When the porosity of a certain ceramic is reduced from 2.3% to 0.5% the fracture stress drops by 12%. Assuming Equation ( 19.8), how much would the fracture stress increase above the level for 1/2% porosity if all porosity were removed?

$\eta =A\exp\left[-Q/(R \ T)\right].$ (19.8)

Question

When the porosity of a certain ceramic is reduced from 2.3% to 0.5% the fracture stress drops by 12%. Assuming Equation ( 19.8), how much would the fracture stress increase above the level for 1/2% porosity if all porosity were removed?

$\eta =A\exp\left[-Q/(R \ T)\right].$ (19.8)

[latex] \eta =A\exp\left[-Q/(R \ T)\right]. [/latex] (19.8)

Accepted Answer

[latex] \sigma_{2}/\sigma_{1} =\exp(-b P_{2})/\exp( -b P_{1})=\exp \left[b( P_{1}- P_{2})\right], b=\ln (\sigma_{2}/\sigma_{1})/ ( P_{1}- P_{2}). [/latex] Substituting [latex]\sigma_{2}/\sigma_{1}=1/0.88[/latex] and [latex] P_{1}- P_{2}=0.023-0.005=0.018, b=\ln (1/0.88)/0.018=7.1. [/latex] [latex]\sigma_{3}/\sigma_{2}=\exp[-b(P_{3}- P_{2})] =\exp[-7.1(0- 0.005)]) =1.036 [/latex] or a 3.6% increase.

Question 19.3: When the porosity of a certain ceramic is reduced from 2.3% ......

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