Work Hardening percentage calculation

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SUMMARY

The calculation of total percent cold work (CW) for a plate that has undergone multiple cold-working processes is determined using the formula %CW = (Ao - Ad) / Ao x 100. In this discussion, the initial thickness (Ao) is derived from the first cold work at 50 mm, and the final thickness after further cold work is 33 mm. The correct calculation yields a total percent cold work of 47.2%. It is essential to maintain proper parentheses in the formula to avoid calculation errors.

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Ben James
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Plate previous cold-worked 20% is 50 mm thick. It is then cold-worked further to 33 mm. What is the total percent cold work?

I know %CW= (Ao − Ad/ Ao) x 100

I know the answer should be 47.2%, but I don't get that. What are the first steps I need to take?
 
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Start with what you know. I assume Ao is initial thickness and Ad is thickness after work. If not, please provide more detail on what these variables are.
.20 = (Ao -Ad1/Ao) --- Are you sure this shouldn't be (Ao-Ad)/Ao?
Solve that to find Ao.
Then plug into find your percentage::
x = (Ao-Ad2/Ao). Or maybe (Ao-Ad2)/Ao.
 
I worked it out, and yes... it is clear that using the assumptions I made above, you need to use ##.20 = \frac{Ao -50}{Ao}## to find Ao. And then apply the same formula to find ##x = \frac{Ao -33}{Ao}\times100\%##.
Please be careful with your parentheses.
 

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