PSI - Issue 2_A

Gunter Kullmer et al. / Procedia Structural Integrity 2 (2016) 2994–3001 Author name / Structural Integrity Procedia 00 (2016) 000–000

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FE-mesh of the initial crack model

Fig. 5. FE-meshes for the CT-specimen with an orientation angle α = 45° for the region boundary and the initial crack model

For the crack growth simulation with ADAPCRACK3D the global mesh is unstitched along the crack surface with the aid of a crack model. The crack model is a surface mesh that represents only the surface of the crack. At the beginning of the simulation, the crack model is the mesh of the initial crack model shown in Fig. 5. The rectangular surface of the initial crack is evenly meshed with 10 linear triangle elements in thickness direction and 5 linear triangle elements in longitudinal direction. The initial crack has a lateral length of 1mm. For a growing crack the crack model is incrementally extended with additional crack surfaces in the direction depending on the estimated mixed mode ratio. Since the present investigation in principle represents a plane problem ADAPCRACK3D is modified in a way that with every simulation step a uniform crack increment over the specimen thickness with a fixed lateral length of 0.2mm is achieved. For the calculation of the stress intensity factors ADAPCRACK3D uses the modified virtual crack closure integral (MVCCI) after Rybicki and Kanninen 1977 applied to a comoving submodel composed of a regular linear hexahedral mesh containing the crack front. First for every node at the crack front, the energy release rates G I , G II and G III for the respective crack opening modes are calculated. For the calculation of the stress intensity factors from the energy release rates a state of plane stress is assumed. The equations valid for the state of plane stress read ܭ ூ ൌ ඥ ܩ ூ ܧ and ܭ ூூ ൌ ඥ ܩ ூூ ܧ . Since plane mixed mode loading is existent, the mean values of the stress intensity factors K I and K II over the thickness of the specimen are used to calculate the crack deflection angles with the maximum tangential stress criterion after Erdogan and Sih 1963. The stress intensity factor K III is neglected to avoid a twisting of the crack surface. Furthermore it is meaningful to use the mapped mesh-method for the meshing of the initial crack as shown in Fig. 5 to achieve constant crack deflection angles over the thickness of the specimen, because ADAPCRACK3D uses local coordinate systems based on the mesh of the previous crack surface to calculate the coordinates of the new crack front nodes. Thus, the mesh of crack remains uniform even during the extension of the crack. 3. Verification of the crack growth simulations Prior to executing the actual numerical simulations of CT-specimens with regions of differing stiffness, it is verified if the simulation model and the modified version of ADAPCRACK3D are suitable for the planned investigations. Therefore, simulations with the intended different values of Young´s modulus in both regions and a constant orientation angle α = 90° of the region boundary are conducted. Due to symmetry, the portion of mode II should be zero and the crack should grow straight independent of Young´s modulus in both regions. The evaluation of the numerically determined resulting crack paths for all cases with α = 90° shows, that only small varying portions of mode II occur and that crack paths are almost straight with slight deviations from zero in y-direction corresponding to the typical numerical oscillations. Already numerical inaccuracies due to an asymmetric FE-mesh, typical for using the free mesh option, cause slight deviations from a straight crack path. Additionally it is verified if the application of mean values for the stress intensity factors has a significant influence on the calculated crack paths or the course of the stress intensity factors along the crack paths. For this purpose, various evaluation methods for the course of the stress intensity factors over the thickness of the specimen are compared. Fig. 6 shows an exemplary distribution of the raw data of K I along the crack front over the thickness of the specimen compared with the courses of K I smoothed with a 4 th degree polynomial regression and as mean value. The smoothing of the courses of the