Answered: Why the volume change as low as 0.5…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Why the volume change as low as 0.5 percent can cause grain fractures during phase transformation of ceramics? Given that the elastic modulus of the ceramic is 250 GPa and Poisson ration is 0.2.

You need to calculate the thermal stress due to the volume change

Expert Solution

Step 1

Given data as per question

volumetric change =0.5%

Elastic modulus of ceramic =250 Gpa

Poisson ratio =0.2

Volumetric change of 0.5 % is very high change in the dimensions of the object ,so it increases the vale of the stress induced in it.

$\begin{array}{l} we know that \\ volumetric strain \\ ε_{v} = \frac{σ_{t h}}{E_{c e r a m i c}} (1 - 2 μ) \end{array}$

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