Short answer
No, not because the visa expired. Your visa is what you use to ask for entry into the United States. Once you are here, your I-94 controls how long you were admitted for, unless your record shows D/S. You still have to follow the rules of your status. You can check your latest I-94 at the official CBP I-94 site. If you leave the United States, you will usually need a valid visa to come back unless an exception applies.
Useful official link: U.S. Department of State, What the Visa Expiration Date Means
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