draw a line in the sand vs throw down the gauntlet

draw a line in the sand

verb
  • To lay down a challenge; to provide a test of commitment (often one which carries a high risk) to a cause. 

  • To create a real or artificial boundary or distinction between (two places, people or things). 

  • To indicate the threshold or level above which something will become unacceptable or will provoke a response; to create a boundary and imply or declare that its crossing will provoke a (negative) response. 

throw down the gauntlet

verb
  • To issue a challenge. 

How often have the words draw a line in the sand and throw down the gauntlet occurred in a corpus of books? (source: Google Ngram Viewer )