13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- During the continuous cyclic change from elongation to compression different stages of the system appeared (see Figure 2). Stage I: Configuration under no pressure. Stage II: Initiation of reversible local restructuring under tensile loading. Stage III: Formation of one continuous plane with hcp structure. Stage IV: Compression leads to a resolution of the deformation introduced in the previous steps into the structure and to bending of the middle of the notch surfaces towards each other up to a minimum distance of 6.8 Å. Stage V: During the fourth loading cycle dislocations are initiated. The Dislocation Extraction Algorithm (DXA) [4] detects “defect surfaces”. “The defect surface consists of those parts of the interface mesh, which have not been swept by elastic Burgers circuits.” [5] Stage VI: Dislocations still remain in the structure even though no pressure remains in the system. 3. Microstructural crack nucleation and propagation To solve problems of micro-crack nucleation the Tanaka-Mura model [16] is frequently used. The number of stress cycles Nc required for micro-crack nucleation can be determined as follows: ܰ ൌ 8 ܹܩ ௦ ߨ ሺ1െ ߥ ሻ݀ ሺΔ߬̅ െ2݇ ሻଶ (3) Eq. (3) presumes that micro-cracks form along slip bands within grains, depending on slip band length ݀ and average shear stress range Δ߬̅ on the slip band. Other material constants (shear modulus ܩ , specific fracture energy per unit area ܹ ௦, Poisson‘s ratio ߥ and frictional stress of dislocations on the slip plane can be found in the specialized literature [17]. Jezernik et al. [18] used the Tanaka-Mura model to numerically simulate the small crack formation process. Three improvements were added to this model: (a) multiple slip bands inside each crystal grain as potential sites for crack nucleation, (b) micro-crack coalescence between two grains and (c) segmented micro-crack generation inside one grain. A numerical model was directed at simulating fatigue properties of thermally cut steel. The authors took into account accompanying residual stresses in order to simulate the properties of the thermally cut edge as faithfully as possible. micro-crack nucleation micro-cracks coalescence Figure 3. Micro-crack nucleation and subsequent coalescence [18]
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