Question

Problem 2 (20 pts): Determine the range of acceptable initial thicknesses for a cold rolled plate with a final thickness of 0.5 cm having at least 65,000 psi tensile strength, 60,000 psi yield strength, and 5% elongation. [Hint: Assume a constant or infinite width.] 1 100 90 80 -70 60 100,000 90,000 a) Illustrate how you use the chart for this problem (4 pts) 70,0001-ensile strength 60,000 50,000 40,00아 Yield strength50 -40 30 20 10 30,000 20,000 10,000 % Elongation what is the range of %cw for each of the three criteria (tensile strength, yield strength and ductility (5 pts)? b) 0 0 20 40 60 80 100 Percent cold work range to satisfy all three criteria (3 pts)? What is the proper working c) What is the acceptable range of initial thickness (min and max thicknesses) to use for the cold rolling process (8 pts)? d)

Answer 1

a) Due to cold working, that is deforming a ductile material under load, the strength of material increases because of strain hardening. At the same time, its ductility reduces that is measures as % elongation of the material before ultimate fracture.

The chart represents, increase the yield and ultimate tensile strength and decrease in % elongation as function of percentage of cold work. Percentage of cold work is a measure of permanent strain due to cold working, that can be given by formula:

% cold work= (Tinit-Tfinal)/Tinit=1-Tfinal/Tinit

Therefore if we know target yield and tensile strength and % elongation, we can estimate the % cold work required and therefore the initial thickness can be determined for given final thickness of the plate.

b and c)

Looking at chart, for tensile strength to be above 65000psi and yield strength to be above 60000psi, we need minimum 40% cold work.

Also, to have atleast 5% elongation, we need maximum of 50% cold work.

So, cold work of 40% to 50% range satisfies all criteria.

d)

Using formula stated above in a,

Tfinal=0.5cm, and range of CW is 0.4 to 0.5

So,

Minimum of 0.4=1-0.5/Tinit

Gives Tinit=0.83cm

Maximum of 0.5=1-0.5/Tinit

Gives Tinit=1cm

So, acceptable range of initial thickness is min 0.83cm and max 1cm

100 100,000 90,000 80,000-Tensile str ng 70,000 e60,000 50,000 40,000 30,000 20,000 10,000 90 80 60 iel strength0 30 -120 10 96 Flor gation 0 0 20 40 60 80 100 Percent cold work