13th International Conference on Fracture June 16–21, 2013, Beijing, China 4 It is known that the creep ductility significantly depends on the stress state. In this work, a modified multi-axial ductility model, which can describes the behavior of creep cavity growth more appropriately than the widely-used Cocks-Ashby model [23], is employed: * 2 0.5 0.5 exp exp 2 3 0.5 0.5 f m e f n n n n , (7) where f is the uniaxial creep failure strain and m is the hydrostatic stress. In this work, the optimum value of f for tests of uniaxial specimens of 316 stainless steel at 600ºC is found to be 0.27, as listed in Table 2. 3. Finite element framework 3.1 Using fracture mechanics approach To predict the crack growth behavior of thumbnail crack specimens under creep conditions, fracture mechanics approach has been used in conjunction with the FE method. Numerical simulations of creep crack growth, which have been based on a step-by-step analysis procedure, are described as follows: (a) Creating of the FE models. One quarter of the specimen containing a semi-elliptical surface crack has been created using the codes ABAQUS [24] and ZENCRACK [25] due to symmetry of both the geometry and loading. About 10,000 elements of type C3D8I for each model have been adopted. Note that extremely refined meshes are generated in the crack tip zone to obtain accurate results. (b) Calculations of values of C*. Values of C* at a set of points which constitute the crack front can be calculated using the equivalent domain integral (EDI) method provided by the codes ABAQUS. In the study, the crack front has been divided into 16 sections, so values of C* at 17 points are recorded in every step. (c) Calculation of the increment of the crack size. The steady-state creep crack growth can be represented by Eq. (2), according to which, the creep crack growth increment at each point along the crack front, ia , can be calculated as * max * max ( ) i q i C a a C , (8) where * iC and * max C are C* at an arbitrary point and the maximum value along the crack front, respectively; max a denote the maximum crack growth increment at the point where * max C occurs.
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