Experimental investigations on fatigue crack growth of repaired thick aluminium panels in mixed-mode conditions

In this paper, experimental fatigue crack growth of thick aluminium panels containing a central inclined crack of 45° repaired with single-side glass/epoxy composite patch are performed. It is shown that, the technique of single-side repair using glass/epoxy composite patch is effective in the crack growth life extension of the thick panels in mixed-mode conditions. It is also shown that the crack-front of the propagated cracks of the repaired panels has a curvilinear shape which is the effect of the existed out-of-plane bending due to the asymmetry conditions in the single-side repaired panels. It is indicated that the crack propagation path at patched surface is different from the un-patched surface of the panels. In the primary stages of the crack growth, the crack surfaces through the thickness, in the vicinity of the mid-plane propagate without surface twisting. There are considerable differences between the obtained crack growth path at patched and un-patched surfaces of the panels which mean that the crack propagation surfaces have three-dimensional patterns. Using the various thin patch lay-ups has minor effects on the crack re-initiation life of the repaired thick panels. It is shown that using various four layers patch lay-up configurations, the crack propagation life of the cracked panels may increase by the order of 30–85%. The most fatigue crack growth life extension belongs to the repaired panel with the patch lay-up of [90]₄.     

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.     

Mixed-mode 3-D crack propagation of repaired thin aluminum panels using single-side composite patches

Three dimensional finite element analyses of the single-side repaired panels using glass/epoxy composite are performed considering the general mixed mode conditions and real crack-front shape modeling (RCFM) during the crack propagation procedure. Variations of the fracture parameters through the thickness of the panels for the initial crack configuration and crack growth behavior of the repaired panels with various patch lay-ups are investigated. The effect of considering K _III on the small and large crack growth of repaired panels are also studied. The obtained lives are compared with the previously obtained lives using simplified FEM procedure and experimental results by the authors.     

Prediction of shape change of corner crack by fatigue crack growth circles

As a fatigue crack grows, its shape changes. Conventional method for predicting the shape change typically requires the computation of several hundred increments to get accurate results. In this paper, a new finite element simulation technique that uses fatigue crack growth circles is developed. Since the circles are perpendicular to the new crack front as well as to the current crack front, they can represent the real path of the fatigue crack well and yield more accurate results. The new technique is validated by applying it to the case of a quarter-elliptical corner crack in a plate with an open hole subjected to tension loading. The effect of the Paris–Erdogan exponent is also investigated.     

Numerical simulation study of fatigue crack growth behavior of cracked aluminum panels repaired with a FRP composite patch using combined BEM/FEM

A combined boundary element method and finite element method (BEM/FEM) is employed to investigate the fatigue crack growth behavior of cracked aluminum panels repaired with an adhesively bonded fiber-reinforced polymer (FRP) composite patch. Numerical simulation of crack growth process of a cracked aluminum panel repaired with a FRP composite patch under uniaxial cyclic loading has been carried out. The curve of crack length on unpatched side of the cracked panel versus the number of cyclic loading is determined by the numerical simulation, and it agrees well with experimental data. Furthermore, the crack front profiles of the cracked panel during fatigue crack growth and the distributions of stress intensity factors along crack fronts are also numerically simulated.     

Modelling of damage and failure of glass/epoxy composite plates subject to impact fatigue

An investigation has been carried out to study the impact fatigue damage of glass/epoxy laminated composites. Accumulation of damage, such as matrix cracking, delamination and fibre breakage, with repeated impact of the composite material may reduce the overall stiffness. These damage modes have been combined in a very complicated way to describe damage growth and fracture. A model is proposed for characterising the damage as a function of the normalised impact number. The scalar variable D, which characterises the material damage, is written as a function of the life duration β, using a modified form of the Mankowsky empirical law [Int J Solids Struct 32(11) (1995) 1607]. The macroscopic failure mode and the internal damage in laminated specimens of glass/epoxy as a consequence of impact fatigue are analysed at different levels of incident impact energy. The impact fatigue tests have been conducted on an apparatus built in our laboratory.     

Microstructure dependent fatigue crack growth in aged hardened aluminium alloys

Fatigue crack propagation tests in constant amplitude loading, as well as with single peak overloads, have been performed in AlMgSi1-T6 aluminium alloys with different Mn and Cr contents. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. A moderate stress ratio and a strong material dependence effects on the fatigue crack growth were observed. These effects are discussed in terms of the different dominant closure mechanism (plasticity-induced closure or roughness-induced closure). Roughness-induced closure dominates crack closure in the alloys with higher contents of Mn and Cr elements. In the alloy with a lower content of these elements, plasticity-induced closure is dominant. When roughness-induced closure is the prime pre-overload closure mechanism, the retardation effect is decreased in comparison to when plasticity-induced closure is dominant.     

