A study of cracks in a three-dimensional finite medium employing the boundary element method

The work presented herein is a method for analyzing cracked, finite, linearly elastic bodies. A mathematical model for the behavior of cracks in a finite medium is presented that is capable of handling any shaped crack in a given domain. The model employs the boundary element method using Somigliana's displacement identity and a traction boundary integral equation. The model was tested using a circular crack embedded inside a circular cylinder subjected to axial tension. For infinitely long cylinders of various radii, results obtained from the method agreed with the analytical solution. For cylinders of finite length, the model gave results that are qualitatively correct. The significance of the model is that it has the potential of modeling cracks with irregular shapes where interference is possible due to crack face closure. It is concluded that the method is capable of accurately predicting the behavior of embedded cracks in a finite body and has the potential for handling crack-face interference and calculation of stress intensity factors.