Following is tabulated data that were gathered from a series of Charpy impact tests on a ductile cast iron. $$ \begin{array}{cc} \hline \text { Temperature }\left({ }^{\circ} \boldsymbol{C}\right) & \text { Impact Energy }(\boldsymbol{J}) \\ \hline-25 & 124 \\ -50 & 123 \\ -75 & 115 \\ -85 & 100 \\ -100 & 73 \\ -110 & 52 \\ -125 & 26 \\ -150 & 9 \\ -175 & 6 \\ \hline \end{array} $$ (a) Plot the data as impact energy versus temperature. (b) Determine a ductile-to-brittle transition temperature as that temperature corresponding to the average of the maximum and minimum impact energies. (c) Determine a ductile-to-brittle transition temperature as that temperature at which the impact energy is \(80 \mathrm{~J}\).

Step by step solution

01

Find the maximum and minimum impact energy values

From the given data, we can see that the maximum impact energy is 124 J at -25°C, and the minimum impact energy is 6 J at -175°C.

02

Calculate the average of the maximum and minimum impact energies

\(\frac{6 + 124}{2} = \frac{130}{2} = 65\) J

03

Estimate the ductile-to-brittle transition temperature

Looking at the given data, we find that the impact energy is between 73 J and 100 J at -100°C and -85°C, respectively. Since 65 J lies between these two values, we can estimate the transition temperature using linear interpolation: Transition temperature \(= -85 + \frac{65-73}{100-73}(-100 - (-85)) = -85 - \frac{8}{27}(-15) \approx -89.4 ^{\circ}C\) Therefore, the ductile-to-brittle transition temperature estimated based on the average of the maximum and minimum impact energies is approximately -89.4°C. #c# Determine a ductile-to-brittle transition temperature as that temperature at which the impact energy is 80 J.

04

Estimate the transition temperature for 80 J impact energy

We look at the given data and find that 80 J impact energy lies between 73 J and 100 J at -100°C and -85°C, respectively. We can again use linear interpolation to estimate the required transition temperature at 80 J: Transition temperature \(= -85 + \frac{80 - 100}{73 - 100}(-100 - (-85)) = -85 - \frac{-20}{-27}(-15) \approx -91.1 ^{\circ}C\) So, the ductile-to-brittle transition temperature corresponding to an impact energy of 80 J is approximately -91.1°C.

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