Fast multipole DBEM analysis of fatigue crack growth

A fast multipole method (FMM) based on complex Taylor series expansions is applied to the dual boundary element method (DBEM) for large-scale crack analysis in linear elastic fracture mechanics. Combining multipole expansions with local expansions, both the computational complexity and memory requirement are reduced to O(N), where N is the number of DOF. An incremental crack-extension analysis based on the maximum principal stress criterion and the Paris law is used to simulate the fatigue growth of numerous cracks in a 2D solid. Some examples are presented to validate the numerical scheme.     

A multifractal analysis of fatigue crack growth and its application to concrete

As is well-known, strength of materials is influenced by the specimen or structure size. In particular, several experimental campaigns have shown a decrease of the material strength under static or fatigue loading with increasing structure size, and some theoretical arguments have been proposed to interpret such a phenomenon. As far as fatigue crack growth is concerned, limited information on size effect is available in the literature, particularly for so-called quasi-brittle materials like concrete. In the present paper, by exploiting concepts of fractal geometry, some definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. A multifractal size-dependent fatigue crack growth law (expressing crack growth rate against stress intensity factor range) is proposed and used to interpret relevant experimental data related to concrete.     

Estimation of fatigue crack growth retardation due to crack branching

Quantitative analysis is provided to estimate the reduction of fatigue crack growth rate due to overload crack branching. A recent mixed-mode fatigue crack growth model based on the dilatational component of the accumulated strain energy density near the crack tip is modified to quantify the retardation factor of crack growth rate following an overload. It is found that crack branching due to an overload results in considerable reduction of fatigue crack growth rate. The retardation factor estimated by the proposed methodology is correlated with test results for the 2090-T8E41 aluminum–lithium alloy indicating encouraging agreement.     

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.     

More insights into fatigue crack growth from experiments on steels and aluminium alloys—Thresholds

The paper deals with the influence of the R-ratio on the fatigue crack propagation threshold of different metallic materials. Based up on threshold data of steels, aluminium-alloys and two particulate-reinforced aluminium-alloys the threshold behaviour has been analyzed and a new model to describe the threshold behaviour has been deduced. With this model, which contains two quantities that can be deduced from special fatigue crack propagation tests, the threshold behaviour of different kind of materials can be explained. Finally, the existence of the threshold can be attributed to specific elastic parameters of the materials (shear modulus) and their microstructure.     

Modelling fatigue crack propagation of a cracked metallic member reinforced by composite patches

The concept of fracture for material elements at front of a crack for fatigue crack propagation was extended to the fatigue crack propagation of a cracked metallic member reinforced with a composite patch in this paper. From static mechanics and linear elastic fracture mechanics, force transfer on a cracked member through a composite patch was analyzed and a formula connecting the stress intensity factor with crack length was obtained. Thereafter, a fracture model for fatigue crack propagation of a repaired cracked metallic member was proposed. A new expression for the fatigue crack propagation rate has thus been derived. The expression was verified objectively by the test data. It is in good agreement with the test results.     

Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.     

Identification of crack and disbond fronts in repaired aircraft structural panels with bonded FRP composite patches

Structural health monitoring of fatigue-cracked aircraft structural panels repaired with bonded FRP composite patches for extending the service life of aging aircraft has received wide attention. In this paper a method for identifying the locations and shapes of crack and disbond fronts in aircraft structural panels repaired with bonded FRP composite patches is presented. The identification is performed by minimizing the residual norm between the measured in-plane strain range on a strain measurement plane in the FRP composite patches and the calculated in-plane strain range. Several numerical examples of identification of the locations and shapes of crack and disbond fronts are examined. The effects of the number of strain measurement points, position of the strain measurement plane, and measurement errors of the in-plane strain ranges on the identification results are discussed. The validity of this identification method is verified by comparing the identification results with the exact ones.     

