grate vs eat into

grate is a noun but eat into is not a noun.

Word	Noun	Adjective	Verb	Adverb
grate	Yes	No	Yes	No
eat into	No	No	Yes	No

As verbs, grate and eat into are synonyms defined as:

Other synonyms of grate include fret, rankle.

grate (noun)	eat into (noun)
a frame of iron bars to hold a fire
a barrier that has parallel or crossed bars blocking a passage but admitting air
a harsh rasping sound made by scraping something

grate (verb)	eat into (verb)
make a grating or grinding sound by rubbing together	gnaw into; make resentful or angry
scratch repeatedly
reduce to small shreds or pulverize by rubbing against a rough or sharp perforated surface
gnaw into; make resentful or angry
furnish with a grate