13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- on the resonant behavior is investigated. The slip band model adopted in this study is applied on a mesoscopic scale and accounts for the mechanisms of slip band formation, motion and multiplication of dislocations (expressed with the term sliding), its cyclic irreversibility and cyclic hardening. To investigate the effect of the suggested slip band model on the resonant behavior it is adapted to the simulation of real microstructures. Several studies in the field of microstructural modeling and simulation of fatigue damage use the finite-element method (FEM) in conjunction with crystal plasticity models. Although the FE-method combined with crystal plasticity models has been devoted to a wide range of applications the implementation of the newly proposed slip band model of this study would present some difficulties: formation of new slip bands would require a remeshing algorithm and computation of sliding displacement in slip bands would necessitate special finite elements like cohesive-zone elements. In this study a two-dimensional boundary element method (BEM) is applied, in which the proposed slip band model can be implemented very effectively. The most outstanding feature of this method is that it uses displacement differences or sliding displacements directly as unknowns on slip band layers and element discretization is confined to outer boundaries such as grain boundaries and on slip bands. The proposed BEM can simulate slip bands in a two-dimensional microstructure consisting of grains with individual anisotropic elastic properties. In the following paragraphs at first the results of experimental examinations are given and then the simulation model with its slip band mechanisms is presented and the numerical method is specified. After presenting a procedure to determine the resonant behavior resulting from simulations, the effect of damage accumulation in slip bands on the resonant behavior is investigated in a model representing the morphology of a real microstructure. 2. Experimental Characterization The resonant behavior of a metastable austenitic stainless steel (AISI304) is studied experimentally by means of a resonance-testing-machine, which readjusts the excitation resonant frequency during testing. The material shows a distinct transient characteristic, as shown in Fig. 1a. The lower curve in Fig. 1a indicates the test frequency at a stress amplitude of 240MPa, representing the damped resonant frequency fres of the specimen-machine system. The upper curve in Fig. 1a indicates the testing frequency at low stress levels (50MPa) at distinct fatigue life stages (due to testing at 240MPa). It shows the resonance frequency f0 of the sample without the damping effect of plastic deformation. Fig. 1b shows a transmission electron microscopy (TEM) micrograph of the dislocation arrangement in metastable austenitic stainless steel in the fully austenitic condition fatigued under VHCF condition. The micrograph indicates that dislocations in slip bands are arranged in pile-ups at grain boundaries. Figure 1. (a) Damped (fres) and undamped (f0) resonant frequency during cyclic loading of metastable austenitic stainless steel; (b) TEM micrograph of dislocation pile-ups at a grain boundary in metastable austenitic stainless steel (loading amplitude: 240MPa, number of cycles: 107)
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