Relationship Between Crack-Tip Constraint and Dynamic Fracture Initiation Toughness

Two-dimensional finite element analyses are performed to study the crack-tip constraint in an elastic-plastic, three point bend specimen under dynamic load. Both strain rate-independent and strain rate-dependent materials are considered to elucidate the difference in response due to the material rate effect. It is first demonstrated that the crack-tip stress fields can be adequately characterized by the $J-A2$ three-term solution within the region of interest $1<r/(J/σo)<5$⁠. Consequently, $A2$ is used as a constraint parameter in constraint evaluations. Results show that the crack-tip constraint decreases with increasing loading rate in rate-independent material. On the other hand, in rate-dependent material, the crack-tip constraint first increases at low loading rate but later decreases at high loading rate. It appears that there is a competition between constraint loss due to dynamic load and constraint gain due to material sensitivity to strain rate. The effect of crack-tip constraint on fracture initiation toughness under dynamic load $Kdyn$ is then studied using a critical stress failure criterion. The results are consistent with experimental data in (a) reduced dynamic fracture initiation toughness, as compared with the static fracture toughness, at low loading rate such as those obtained by ASTM E23 Charpy tests and (b) elevated fracture toughness at high loading rate as frequently reported by experimental researchers.