Fatigue crack growth analysis of adhesively repaired panel using perfectly and imperfectly composite patches

Fatigue crack behavior of cracked aluminum panel repaired with the imperfectly bonded composite patch is analyzed. The imperfection is in the form of debond which could result during the bonding of patch or the service life of the repaired structure. Debonds, of various sizes and at different locations with respect to the crack front, are investigated. An analytical procedure, involving two-dimensional finite element method having three layers to model cracked plate, adhesive and composite patch, is used to compute the stress intensity factors of test coupons. From the computed stress intensity factors, the crack growth rates are obtained analytically by assuming that the relationship between the stress intensity factor and the crack growth rate after repair is the same as the fatigue crack growth relationship for cracked panel material. The fatigue crack growth rates obtained experimentally and analytically are in good agreement with each other and they vary linearly with crack length inside the patch. The experimental results are bounded between its analytical counterparts at the mid-plane and free edge surfaces of the cracked panel. The present analytical procedure can, thus, be used to characterize the effects of imperfectly and perfectly bonded composite patch repairs on the durability and damage tolerance of the repaired structure.     

Thermal effects on adhesively bonded composite repair of cracked aluminum panels

This study introduces the two-dimensional finite element analysis involving three layer technique to investigate the adhesively bonded composite repair of cracked metallic structure under thermo-mechanical loading. The thermal loading involves, in this study, the temperature drop such as seen during the bonding process. Three patch materials having different stiffnesses and coefficients of thermal expansion are investigated to analyze the thermal effects on the damage tolerance of the crack in the repaired structure and of the debond in the adhesive bondline. For the single sided repair, the patch material having the maximum mismatch in the coefficient of thermal expansion with that of the cracked aluminum plate provides the better damage tolerance capability for both the crack in the panel and the debond in the adhesive. On the other hand, for double sided repair, the patch material having the minimal mismatch in the coefficient of thermal expansion with that of the cracked plate provides the better damage tolerance capability.     

Plasticity induced fatigue crack growth retardation model for steel elements reinforced by composite patch

Fatigue tests on notched steel plates reinforced by composite patch showed that the application of carbon fiber reinforced polymers (CFRP) strips with pretension of the overlays prior to bonding. This resulted in a significant amount of additional fatigue life. In particular, the pre-tension produces a compressive field in the steel plate which reduces the stress ratio that enhances crack growth retardation. The fatigue crack propagation rate is postulated to be a function of the effective strain energy density factor range. Fatigue crack growth data showed that standard crack growth retardation model cannot be used to evaluate the minimum effective stress. Hence, an ad hoc plasticity model is introduced and validated using experimental results. The proposed technique is an extension of the well know Newman’s model. The bridging effect due to the reinforcing strips is analytically modeled in order to estimate the reduction of crack opening displacement and finally the magnification of the crack growth retardation. Numerical and experimental results match well and show a significant influence of the pre-tension level on the expected fatigue crack growth rate of a reinforced steel plate.     

Stress-intensity factors in plates with a partially patched central crack

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of patches is related to the reduction they cause in the stress-intensity factor of the crack. Hence, an accurate evaluation of SIF in terms of various parameters is required for reliable patch design.In this paper, the influence of patch parameters on the opening-mode stress-intensity factor for a plate with a central crack is studied by employing transmission photoelasticity. Cracked plates made of photoelastic material are patched on one side as well as both sides by epoxy, phenolic and E glass-epoxy composite materials. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of 50 magnification, converted into a polariscope. Irwin's method with extrapolation is employed to compute the stress-intensity factor from photoelastic data. The reduction in the stress-intensity factor is presented in graphic form as a function of pathch parameters, namely stiffness, width and length.     

