Love, A.J.; (2008) Interpolation of SIF weight functions in fracture mechanics analyses. Doctoral thesis , University of London.

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Abstract

Engineers are commonly confronted by complex, linear elastic crack problems, typically cracks situated at notches, for which relevant and readily available SIF solutions are sparse. The difficulty in accurately determining such solutions for rapid engineering defect assessment without resorting to specialist analyses, e.g. numerical or experimental methods, is well known and longstanding. The thesis documents the development of a novel methodology for the calculation of SIF solutions for cracks in complex geometries subject to non-simple loading arrangements. A methodology, termed an 'interpolation of base geometry weight functions' was designed to empower the engineer with a tool to generate broad ranging solutions accurately and rapidly in a manner that is robust and requires minimal specialist insight. The methodology utilises constituent geometry SIF solutions, of more simple form, to isolate the geometric influence of the notch upon SIF. Expressed as an interpolation factor the geometric influence is used to interpolate two extreme, plane geometry (or 'base' geometry) weight functions to determine a weight function for the notched geometry. Once determined the notched geometry weight function is used with crack-line stress distributions to efficiently calculate new SIF solutions for a number of loading arrangements. The interpolation methodology allows large numbers of new SIF solutions to be readily generated from a relatively small, 'library' of constituent geometry solutions. The primary body of work details development and validation of the methodology, applied to a wide range of two-dimensional notch geometry types, both symmetric and asymmetric. Generation of constituent geometry SIF solutions, using FEA their subsequent manipulation, dictated by the interpolation scheme and formulation of base geometry weight functions, using a contemporary methodology are presented. New SIF solutions obtained are rigorously validated against those developed from finite element and experimental methods and compared to existing, closely related weight function methodologies. The interpolation scheme was shown to display excellent performance, economy and versatility and universal applicability to all notch types. Application of the interpolation methodology was extended to determine deepest point SIF solutions for surface cracks in complex three-dimensional bodies. Weight function formulation utilises two-dimensional constituent geometry solutions together with three-dimensional 'base' geometry weight functions. Though presently restricted by a number of approximations, results achieved for surface cracks in notched flat plates compared well to those determined via full three-dimensional FEA. The broad ranging scope for applications and future developments of the interpolation scheme are identified and cited.

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