Mixed mode fatigue growth of curved cracks emanating from fastener holes in aircraft lap joints

The finite element alternating method is extended further for analyzing multiple arbitrarily curved cracks in an isotropic plate under plane stress loading. The required analytical solution for an arbitrarily curved crack in an infinite isotropic plate is obtained by solving the integral equations formulated by Cheung and Chen (1987a, b). With the proposed method several example problems are solved in order to check the accuracy and efficiency of the method. Curved cracks emanating from loaded fastener holes, due to mixed mode fatigue crack growth, are also analyzed. Uniform far field plane stress loading on the plate and sinusoidally distributed pin loading on the fastener hole periphery are assumed to be applied. Small cracks emanating from fastener holes are assumed as initial cracks, and the subsequent fatigue crack growth behavior is examined until long arbitrarily curved cracks are formed near the fastener holes under mixed mode loading conditions.     

Composite repairs to cracked holes under bi-axial loading

This paper begins by briefly discussing a simple method for calculating the stress intensity factors for cracks emanating from a notch under arbitrary loading. A range of examples are presented to demonstrate the accuracy of the present method. This technique is then used to extend existing design formulae for the composite repairs to cracks in thin metallic skins [J. Compos. Struct. 11 (1) (1989) 57; Int. J. Solid Struct. 17 (1981) 827] to allow for the repair of cracks at holes or notches under complex bi-axial loading.     

Modelling of a patch repair to a thin cracked sheet

Integrity enhancement of damaged or design deficient structures through repairs is attracting considerable engineering attention. Bonded composite patch repairs to cracked metallic sheets offer various advantages over riveted doubler type, particularly for airframe applications. This paper first reviews the R&D activity in the area of structural repairs. It then approaches the problem of a composite patch repair to a cracked aluminium sheet with different finite element modelling strategies and compares their outcome. The efficient finite element modelling approach thus established is used to study the effect of patch material, patch size, patch symmetry and adhesive thickness on repair performance as the crack grows in the repair configuration.     

Retardation of cracks emanating from fastener holes

A limited number of cold expansion and interference fit fastener systems were evaluated to determine their capability to retard the growth of cracks emanating from fastener holes. The fastener systems were applied to specimens fabricated from 7075-T6 aluminum. In all cases the fastener holes had fatigue cracks emanating from them before the fastener system was applied. Some samples that were used as baseline were fitted with non-interference fit fasteners. All samples were tested in constant amplitude fatigue at an R ratio of 0.5 at maximum stresses of 20 or 30 ksi. The results show that a cold expansion or properly installed interference fit fastener system significantly retards the growth of preexisting cracks emanating from fastener holes irrespective of the amount of load transfer through the joint.     

Compressive behaviour of CFRP laminates repaired with adhesively bonded external patches

Composite patches can be used to reinforce and repair both cracked composite and metallic aircraft structures. The repair of a composite structure with a composite patch may use mechanical fastening, which often introduces undesirable stress concentrations or adhesive bonding, external or flush patches. To ensure a reliable and durable bond, various parameters such as the quality of surface preparation and the design of the composite patch (size, shape, stiffness) are very important. This paper describes the testing of bonded external patch repaired CFRP laminates loaded in compression. It is found that the critical failure mechanism is fibre microbuckling in the 0° plies accompanied by matrix cracking and delamination, triggered by failures at the adhesive/adherend interface. A three-dimensional finite element analysis is performed to estimate the stress field in the repaired region. The calculated stresses are then used with the maximum stress and average stress failure criteria to predict damage initiation, mode and location. Carefully designed external patch repairs can recover more than 80% of the undamaged compressive strength.     

