D.J. Cartwright

Analysis of patched and stiffened cracked panels using the boundary element method

Abstract The Boundary Element Method is combined with the method of compatible deformations to analyse the stress distributions in cracked finite sheets symmetrically reinforced by bonded patches and stiffeners. The two-dimensional theoretical model involves an exact representation of the crack tip stress singularities and the stress intensity factors may be calculated directly. Examples of configurations are studied in order to demonstrate the practical use of the method, and it is shown that converged results from the model are representative of adhesively bonded structures.

Approximate stress intensity factors compounded from known solutions

Abstract A versatile method for determining approximate stress intensity factors is presented. The accuracy of the method is assessed using three widely differing configurations for which alternative solutions are available. Finally an approximate solution is then obtained to a configuration for which no alternative solution exists.

Strain energy release rates for a straight-fronted edge crack in a circular bar subject to bending

Abstract The strain energy release rate for a straight-fronted edge crack in a bar of circular cross section subjected to pure bending is determined. The cracked bar is modelled with two-dimensional plane-stress finite elements and strain energy release rates, determined from this model, are shown to be in close agreement with existing results for a bar subjected to three-point bending in which strain energy release rates were determined by measuring the compliance of the bar experimentally. The strain energy release rates for a crack in the circular cross section bar are found to be lower than those in a rectangular cross section bar having the same relative crack length and subjected to the same bending moment. Previously determined results for uniform tension are superimposed to obtain strain energy release rates for a circular cross section bar which is subjected simultaneously to a tensile load and a bending moment.

Simple methods of determining stress intensity factors

Abstract A prerequisite for any fracture mechanics analysis of a cracked structure, is a knowledge of the stress intensity factor at the tip of the crack. Many methods are available for evaluating stress intensity factors, but if the structural configuration is complex, they are usually costly in time and money. This paper describes some simpler approximate methods which are both quick and cheap. Their use is illustrated by examples typical of aerospace applications, e.g. cracks at holes and cracks in stiffened sheets. The errors introduced into calculations of residual static strength and fatique lifetimes by the use of such approximations are acceptable for many practical cases: They are usually no greater and often smaller than those due to uncertainties in other parameters such as service loads, material toughness, etc.

An improved boundary element formulation for calculating stress intensity factors: Application to aerospace structures

Abstract In order to compute stress intensity factors accurately, the standard boundary element method is modified to take explicit account of the singularity in the stresses at a crack-tip. The known expansion terms of the crack tip displacement and stress fields are subtracted to remove the numerical difficulties associated with the representation of a singular stress field at the crack-tip. Hence the accuracy of calculation is much improved, without appreciably increasing the amount of computation involved. Furthermore, the stress intensity factor is directly obtained as a part of a solution and no extrapolations are required. The improved formulation is applied to a configuration, which is representative of a part of the wing in a civil transport aeroplane. This configuration consists of a pair of circular cut-outs (supply ports) near to which smaller holes exist; these small holes are particularly susceptible to cracking.

An analytical solution for two equal-length collinear strip yield cracks

Abstract The development of plasticity at the tips of two equal-length collinear cracks is assessed through the strip yield model of Dugdale and Barenblatt. For this simple configuration, the necessary conditions ensuring a bounded stress field in the vicinity of the crack tips, from which the unknown plastic zone sizes may be obtained, are established in closed form. This analytical solution, which corrects a previously published solution, may be of service in the validation of more general iterative or numerical procedures.

The boundary element method for analysing repair patches on cracked finite sheets

The boundary element method is combined with the method of compatible deformations to obtain stress intensity factors for a cracked sheet reinforced with a repair patch. The method is applied to the analysis of a circular patch over a central crack in a rectangular uniaxially stressed sheet. It is shown that the proximity of the edges of the sheet to the patch edge has a negligible effect on the stress intensity factor of a crack completely under the patch.

On the development of the strip yield model for the assessment of multiple site damage

Abstract The strip yield model is used to assess the link-up of multiple fatigue cracks in a simple open hole configuration. This analysis is based upon the complex stress function formulation of the problem of multiple straight collinear cuts in an infinite sheet. The predictions of link-up and fracture are compared to results from a fatigue crack propagation test on an open hole specimen, and are shown to be in very close agreement.

Boundary effects for a reinforced cracked sheet using the boundary element method

Abstract A Boundary Element procedure for analysis of cracked reinforced finite sheets is developed. The kernel functions used in the Boundary Element procedure are chosen to satisfy the traction free conditions on the crack surface and to avoid explicit modelling of the crack. This allows the stress intensity factor of the crack to be determined accurately using known Greens functions. The method is shown to give stress intensity factors which are in agreement with known results from other methods. New results are obtained which show that the stress intensity factor of the crack in a stiffened sheet is strongly affected by nearby boundaries, although this affect may be considerably relieved by an appropriately positioned stiffener.

the compounding method applied to cracks in stiffened sheets

Abstract The compounding method for determining approximate stress intensity factors is extended and applied to cracks in stiffened sheets. The accuracy of the method is assessed by using configurations for which alternative solutions are available. An approximate solution is obtained for a crack located asymmetrically between stiffeners.