Composite patch reinforcement of cracked aircraft upper longeron: analysis and specimen simulation

The use of composite patches on cracked portions of metallic aircraft structures is an accepted means of improving fatigue life and attaining high structural efficiency. As more and more advanced composite materials are beng developed, the wider use of the repair technology is anticipated even for the reinforcement of primary aircraft structure. The objective of this work is to illustrate how the composite patch repair technology can be successfully applied to restore the structural integrity of cracked components.The Phosphoric Acid Anodize (PAA) surface treatment on aluminum when applied in conjunction with the AVI13/HV998 adhesive were essential for achieving the appropriate patch bonding strength. Such a process was done without immersing the component into the PAA tank; dismantling the component from the aircraft was not necessary. Boron/epoxy and carbon/epoxy patches were applied at room temperature to the 7075-T6511 cracked specimens and tested under fatigue simulating the load spectrum for the upper longeron attached to the access door of the electronic equipment bay. Considerable improvement in the fatigue life was observed after the repair. Equivalent flight test hours were increased from approximately two thousand hours at which the component fractured completely when not repired to twelve thousand hours when the repair was made with only a small amount of crack growth. A six times increase fatigue life is obtained. The laboratory developed technique has been applied to several in-service aircraft which have now been flown for more than 700 h without detection of crack growth.     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

A crack bridging model for bonded plates subjected to tension and bending

A crack bridging model is presented for analysing the tensile stretching and bending of a cracked plate with a patch bonded on one side, accounting for the effect of out-of-plane bending induced by load-path eccentricity inherent to one-sided repairs. The model is formulated using both Kirchhoff–Poisson plate bending theory and Reissners shear deformation theory, within the frameworks of geometrically linear and nonlinear elasticity. The bonded patch is represented as distributed springs bridging the crack faces. The springs have both tension and bending resistances ; their stiffness constants are determined from a one-dimensional analysis for a single strap joint, representative of the load transfer from the cracked plate to the bonded patch. The resulting coupled integral equations are solved using a Galerkin method, and the results are compared with three-dimensional finite element solutions. It is found that the formulation based on Reissners plate theory provides better agreement with finite element results than the classical plate theory.     

Scale effect in molding-composition plates with cracks

In [5–7], the influence of the relation between the plate width and the crack length on the limiting load for steel was investigated. The hazardous defect dimension in steel is determined by the grain size, and may be neglected in practice. For molding compositions reinforced by glassfiber or glass-strip sections, the hazardous defect dimension may be comparable with that of a visually observable crack. In that case, the failure criterion and the scale effect for a cracked plate depends on the relation between the plate width and the crack length, and on the crack-resistance characteristic of the material, which is the length of the crack equivalent to the hazardous defect in the material. The aim of the present work is to investigate this characteristic experimentally in various loading conditions, for the example of AG-4V molding composition and to develop a simple model permitting the prediction of the scale effect in analogous materials.S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 62–67, January, 1994.     

Investigation on 3D fatigue crack propagation in surface-cracked specimens

In the present work the fatigue crack growth in AISI304 specimens is investigated experimentally. In 3D finite element analysis the virtual crack closure technique is applied to calculate distributions and variations of the stress intensity factor along the surface crack front. It is confirmed that the stress intensity factor along the surface crack front varies non-uniformly with crack growth. Crack growth rate is proportional to the stress intensity factor distribution in the 3D cracked specimen. The fatigue crack growth in surface cracked specimens can be described by the Forman model identified in conventional compact tension specimens. For crack growth in the free specimen surface the arc length seems more suitable to quantify crack progress. Geometry and loading configuration of the surface cracked specimen seem to not affect the fatigue crack growth substantially.     

Fatigue crack growth in high and low strength steel under torsional loading

During loading of a crack in mode III the crack surfaces in contact slide against each other giving rise to friction, abrasion and mutual support, thereby reducing the effective stress at the crack tip (“sliding mode crack closure”). This phenomenon was investigated in a high strength steel (AISI 4340) and in a low strength steel (AISI C1018) in circumferentially notched specimens under pure cyclic torsion and combined loading (cyclic torsion plus static axial load). The influence of sliding mode crack closure on fatigue crack propagation is shown and “true” crack growth values (without the sliding mode crack closure influence) are determined on the basis of an extrapolation procedure. Explanations are given for causes of the various fracture modes observed, such as “factory roof” fracture, macroscopically flat mode III fracture and “lamella” fracture. Finally the scientific and technical importance of sliding mode crack closure is demonstrated.     

