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

Answer:

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

Explanation:

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

Original Dimension                       18.0                                  20 x 50

Deformed Dimension                   15.9                               13.7 x 55.1

%CW =  $(\frac{A_{0}-A_{d}}{A_{0}}) * 100$

Circular %CW = $(\frac{(\frac{18}{2} )^2-(\frac{15.9}{2} )^2}{\frac{18}{2} )^2}) * 100$ = 21.97%

Rectangular %CW = $(\frac{(20 *50)-(13.7*55.1)}{20*50}) * 100$ = 24.51%

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