Abstract
The stress intensity factor for the crack under mode III loading in the three dimensional elastic body is analyzed numerically by the finite element method. After obtaining the energy release rates, these energy release rates are converted into stress intensity factors. The method considering the difference of the strain energy between the analysis model and the crack extension model is used for the approach obtained the energy release rate in this study. The ratio of the model width(W), the model thickness(T) and the model length(L) for the basic finite element model are in the ratio 1:1:4. After the analytical accuracy is investigated by three point bending model with the mode I loading, the stress intensity factor for mode III loading is analyzed by the same basic finite element model with the different boundary condition. As a result, the result for mode I loading using the basic model agrees well with the two dimensional analytical solution. However, the result for mode III loading has the some differences for the two dimensional exact solution. Therefore, the numerical analyses of the model with different thicknesses are conducted for mode III loading. As a result of those analyses, it is clear that the numerical results approach the exact solution with the increase of thickness length. That is to say, the model thickness needs about twenty times as long as the model width to obtain the result close to two dimensional exact solution by the three dimensional analysis. However, the model length(L) requires eight times(L=8W) of the model width(W) in connection with the influence of the boundary condition.
