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.     

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.     

FE analysis of the behaviour of octagonal bonded composite repair in aircraft structures

Bonded composite repair has been recognized as an efficient and economical method to extend the fatigue life of cracked aluminium components. In this work, the finite element method is applied to analyze the central crack’s behaviour repaired by a boron/epoxy composite patch. The knowledge of the stress distribution in the neighbourhood of cracks has an importance for the analysis of their repair according to the patch geometry. The effects of mechanical and geometrical properties of the patch on the variation of the stress intensity factor at the crack tip were highlighted. The obtained results show that the stress intensity factor at the repaired crack with composite patch of height 2c/3 is reduced about 5% compared to cracks repaired with octagonal patch of size c. For patch height of c/3 the reduction is about 7%. The adhesive properties must be optimised in order to increase the repair performances and to avoid the adhesive failure.     

Numerical analysis of the beneficial effect of the double symmetric patch repair compared to single one in aircraft structures

This paper concerns a numerical study by the finite element method of the cracked structure repaired by single and double bonded composite patches. The stress intensity factor is used as fracture criteria. The obtained results showed the advantage of the double patch compared to single on the reduction of the stress intensity factor at the crack tip. The effects of the properties of the plate and the patch and the adhesive on the beneficial effect of the double patch are highlighted. The adhesive properties must be optimised in order to increase the advantage of the double patch and to avoid the adhesive failure. The patch properties have a significant effect on the beneficial effects of the double symmetric patch.     

Comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: A numerical analysis

The optimization of the patch shape of bonded composite repair in aircraft structures is a good way to improve the repair performance. In this study, the three-dimensional finite element method is used to compare the repair performance of patches with rectangular and trapezoidal shapes in aircraft structures. The comparison is done by analysing the stress intensity factor (SIF) at the tip of repaired crack and the distribution of the adhesive stresses for the two patch shapes. The obtained results show that, when the crack length is ranged from 5 to 20 mm, the trapezoidal shape presents lower stress intensity factor at the crack tip, which is beneficial for the fatigue life and lower adhesives stresses, which is beneficial for the repair durability. These advantages disappear when the crack length reaches the value of 40 mm. It is also shown that the use of the trapezoidal shape reduce the mass of the patch, which can reduce the repair cost.     

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.     

Fracture analysis of Kevlar-49/epoxy and e-glass/epoxy doublers for reinforcement of cracked aluminum plates

Adhesively bonded composite patch repair is efficient means to regain load carrying capacity, alleviate the crack growth, and improve the service life of the damaged structure. In this paper, three dimensional finite element models are developed to examine the fracture behavior of a single edge V-notched Aluminum plate repaired with Kevlar-49/epoxy or e-glass/epoxy pre-preg patches on both sides. Contour integral method was used for evaluating the stress intensity factor (SIF), an indicator of the crack stability. The load transfer mechanisms, stress distribution, damage variable (D), and crack mouth opening displacement (CMOD), were also presented to estimate the effectiveness of composite patch repair. The influence of the patch material, crack length and the adhesive thickness has been investigated. Results have shown that the crack induced damage increased nonlinearly with a larger crack size. With the composite patch repairs, SIF is reduced to 1/7–1/10 of that of the bare plate and CMOD decreased by 79%. The damage variable is reduced significantly and the load capacity is increased. A thinner adhesive layer results in a higher percentage of load shared by the composite patch.     

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.     

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.     

Progressive edge cracked aluminium plate repaired with adhesively bonded composite patch under full width disbond

In this study, the crack growth behaviour of an aluminium plate cracked at the tip and repaired with a bonded boron/epoxy composite patch in the case of full-width disbond was investigated. This effect is the imperfection which could result during the bonded patch of the repaired structure. Disbonds of various sizes and situated at different positions with respect to the crack tip as well as the effect of adhesive and patch thickness on repair performance were examined. An analysis procedure involving the efficient finite element modelling applied to cracked plate, adhesive and composite patch was used to compute the stress intensity factors. The crack growth rate is dominated by the stress intensity factor near the location and size of the pre-existing disbonds. The cracked plate and disbond propagation result in an increase in the patch deformation. The patch does not have an influence on the crack growth when the ratio 2a/d_R exceeds 0.8.     

Effects of the adhesive disband on the performances of bonded composite repairs in aircraft structures

In this study, the effects of the adhesive disband on the efficiency of bonded composites repair in aircraft structures were analyzed. The three-dimensional finite element method was used to achieve the objectives of the study. The stress intensity factor at the crack tip was chosen as fracture criteria. The analysis was extended to the single and double symmetric bonded composite patches. The obtained results show that the repair efficiency is negatively influenced if the adhesive disband growths perpendicularly to the crack. In the case of double symmetric patch, the presence of double adhesive disband highly decreases the repair efficiency and increases the risk of adhesion failure between the composite patch and the cracked aluminum structures.     

Nonlinear analysis of bonded composite patch repair of cracked aluminum panels

Analyses of adhesively bonded composite patches to repair cracked structures have been the focus of many studies. Most of these studies investigated the damage tolerance of the repaired structure by using linear analysis. This study involves nonlinear analysis of the adhesively bonded composite patch to investigate its effects on the damage tolerance of the repaired structure. The nonlinear analysis utilizes the three-layer technique which includes geometric nonlinearity to account for large displacements of the repaired structure and also material nonlinearity of the adhesive. The three-layer technique uses two-dimensional finite element analysis with Mindlin plate elements to model the cracked plate, adhesive and composite patch. The effects of geometric nonlinearity on the damage tolerance of the cracked plate is investigated by computing the stress intensity factor and fatigue growth rate of the crack in the plate. The adhesive is modeled as a nonlinear material to characterize debond behavior. The elastic-plastic analysis of the adhesive utilizes the extended Drucker-Prager model. A detailed discussion on the effects of nonlinear analysis for a bonded composite patch repair of a cracked aluminum panel is presented in this paper.     

