Research report | Beta Factors for Collinear Asymmetrical Cracks Emanating from an Offset Circular Hole in a Rectangular Plate

Abstract

Beta factors, a nondimensional form of stress intensity factor, are a key input used in generating crack-growth curves as part of Damage Tolerance Analysis work. One specific damage scenario that is of interest is the case of collinear asymmetrical cracks emanating from an offset circular hole in a finite-width rectangular plate, which is representative of circumstances that can occur in aircraft fleets. Unfortunately, no handbook results are available for this geometry. Using a custom-written FORTRAN computer program, interfaced with an existing two-dimensional boundary element fracture analysis code, the present report provides an extensive set of Beta factor solutions covering a wide range of hole offsets and crack lengths. This work has also led to the derivation of an improved closed-form analytical two-dimensional Beta factor solution for the related case of symmetrical cracks emanating from a central hole in a finite-width strip. The availability of accurate Beta factors is an important element in the structural integrity management of aircraft in service with the Royal Australian Air Force. The database of results presented here supports research into probabilistic analysis of multi-site fatigue damage scenarios, as well as assisting the long-term ongoing structural integrity management of aircraft in service with the Royal Australian Air Force.

Executive Summary

Aerospace Division has been deeply involved in the development and application of technologies that help to ensure the safety and enhance the availability of aircraft in service with the Royal Australian Air Force by extending the fatigue lives of airframe structural components. Many of these aircraft structures typically contain large numbers of circular holes that are fitted with fasteners. Fatigue damage often occurs at such holes during the service life of the aircraft, with attendant increases in operating costs and maintenance times. The determination of Beta factors, a nondimensional form of stress intensity factor, that are associated with cracks that occur at holes and other locations, is therefore of significant importance in fatigue life studies, many of which involve extensive and costly experimental fatigue testing.

The particular geometry of interest considered here consists of two asymmetrical collinear cracks emanating from an offset circular hole in a finite-width rectangular plate. These two through-thickness cracks are deemed to interact with each other. As there are no known prior solutions available for this particular scenario, even though there are many handbook solutions for other geometries, the aim of the present work is to determine the required Beta factor solutions in a form that will enable them to be readily utilised in fatigue life computations.

This report details the development and use of a FORTRAN 90 computer program that has been developed to determine Beta factors for two asymmetrical collinear cracks emanating from an offset circular hole in a finite-width rectangular plate. The software is comprised of a small library of subroutines that are used to compute Beta factors for the various cases of interest, which involve different combinations of plate size, hole diameter, hole offset and crack lengths. These subroutines interface with a two-dimensional boundary element program in order to perform the requisite fracture mechanics stress intensity factor calculations, which are then converted to Beta factors. The direct use of these subroutines saves considerable time and effort that is typically needed for developing interpolation routines to handle the tabulated Beta factor data, which are also supplied here in order to provide a comprehensive database of results. The extensive Beta solutions and software tools that have been developed and presented in this report are providing support for research into the probabilistic analysis of multi-site fatigue damage scenarios of aerospace significance. They will also assist in the long-term ongoing structural integrity management of aircraft in service with the Royal Australian Air Force. The computational approach developed and used in the present work is also very amenable to customisation to obtain Beta factors for other geometries. The present work has also led to the derivation of an improved closed-form analytical two-dimensional Beta factor solution that is applicable to symmetrical cracks emanating from a central hole in a finite-width strip.