13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- very close to the detector plane. a b Figure 8: (a) Illustration of the working principle of the diffraction-contrast tomography (DCT) [7], (b) reconstructed slice of a duplex steel fatigue specimen mapped with DCT. The beam is confined by slits to limit the number of penetrated grains. During the rotation of the sample, some of the grains fulfill the Bragg condition; therefore, the grains are producing diffraction spots on the detector plane. Afterwards, a semi-automated computer code reconstructs the individual grain shape and position in the volume from the pictures taken during the rotation of the sample, cf. Figure 8 b. The data will be used for a more detailed prediction of local crack or slip band nucleation sites by means of the finite-element method (FEM). An example of the application of the FEM is given in Figure 9. The microcracks (see arrows in Figure 9 a) were initiated at a stress amplitude of Δσ/2365 MPa. The emanation process of the slip bands within the austenite grain γ1 leads to stress intensities at the phase boundaries and in the neighboring ferrite grain α1. a b c Figure 9: (a) intercrystalline und transcrystalline fatigue crack initiation (arrows) in the ferrite, introduced by local stress intensities caused by slip bands within the austenite, (b) plastic slip on the slip system with the highest stress, (c) plastic slip on discrete slip bands. Eventually, the initiated dislocation motion in the ferrite leads to the crack initiation process described by Tanaka and Mura [1]. The transport of the plastic deformation was supported by the low twist and tilt angle between the austenite γ1 and ferrite α1 grains. With the help of a material model according for crystal plasticity, the slip on adjacent slip systems have been calculated by FEM [8]. The model is considering the elastic and plastic anisotropic deformation of the grains, which is leading to the inhomogeneous stress distribution. Figure 9 b shows the displacement on slip system in the austenite grain γ1 with the highest stress, leading to pronounced slip band formation. To analyze the stress distribution at the phase boundaries, discrete slip bands have been integrated on the highly stressed austenite grain (cf. Figure 9 c), according to the results of Figure 9 b. These slip bands are activated when the local friction stress τfr is exceeded. Meanwhile, the other areas of the austenite grain are deforming only anisotropic-elastic. This approach allows to calculate a global stress value which is not sufficient to initiate any plastic deformation within the ferrite phase. Accordingly, the endurance limit for a certain area of the microstructure can be estimated.
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