Fracture Analysis of Double-Side Adhesively Bonded Composite Repairs to Cracked Aluminium Plate Using Line Spring Model

A line spring model is developed for analyzing the fracture problem of cracked metallic plate repaired with the double-sided adhesively bonded composite patch. The restraining action of the bonded patch is modeled as continuous distributed linear springs bridging the crack faces provided that the cracked plate is subjected to extensional load. The effective spring constant is determined from 1-D bonded joint theory. The hyper-singular integral equation (HSIE), which can be solved using the second kind Chebyshev polynomial expansion method, is applied to determine the crack opening displacements (COD) and the crack tip stress intensity factors (SIF) of the repaired cracked plate. The numerical result of SIF for the crack-tip correlates very well with the finite element (FE) computations based on the virtual crack closure technique (VCCT). The present analysis approaches and mathematical techniques are critical to the successful design, analysis and implementation of crack patching.     

Design and analysis of mechanically fastened composite joints and repairs

In this paper, a boundary element formulation is developed to analyze mechanically bolted composite joints and repairs. Boundary equations are formulated for all the member panels of the composite joints/repairs. These equations are solved together with the fastener equations to get the resultant contact forces for all the fasteners involved. The fasteners are modeled as 1-D springs that are governed by linear relationships between the fastener forces and the displacements of member panels at the respective fastener centers. After obtaining the fastener forces from the so-called global analysis, detailed stress analyses are conducted for regions around individual fasteners. The stress distributions around fastener holes are then used to evaluate the margin of safety of the composite panels. The numerical predictions on the fastener forces, failure modes and failure loads of two composite joints using this method agree very well with experimental results. The boundary element formulation presented here is especially suitable for design and analysis of aircraft battle damage repairs where time and facility availability is the prime concern.     

Tensile cracks in polycrystalline ice under transient creep: Part II — Numerical simulations

This paper discusses predictions of a numerical model presented in the companion paper (Nanthikesan and Shyam Sunder, 1995) to analyze tensile cracks in polycrystalline ice undergoing transient creep. The numerical model is based on the internal state variable constitutive theory of transient creep in ice developed by Shyam Sunder and Wu (1989a,b, 1990). The finite element model uses the boundary layer approach of Rice (1968), in conjunction with a mid-point crack-tip element and reduced integration, to simulate the asymptotic stress and deformation fields in the vicinity of the crack tip, including incompressible creep deformations.

The problem of a stationary, traction-free, tensile (mode I) crack is analyzed to predict the size, shape and time evolution of the creep-dominated fracture process zone surrounding the crack-tip. The numerical simulations quantify the effects of transient creep, material strain hardening, fabric anisotropy, loading rate, temperature, and finite fracture test-specimen boundary on the development of the creep zone. A range of stress-intensity rates from 1 to 100 kPa s⁻¹ and temperatures from −5° to −25°C is considered in the simulations.

The results from a comprehensive numerical simulation study show that: (i) transient creep increases the creep zone size by more than an order of magnitude over that for a power-law creeping material, i.e., about 40 times for the isotropic, equiaxed granular ice tested by Jacka (1984); (ii) material strain hardening significantly affects the creep zone size, i.e., the creep zone for the transversely-isotropic columnar-grained ice tested by Sinha (1978), with the crack loaded in the plane of isotropy, is about 4 times smaller than that for the granular isotropic ice; (iii) fabric anisotropy increases the size of the creep zone by a factor of at least two for cracks in the transversely-isotropic, columnar-grained ice loaded in the plane of isotropy; (iv) the Riedel and Rice (1980) equation, which was derived for an isotropic power-law creeping material subjected to a suddenly applied constant stress-intensity, overestimates the creep zone size by a factor of 4.2 for a constant stress-intensity rate loading; and (v) as the crack size increases, linear elastic fracture mechanics becomes increasingly applicable at lower loading rates and higher temperatures.     