Analysis of the plastic zone size ahead of repaired cracks with bonded composite patch of metallic aircraft structures

In this study, the three-dimensional and non-linear finite element method is used to estimate the performance of the bonded composite repair of metallic aircraft structures by analyzing the plastic zone size ahead of repaired cracks. Several calculations have been realized to extract the plasticized elements around the crack tip of repaired crack. The obtained results show that the presence of the composite patch reduces considerably the size of the plastic zone ahead of the crack. The effects of the adhesive properties and the patch thickness on the plastic zone size ahead of repaired cracks were analyzed.     

Fatigue crack growth behavior of cracked aluminum plate repaired with composite patch

In this study, we investigated the fatigue crack growth behavior of cracked aluminum plate repaired with bonded composite patch especially in thick plate. Adhesively bonded composite patch repair technique has been successfully applied to military aircraft repair and expanded its application to commercial aircraft industry recently. Also this technique has been expanded its application to the repair of load bearing primary structure from secondary structure repair. Therefore, a through understanding of crack growth behavior of thick panel repaired with bonded composite patch is needed. We investigated the fatigue crack growth behavior of thick panel repaired with bonded composite patch using the stress intensity factor range (ΔK) and fatigue crack growth rate (da/dN). The stress intensity factor of patched crack was determined from experimental result by comparing the crack growth behavior of specimens with and without repair. Also, by considering the three-dimensional (3D) stress state of patch crack, 3D finite element analyses were performed to obtain the stress intensity factor of crack repaired by bonded composite patch. Two types of crack front modeling, i.e. uniform crack front model and skew crack front model, were used. The stress intensity factor calculated using FEM was compared with the experimentally determined values.     

Finite element analysis of the integrity of an API X65 pipeline with a longitudinal crack repaired with single- and double-bonded composites

The objective of this study was to compare the performance of the repaired longitudinal cracks in API X65 pipelines under two different conditions: with patches (i.e., single and double patches) and without patches. The three-dimensional finite element method (FEM) was used to compute the stress intensity factors (SIF) at the crack tip. Repairing cracks under internal pressure using carbon-epoxy composites was investigated where the influence of both the single- and double-sided patches made of composite and adhesive were included. In the evaluation of the repair of the pipeline, the failure assessment diagram (FAD) was introduced to obtain the safety factor value. The obtained results indicated that the value of the factor of safety depends on both the crack length and the pressure. In addition, the results showed that the suggested technique is sufficient in predicting the behavior of the repairs.     

Comparison between composite and metallic patches for repairing aircraft structures of aluminum alloy 7075 T6

In this study, experimental and numerical investigations were carried out in order to compare the performances of composite and metallic patches for repairing aircraft structures. In the experimental part, an accelerating aging of the composite was realized by the immersion of the composite patch in distilled water. The fatigue lives of notched plates repaired with aged composite patch, non-aged composite patch and aluminum patch were measured. The obtained results show that the composite patch is more beneficial than the aluminum patch if there is no significant water absorption by the composite. In the numerical part, the stress intensity factor at the crack tip was computed for aged and non-aged composite patches and for aluminum patches. The numerical results confirm the experimental ones, the reduction of the stress intensity factor by the composite patch is more significant than the aluminum patch but the water absorption reduces significantly the repair efficiency.     

A scientific evaluation of the approximate 2D theories for composite repairs to cracked metallic components

In this paper, we show how the published literature reveals that the approximate two-dimensional solution for the stress intensity factor associated with cracked panel repaired using an externally bonded composite repair is inconsistent with experimental data, and that for short to mid-size cracks the fibre bridging effect is often a second-order effect. The result of this finding is that prediction of the effect of a composite repair on the structural integrity of cracked components repaired by an externally bonded composite repair is dramatically simplified. We also show why structures repaired using Glare patches have a fatigue performance that is superior to structures repaired using boron epoxy or carbon fibre patches.     

金属裂纹板复合材料修补结构的超奇异积分方程方法

根据应力强度因子在线弹性范围内具有可叠加性,将金属裂纹板复合材料修补结构进行简化,在表面裂纹线弹簧模型的基础上,建立了基于超奇异积分方程的Line-Spring模型。利用第二类Chebyshev多项式展开的方法,将超奇异积分方程转化为线性方程组,推导出以裂纹面位移表示的应力强度因子表达式,得到了裂纹尖端应力强度因子的数值解,并利用虚拟裂纹闭合法加以验证。参数分析确定了影响对称修补裂纹板应力强度因子的两个主要参数:胶层界面刚度和补片与金属板刚度比,为胶接修补结构的承载能力分析以及改进设计提供理论依据。     

Study of composite patch repair by analytical and numerical methods

A combined analytical and numerical study of an isotropic cracked plate that was repaired by using a bonded composite patch was conducted. The analytical work was based on Rose's equations, whereas for the numerical investigation a three-dimensional finite element analysis was implemented. A number of cracked plates with different crack lengths and overall dimensions of the composite repair were considered. The composite patch was made of unidirectional laminates with different stacking sequences. Both, one- and two-sided patches were analysed. Results are presented for the stress intensity factor in the patched crack and the maximum stress reinforcement stress and adhesive strain. It was found that for the case of a two-sided reinforcement the results obtained by both methods were in good agreement. However, for the case of a single reinforcement the accuracy of the analytical method decreased due to the tendency to out-of-plane bending as a result of bonding a reinforcing patch to only one face of a plate, which is ignored in the analysis.