Crack paths formed by multiple debonds in LFRP composites

Onset and growth of debonds at fibre-matrix interfaces in a bundle of fibres subjected to transverse loads are studied numerically. In particular, the crack path formed by debonded neighbour fibres is analysed. The Linear Elastic–Brittle Interface Model (LEBIM) is used to model the fibre-matrix interface behaviour. This simple model of a Long Fibre Reinfoced Polymer (LFRP) composite includes ten parallel fibres embedded in a matrix cell whose external dimensions are much larger than the fibre radius. The advantage of the present LEBIM formulation of the so-called matrix cracking lies in its ability to make quantitative predictions about the concurrent fibre-matrix debond onset and mixed-mode interface crack growth in a fibre bundle. The numerical analysis predicts failure loads producing the first and subsequent debond onsets, leading to a crack path. A discussion on the position where debond occurs is also included. Finally, the effect of the load biaxiality on the crack path is studied in detail.     

Transient dynamic response of debonded sandwich plates predicted with finite element analysis

Dynamic transient response of a composite sandwich plate with a penny-shaped debonded zone has been studied by using the finite element analysis within the ABAQUS/Explicit code in this paper. In order to accurately predict the response of the debonded sandwich plate to impulsive loading, contact–impact and sliding conditions along the damaged skin-to-core interface were imposed in the model through a kinematic predictor/corrector contact algorithm. The accuracy of the finite element (FE) model used was verified by comparing between numerical predictions and experimental data known in literature for the frequency spectrum of a cracked polycarbonate laminated beam containing a delamination. By analyzing nonlinear aspects of the transient dynamics of the sandwich plate, it is shown that the presence of the debond significantly alters its short-term response. In this respect, a considerable influence of contact events within the debonded region on the plate’s global dynamic response was found out. These results were presented in both time and frequency domains. The predictions performed also showed that the FE model applied would be useful for nondestructive evaluation of defects in composite sandwich plates, and for studying dynamic response of such plates to impact.     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

考虑界面滑移效应的组合裂纹梁弯曲解析解

将上部子梁的裂纹等效为线性扭转弹簧,考虑组合梁连接面的滑移位移,建立了以组合裂纹梁挠度和滑移位移为基本未知量的组合裂纹梁弯曲变形一维数学模型．利用Laplace变换及其逆变换,给出了组合裂纹梁弯曲变形一维数学模型的解析通解．在此基础上,研究了均布载荷作用下简支组合裂纹梁的弯曲变形问题,数值分析了连接面剪切刚度、裂纹深度、数目和位置等参数对组合裂纹梁弯曲变形的影响,结果表明：在裂纹处,组合裂纹梁挠度曲线存在尖点,而横截面转角曲线存在跳跃,且随着裂纹数目和深度的增加,挠度和横截面转角跳跃值增大;随着连接面剪切刚度的增加,挠度和横截面转角减小,并最终趋于定值．并且,随着组合梁跨高比的增加,连接面剪切刚度对梁挠度影响逐渐减弱．     

A Piezoelectric Technique for Evaluation of Crack Closure

The ability of the piezoelectric materials to work as sensors and actuators was employed in a technique for monitoring the degree of crack closure and to detect the crack opening load. The technique is demonstrated through experiments with a cracked beam. It consists in exciting the specimen with a piezoelectric actuator and recording the electromechanical response of piezoelectric sensors placed near the crack mouth, while applying a bending moment to open the crack. The sensors in the neighborhood of the crack present a reduction in the amplitude response signal due to the progressive decrease of the dynamic strains near the crack, as the bending load causes the crack to open, reducing the contact between the surfaces of the fatigue crack and the load transmission through the contact area. The results show that the method has a high sensitivity to the state of crack closure, allowing for the direct determination of the crack opening load.     

Numerical and experimental determination of three-dimensional multiple crack growth in fatigue

This work is concerned with the assessment of propagation of multiple fatigue cracks in three-dimensions. Computational modelling of fatigue crack propagation is made together with detection and monitoring of the crack shape development. The boundary element method (BEM) is used for automating the modelling of crack propagation in linear elastic as well as elastic–plastic regimes. Strain at several positions on the specimen surface near the crack mouth is measured to monitor crack initiation, shape development and closure levels. Examples are provided to validate the model by comparing the experimental results with those obtained by numerical predictions.     