Comparison of the effectiveness of boron/epoxy and graphite/epoxy patches for repaired cracks emanating from a semicircular notch edge

The adhesively bonded composite patch repair technique has been used to restore or extend the service life of the cracked aluminium structural components because of its efficiency. In this study, the finite element method is used to analyse the performance of the different bonded composite patches at a semicircular lateral notch and the repair of cracks emanating from this kind of notch. The knowledge of the stress distribution in the neighbourhood of the cracks is important for the analysis of their repair according to the geometry of the patch. The effects of the mechanical and geometrical properties on the variation of the stress intensity factor in the crack tip were highlighted. The effects of the adhesive properties and of the patch size on the stress intensity factor variation at the crack tip in mode I were also highlighted. The comparison between the double and single patch repairs is also given in this study. The results obtained show that the stress intensity factor of the crack tip repaired by two composite patches, is reduced to a half compared to the one that is repaired only by one patch. The orientation of fibres possessing a higher rigidity perpendicularly to the crack propagation considerably influences the reduction of the stress intensity factor. The adhesive properties must be optimised in order to increase the performance of the patch repair or the reinforcement.     

The effects of size and stacking sequence of composite laminated patch on bonded repair for cracked hole

The performance of a bonded repair for cracked holes has been studied using the three dimensional finite element method, linear elastic fracture mechanics and strain energy density theory. Increasing the composite patch size reduces the strain energy level at the crack tip; increasing the patch length normal to the crack is a better choice. The stacking sequences of the laminated patch have little influence on the strain energy distribution in the vicinity of the crack. To repair the cracked holes of aircraft components subjected to variable direction loading during flight, the orientations of the patch ply, 90° and ±45° with respect to the crack direction, are the optimum selection in bonded repairs.     

The mechanics of matrix cracking in fiber reinforced ceramic composites containing a viscous interface

A detailed fracture mechanics analysis of matrix cracking in a fiber reinforced ceramic composite is presented for the case where the fiber—matrix interface exhibits viscous flow as can be the case when ceramic composites containing amorphous interfacial layers are subjected to loads at elevated temperatures. The analysis considers the case where matrix cracks are fully bridged by fibers, and the role of the viscous interface is to introduce a time dependence into the stress-intensity formulations. Such time-dependence arises because the bridging fibers are able to pull out of the matrix by viscous interfacial flow, with the result that the crack opening, as well as the actual (or shielded) matrix crack-tip stress-intensity factor, increase with time under the action of a constant externally applied load to the composite. The differential equation governing the mechanics of the fiber pull-out is derived. This is then applied to obtain expressions for the time-dependence of the crack opening and the effective crack-tip stress-intensity factor in terms of material and microstructural factors. These expressions predict that the matrix crack will exhibit stable crack growth, with the crack growth rate being essentially crack length (and time) independent and a function only of the applied stress and of material and microstructural factors. It is also shown that the composite lifetime is independent of the sizes of pre-existing cracks and is dependent only on a critical microstructure dependent flaw size, applied stress and microstructural factors.     

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.     

Disbond effect on the stress intensity factor for repairing cracks with bonded composite patch

It is well known that the stress intensity factor is considerably reduced by the bonded composite repair. The finite element method is used to compute the stress intensity factor for repairing cracks with bonded composite patch taking account of the disbond. In the case of a disbond, the increase of patch thickness reduce the negative effects of disbond. The curves plotted show the concordance with the model [Thermal residual stresses in composite repairs on cracked metal structures, Ph.D. Thesis, University of British Columbia, 1998].     

Design of Emergency Aircraft Repairs Using Composite Patches

The increasing demand for fatigue life extension of both military and civilian aircraft has led to advances in repair technology for cracked metallic structures. Conventional structural repairs may significantly degrade the aircraft fatigue life and lower its aerodynamic performance. Adhesively bonded composite reinforcement is a new technology of great importance due to the remarkable advantages obtained, such as mechanical efficiency and repair time and cost reduction. In this article, bonded composite patch repairs were designed for quick application to aircraft under emergency conditions, such as aircraft battle damage repair (ABDR). A formulated method was developed, to be applied when damage has to be restored quickly, without restrictions to safety of flight. Different damage cases were investigated using finite-element analysis (FEA), taking into account specific parameters of the structure under repair. Based on the FEA results, a quick design procedure using composite patch repairs for the most frequent damage cases is proposed.     

