A review and verification of analytical weight function methods in fracture mechanics

Abstract

The weight function method is a powerful method for the determination of key parameters of stress intensity factors and crack opening displacements that are fundamental for crack analyses in fracture mechanics. The method has a remarkable computational efficiency without compromising solution accuracy and is especially suited for cracks in real‐world components with complex stress gradients. A critical issue for successful development and reliable application of the weight function method is how to achieve verifiable and high solution accuracy. This paper provides several reflections on the current state of the art in weight function methods, including a brief historical perspective and description of several analytical and numerical weight methods, with main focus on the two‐dimensional (2D) analytical approaches. A variety of typical application examples are presented. A platform for point‐by‐point accuracy assessment by using the Green's functions is established on a completely independent numerical approach with validated accuracy. Rigorous and systematic verification of the accuracy levels of different 2D analytical weight function approaches are conducted using several benchmark crack geometries. The sources of inaccuracy of different analytical weight function methods are analysed. A brief account on weight function methods for analysing three‐dimensional (3D) crack problems with arbitrary univariant and bivariant stress distributions is provided.

Wide‐range and accurate mixed‐mode weight functions and stress intensity factors for cracked discs

“…Once the weight function for a given crack configuration together with its load‐displacement boundary composition is determined, the SIF for any crack length subjected to arbitrary load can be obtained by simply integrating the product of the stress distribution and the weight function along the crack. By using the Wu‐Carlsson WFM, the present paper has obtained highly accurate mixed‐mode weight functions for the edge‐ and centre‐cracked discs. Furthermore, SIFs for various mode I and mod II load cases have been determined with these weight functions.…”

“…It was pointed out by Wu et al that the best way to verify the accuracy of the weight function is the point‐by‐point comparisons of the corresponding Green's function. The relationship between the weight function m ( α , ξ ) and Green's function G ( α , ξ ) is Figure shows the mode I and mode II Green's functions for the double edge‐cracked disc obtained from Equations (11) and , respectively.…”

“…The maximum difference between Green's functions obtained from the DAM and FEM is 10.7% for mode I and 4.1% for mode II, respectively. A detailed discussion on the limitation of Fett's DAM was given by Wu et al, 18,19 recently. Therefore, compared with Fett's DAM, the present weight function is more accurate and has wider range of validity in term of crack length.…”

“…Fett's weight functions 10,11 are very powerful and widely used for calculating SIFs for cracked discs subjected to various loads. However, it is recently found 18,19 that the accuracy of the mode I weight function for single edge-cracked bodies provided by Fett's direct adjustment method (DAM) can be further improved by the Wu-Carlsson displacement-based WFM. In this paper, the Wu-Carlsson WFM will be extended to determine the mixed-mode weight functions for cracked discs.…”

Weight function for an external circumferential semielliptical crack in a cylinder

“…The WF method proposed by Bueckner 27 and Rice 28 provides the possibility of the determination of the SIF in a linear elastic solid. Wu 29 provided several reflections on the current state of the art in WF methods, including a description of several analytical and numerical WF methods, with main focus on the two‐dimensional (2‐D) analytical approaches. The WF is dependent only on the crack geometry, that is, it is independent of loads.…”