13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- ligament and the size of the element is 0.125mm. The details for the finite element model are depicted in Figure 5. ΔF boundary condition ux=0 boundary condition ux=uy=0 crack cohesive elements Figure 5. Finite element model for simulated compact tension specimen In the calculation, three different cyclic loading ranges are used: ΔF=1200N, ΔF=950N and ΔF=800N. All loading ratios are R=0. The fatigue crack growth rate Δa/ΔN can be calculated directly from the numerical model, but the cyclic ΔJ integral will be computed by another approach. A finite element model of the CT specimen without cohesive zone is built. The crack length inserted in this model is (a0+Δa). One cycle is calculated and the cyclic ΔJ integral is computed by Equation (12) [23]. 0 i i ij ij u J Wdy t ds W d x ε σ ε Δ Γ ∂Δ ⎛ ⎞ Δ = Δ −Δ Δ = Δ Δ ⎜ ⎟ ∂ ⎝ ⎠ ∫ ∫ (12) σ Δ ij and ε Δ ij are the cyclic stress and strain range. W is the cyclic deformation energy. x and y are the Cartesian coordinates with the x-axis parallel to the crack surface. Γ is the integration path. ds is the line element lying on the integration path. Δit is the cyclic stress vector on the integration path. Δ iu is the cyclic displacement variation. The simulation results under three loading ranges are plotted together with the scatter band of experimental data in Figure 6. Figure 6. Comparison of fatigue crack growth rates curve for material S460N A reasonable accordance of experimental and simulated results is achieved. The simulated fatigue crack growth rates are a little bit faster than the experimental data, but the total trend for fatigue
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