sink one's teeth into, to

sink one's teeth into

Also, get one's teeth into. Become fully engaged in, as in He couldn't wait to sink his teeth into that problem. This metaphoric expression alludes to an animal biting vigorously into its prey. [Early 1900s]
See also: sink, teeth
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

sink (one's) teeth into

Informal
To undertake an endeavor energetically: She sank her teeth into the challenging project.
See also: sink, teeth
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

sink one's teeth into, to

To become fully engaged or engrossed in something. The analogy in this term, which began to be used figuratively only in the early twentieth century, is to the animal that bites deeply and vigorously into food. Dorothy Sayers used it in Gaudy Night (1935), describing a scholarly effort: “If one could work . . . getting one’s teeth into something dull and durable.”
See also: sink, teeth
The Dictionary of Clichés by Christine Ammer Copyright © 2013 by Christine Ammer
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