A little trunk damage alone will not kill the tree. However if the damage completely goes around the tree it could prove fatal. There is little you can do now but give it time and proper care. Cut away any loose bark and keep the plant adequately watered throughout the summer. Fertilize with a cup of turf fertilizer per inch of trunk diameter now and again in mid summer. Apply a 3-4 inch layer of mulch to the soil surface all around the trunk extending a few feet out from the trunk in all directions. This will conserve moisture and deter weeds which compete with the tree for water and nutrients. Most importantly the mulch will help to keep the mower and weed eater away!
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