13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- 2.3 Validation As highlighted in the Introduction section due to complexity of the numerical analysis and interpretation of the computational results there were almost no works investigating this singular mode. However, the three-dimensional effects, specifically the coupling of fracture modes II and III, were often recognised and acknowledged in many papers on stress analysis of cracked structural components, fracture and fatigue. A comparison of the present results obtained with ANSYS 11 and those published in [11] in terms of the ratio of the induced to applied stress intensity factors III C II K /K as a function of the position along the crack front, z/H, are shown in Fig.3, demonstrating a good agreement. Description of all parameters of the modelling is given in [10] and the definition of the stress intensity factor of the coupled mode C II K will be provided in the next Section. 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 Normalized coordinate z/H Normalized coupled SIF Kc II/KIII Fig.3 Comparison of the present FE calculations and published results: line is the current numerical results and filled circles are data from [11] 3. Numerical Results 3.1 Stress State First, the results for the out-of-plane shear stress components along the bisector line for different distances from the crack tip are considered. The results can also be represented in non-dimensional form; however, the non-dimensional results are sometimes difficult to relate to practical situations. Therefore in the following computational examples, if it is not specified separately, the applied remote stress intensity factor, KIII= 1 MPa m, Poisson’s ratio ν=0.3 and the thickness of the plate, H= 40 mm. The intensity of the computed stress component τyz defined similar to the classical definition of the stress intensity factor for mode II in plane problems of elasticity as ( ) ( ) III 1 yz x 0 III z x K z 2 lim −λ → = π τ (3) can be obtained using a standard log-log regression analysis of the stress distribution. The singular power describes the asymptotic rate at which the stress components increase as the crack tip is approached. As expected, the stress field everywhere has been found to have a degree of singularity
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