I work for a large US foundry and we use the word "coupon" to describe
a small sample piece of iron we use to test metallurgical properties.
We would like to know where and/or how the word "coupon" originated
when it is used to refer to a small piece or sample of something?

Hello krahmer-ga,

The administrator of OLD-ENGLISH-L, using the Oxford English
Dictionary, explains that the now-obsolete English word "culpon" meant
"A piece cut off, a cutting; a portion, strip, slice, bit, shred". 
She also notes that the word is "now adopted from Modern French as
'coupon.'"

"[OEL] Word for 2000-01-06: culpon", by Judith K Werner (5 Jan 2000)
OLD-ENGLISH-L Archives 
http://newsarch.rootsweb.com/th/read/OLD-ENGLISH/2000-01/0947138471

So it appears that this sense of "coupon" as "small piece" has
remained from the older word "culpon".  It is possible that the
original meaning was preserved through continuation of the word in
Scottish, which kept the word in the forms "coupoun", "cowpon", and
"coopin".  (The preservation of this word in Scottish is noted in the
hard copy of the original Oxford English Dictionary, page 1085 of
volume "C".)

- justaskscott-ga


Search strategy:

Looked up "coupon" and then "culpon", in hard copy of Oxford English
Dictionary.

Searched on Google for: coupon culpon

Excellent job! Extremely quick response.
Thank you!