Question

Two previously undeformed specimens of the same metal are to be plastically deformed by reducing heir cross-sectional areas. One has a circular cross section, and the other is rectangular, during deformation the circular cross section is to remain circular, and the rectangular is to remain as such. Their original and deformed dimensions are as follows:
Circular diameter, ( mm) Rectangular (mm)
Original dimensions 15.2 125 × 175
Deformed dimensions 11.4 75 x 200
Which of these specimens will be the hardest after plastic deformation, and why?

Answer 1

Answer:

Circular will be the hardest after plastic deformation because % of deformation is more in circular than in rectangular.

Step-by-step explanation:

Since we have given that

                            Circular diameter, ( mm) Rectangular (mm)

Original dimensions       15.2                         125 × 175

Deformed dimensions      11.4                               75 x 200

So, Percentage of deformation is given by

$=\dfrac{Area_{original}-Area_{Deformed}}{Area_{original}}\times 100$

$=\dfrac{\pi (\dfrac{15.2}{2})^2-\pi (\dfrac{11.4}{2})^2}{\pi (\dfrac{15.2}{2})^2}\times 100$

$=\dfrac{\pi (7.6^2-5.7^2)}{\pi 7.6^2}\times 100$

$=\dfrac{25.27}{57.76}\times 100$

$=43.75\%$

Similarly, for rectangular ,

Percentage of deformation is given by

$=\dfrac{Area_{original}-Area_{Deformed}}{Area_{original}}\times 100$

$=\dfrac{125\times 175-75\times 200}{125\times 175}\times 100$

$=\dfrac{21875-15000}{21875}\times 100$

$=\dfrac{6875}{21875}\times 100$

$=31.4\%$

Hence, circular will be the hardest after plastic deformation because % of deformation is more in circular than in rectangular.