Question

Two previously undeformed specimens (i.e. 0% cold work) of the same metal are to be plastically deformed by reducing their cross-sectional areas. One has a circular cross-section, and the other is rectangular; assume the shapes do not change during the process. Their original and deformed dimensions are as follows:

Circular (diameter, mm) Rectangular (mm)
Original dimensions 18.0 20 × 50
Deformed dimensions 15.9 13.7 × 55.1

Which of these specimens will be the hardest after plastic deformation, and why?

Answer 1

The metal with the hardest CW will be the strongest = Rectangular

Step-by-step explanation:

Circular(di, mm) Rectangular(di, mm)

Original Dimension 18.0 20 x 50

Deformed Dimension 15.9 13.7 x 55.1

%CW =
`((A_(0)-A_(d))/(A_(0))) * 100`

Circular %CW =
`((((18)/(2) )^2-((15.9)/(2) )^2)/((18)/(2) )^2)) * 100` = 21.97%

Rectangular %CW =
`(((20 *50)-(13.7*55.1))/(20*50)) * 100` = 24.51%

The metal with the cross-section rectangular would be the best because it has the largest percentage of CW.