13th International Conference on Fracture June 16–21, 2013, Beijing, China Realistically, an initial stage of crack tip blunting is expected to occur with the non-local GTN-model before the fracture initiation [9,10]. In order to handle the associated strain singularity an initial radius rt is introduced in the FE-model. The radius rt has to be small compared to lnl preventing an inadmissible perturbance of the solution. The mesh in Fig. 5 fulfills this requirement. For the computations the commercial FE-code Abaqus/standard is employed. Dynamic simulations are performed with implicit time integration under plane-strain conditions. The loading is applied quasi-statically. The elements for non-local GTN-model and the cohesive elements are both implemented with quadratic shape functions as user-defined elements via the UEL-interface. The crack propagation is simulated in the following for a three-point bending specimen (Fig. 6) or under a KI-dominated far-field (boundary-layer model, see [10]). 3. Results First, the influence of the cohesive strength σc is investigated. In order to exclude possible effects of the geometry of a particular specimen, the limit case of a KI-dominated far-field is considered. A dimensional analysis shows that under these conditions the ratio of σc and initial yield stress σy is the only relevant parameter. In metals σy increases with decreasing temperature. If σc is assumed to be independent of the temperature, σc/σy increases with increasing temperature. Computed crack growth resistance curves (R-curves) are shown in Fig. 7 for several values of σc/σy. In addition, the active damage mechanism is marked. It has to be noticed that the crack growth resistance JR is normalized with respect to the yield stress σy and the non-local length lnl. The amount of crack growth Δa is normalized by lnl as well. The results show that the crack growth resistance increases with the ratio σc/σy, i.e. with increasing temperature. For σc/σy=2.6 the crack growth resistance is determined by the work of separations Γ0. In the lower ductile-brittle transition Fig. 7: Crack growth resistance curves region at σc/σy=3.05 there is still pure cleavage but already a considerably higher crack growth resistance JR. The difference between JR and Γ0 is caused by the dissipation due to the plastic -5-
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