13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure 5. Correlation between reference strain and creep rupture strain 3. Investigation of small cracks To analyse the dependence of the pre-loading crack size alimit on the material’s ductility, 3D models of specimens with DENT geometry have been used. The crack was modelled with a crack tip radius of 0.1 mm, which is valid for the experiments. The crack tip was meshed with a fine mesh to represent the stress and strain gradients correctly. For the description of the material’s behaviour a modified Graham-Walles formulation have been implemented, [14]. The calculations were conducted with the Finite-Element-Code ABAQUS ©. The numerical analysis of specimens with loading times up to 200.000 h requires a failure criterion to correlate with crack initiation. Within the creep regime and with respect to the dependence on ductility, a strain based formulation of the failure criterion is appropriate. Since the creep deformation and the creep damage is dependent on the multiaxiality of the stress state, this must also be considered, [15], [16], [17], [18]. With higher multiaxiality, the deformability is reduced. To account for that effect, the concept of Cocks&Ashby is applied, [19]. To correlate the calculated strains with the material dependent reference strain, a characteristic point within the crack tip region to evaluate the strains and the multiaxiality must be chosen. The calculated strains were evaluated at the point of maximum triaxiality near the modelled crack tip. Due to the high constraints, crack initiation begins at this point by formation, growth and coalescence of creep cavities. In addition a definition of crack initiation in the experiment must be set up. Crack initiation is defined for a crack growth of a = 0.1 mm. Figure 6. Schematic overview of calculation of alimit 0 5 10152025303540 0 5 10 15 20 30CrMoNiV4-11 / AMA, T = 550 °C 28CrMoNiV4-9 / AGB, T = 550 °C X12CrMoWVNbN10-1-1 / 1A, T = 600 °C Reference Strain r, 1 / % Creep rupture strain Au / % Definition of Loading F a = a 0 limit Failure Criterion met Ligament strain reached yes yes no no Definition of initial crack length a0 Specimen geometry
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