Boundary element analysis of curved cracked panels with adhesively bonded patches

A new boundary element formulation for analysis of curved cracked panels with adhesively bonded patches is presented in this paper. The effect of the adhesive layer is modelled by distributed body forces (i.e. two in‐plane forces, two moments and one out‐of‐plane force). A coupled boundary integral formulation of a shear deformable plate and two‐dimensional plane stress elasticity is used to determine bending and membrane forces along the adhesive layer taking into consideration the compatibility conditions in the patch area. Two numerical examples are presented to demonstrate the efficiency of the proposed method. It is shown that the out‐of‐plane bending behaviour and panel curvature have significant influence on the magnitude of the stress intensity factors. Copyright © 2003 John Wiley & Sons, Ltd.     

The boundary element analysis of cracked stiffened sheets,reinforced by adhesively bonded patches

This paper presents a formulation based on the Dual Boundary Element Method and on the Dual Reciprocity Method for the analysis of thin cracked metal sheets to which thin metal patches and stiffeners are adhesively bonded. The stiffened cracked sheet is modelled with the Dual Boundary Element Method. Adhesive shear stresses are modelled as action–reaction body forces exchanged by the sheet and patches. The Dual Reciprocity Method is used to avoid the discretization of the patches attachment domain into internal cells. Several examples are presented to demonstrate the efficiency and robustness of the method developed. The examples include sheets with embedded or edge cracks, stiffened or not, to which single or double patches are adhesively bonded. © 1998 John Wiley & Sons, Ltd.     

Fatigue crack growth analysis of stiffened cracked panel repaired with bonded composite patch

Fatigue crack growth behavior in a stiffened thin 2024-T3 aluminum panel repaired with one-sided adhesively bonded composite patch was investigated through experiments and analyses. The patch had three plies of unidirectional boron/epoxy composite. 2024-T3 aluminum stiffeners were riveted as well as bonded on the panel. Stiffeners were oriented in the loading direction and were spaced at either 102 mm or 152 mm with a crack centered between them. Also, un-repaired cracked panel with and without stiffeners were studied. Experiment involved tension-tension fatigue at constant amplitude with maximum stress of 120 MPa and stress ratio of 0.05. Bonded composite patch repair increased fatigue life about five-fold in the case of stiffened panels while it increased about ten fold in the case of un-stiffened panels. Fatigue life also increased with decrease of the distance between the stiffeners for both repaired and un-repaired panels. A three-dimensional finite element method was used to analyze the experiments. Residual thermal stresses, developed during patch bonding, requires the knowledge of temperature at which adhesive becomes effective in creating a bond between the structure and patch in the analysis. A simple method to estimate the effective curing temperature range is suggested in this study. The computed stress intensity factor versus measured crack growth relationships for all panel configurations were consistent and in agreement with the counterpart from the test material. Thus, the present approach provides a means to analyze the fatigue crack growth behavior of stiffened structures repaired with adhesively bonded composite patch.     

The stress intensity factor for a cracked stiffened sheet repaired with an adhesively bonded composite patch

The problem of a cracked, stiffened metallic sheet adhesively bonded by a composite patch is analyzed. The composite patch is assumed to be either an infinite orthotropic sheet or an infinite orthotropic strip normal to the crack. Due to the high stress concentration around the crack and on the interface, an elliptical disbond is assumed to exist around the crack. The crack is asymmetric with respect to the stiffener's locations as well as to the patch's center. The effect of thermal stresses in curing process is also considered. The fracture problem is solved by the displacement compatibility method, using the complex variable approach and the Fourier integral transform method.The problem is dealt with in two steps. First, starting with an uncracked, patched stiffened sheet, the stress at the prospective location of the crack is determined in a closed-form solution. The second step is to introduce a crack into the stiffened patched sheet. The multivalue of the analytical formulation is treated in detail to ensure proper implement in the computer. The results show that the effect of the stiffeners on the stress intensity factor is not significant for a crack fully covered by a patch.For the repairs by Boron/Epoxy patches, the difference in KI between the infinite sheet patch and the infinite strip model is only minor (less than 5 percent) in the absence of the curing thermal stresses and it becomes more pronounced when these stresses are taken into consideration. The stress intensity factor for a crack repaired by an infinite composite strip also can be estimated with a good or reasonable accuracy via a simplified analysis in which the patch is considered as an infinite strip in the first step and is treated as an infinite sheet in the second step of the solution procedure mentioned above.The latter simplified analysis is based on the approach originally proposed by Rose for a relatively simple repair configuration. For most cases, that approach seems to work well for the repair of a stiffened sheet by an infinite composite strip with the effects of thermal stresses and a disbond included. It should be emphasized that the present methodology can apply to the problem of a crack in a metallic stiffened sheet growing beyond the patch's boundary and also to the repairs by an infinite adhesively bonded composite strip parallel to the crack.     

