When polymer-bonded explosives （PBX） charges are rapidly extruded in a crack in the warhead′s case， it′s required to accurately predict unexpected ignition of cased PBX for safety reasons. Using the combined microcrack and microvoid model （CMM）， damage-ignition responses of crack-extruded PBX are investigated in three aspects： （i） interactions between crack and extruded PBX； （ii） mechanical-thermal-chemical responses of PBX at the macroscale； and （iii） underlying mechanisms of damage-ignition at the mesoscale. Meanwhile， the difference between two typical PBXs （pressed PBX-5 and casted GOFL-5） in response to crack-extruded loading is compared. The results show that， under 200 m·s^-1 extruded velocity， pressed PBX-5 exhibits brittle failure （extruded 3 mm at 60 μs） and shows a stress concentration near the crack； microcrack shows a rapid growth along the 45° angle with the extruded surface. In contrast， under the same extruded condition， casted GOFL-5 exhibits a rapid flow rate near the crack； large quantities of material are extruded （extruded 9 mm at 60 μs）. Both pressed and casted PBXs show an ignition near the crack. Shear-crack hotspot is the dominated ignition mechanism for PBX-5， while locally plastic dissipation is a possible dominated ignition mechanism for GOFL-5.