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"Mrs. Clark took it upon herself to go on with his husband's work ."

The phrasal verb is "take upon", meaning to assume an obligation, often of a personal nature. "The colonel took it upon himself to check the sentry posts each evening". So Mrs. Clark took charge of her husband's work after his untimely death as a personal obligation.

take it upon yourself = you take up the responsibility make your own decision and take responsibility for that decision

http://legal-dictionary.thefreedictionary.com/take+upon+oneself