PSI - Issue 13

Katharina Dibblee et al. / Procedia Structural Integrity 13 (2018) 322–327 Katharina Dibblee et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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The cyclic stress intensity factor which indicates the minimum value corresponds to the relevant stress intensity factor. This is used to determine the relevant stress function and also provides the angle of deflection phi3D under which the crack will spread when the material grading is reached.       M th,3D I 0 th,3D I 3D I,th Δ ; Δ MIN Δ        K K K (5)

3. Numerical investigation of crack growth behaviour in fracture mechanically graded materials

In order to be able to calculate crack growth simulations considering an existing fracture mechanical material grading, the new 3D concept presented here was implemented in the already established simulation program A DAP C RACK 3D. With the resulting extended program A DAP C RACK 3D Version_KD15 it is now possible to calculate crack growth processes for homogeneous, isotropic and also for functionally graded materials.

3.1. Crack growth simulations using CT and CTMM specimen

To illustrate the influence of fracture mechanical material grading on crack propagation behaviour, crack growth simulations were performed on standard compact tension (CT), ASTM (2008), and compact tension mixed mode (CTMM) specimen. Two material areas were created in the required FE-models. Material range M1 represents the range with the fracture mechanically seen less favourable characteristic values compared to the range M2 with the more favourable characteristic material values. In the model of the CT specimen a grading angle of φ M = 40° and in the CTMM specimen an angle of φ M = -75° and φ M = 30° were realized. As can be seen in Fig. 3, the crack paths in both the CT specimen and the CTMM specimen using a grading angel of φ M = -75° change depending on the existing material property areas. If the crack growth starts in the material area with the less favourable mechanical properties, the crack growth depending on the stresses prevailing.

Fig. 3. Crack growth simulations under consideration of fracture mechanical material grading: (a) & (b) CT-specimen with a grading angle of φ M = 40° and changing material areas (c) & (d) CTMM-specimen with a grading angle of φ M = -75° and changing material areas (e) & (f) CTMM-specimen with a grading angle of φ M = 30° and changing material areas