Very likely - When you file an I-90 application to renew your expiring green card, the next thing that will happen after USCIS issues a receipt is that you will be scheduled for an appointment to complete biometric processing at an Application Support Center.
Biometrics include both a digital photo - which they will compare to the physical photos submitted with your application - and 10 digital fingerprints, which they will forward to the FBI and run through all available databases to check for arrest history, to see if you have committed any offenses that render you deportable or inadmissible since your green card was issued.
The fact that your convictions were misdemeanors is not meaningful; because (1) many offenses that are only misdemeanors under state criminal laws may be treated "aggravated felonies" under immigration law, and (2) for purposes of determining inadmissibility, and thus whether you remain entitled to your green card after foreign travel following an incident, a "conviction" can include any situation where you admitted to the elements of an offense, even if you were not convicted and did not take a plea - this can cover many forms of pre-trial intervention. Even if the specific state laws to which you pled guilty are not "aggravated felonies," they may still fall into other groups that have serious immigration consequences, such as crimes of domestic violence, or crimes involving moral turpitude.
Do not take further action without consulting a qualified immigration attorney in person, with final records of both convictions. You must get original Certificates of Disposition for any arrests and bring them to an immigration attorney for assessment of your individual circumstances, and whether the two offenses in question render you deportable or inadmissible.
This is general information only. It is not intended as a substitute for legal advice, and does not create an attorney-client relationship.