D. P. Rooke

Mixed-mode Bueckner weight functions using boundary element analysis

A Bueckner singular displacement field is incorporated into the boundary element method in order to calculate weight functions for mixed mode stress intensity factor in a two-dimensional cracked body. Weight functions for modes I and II can be calculated independently and hence the factors KI and KII can be obtained for any arbitrary loading on any boundary. Results are obtained for some slant crack problems in finite sheets and compared with known results where available.RésuméOn incorpore à la méthode des éléments dans un contour un champ singulier de déplacements de Bueckner en vue de calculer les fonctions pondérales qui caractérisent le facteur dintensité pour un mode mixte dans un corps bidimensionnel fissuré. Les fonctions pondérales relatives aux Modes I et II peuvent être calculées indépendamment. Dès lors, les facteur KI et KII peuvent être obtenus pour toute charge arbitraire agissant sur un contour quelconque. On obtient des résultats pour divers problèmes de fissures et on les compare à des résultats connus, lorsque ceux-ci sont disponibles.

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.

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.

Fracture-mechanics weight-functions by the removal of singular fields using boundary element analysis

A new technique is described for the derivation of weight functions for stress intensity factors. The derivation involves the use of the singular field for a point force acting at the tip of a crack. By using explicit expressions (valid near the tip) for this field, it is possible to solve for the weight functions without the need for detailed modelling in the vicinity of the crack tip. Some test results are shown which demonstrate the accuracy of the technique.RésuméOn décrit une technique nouvelle pour obtenir les fonctions pondérales relatives aux facteurs dintensité de contraintes. Cette technique comporte lusage dun champ singulier pour une charge ponctuelle agissant à lextrémité dune fissure.En utilisant pour ce champ des expressions explicites, applicables au voisinage de cette extrémité, il est possible de résoudre les fonctions pondérales sans avoir à recourir à une modélisation détaillée au voisinage de lextrémité de la fissure.On fait état de certains résultats dessai, qui démontrent lexactitude de la technique.

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.

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.

Compounded stress intensity factors for cracks at fastener holes

The compounding technique, a method for obtaining stress intensity factors for complex geometrical configurations from those for simple configurations, is applied to cracks at the edges of the holes in a row of fastener holes. The holes are assumed to be loaded on their perimeters; the original technique requires modification in order to incorporate these loads into the equivalent crack concept. The accuracy of the method is tested by comparing the solution obtained by compounding with that obtained by a collocation technique for cracks at the edges of a row of pressurized holes. Finally stress intensity factors are obtained for cracks at a row of fastener holes near the edge of a sheet.

Stress intensity factors for cracks at a row of holes

Cracks frequently occur in engineering structures at some time during the service life. To ensure safety and optimise inspection schedules it is necessary to be able to calculate the residual strength of the cracked structure and how fast the crack will grow. Both depend on the stress intensity factor which is known for many simple configurations [I]. A compounding method, developed by Cartwright and Rooke [2], can be used to obtain stress intensity factors for complex configurations using the results known for simple configurations. The method has been applied to the problems of one or two cracks at the edge of one of the holes in a row of holes [3]. In this report the method is used to study a configuration with a multiple collinear cracks, i.e., cracks at every hole in a row. The resultant stress intensity factor K at the tip of one of the cracks in a complex configuration can ~e expressed [2] in terms of the stress intensity factors for N simpler configurations: K = K + 2 K) + K (1) Kr (Kn e n=l

Green's Functions in Fracture Mechanics.

The use of Greens functions in the determination of stress intensity factors is described and applied to the solution of problems in fracture mechanics. Methods of obtaining further Greens functions from existing ones are presented. It is shown that several commonly used simple methods of determining stress intensity factors can be expressed in terms of approximate Greens functions. Many important Greens functions are presented and some of these are used to solve several problems of practical importance to the aerospace industry e.g. cracks in stiffened sheets and cracks in pin-loaded lug-joints.