Mixed-mode fatigue crack growth of thin aluminium panels with single-side repair using experimental and numerical methods

In this paper, experimental and numerical fatigue crack growth of thin aluminium panels containing a central inclined crack of 45° with single-side glass/epoxy composite patch are performed. Effects of patch lay-up configuration on the restarting crack growth (crack re-initiation) life and crack growth rate of the repaired panels are investigated. The obtained experimental results are compared with those predicted using finite element analysis based on both mid-plane and unpatched surface fracture parameters. In the finite elements analyses, it is assumed that the crack-front remains perpendicular to the panel's surfaces during its propagation. It is shown that the finite element crack re-initiation and propagation lives predictions using the unpatched surface results are too conservative. However, the finite element mid-plane results lead to a non-conservative life prediction. It is experimentally shown that, the most effective patch lay-up configurations to retard the crack growth of the repaired panels is [−45/+45]₂; however, the most life extension including the crack propagation cycles belongs to the patch lay-up of [90₄]. It is also shown that using the asymmetric patch lay-up configuration similar to [90₂/0₂] with a proper bonding process may lead to a very slow crack growth rate, even slower than the patch lay-up of [90₄].     

铝合金板厚度对硼/环氧补片单面修复试件疲劳性能的影响

采用单向硼/环氧复合材料补片真空袋压工艺单面修复含中心裂纹不同厚度铝合金板,测试了修复试件的疲劳性能,从疲劳寿命、疲劳裂纹扩展速率和裂纹扩展纹线考察不同厚度铝合金板修复后疲劳性能的差异。结果表明：硼/环氧补片胶接修复后,铝合金板的疲劳寿命大幅度提高,且疲劳寿命提高幅度随铝合金板厚度增大而降低。厚度为1.76mm、5.20mm和10.20mm 3种铝合金板修复试件的疲劳寿命分别是未修复试件的22.30倍、12.84倍和8.40倍。厚度为1.76mm铝合金板修复试件在铝合金板完全断裂后还能继续承担疲劳载荷,而厚度为5.20mm和10.20mm 2种铝合金板修复试件在铝合金板断裂后完全破坏。裂纹扩展速率和归一化裂纹长度差均随铝合金板厚度增大而增大。     

Fatigue and fracture analysis of aluminum plate with composite patches under the hygrothermal effect

In this paper, fatigue life of the repaired cracks in 2024-T 3 aluminum with bonded patches made of unidirectional composite plates has been investigated experimentally and numerically for hygrothermal effect. The problem is handled in plane stress and Mode I condition. In the experimental study the mechanical properties of the aluminum plate and patch materials are determined and fatigue experiments are conducted. The results obtained from these experiments and numerical solutions are compared. Thus the reliability of the numerical solution has been proven. For all conditions, numerical solutions have been made and stress intensity factor (K_I) and fatigue life are calculated. Different plate and patch thicknesses are also considered in the experiments.     

Characterization of fatigue crack growth in aluminium panels with a bonded composite patch

This study introduces an analytical procedure to characterize the fatigue crack growth behavior in an aluminium panel repaired with a bonded composite patch. This procedure involves the computation of the stress intensity factor from a two-dimensional finite element method consisting of three layers to model cracked plate, adhesive and composite patch. In this three layer finite element analysis, as recently introduced by the authors, two-dimensional Mindlin plate elements with transverse shear deformation capability are used. The computed stress intensity factor is then compared with the experimental counterpart. The latter was obtained from the measured fatigue crack growth rate of an aluminium panel with a bonded patch by using the power law relationship (Paris Law) of an unpatched aluminum panel. Both a completely bonded patch (with no debond) and a partially bonded patch (with debond) are investigated in this study. This procedure, thus, provides an effective and reliable technique to predict the fatigue life of a repaired structure with a bonded patch, or alternatively, it can be used to design the bonded composite patch configuration to enhance the fatigue life of cracked structure.     

Torsion fatigue behavior of unidirectional carbon/epoxy and glass/epoxy composites

This paper presents results of the feasibility of carbon/epoxy composites (CFRP) as a future helicopter flexbeam material. Torsional behaviors of unidirectional CFRP and glass/epoxy composites (GFRP) with the same resin matrix were investigated. The initial torsional rigidity of CFRP was almost identical to that of GFRP. The torsional rigidities calculated using finite element analyses (FEA) agreed with the experimental results: the torsional rigidities are governed mainly by the material’s shear stiffness. Torsion fatigue tests were also conducted by controlling the angle of twist of the sinusoidal wave under a constant tensile axial load. No catastrophic failure occurred with either GFRP or CFRP, although decreased amplitudes of torque and torsional rigidities were observed according to the number of cycles. Results of X-ray CT inspections and numerical calculation by FEA revealed that degradation of a torsional rigidity is caused mainly by splitting crack propagation along the fiber direction. The torsion fatigue life of CFRP was superior to that of GFRP. Consequently, results confirmed that CFRP exhibits excellent properties as a torsional element of a helicopter flexbeam in terms of torsional rigidity and tension–torsion fatigue behaviors.