NOSE GEAR DOWN LOCK BREAKS ON LNDG ROLL.

Narrative

WENT FLYING IN A PIPER ARROW BASED OUT OF FELTS FIELD WITH 2 POTENTIAL STUDENT PLTS AS PAX. I WAS DEMONSTRATING A LNDG AT DEER PARK ARPT; WA; AND THE NOSE GEAR OF THE PIPER ARROW I WAS FLYING COLLAPSED! DURING THE LNDG ROLL A FEW SECONDS AFTER TOUCHDOWN; AFTER I LET PRESSURE OFF YOKE (WT ON THE NOSE GEAR); AND STARTED TO RETRACT THE FLAPS FOR A TOUCH-AND-GO; THE NOSE MOVED OUT OF OVER-CTR AND IN THE DIRECTION OF RETRACTION. THE NOSE OF THE ACFT CONTINUED TO DROP UNTIL THE PROP HIT THE PAVEMENT BENDING IT OUT OF SHAPE AND STOPPING THE ENG. AS SOON AS I NOTICED THE PROP HIT; I YANKED BACK ON THE YOKE AND FORTUNATELY I HAD ENOUGH AIRSPD TO KEEP THE ACFT'S NOSE OFF OF THE GND HIGH ENOUGH TO LET THE NOSE GEAR FOLD BACK OUT. WITH THE NOSE FOLDED BACK OUT I EASED IT BACK DOWN AND WAS ABLE TO AVOID ANY DAMAGE TO THE UNDERCARRIAGE. THE NOSE GEAR STAYED DEPLOYED -- PAST THE OVER-CTR POS. LOOKING IN THE NOSE GEAR WELL; I NOTICED A MISSING; BROKEN PART THAT LOOKED LIKE A LATCH BAR -- THE ACTUAL DOWN LOCKING LEVER. SEARCHING THE RWY WE FOUND THE BROKEN OFF PART ABOUT 30 FT FROM THE TOUCHDOWN SKID MARKS.