LJ45 CREW DEPARTED IN IMC CONDITIONS WITHOUT GETTING THEIR IFR CLRNC. EXTREME CREW FATIGUE WAS INDICATED.

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JUST AFTER ROTATION I ASKED MY FO IF WE HAVE OBTAINED A DEP RELEASE FROM BANGOR APCH. WE HAD AT THAT TIME CLBED TO 1000 FT AGL AND IMMEDIATELY CONTACTED BANGOR TO ADVISE THAT WE HAD DEPARTED VFR AND WERE CURRENTLY AIRBORNE. THE WX DEPARTING THE FIELD WAS 600 FT OVCST AND 10 MI VISIBILITY. BY 1000 FT AGL WE HAD BECOME VFR ON TOP. BANGOR ADVISED US TO MAINTAIN VFR; OUR TCASII INDICATED NO TFC WITHIN 12 NM RADIUS. WE MAINTAINED VFR FOR APPROX 30-45 SECONDS BEFORE OUR IFR RELEASE BECAME AVAILABLE. ONCE RECEIVED WE CONTINUED PER OUR PRE-DEP CLRNC. I KNOW THE CAUSE OF THIS SIT WAS FATIGUE. THIS EVENT HAPPENED ON THE 7TH STRAIGHT DAY OF FLYING FOR MYSELF AND MY FO. DURING THE PRIOR 6 DAYS; OUR FLT TIME WAS BTWN 6-9 HRS PER DAY; WHILE DUTY TIME WAS BTWN 10 TO 13+ HRS PER DAY. WE WOULD NEVER INTENTIONALLY HAVE DISREGARDED ANY FARS OR ATC PROTOCOL. AS FAR AS CORRECTIVE ACTIONS; I BELIEVE CREWS SHOULD BE GIVEN ADEQUATE REST AND CONSIDERATION AFTER EXTENDED 12+ HR DUTY DAYS; 8+ FLT HR DAYS; AND 6+ DAY ROTATIONS. I ALSO BELIEVE AS CAPT ON THE ABOVE FLT I SHOULD HAVE BEEN MORE VOCAL TO THE COMPANY THAT WE AS A CREW WERE OPERATING ON THE VERGE OF STUPIDITY.