burn through vs damage

burn through

damage

noun
  • Cost or expense. 

  • Injury or harm; the condition or measure of something not being intact. 

verb
  • To impair the soundness, goodness, or value of; to harm or cause destruction. 

  • To remove a damaged or unsalable item from the sales floor for processing. 

How often have the words burn through and damage occurred in a corpus of books? (source: Google Ngram Viewer )