Numerical analysis of the stress intensity factors for repaired cracks from a notch with bonded composite semicircular patch

In this paper, we investigated the crack growth behaviour of cracked thin aluminium plate repaired with bonded composite patch. The finite element method is used to study the performance of the bonded composite reinforcement or repair for reducing the stress concentration at a semicircular lateral notch and repairing cracks emanating from this kind of notch. The effects of the adhesive properties and the patch size on the stress intensity factor variation at the crack tip in mode I were highlighted. The obtained results show that the stress concentration factor at the semicircular notch root and the stress intensity factor of a crack emanating from notch are reduced with the increase of the diameter and the number of the semicircular patch. The maximal reduction of stress intensity factor is about 42% and 54%, respectively, for single and double patch. However, the gain in the patch thickness increases with the increase of the crack length and it decreases when the patch thickness increases. The adhesive properties must be optimised in order to increase the performance of the patch repair or reinforcement.     

The distribution of stress around a flat parabolic crack in an elastic solid

A simple limiting procedure is revealed whereby the three-dimensional state of stress and deformation around parabolic cracks or flaws embedded in elastic solids may be obtained. Several results are derived from available solutions concerning elliptical cracks or thin-sheet rigid inclusions. In particular, stress-intensity factors used in the Griffith-Irwin theory of fracture are evaluated and shown in curves. The findings of this investigation may also be exploited to determine the stress-strain field in thin sheets containing parabolic boles (and hence semi-infinite cracks) from existing solutions concerning similar bodies with elliptic holes.     

EXPERIMENTAL INVESTIGATION ON THE EFFECTS OF COLD EXPANSION OF FASTENER HOLES

A series of experimental investigations concerning the residual stress fields at cold-expanded fastener holes and of the behavior of fatigue cracks at such holes has been conducted. These studies have included measurement of the initial, cold-work-induced residual stress fields at both uncracked and cracked holes and the performance of both constant amplitude and spectrum fatigue crack growth tests.     

Stress intensity factors for some through-cracked fastener holes

A stress intensity factor solution is developed for a large plate containing radial hole cracks loaded with arbitrary crack face pressure. When the pressure is defined as the unflawed hoop stress surrounding a mechanical fastener, stress intensity factor calibrations are readily computed by the linear superposition principle. Results obtained in this manner agree well with previous solutions determined for open holes loaded in remote tension. The potential usefulness of the present analysis is further demonstrated with application to specific fastener configurations, including interference fit fasteners, pin-loaded plates, and cold-worked holes.     

Adhesive elements for stress analysis of bonded patch to curved thin-walled structures

 Bonded composite patching has been recognized as an efficient and economical method to extend the service life of cracked aluminum components. However, current analysis methods and empirical databases for designing composite bonded joint and patch repair are limited to flat plate and/or flat laminate geometries, and the effect of curvature on the performance and durability of composite bonded joints and repairs is not known. This paper presents a novel finite element formulation for developing adhesive elements for conducting quick stress analysis of bonded repairs to curved structures. Illustrative examples are presented to demonstrate the effect of curvature and the effect of patch location, i.e., internal and external patches, patch size and patch thickness on stresses in adhesive layer. Received: 24 April 2002 / Accepted: 10 October 2002     

Bonded repairs to rib stiffened wing skins

The present paper extends existing design formulae [Int. J. Solid Struct. 17 (1981) 827; J. Compos. Struct. 47 (1999) 737] for composite repairs to cracked metallic skins to include the bonded repair of rib stiffened wing skins. These design formulae are validated by comparison with the results of a series of 3D finite element studies and an experimental test program.