On the trunks of my 8 year old, otherwise healthy, crepe myrtles it looks like bugs are getting under the bark and pushing it off. The shapes are generally oblong, about 1/2' to 3/4" long by 1/4" wide. I fertilize and prune the interior branches. This started last year, and I removed one of the trunks, but it appears to be spreading. No bugs or fungus or mold is visible.
Crepe Myrtle Bark Disease or Pests
Certified GKH Gardening Expert
Peeling bark on crepe myrtle is normal. It occurs after the tree has reached full maturity, which may be a several years after you plant it. I really think this is the case since you said that no bugs or fungus/mold is visible. For more information please visit the following article:
For a frame of reference, here is a photo of a crepe myrtle that is exfoliating its bark: