STUDENT PLT AND INSTRUCTOR EXPERIENCE A RWY EXCURSION AFTER LANDING AT CMI. APPARENT CAUSE IS ICE ACCUMULATION ON LEFT BRAKE ASSEMBLY DISCOVERED ON INSPECTION.

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MY STUDENT HAD LANDED ON RWY 32R AT CHAMPAIGN; IL. AT THE TIME WINDS WERE 290 DEGS AT 19 KTS. THE STUDENT'S TOUCHDOWN WAS SMOOTH WITH A FULL STALL LNDG. ON THE LNDG ROLLOUT THE STUDENT APPLIED BRAKES AND THE L BRAKE LOCKED. THE ACFT VEERED SHARPLY TO THE L. AT THAT POINT I TOOK OVER CTL OF THE ACFT; RELEASED ANY BRAKING AND APPLIED FULL NOSE-UP ELEVATOR AND FULL R RUDDER IN AN ATTEMPT TO KEEP THE PLANE ON THE RWY. THE L BRAKE REMAINED LOCKED AND WHEN IT WAS APPARENT THE ACFT WOULD DEPART THE SIDE OF THE RWY I SHUT DOWN THE ENG TO PREVENT A PROP STRIKE. THE ACFT STOPPED APPROX 20 FT OFF THE L SIDE OF THE RWY; MISSING ANY OBSTRUCTIONS. NO DAMAGE WAS DONE TO THE ACFT OR THE ARPT FACILITIES. AFTER GETTING THE ACFT BACK TO THE PAVEMENT IT WAS INSPECTED AND WITH APPROVAL FROM THE MAINT DEPT WAS FLOWN HOME. FACTORS CONTRIBUTING TO THIS INCIDENT WERE THE COLD CONDITIONS AND POSSIBLY ICE ON THE BRAKES. NEXT TIME I FLY IN THAT TYPE OF WX I WILL DELAY BRAKE APPLICATION UNTIL AT A LOWER SPD TO HOPEFULLY MAINTAIN CTL OF THE ACFT SHOULD THE BRAKES LOCK; OR NOT APPLY BRAKES AT ALL. SUPPLEMENTAL INFO FROM ACN 725883: AFTER A QUICK INSPECTION OF THE ACFT; A CHUNK OF ICE FROZEN ONTO THE L BRAKE PAD WAS DISCOVERED. ICING ON THE L BRAKE WAS THE PROBABLE FACTOR IN THE RWY EXCURSION.