falling tree twigs? or bug damage, you decide
Here is a picture of it, and the description of the damage it does:
Many trees are targeted such as oak, pecan, hickory, dogwood, and other shade, nut, and fruit trees.
A stout, gray-brown, hard-shelled beetle about 3/4 inches long. Distinguishing marks include a light stripe across the wings and antennae, as long as its body. Adult beetles emerge from mid-August through early October. Adult females chew V-shaped grooves into twigs near the ends of the branches and deposit 3 to 8 eggs into each groove. Then they chew a continuous notch around the twig, girdling it. The notch restricts the flow of sap into the twig, killing it, but provides the necessary conditions for the larvae to develop. The twig breaks and falls to the ground, where the larvae overwinter in the twig.
Adult females girdle small pencil-sized twigs during late summer and fall. Twigs up to 3 feet long drop to the ground beneath the tree. The broken end of the twig seems to have been ground smooth all the way around, although the center may appear cracked. Girdled stem will have beveled ends. Stems weakened by this pest will break off during wind storms or may hang in the tree. Young trees can be severely affected.
For prevention and control, gather and burn all girdled twigs that fall to the ground.
This info is from the Tulsa Master Gardeners website.