Chapter 7, Problem 7.50P

Interpretation Introduction

Interpretation:

The values of temperature should be determined for specimens made up of tin, molybdenum, iron, gold, zinc, and chromium.

Concept introduction:

At constant stress and elevated temperature, when a progressive deformation occurs in any material or component, it is known as creep deformation.

It is also known as time-dependent deformation because this deformation occurs depending on time for how long the materials are exposed to stress.

Answer to Problem 7.50P

The values of temperature are $\left(-71.04\right)C$, $885.4C$, $451.4C$, $261.96C$, $4.2C$, and $599C$ at which creep deformation occurs in the specimens made up of tin, molybdenum, iron, gold, zinc, and chromium respectively.

Explanation of Solution

With respect to absolute melting temperature, we have below-mentioned formula which can be taken into consideration for determining creep deformation.

$T=0.4T_m\mathrm{......}(1)$

Here,

$T_m$ = absolute temperature at which metal melts

With the help of Appendix-A, 'Selected Physical Properties of Metals', one can get the values of melting points of the given specimens of materials as follow.

$\begin{array}{l}\text{Tin, }{\left(T_m\right)}_{Sn}=231.9C\\ \text{Molybdenum, }{\left(T_m\right)}_{Mo}=2623C\\ \text{Iron, }{\left(T_m\right)}_{Fe}=1538C\\ \text{Gold, }{\left(T_m\right)}_{Au}=1064.4C\\ \text{Zinc, }{\left(T_m\right)}_{Zn}=420C\\ \text{Chromium, }{\left(T_m\right)}_{Cr}=1907C\end{array}$

Now, by using equation (1), determine the temperature at which the given materials will experience creep deformations.

1. For Tin,
$\begin{array}{l}T=0.4T_m\\ T=0.4{\left(T_m\right)}_{Sn}\\ T=0.4\left[231.9C+273\right]K\\ T=201.96K\\ T=\left(201.93-273\right)C\\ T=-71.04C\end{array}$
2. For Molybdenum,

$\begin{array}{l}T=0.4T_m\\ T=0.4{\left(T_m\right)}_{Mo}\\ T=0.4\left[2623C+273\right]K\\ T=1158.4K\\ T=\left(1158.4-273\right)C\\ T=885.4C\end{array}$

3. For Iron,

$\begin{array}{l}T=0.4T_m\\ T=0.4{\left(T_m\right)}_{Fe}\\ T=0.4\left[1538C+273\right]K\\ T=724.4K\\ T=\left(724.4-273\right)C\\ T=451.4C\end{array}$

4. For Gold,

$\begin{array}{l}T=0.4T_m\\ T=0.4{\left(T_m\right)}_{Au}\\ T=0.4\left[1064.4C+273\right]K\\ T=534.96K\\ T=\left(534.96-273\right)C\\ T=261.96C\end{array}$

5. For Zinc,

$\begin{array}{l}T=0.4T_m\\ T=0.4{\left(T_m\right)}_{Zn}\\ T=0.4\left[420C+273\right]K\\ T=277.2K\\ T=\left(277.2-273\right)C\\ T=4.2C\end{array}$

6. For Chromium,

$\begin{array}{l}T=0.4T_m\\ T=0.4{\left(T_m\right)}_{Cr}\\ T=0.4\left[1907C+273\right]K\\ T=872K\\ T=\left(872-273\right)C\\ T=599C\end{array}$

Conclusion

Thus, different temperatures corresponding to given specimen of materials of tin, molybdenum, iron, gold, zinc and chromium at which they experiences creep deformation are $\left(-71.04\right)C$, $885.4C$, $451.4C$, $261.96C$, $4.2C$, and $599C$.