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.     

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.     

Crack opening displacement in plate with bonded repair patch

Mathematical techniques are extended to compute crack opening displacements in a cracked plate with an adhesively bonded composite patch. The plate and the patch are considered as orthotropic materials. The problem is reduced to the solution of integral equations. A software program is written to compute shear stresses in adhesive, stress intensity factors in the plate and the crack openings at the centreline of the crack. The effects of adhesive thickness, adhesive modulus, patch thickness and plate thickness on crack openings are investigated. A test program is carried out to obtain crack opening displacements in plate with bonded patch. A good agreement with analytical predictions is obtained. The effects of patches bonded on one or both sides of a plate on stress intensity factors are evaluated.     

Three-dimensional stress intensity factor calibration for a stiffened cracked plate

Three-dimensional finite element analyses are used in this paper to calibrate the stress intensity factor in a cracked stiffened plate subjected to remote uniform traction. An accurate numerical determination of the stress field and stress intensity variation through the thickness of a central cracked plate was first carried out in order to evaluate three-dimensional effects. A stiffened cracked plate was then analysed, taking into account the results and the conclusions obtained in the previous study. Such a structure was chosen due to the growing interest for large integral metallic structures for aircraft applications, following the continuous need for low cost and the emergence of new technologies. The J-Integral technique was used to calculate the values of the stress intensity factor along the plate thickness. The plane strain behaviour near the crack front and the variation of the opening stress are discussed.     

金属裂纹板复合材料单面胶接修补结构应力分析

考虑金属裂纹板复合材料单面胶接修补结构的几何非线性和边界条件,建立了考虑弯曲变形单面修补结构力学分析模型,计算出承受面内载荷时修补结构的弯矩和挠度,将补片自由端和金属板裂纹处的弯矩作为胶层应力控制微分方程的边界条件,推导出剪应力和剥离应力的解析解,及裂纹张开位移的表达式,并与有限元数值结果进行对比。分析结果表明,胶接修补结构应力分析理论模型和相关简化假设合理、正确。利用所建立的解析模型研究了金属裂纹复合材料单面胶接修补结构的应力分布特点及胶层主导破坏模式的失效机制,为胶接修补结构的承载能力分析以及结构改进设计提供了一定的理论依据。     

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.     

Boundary element analysis of flat cracked panels with adhesively bonded patches

Adhesively bonded patch repairs for cracked finite sheets are analysed by the boundary element method. The interaction between the plate and the patch on a repaired sheet is modelled as a distribution of forces which include in-plane, out-of-plane and two moment body forces. The coupled boundary integral formulations of shear deformable plate (Mindlin theory) and two-dimensional plane stress elasticity are presented. Stress intensity factors, three for the bending problem and two for the membrane problem, are evaluated from crack opening displacements. Several examples are presented to demonstrate the accuracy and efficiency of the proposed method. Comparison with two-dimensional solutions demonstrate the significance of the bending loads on the stress intensity factors.     

加载速率对复合材料粘接修理金属结构力学性能的影响

基于复合材料补片基体和胶层树脂黏弹性的特点, 分别采用光固化和传统热固化方式制备了一系列不同树脂配方的试样, 实验研究了树脂配方对修理结构应变率效应的影响, 测定了复合材料粘接修理结构在不同加载速率下的力学性能。结果表明, 树脂体系的交联度较低时, 应变率效应更明显; 加载速率的提高通常会使补片更好地发挥分担载荷的作用, 但是也会导致变形协调能力的下降; 这两个因素共同影响复合材料粘接结构的最终修理效率。加载速率对于复合材料粘接修理结构的破坏模式也有影响。     

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.     

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 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.     

基于全试验设计方法的含裂纹铝合金板复合材料修补参数优化

建立含穿透裂纹铝合金板复合材料单面胶接修补板条的三维有限元模型,基于位移外推法对裂纹尖端的应力强度因子(SIF)进行求解。使用全试验设计的方法对不同修补参数下修补板条的单向拉伸试验进行仿真模拟,利用二次方程描述并研究了补片长度、补片厚度及胶层弹性模量共同作用时对SIF的影响,确定了以SIF为评价指标时对修补效果影响最大的修补参数,优化了修补设计,并应用优化修补参数进行单向静拉伸试验。结果表明,当三类修补参数共同作用时,补片长度对修补效果影响最大;使用优化修补参数单面修补试验件的破坏强度比未修补板的提高了12.1%,恢复到完好板的90.5%。     

SIFs of CCT plate repaired with single‐sided composite patch

Constant amplitude load fatigue tests are performed to obtain crack propagation data for LF2‐aluminium centre crack tension (CCT) plates un‐repaired and repaired with single‐sided composite patches. Then, the James–Anderson method, an experimental method, is used to obtain the stress intensity factor (SIF) formula for the repaired CCT plates with carbon–fibre composite patches. At last, crack propagation life prediction and finite element (FE) calculation are carried out to validate the experimental SIF formula. It is shown that the present SIF formula can exactly predict the fatigue‐crack propagation life of the patched CCT plates and is close to the FE results, which implies the effectivity of the experimental SIF formula in the present paper.     

Free out-of-plane vibration of cracked curved beams on elastic foundation by estimating the stress intensity factor

Abstract

This paper is concerned with evaluating stress intensity factors (SIFs), for a cracked curved beam of rectangular cross section, applying an approach which allows us to estimate the strain energy release rate. The beam is located on an elastic foundation. The out-of-plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach, namely differential quadrature element method (DQEM), to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam.     

Extended finite element fracture analysis of a cracked isotropic shell repaired by composite patch

An extended finite element method (XFEM) is developed to study fracture parameters of cracked metal plates and tubes that are repaired on top of the crack with a composite patch. A MATLAB® stand‐alone code is prepared to model such structures with eight‐noded doubly curved shell elements in the XFEM framework. Crack trajectory studies are performed for a diagonally cracked panel under fatigue loading. Verification studies are investigated on different shell type structures such as a cracked spherical shell and cracked cylindrical pipe with different crack orientations. The effects of using patch repairs with different fibre orientations on the reduction of stress intensity factors (SIFs) is also studied which can be useful for design purposes. XFEM is selected as any crack geometry can be embedded in the finite element mesh configuration with no need to coincide the crack geometry with meshed elements and so re‐meshing with fine mesh generation is not needed in the current method.     

Stress intensity factor for a cracked specimen under compression

For a cracked specimen under compression, a set of complex stress functions is proposed and by using the boundary collocation method, the unknown coefficients of these complex stress functions are determined. Based on the calculation results of the boundary collocation method, the formulas of the stress intensity factor for a cracked specimen under compression are obtained, and by using these formulas, the influence of confining stress on stress intensity factor is analyzed.     

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].     

General expressions for the stress intensity factor of a one-point bend beam

The aim of this work is to find general expressions to determine the stress intensity factor of a one-point bend beam-like specimen, whether from the measurement of the applied load or the crack mouth opening displacement. The expressions, obtained by applying the superposition principle, involve the decomposition of the general case into three auxiliary problems. The solution of two of them (pure bending and three-point bending) is well known, while the solution of the third (one-point bending) is developed in the present work. The proposed expressions are compared to numerical results obtained by the finite element method and their accuracy is equal to or better than available expressions published elsewhere.     

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.