13th International Conference on Fracture June 16–21, 2013, Beijing, China 5 (d) Establishment of a new crack profile. Based on the creep crack increment at each point along the crack front, a set of new points can be determined. And then, a new crack profile can be created by using codes ZENCRACK. (e) Returning to stage (a). The crack continued to extend through the stages from (a) to (d) until a termination condition is reached. 3.2 Using continuum damage mechanics approach Creep damage modeling has been also carried out using the codes ABAQUS with the elastic-plastic-creep properties of 316 stainless steel tested at 600ºC [1, 9, 15]. The total strain can be calculated by tol e p c , (9) where e , p and c are elastic, plastic and creep strain components, respectively. The true stress-strain data beyond the yield point is used as input to FE analysis and a Mises flow rule with isotropic strain hardening is employed. To define the time-dependent and damage-coupled creep behavior, Eq. (3) is implemented into the ABAQUS user subroutine, CREEP. Eq. (4) is also embedded in CREEP to determine the damage accumulation. Creep damage variable, , is in the range of 0 to 0.99. When at a Gauss point reaches 0.99, all the stress components are sharply reduced to a small plateau and thus crack growth can be characterized by a completely damaged element zone ahead of the initial crack tip. Another user subroutine, USDFLD, is employed to embody this failure simulation technique. Using this numerical method, three-dimensional creep damage analyses are performed to simulate the creep crack growth in thumbnail crack specimens. One quarter of the model consisting of about 10,000 eight-node C3D8R elements is modeled exploiting the symmetry conditions. The mesh size in the vicinity of the crack front is 200µm, which has been proved to provide excellent predictions in Ref. [21]. 4. Results and discussion 4.1 Predictions using fracture mechanics approach To achieve accurate predictions of crack growth using fracture mechanics approach, it is essential to choose a proper maximum crack growth increment, max a , in Eq. (8). Comparison of crack depth variations predicted using five different maximum crack growth increments, max a = t/300, t/150, t/75, t/30 and t/15, for the thumbnail crack in specimen 5 is shown in Fig. 2. It can be seen that the difference between the crack depth variations cannot be neglected when the maximum crack growth increment is relatively large ( max a = t/30 and t/15). For max a = t/300, t/150 and t/75, however,
RkJQdWJsaXNoZXIy MjM0NDE=