eat into vs etch

eat into

verb
  • To consume gradually, especially by erosion. 

etch

verb
  • To engrave a surface. 

  • To make a lasting impression. 

  • To cut into a surface with an acid or other corrosive substance in order to make a pattern. Best known as a technique for creating printing plates, but also used for decoration on metal, and, in modern industry, to make circuit boards. 

  • To sketch; to delineate. 

How often have the words eat into and etch occurred in a corpus of books? (source: Google Ngram Viewer )