FO OF AN AIRBUS 320 FAILED TO INTERCEPT JET AIRWAY DURING CLBOUT DUE TO NOT HEARING CLRNC TO JOIN AIRWAY WHILE MAINTAINING THE LAST VECTOR HDG.

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FLYING A SCHEDULED FLT FROM MEM TO IND; WE DEPARTED ON RWY 9 AND WERE BEING VECTORED. DURING OUR CLB WE WERE GIVEN A HDG WHICH I BELIEVE WAS TO INTERCEPT J29; AND I BELIEVE I ACKNOWLEDGED SAME. THE FO WAS FLYING THE ACFT ON AUTOPLT AND I WAS HANDLING RADIOS; CHKLISTS; ETC. LATER; ATC ASKED 'DIDN'T I TELL YOU TO INTERCEPT J29?' I LOOKED AND NOTICED WE WERE STILL ON A HDG APPROX 10 NM L OF J29. THE FO DID NOT PROGRAM THE ACFT TO INTERCEPT THE AIRWAY PERHAPS BECAUSE HE NEVER HEARD THE INSTRUCTIONS FROM ATC. I TOLD ATC WE WERE ON A HDG; ASKING HIM IF HE WANTED US TO JOIN J29. WE VERIFIED IT WAS OUR FILED RTE AND HE CLRED US DIRECT PXV WHICH WE IMMEDIATELY DID; CONTINUING TO IND. WE WERE CLBING THROUGH APPROX FL200-FL220 WHEN HE HAD QUERIED US. I BELIEVE THE ATC CTLR WAS CORRECT AND HAD GIVEN US A CLRNC TO INTERCEPT J29. AFTER ACKNOWLEDGING THIS CLRNC; I BELIEVE I VERBALLY REPEATED IT ASSUMING THE FO UNDERSTOOD THE CLRNC. I THEN FINISHED THE CHKLIST AND MADE SOME LOGBOOK ENTRIES. FATIGUE WAS MOST CERTAINLY A FACTOR. IT WAS THE LAST LEG OF A LONG DAY. 8 HRS SCHEDULED FLYING; 12 HRS 30 MINS SCHEDULED ON DUTY. LATE AT NIGHT. I SHOULD HAVE VERIFIED THE FO HAD PROPERLY PROGRAMMED THE ACFT; NOT ASSUMED -- AND FATIGUE MOST DEFINITELY CONTRIBUTED TO THIS ERROR.