COHESIVE MODELING OF PROCESS REGIONS FOR CRACKS IN LINEAR ELASTIC STRUCTURES - FUNDAMENTAL-ASPECTS

The process region at the tip of a crack in a linear elastic structure has been modelled by a cohesive zone. Growth of the front end of the cohesive zone is governed by a critical stress intensity factor criterion, and advance of the original traction free crack is determined by a critical crack opening at the rear end of the cohesive zone. Damage resistance curves relating the applied stress intensity factor to the growth of the cohesive zone have been calculated for an idealized structure containing two characteristic dimensions. Instability resulting in failure of the structure is found to occur either by unstable growth of the front end of the cohesive zone, without a fully developed cohesive zone, or by unstable growth of the original flaw, when the crack opening displacement at the rear end of the cohesive zone reaches a critical value. The influence of the size of the structure compared to the length of the cohesive zone is investigated, and conditions for the limits of validity of the small scale yielding assumption are discussed. Comparisons are made between the maximum load and the length of the cohesive zone at instability resulting from the present analysis, and the values predicted by linear elastic fracture mechanics.