13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure 4 Analysis model and boundary condition 3.2. Characteristics of singular stress field at the edge corner The characteristics of the singular stress field at the corner edge are mentioned using the analysis results of the specimens A25, A50 and A25-90. Figure 5 shows the relationship between the A25 , A50 ,y FEM y FEM σ σ , A25, A50 , xy FEM xy FEM τ τ and r under the applied stress σ0 = 1MPa. Then, Figure 6 shows the relationship between the A25 0, A50 0, y FEM y FEM σ σ , A25 0, A50 0, xy FEM xy FEM τ τ and emin. When t2 are set constant, the stress ratios almost become constant independent of emin. Figure 7 shows the relationship between the A25 , A25 90 , y FEM y FEM σ σ − , A25, A25-90 , xy FEM xy FEM τ τ and r under the applied stress σ0 = 1MPa. Then, Figure 8 shows the relationship between the A25 0, A25-90 0, y FEM y FEM σ σ , A25 0, A25 90 0, xy FEM xy FEM τ τ − and e min. The stress distributions of the specimen A25-90 are different from those of the specimen A50. That is because the moment which is applied to the adhesive layer changes depending on the adhesive thickness. However, when the r is smaller than about 10-4 mm, the A25 0, A25-90 0, y FEM y FEM σ σ and A25 , A25 90 , xy FEM xy FEM τ τ − almost become constant. Then, the stress ratios at the edge corner, A25 , A25-90 ,y FEM y FEM σ σ and A25 0, A25 90 0, xy FEM xy FEM τ τ − , become constant independent of the e min. From the results, the stresses on the interface near the corner edge are expressed with as follows independent of the t2 and l2. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = + ≅ − − − − 2 1 2 1 1 1 1 2 1 1 1 λ σ λ σ λ σ λ σ σ r C r K r K r K y , (2) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = + ≅ − − − − 2 1 2 1 1 1 1 2 1 1 1 λ τ λ τ λ τ λ τ τ r C r K r K r K x y (3) Here, Cσ and Cτ are constant. The intensities of singular stress field of the reference problem and the unknown problem are denoted with σK and * σK , respectively. Then, the stresses in the y direction at the edge corner of the unknown problem and the reference problem, which are obtained from the FEM analysis, are denoted with y FEM 0, σ and * 0, y FEM σ , respectively. From Equation (2), the relation between * σ σ K K and * 0, 0, y FEM y FEM σ σ can be expressed as follows. * 0, 0, * y FEM y FEM K K σ σ σ σ = (4) If the * σK has been solved, the y FEM 0, σ is equivalent with the σK because the * 0, y FEM σ can be obtained from the FEM analysis of the reference problem. The xy FEM 0, τ is also equivalent with the τK . As shown in Figure 6, it is found that the different between A25 0, A50 0, y FEM y FEM σ σ and A25 0, A50 0, xy FEM xy FEM τ τ tends to become small with the r decreasing. Then, from Figure 8, the different between A25 0, A25-90 0, y FEM y FEM σ σ and A25 0, A25-90 0, xy FEM xy FEM τ τ tends to become small with the r decreasing. From Figures 6 and 8, the relations of A25 0, A50 0, A25 0, A50 0, xy FEM xy FEM y FEM y FEM τ τ σ σ = and A25 0, A25-90 0, y FEM y FEM σ σ A25 0, A25-90 0, xy FEM xy FEM τ τ = can be confirmed. This means * 0, 0, * 0, 0, xy FEM xy FEM y FEM y FEM τ τ σ σ = , that is, following equation.
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