex]\sigma[/tex] the subject where [tex]\sigma[/tex] is applied stress, Y is shape factor, a is crack length

[tex]\sigma=\frac {K}{Y\sqrt{\pi a}}[/tex] substituting the given figures and assuming shape factor, Y of 1

[tex]\sigma=\frac {3}{1\sqrt{\pi 100*10^{-6}}}= 169.2569\approx 169.26 Mpa[/tex]

Stabilized zirconia

Stress intensity, K is given by

[tex]K=\sigma Y\sqrt{\pi a}[/tex] hence making [tex]\sigma[/tex] the subject where [tex]\sigma[/tex] is applied stress, Y is shape factor, a is crack length

[tex]\sigma=\frac {K}{Y\sqrt{\pi a}}[/tex] substituting the given figures and assuming shape factor, Y of 1

[tex]\sigma=\frac {9}{1\sqrt{\pi 100*10^{-6}}}= 507.7706\approx 507.77 Mpa[/tex]

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