Boundary elements analysis of adhesively bonded piezoelectric active repair

This paper presents the analysis of active piezoelectric patches for cracked structures by the boundary element method. A two-dimensional boundary integral formulation based on the multidomain technique is used to model cracks and to assemble the multi-layered piezoelectric patches to the host damaged structures. The fracture mechanics behavior of the repaired structures is analyzed for both perfect and imperfect interface between patches and host beams. The imperfect interface, representing the adhesive between two different layers, is modeled by using a “spring model” that involves linear relationships between the interface tractions, in normal and tangential directions, and the respective discontinuity in displacements. Numerical analyses performed on a cracked cantilever beam repaired by single and multi-layered patches are presented. It is pointed out that the adhesive deeply influences the performances of the repair as highlighted by an increasing of the repairing voltage values with respect to perfect bonding case.     

The effects of disbonds on the pure mode II stress intensity factor of aluminium plate reinforced with bonded composite materials

Adhesively bonded composite patch repair has been widely used to restore or extend the service life of cracked structural components due to its effectiveness to mechanical repair technique. In this work, the finite element method is applied to analyse the performance of the bonded composite patch for repairing cracks emanating from semicircular notch root in pure mode II. The stress intensity factor was computed at the crack tip repaired using a boron/epoxy patch for different orientation of fibers, taking into account the disbond. In this case, the increase of a patch thickness reduces the negative effects of disbond. When this effect is significant between the patch and the plate, it reduces the repair effectiveness. The maximum reduction obtained by using a boron/epoxy of fibers in the x-direction is of the order of 20% more important compared to a patch having its fibers in the y-direction. The stress intensity factor exhibits an asymptotic behaviour as the disbond size increases.     

Numerical analysis of the notch effect and the behaviour of notch crack in adhesively bonded composite laminates

In this study the finite element method is used to analyse the notch effect and the behaviour of notch cracks in adhesively composite laminate under tension by computing respectively the stress concentration factor at the notch tip which characterize the notch strength and the stress intensity factor at the crack tip which characterize the resistance to the crack propagation. The effects of the adhesive properties and fiber orientation on the variation of both stress concentration and stress intensity factors are highlighted. The obtained results show that the notch strength is reduced in the layer of the laminate of which the fiber orientation is in the applied load direction; the resistance to the crack propagation is also reduced in this type of layer. The stress intensity factor at the tip of notch crack exhibits an asymptotic behaviour as the crack length increases.     

Analysis of cracked plates using an iterative hybrid technique of boundary element method and distributed dislocation method

An iterative hybrid technique of boundary element method (BEM) and distributed dislocation method (DDM) is introduced for solving two dimensional crack problems. The technique decomposes the problem into (n + 1) subsidiary problems where n is the number of crack branches. The required solution will be the sum of these (n + 1) solutions. The first subsidiary problem is to find the stress distribution induced in the plate in the absence of the crack using BEM. All of the remaining subsidiary problems, are stress disturbance ones that will be solved using DDM. The results will be added and compared with the boundary conditions of the original problem. Iteration will be performed between the plate boundaries and crack faces until all of the boundary conditions are satisfied.     

Computation of the stress intensity factors for repaired cracks with bonded composite patch in mode I and mixed mode

In this study, the finite element method is used to analyse the behaviour of repaired cracks with bonded composite patches in mode I and mixed mode by computing the stress intensity factors at the crack tip. The effects of the patch size and the adhesive properties on the stress intensity factors variation were highlighted. The plot of the stress intensity factors according to the crack length in mode I, shows that the stress intensity factor exhibits an asymptotic behaviour as the crack length increases. In mixed mode, the obtained results show that the Mode I stress intensity factor is more affected by the presence of the patch than that of mode II.     

金属裂纹板复合材料胶接修补强度的弹塑性有限元预测

金属裂纹板经复合材料补片胶接修补后,其结构强度明显提高,但裂纹板中的裂纹会导致严重的应力集中现象,并易产生塑性变形,呈现强烈的材料物理非线性特性,需要采用弹塑性力学原理,进行复合材料胶接修复结构的静强度预测。为此,考虑金属板材料的非线性特性,建立了金属裂纹板复合材料胶接修补结构的弹塑性有限元模型,并通过试验验证了模型的有效性。在此基础上,提出了基于裂纹尖端的张开位移(COD)判据的拉伸强度预测方法,分析了修复结构的塑性应变、COD以及静拉伸强度。结果表明:相对于应力强度因子K判据, COD判据能更有效地预测修复试件的静拉伸强度。      

Stress intensity factors of a central interface crack in a bonded finite plate and periodic interface cracks under arbitrary material combinations

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combinations. This paper deals with a central interface crack in a bonded finite plate and periodic interface cracks. Then, the effects of material combination and relative crack length on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method.     

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.     

Analysis of the distribution of thermal residual stresses in bonded composite repair of metallic aircraft structures

In this study, the distribution of the thermal residual stresses due to the adhesive curing in bonded composite repair is analysed using the finite element method. The computation of these stresses comprises all components of the structures: cracked plate, composite patch and adhesive layer. In addition, the influence of these residual stresses on the repair performance is highlighted by analysing their effect on the stress intensity factor at the crack tip. The obtained results show that the normal thermal stresses in the plate and the patch are important and the shear stresses are less significant. The level of the adhesive thermal stresses is relatively high. The presence of the thermal stresses increases the stress intensity factor at the crack tip, what reduce the repair performance.     

