Unless you have really fouled things up, you will always have complete conversion in 40 minutes or so, sometimes less. It is so easy to get a false reading doing the iodine test, it is really a waste of time to even do it.
If you are doing the test in an effort to cut your mash time to an absolute minimum (in the 15-20 minute range), you may get an indication of complete conversion. However, what the test will not tell you is whether the enzymes are done working on the wort. The initial conversion will produce a lot of long chain sugars that are not very fermentable. The additional time (normally an hour total) allows the enzymes to keep working to break down those chains into shorter pieces that the yeast can use. If you do a very short mash with complete conversion, you may end up with beer with a high finishing gravity. If you get a false indication that conversion is not complete, you can end up mashing way too long and getting a beer that finishes too dry.
Forget the iodine test and do a mash of a consistent length at the proper temperature and everything will be fine. There are places to cut the length of the brew day, but the mash isn't really one of them.
Wayne
Bugeater Brewing Company