ZAU CTLR EXPERIENCED OPERROR AT FL370 WHEN EXPECTED SEPARATION BTWN 2 ENRTE ACFT FAILED AND ACTION TAKEN WAS TOO LATE.

Narrative

ACFT #1 WAS SBOUND AT FL370. ACFT #2 WAS NEBOUND ALSO AT FL370. ACFT #1'S RTE TURNED SHARPLY EBOUND AT TNV; 10 MI W OF THE PATH OF ACFT #2. I WAS AWARE THE 2 ACFT WERE A POTENTIAL CONFLICT; BUT AFTER EVALUATION; I FELT ACFT #1 WOULD PASS BEHIND ACFT #2 WITH NO ACTION TAKEN. AS ACFT #1 BEGAN THE TURN I REALIZED I WOULD LOSE SEPARATION. I ISSUED A CLRNC TO ACFT #1 TO DSND BUT DID NOT USE THE WORD 'IMMEDIATELY' AND ADDITIONALLY; I USED THE WRONG CALL SIGN. AFTER THE PLT ASKED IF THE CLRNC WAS FOR HIM; I REISSUED THE CLRNC TO DSND IMMEDIATELY USING THE CORRECT CALL SIGN. THE DELAY IN DSNDING ACFT #1 CAUSED SEPARATION TO BE LOST. THERE WERE SEVERAL FACTORS CONTRIBUTING TO THE ERROR. I WAS AT THE SECTOR FOR OVER 1 HR AND HAD WORKED VERY COMPLEX TFC THE WHOLE TIME. DFW DEP TFC WAS ROUTED OVER HOUSTON; TAKING MANY MORE ACFT THROUGH MY AIRSPACE THAN USUAL AND ON NON-STANDARD RTES. AS A RESULT; I WAS FEELING FATIGUED AT THE TIME OF THE INCIDENT. I WAS SO CONVINCED THE 2 ACFT WERE GOING TO BE SEPARATED. I WAITED UNTIL IT WAS TOO LATE TO DO ANYTHING TO PREVENT THE ERROR. THERE WERE ALSO SEVERAL DISTRACTING SITUATIONS THAT MAY NOT HAVE ALLOWED ME TO GIVE THE CONFLICT MORE ATTN.