"cause of damage" is correct and usable in written English.
You can use it when you want to provide an explanation for why something has been damaged. For example: "The fire was quickly extinguished, but there was still some cause of damage to the building."
On each damaged tree, the following parameters were recorded after logging: diameter at breast height (DBH, 1.30 m) and diameter at wound height (DWH) (measured by dendrometric calliper in mm), damage severity (i.e. type of damaged tissues: bark, phloem, wood fibres), cause of damage (i.e. felling or extraction), and position and size of wounds.
Flooding is the No.1 cause of damage and fatalities caused by natural disasters in Connecticut each year, according to the State Department of Environmental Protection.
Dr. Song argues that misuse of the land, spurred by the rising population of people and livestock, is the overriding cause of damage in most areas and that there is no proof of a general drying of the climate.
Thirty-four growers accused DuPont of racketeering and fraud for allegedly hiding test results implicating Benlate DF, rather than a contaminant, as the cause of damage primarily to nursery plants and especially in humid climates.
Speaking for the Bush administration in an April 18 letter, Phillip Larsen, the director of the White House Office of Administration, told the G.A.O. that it could not document any damage, saying, "After investigating, we have located no such records and our repair records do not contain information that would allow someone to determine the cause of damage being repaired".
To identify the cause of damage, the LGRB made several exploration drillings.