Boundary element analysis of three-dimensional crack problems in two joined transversely isotropic solids

The present paper presents a boundary element analysis of penny-shaped crack problems in two joined transversely isotropic solids. The boundary element analysis is carried out by incorporating the fundamental singular solution for a concentrated point load in a transversely isotropic bi-material solid of infinite space into the conventional displacement boundary integral equations. The conventional multi-region method is used to analyze the crack problems. The traction-singular elements are employed to capture the singularity around the crack front. The values of the stress intensity factors are obtained by using crack opening displacements. The numerical scheme results are verified with the closed-form solutions available in the literature for a penny-shaped crack parallel to the plane of the isotropy of a homogeneous and transversely isotropic solid of infinite extent. The new problem of a penny-shaped crack perpendicular to the interface of a transversely isotropic bi-material solid is then examined in detail. The crack surfaces are subject to the three normal tractions and the uniform shear traction. The associated stress intensity factor values are obtained and analyzed. The present results can be used for the prediction of the stability of composite structures and the hydraulic fracturing in deep rock strata and reservoir engineering.     

Evaluation of bonded and bolted repair techniques with finite element method

In this study, the efficiencies of the patch were checked under mechanical forces using an analytical method for bonded and bolted repairing methods using composite single lap joint, and also compared these analytical results with previous experimental studies.

In the present analytical investigation, glue method was used for bonding and contact-target for bolted repairing. Every material was assumed to be linear isotropic. Central processor unit process time of bolted study was longer than the bonded one. The measured and predicted strain values were in agreement, verifying the accuracy of the predicted tensile loads.

For lower loads, glued repairing was obtained as homogeneous load distribution, but bolted repairing as heterogeneous. As a result of this study, the bonded repair was found to be better than the bolted one for repairing of composite single lap joint.     

Three dimensional boundary element analysis of internal cracks under sliding contact load with a spherical indenter

Using boundary element based three dimensional modelling for linear fracture mechanics, we present an analysis of cracking in a homogeneous medium subject to contact load. The proposed iterative solution procedure allows a simultaneous treatment of a reasonable number of partially closed cracks. It is shown that the most probable direction of propagation of a vertical internal crack is strongly dependent on its size compared to the contact radius and its location with respect to the axis of maximum normal load.     

Dual boundary element method modelling of aircraft structural joints with multiple site damage

The computation of crack growth from a bolt or rivet hole in a structural joint practically requires that the geometry be approximated to some degree. In this paper a simplified quasi-2D stress analysis method, using the boundary element method is presented, where the load transfer rate and the contact stresses at the hole edge for the full 3D geometry are fairly well approximated. Coupled with a dual boundary element formulation for the crack propagation problem, this model is used to evaluate stress intensity factors for through cracks emanating from holes in several double shear lap joint configurations. As the calculated stress intensity factors compare well with experimental data, this procedure is considered to approximate satisfactorily the load transfer rate and the contact stresses at the hole edge of the full 3D geometry, when secondary bending is not a factor.     

Finite element fatigue propagation of induced cracks by stiffeners in repaired panels with composite patches

Fatigue crack growth analyses of aluminum panels with stiffeners repaired by composite patches have been rarely investigated. Generally, cracks may occur around the rivets which are capable to propagate under cyclic loadings. A composite patch can be used to stop or retard the crack growth rate. In this investigation, finite element method is used for the crack propagation analyses of stiffened aluminum panels repaired with composite patches. In these analyses, the crack-front can propagate in 3-D general mixed-mode conditions. The incremental 3-D crack growth of the repaired panels is automatically handled by a developed ANSYS Parametric Design Language (APDL) code. Effects of rivets distances and their diameters on the crack growth life of repaired panels are investigated. Moreover, the obtained crack-front shapes at various crack growth steps, crack trajectories, and life of the unrepaired and repaired panels with various glass/epoxy patch lay-ups and various patch thicknesses are discussed.     

An analytical solution for the analysis of symmetric composite adhesively bonded joints

Analytical solutions for adhesively bonded balanced composite and metallic joints are presented in this paper. The classical laminate plate theory and adhesive interface constitutive model are employed for this deduction. Both theoretical and numerical (finite element analysis) studies of the balanced joints are conducted to reveal the adhesive peel and shear stresses. The methodology can be extended to the application of various joint configurations, such as single-lap and single-strap joints to name a few. The methodology was used to evaluate stresses in several balanced adhesively bonded metallic and composite joints subjected to the tensile, moment and transverse shear loadings. The results showed good agreements with those obtained through FEM.     

Boundary element analysis of anisotropic rock masses

A boundary element formulation is developed for anisotropic elastic rock masses. The boundary element treatment in which the fundamental solutions of Lekhnitskii have been incorporated, and the numerical evaluation of integrals with singularities are discussed. Good agreement found between the numerical and analytical solutions for several example problems demonstrates the capability, accuracy and efficiency of the present formulation. The problem of a deep circular tunnel excavated in a variety of jointed rock masses has also been analysed using the present formulation. The effect of the jointing on the behaviour of the rock mass around the tunnel is evaluated.