13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- surface crack similar to that analysed in this work for both the initial crack and joint geometries, if their result is included in Fig. 6. This further validates the present numerical technique. 4.3. Stress Intensity Factor Variation Figure 7 shows the SIF distributions along the front of the initially circular crack (a/t=0.2) estimated by the 3D finite element method for all six load cases, where the SIF is normalised by a K π = 0 . Obviously, the results vary with the applied load. The distributions along the crack front are basically uniform for Cases I, II and III, but not for Cases IV, V and VI. The SIF for Case IV shows a rapid rise at the plate surface, but that for Case VI drops when the crack front approaches the plate surface. The Case V crack gives a result that the SIF value is zero along the half crack front close to the surface, which means that the crack is in a state of partial closure under the load (Case V). It needs to be indicated that contact elements have been employed for this case. By looking at the crack face load in Fig. 3 for this case, these results are obviously reasonable. Figure 7. Stress intensity factor distributions along the initially circular crack front The degree of the SIF non-uniformity along a crack front with crack growth is more clearly represented for all six loads in Fig. 8, where the ratio of max min K K is plotted against the crack depth ratio, a/t. It can be found that the equal K profile (the SIF value is identical around the crack front), generally, cannot be reached for non-uniform loads. Dependent on the load acting on the crack faces, complex variations exist. For Case V, rapid rise and subsequent drop in the Kmin/Kmax ratio are due to the sine load, whilst for Case VI the zero variation is caused by the existence of partial closure along the crack front. Figure 9 shows the SIF variations for all load cases at both the depth ( θ=0°) and surface ( θ=90°) points, where SIF has been normalized by a K π = 0 . The SIF value at the depth generally increases with the crack advance except Case VI. The SIF decrease for Case VI is due to the rapid drop in stress after the crack propagates to the region of a/t<1/4. The SIF along the surface also tends to increase during crack growth, but that for Case V retains to be zero. CASE I II III IV V VI θ CRACK FRONT POSITION, θ
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