Stress intensity factor evaluation from displacements along arbitrary crack tip radial lines for warped surface flaws

A procedure has been developed to calculate the stress intensity factors from the displacements along any arbitrary crack tip radial line on a quarter-point singular finite element boundary. This procedure enables the conventional finite element method to handle surface and one-dimensional flaws with curved crack lines. The common conversion method which uses the displacements along the crack surfaces is not valid for a flaw with curved crack lines. The developed procedure was validated by analysing an angled edge crack in a flat plate under tension and a weld toe surface flaw in an X-shaped tubular joint under tension and bending loads. This method can also provide a means to assess the accuracy of the stress intensity factor solutions of complex crack geometries through a comparison of the solutions evaluated at variously different angular locations. This paper revealed that when a structural geometry is complex in such a way that the proper binormal plane cannot be defined at the surface crack front points of a finite element mesh of a surface crack, the stress intensity factor cannot easily be calculated at these points by using the conventional finite element method. In this case, it is necessary to use some form of hybrid finite element with built-in crack-tip singularities.