A new weight function expression for through cracks

The application of weight functions for the determination of stress intensi ty factors can be greatly enhanced if simple but accurate expressions are a vailable. A simple weight function expression for through cracks under Mode I (opening mode) loading is proposed in this study. The requirement that w eight functions should be applied to stress fields that do not possess fewe r symmetries than the reference loading case used in the derivation of the weight function, is first examined. It is found that this restriction can b e largely removed by using a more general coordinate axis configuration and an unambiguous definition of crack length in deriving a weight function ex pression. A new expression is then proposed for through cracks by consideri ng the Taylor series expansion of the crack surface displacement as a funct ion of distance from the crack tip. The form of the proposed expression is verified, with different numbers of terms, by using it to curve-fit referen ce weight function values for the following three crack configurations: (a) an array of collinear through cracks in an infinite plate; (b) a central t hrough crack in a rectangular plate; and (c) an eccentric through crack in a rectangular plate. Such reference values are generated either from closed -form expressions or by finite element analysis. The proposed expression is found to produce accurate values for both centrally and eccentrically loca ted cracks. (C) 1999 Published by Elsevier Science Ltd. All rights reserved .