Edge-cracked bimaterial systems under thermal heating

The problem of thermoelastic edge-cracking in two-layered bimaterial systems subjected to convective heating is considered. The medium is assumed to be insulated on one surface and exposed to sudden convective heating on another surface containing the edge crack. It is known that, when a bimaterial system’s surface is heated, compressive stresses arise near the heating surface, forcing the crack surfaces together over a certain cusp-shaped contact length. It is also known that, for a cooled bimaterial systems surface, tensile stresses take place close to the cooling surface and tend to open the crack. So, the edge cracked heating surface problem is treated as an embedded crack with a smooth closure condition of the crack surfaces, with the crack contact length being an additional unknown variable. Superposition and uncoupled quasi-static thermoelasticity principles are adopted to formulate the problem. By using a Fourier integral transform technique, the mixed boundary value problem is reduced to a Cauchy type singular integral equation with an unknown function as the derivative of the crack surface displacement. The numerical results of the stress intensity factors for an edge crack and a crack terminating at the interface, are calculated and presented as a function of time, crack length, heat transfer coefficient, and thickness ratio for two different bimaterial systems, namely a stainless steel layer welded on ferritic steel and a ceramic layer coating on ferritic steel.     

STUDY ON THE SURFACE CRACK GROWTH BEHAVIOR IN 14MnNbq BRIDGE STEEL

Three-dimensional crack closure correction methods are investigated in this paper.The fatigue crack growth tests of surface cracks in 14MnNbq steel for bridge plate subjected to tensile and bending loadings are systematically conducted.The experimentally measured fatigue crack growth rates of surface cracks are compared with those of through-thickness cracks in detail.It is found that the crack growth rates of surface cracks are lower than those of through-thickness cracks.In order to correct their differences in fatigue crack growth rates, a dimensionless crack closure correction model is proposed.Although this correction model is determined only by the experimental data of surface cracks under tensile loading with a constant ratio R=0.05, it can correlate the surface crack growth rates with reasonable accuracy under tensile and bending loadings with various stress ratios ranging from 0 to 0.5.Furthermore, predictions of fatigue life and crack aspect ratio for surface cracks are discussed, and the predicted results are also compared with those obtained from other prediction approaches.Comparison results show that the proposed crack closure correction model gives better prediction of fatigue life than other models.     

Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid

A nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate is presented using the classical plate theory (CPT). The MEE plate material selected is fiber-reinforced \(\hbox {BaTiO}_{3}\)–\(\hbox {CoFe}_{2}\hbox {O}_{4}\) composite, which contains a partial crack at the center. The CPT and the simplified line spring model for crack terms are modified to accommodate the effect of electric and magnetic field rigidities. The analysis considers in-plane forces for the MEE plate, which makes the model nonlinear. The derived governing equation is solved by expressing the transverse displacement in terms of modal coordinates. An approximate solution for forced vibration of cracked MEE plate is also obtained using a perturbation technique. The effect of part-through crack, volume fraction of the composite on the vibration frequencies and structure response is investigated. The frequency response curves presented shows the phenomenon of hard or soft spring. Furthermore, the devised model is extended to the case of cracked MEE plate submerged in fluid. Velocity potential function and Bernoulli’s equation are used to incorporate the inertia effect of surrounding fluid. Both partially and totally submerged plate configurations are considered. The validation of the present results is carried out for intact submerged plate as to the best of the author’s knowledge the literature lacks in results for submerged-cracked plates. New results for cracked MEE plate show that the vibration characteristics are affected by volume fraction, crack length, fluid level and depth of immersion.     

Experimental study and BEM analysis of fatigue crack growth in a cracked heterogeneous body

A model for analysing a soft-hard heterogeneous body with a crack in the hard region is presented in this paper. The result of fatigue experiments shows that mechanical heterogeneity affects the rate of propagation of fatigue crack. Meanwhile the results computed by BEM for cracked heterogeneous bodies under cycling loading indicate that the smaller the distance between the crack and the interface of hard and soft regions is, the smaller the amplitude of crack opening displacement, COD and ofJ-integral as well at the same step during the fatigue crack growth will be. The effect of heterogeneity on the rate of fatigue crack propagation is shown by the variation of J. The smaller the distance of the crack to the interface is, the smaller the rate of fatigue crack growth will be.