Cold Roll Coil Steel Hardness

I am cold rolling bi-metal steel coils (Copper Alloy on steelback). My challenge is correlating the finished steel hardness with the percent reduction. I need this to choose the proper steel size to begin with to ultimately achieve the proper final hardness and size.
I'm an engineer and not an experienced metalurgist. I assume there curves or formulas available to determine the steel hardness vs % reduction? Does anybody know where I can find these and what other factors I should be considering in this process?

Josh wrote:
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Josh,
Bascially your final as-rolled hardness is a fuction of the orginal input hardness transformed by the metal flow model base on the amount of strain (%reduction).
Some stress verses strain curves are published ASM International in a book (check the web site). Unfortunately these will be next to useless fo you. Standard hardness verses % reduction curves (really plots) from steel companies (if you can find them!!) are only applicable to their machinary due to redundant deformation.
What you really need is a metal flow model. Generally for steels hardness follows the tensile strength (other will say yield strength but they don't realize that it only applies to the annealed state - they are ignorant of the process of work hardnening).
The metal flow model for you case must use tensile strength (not hardness - hardness is not a ratio scale - has no zero!) can convert to hardness (using tables from per ASTM A360 or SAE J417)
For % reduction e (measured in true strain only!!!)
OCRT=ICRT* exp (e) for e<n
OCRT= A+B*e for e>n
Where:
ICRT = Input Cold Rolled Tensile Strength (from input hardness) OCRT = Output Cold Rolled Tensile strength (can convert to hardness)
e = natural or true strain from rolling = ln (input thickness/output thickness) + Redundent strain
n = necking strain - strain at tensile load.
A = intercept factor (specific to steel) - in ksi or N/mm² units B = post necking strain hardening factor (specific to steel) ksi/strain or N/mm²/strain
Actually it would be easier IMHO to plot these surves from your product using the flow model above rather than search for data.
Good Luck
Ed Vojcak PE