OK, I'm back.
First , here is a great animated graphic of yaki-ire. The links are in the first post.
http://www.swordforum.com/forums/showthread.php?92559-Yaki-ire-quenching-animated-graphicsHere it the detailed explanation in metallurgical terms:
The down curve is caused by the austenite cooling and thus contracting a bit, plus the pearlite expanding. The upward curve is caused by the expansion is in the martensitic edge as the super-cooled austenite converts to a larger spaced martensite.. The interrupted quench is to prevent the edge from cooling too fast and becoming too brittle martensite before the blade is ready for that. It is also a slight auto-tempering process. The violent force applied to the blade during the martensitic conversion is what breaks many blades with the dreaded "PING".
I use parks 50 and forge in the sori on most blades. If you are going for a hamon, and want all the ashi and clouds, then water is your friend.....but it also is your enemy.
OK, I'll give you the longer explanation.
There are three structures involved in a blade of differential hardness.
Austenite is a compact and rubbery structure.
Pearlite is a larger structure that is soft.
Martensite is a much larger structure and is hard....and brittle when just formed.
Steel changes into austenite as it crosses Ac1 and when it reaches Ac3 it is fully austenitic. As it cools down past Ar1, it will convert to pearlite if cooled slow enough to enter the pearlite range....or stay as austenite if it misses the pearlite nose. As the super-cooled austenite continues down until it hits the Ms, the austenite suddenly converts into martensite.
Now, the austenitic blade with the clay coated back is fully heated to Ac3. It is all austenite, even under the clay. We quench it in a media that will drop the edge to below the pearlite nose around 1000F, and thus keep the edge austenite at this point. At the same time, the coated spine cools a bit slower, and goes into pearlite, which expands a bit. The larger pearlite pushes the soft austenite edge , causing a downward curve. All is happy at this point with a soft pearlite spine and a rubbery austenite edge. Then the martensitic conversion point is hit by the edge, and the edge suddenly gets a lot larger ( relatively), causing a quick push on the soft pearlite ,resulting is a sudden upward curve. This is happening at the same time as the edge becomes hard and brittle. If it all happens at exactly the right time and speed, you get a nice sori and a good hamon. If it happens a few milliseconds out of sync, you get a nice sori and a broken or cracked blade.
All that is fine for a fast water quench, but with oil, which is slower, the martensitic edge is auto tempered and the whole blade just stretches out a bit when the conversion happens.The oil also is slower, and the pearlite gets a bit cooler, and thus stiffer, when the conversion happens. This only slightly reverses the downward curve. Most times you never know that it curved down and then back up to straight or near straight. It is only really an observable feature on longer and thinner blades. I usually figure twice the up curve for every amount down in a water quench, and about 80% up from the down on an oil quench.
