WEIGHT FUNCTION METHODS AND ASSESSMENT FOR AN EDGE CRACK IN A SEMI-INFINITE PLATE

Weight function method (WFM) is highly efficient and accurate for the determination of stress intensity factors (SIFs) and crack opening displacements (CODs) of cracked bodies under arbitrary load conditions. Comparing to the numerical methods such as the finite element method, WFMs have distinct advantage in terms of computational efficiency and reliability. This paper makes systematic analyses and comparisons of three WF approaches by Wu-Carlsson, Glinka-Shen and Fett-Munz, respectively, which are representative in the international fracture mechanics community. By employing the Wigglesworth analytical solutions to CODs of an edge crack in a semi-infinite plate under uniform tension, the WF and corresponding Green's function (SIF for a pair of point forces acting at an arbitrary location along the crack) are derived and used as the base for point-to-point comparison. The results are also compared with other existing WFs in the literature, including those by Bueckner, Hartranft-Sih and Wigglesworth using different analytical approaches. The study also includes the influence of selection of three reference load cases, including uniform, linear and reverse-linear stress distributions and their combinations, and geometric conditions related to CODs on the WF accuracy. Results show that the WF based on COD analytical expression for one reference load case are more accurate than that based on two SIFs due to two reference load cases. Furthermore, solution accuracy of the later approach is considerably affected by the selected reference load case(s). The geometric condition that the third derivative of COD vanishes at crack mouth has little effect on the accuracy of one-reference-load-case-based weight function. Finally, SIFs for four load cases calculated by using various WFMs are presented and compared.