Question
Navajo globe willow trees have bark cracking.  Bark does not fall off by itself but when I pull off a piece it comes on in a size about 12" high and 3 - 4 inches wide.  There are no pests of any kind visible.  There are a few places in the inside of the pieces of bark that looks "webby."  These are mature 8 year old trees and started doing this about 4 years go. My zip is 63760 and zone 7 I think.  Had stressful drought last year and two icy winters past two. No residue, sap or any sight of anything except the webby places and there may be only one of those places on a piece of bark.    

Also my weeping willows have tiny bored holes in the branches of trees that have died.  No holes on the base.  No residue, sap or any indication except those tiny holes on the dear branches.  Older trees.

Answer
The problem with your globe willow could have any of several causes. The globe willow requires water and if it was not irrigated with a deep watering at least once a month, these symptoms could have resulted.

Another potential problem is winter sunlight. In the winter , many plants suffer sunscald, often called southwest injury because it is common on the southwest side of many tree trunks. Any branch exposed to the direct sunlight in the winter can suffer this injury, especially those branches angled directly at the sun. The injury occurs when the thin bark of young trees or branches heats in the day and freezes at night. Shading by branches above or white-washing with a thin water-based white paint can help reduce the problem by reflecting the sunlight in the daytime and reducing the heating of trunks and branches exposed to sunlight. Pruning to remove any damaged branches, once it is determined that there was significant damage, is advisable. However, sometimes some of the outer layers of epidermis on young branches will peel when there is not real damage done to the tree.

Another explanation is that the globe willow is a fast-growing tree, and as a result sacrifices protection from insects and diseases for its rapid growth. This is a tree subject to many problems, only one of which you have described in your message.

Perhaps the peeling bark is just a natural peeling of the epidermis and not a real problem. It may be due to sunscald, or it may be drought related. Insects are probably not a direct cause of what you have seen, but following the injury you described, insects or diseases may enter through the wound. If that occurs, prune the damaged branch.

I think it maybe natural but exasperated by the drought. I would prune the limbs with the holes and remove them form the property. This will get rid of any insect borer in the limbs.

I would also water it with 1 inch of water--place a pan under the tree an turn the sprinkler on and when the pan has 1 Inch of water in it stop. Do this once a week unless it rains significantly.