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The paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.

The fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.

Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.

According to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

The purpose of this paper is to present special nine‐node quadrilateral elements to discretize the un‐cracked boundary and the inclined surface crack in a transversely isotropic cuboid under a uniform vertical traction along its top and bottom surfaces by a three‐dimensional (3D) boundary element method (BEM) formulation. The mixed‐mode stress intensity factors (SIFs), K_I, K_II and K_III, are calculated.

A 3D dual‐BEM or single‐domain BEM is employed to solve the fracture problems in a linear anisotropic elastic cuboid. The transversely isotropic plane has an arbitrary orientation, and the crack surface is along an inclined plane. The mixed 3D SIFs are evaluated by using the asymptotical relation between the SIFs and the relative crack opening displacements.

Numerical results show clearly the influence of the material and crack orientations on the mixed‐mode SIFs. For comparison, the mode‐I SIF when a horizontal rectangular crack is embedded entirely within the cuboid is calculated also. It is observed that the SIF values along the crack front are larger when the crack is closer to the surface of the cuboid than those when the crack is far away from the surface.

The FORTRAN program developed is limited to regular surface cracks which can be discretized by the quadrilateral shape function; it is not very efficient and suitable for irregular crack shapes.

The evaluation of the 3D mixed‐mode SIFs in the transversely isotropic material may have direct practical applications. The SIFs have been used in engineering design to obtain the safety factor of the elastic structures.

This is the first time that the special nine‐node quadrilateral shape function has been applied to the boundary containing the crack mouth. The numerical method developed can be applied to the SIF calculation in a finite transversely isotropic cuboid within an inclined surface crack. The computational approach and the results of SIFs are of great value for the modeling and design of anisotropic elastic structures.

In accord with the literature reviews, there is not a promising examination regarding the several straight and curved cracks interaction with arbitrary arrangement in the rectangular FGP plane. The purpose of this paper is to consider the effect of crack length, position of the point load, material non-homogeneity constant and also the arrangement of cracks on the resulting field intensity factors.

First of all, in order to obtain a set of Cauchy singular integral equations, both the dislocation method and the finite Fourier cosine transform technique are applied. Using the corresponding solution to these equations, the dislocation densities on the crack surfaces are then obtained. Considering the results, both the stress intensity factors (SIFs) and electric displacement intensity factors (EDIFs) for a vertical crack and the interaction between two straight and curved cracks, which have an arbitrary configuration, are determined.

The numerical examples are represented in order to illustrate the interesting mechanical and electrical coupling phenomena induced by multi-crack interactions. At the end, the effects of the material non-homogeneity constant, the crack length and the cracks arrangements on the SIFs and EDIFs are investigated.

The solutions are obtained in series expansion forms which may be considered as Green’s functions in an FGP rectangular plane possessing multiple cracks. The technique of Green’s function provides the ability to analyze multiple cracks having any smooth configuration.

This paper comprehensively addresses the influence of chopped strand mat glass fiber-reinforced polymer (GFRP) patch configurations such as geometry, dimensions, position and the number of layers of patches, whether a single or double patch is used and how well debonding the area under the patch improves the strength of the cracked aluminum plates with different crack lengths.

Single-edge cracked aluminum specimens of 150 mm in length and 50 mm in width were tested using the tensile test. The cracked aluminum specimens were then repaired using GFRP patches with various configurations. A three-dimensional (3D) finite element method (FEM) was adopted to simulate the repaired cracked aluminum plates using composite patches to obtain the stress intensity factor (SIF). The numerical modeling and validation of ABAQUS software and the contour integral method for SIF calculations provide a valuable tool for further investigation and design optimization.

The width of the GFRP patches affected the efficiency of the rehabilitated cracked aluminum plate. Increasing patch width WP from 5 mm to 15 mm increases the peak load by 9.7 and 17.5%, respectively, if compared with the specimen without the patch. The efficiency of the GFRP patch in reducing the SIF increased as the number of layers increased, i.e. the maximum load was enhanced by 5%.

This study assessed repairing metallic structures using the chopped strand mat GFRP. Furthermore, it demonstrated the superiority of rectangular patches over semicircular ones, along with the benefit of using double patches for out-of-plane bending prevention and it emphasizes the detrimental effect of defects in the bonding area between the patch and the cracked component. This underlines the importance of proper surface preparation and bonding techniques for successful repair.

Detecting the orientation of cracks is a major challenge in the development of eddy current nondestructive testing probes. Eddy current-based techniques are limited in their ability to detect cracks that are not perpendicular to induced current flows. This study aims to investigate the application of the rotating electromagnetic field method to detect arbitrary orientation defects in conductive nonferrous parts. This method significantly improves the detection of cracks of any orientation.

A new rotating uniform eddy current (RUEC) probe is presented. Two exciting pairs consisting of similar square-shaped coils are arranged orthogonally at the same lifting point, thus avoiding further adjustment of the excitation system to generate a rotating electromagnetic field, eliminating any need for mechanical rotation and focusing this field with high density. A circular detection coil serving as a receiver is mounted in the middle of the excitation system.

A simulation model of the rotating electromagnetic field system is performed to determine the rules and characteristics of the electromagnetic signal distribution in the defect area. Referring to the experimental results aimed to detect artificial cracks at arbitrary angles in underwater structures using the rotating alternating current field measurement (RACFM) system in Li et al. (2016), the model proposed in this paper is validated.

CEDRAT FLUX 3D simulation results showed that the proposed probe can detect cracks with any orientation, maintaining the same sensitivity, which demonstrates its effectiveness. Furthermore, the proposed RUEC probe, associated with the exploitation procedure, allows us to provide a full characterization of the crack, namely, its length, depth and orientation in a one-pass scan, by analyzing the magnetic induction signal.

This study provides an analysis of patch repair for cracked aircraft structures. Delamination is a type of damage that affects the patch's behavior. The purpose of this study is to assess the influence of delamination on repair performance.

An analytical and numerical study using the finite element method was conducted for a cracked plate repaired with a patch containing a pre-existing delamination defect. The method for defining the contact pair surfaces and modeling the delamination interaction within the patch interface is specified using the virtual crack closure technique (VCCT) approach.

The efficiency of the repair is measured in terms of the J-integral. The effects of delamination initiation, mechanical loading, crack length and patch stacking sequences are presented. It is noted that in mode I, delamination propagation is only significant at node A. The numerical results are in good agreement with those of the analytical solution found in the literature. It is observed that the patch's behavior is strongly dependent on loading, crack size and stacking sequences in terms of reducing the structure's lifespan, especially in the presence of delamination.

The numerical modeling presented by the VCCT approach is highly valuable for studying delamination evolution. The influence of loading, crack size and stacking sequences on repair performance is discussed in this work.

Various types of damage or cracking in the structural components of an airframe can occur during the service lifetimes of aging aircraft. These types of damage are commonly repaired with a patch that can be joined to the original structure by different techniques, e.g., riveting and bonding. The purpose of this paper is to describe the repair of a fatigue crack in the metallic wing structure of a jet trainer aircraft using an adhesively bonded boron composite patch.

The partial analytical design and numerical analysis of the repair is presented. Three different versions of the patch are quantitatively investigated. The efficiency of the designed adhesively bonded boron patch with the parent metallic structure is experimentally verified by panel tests, and two different patch geometries and two surface preparation techniques are investigated. The panels were designed, manufactured and tested as representative structures of the repaired structure.

Adhesively bonded composite repair increases the lifetime by at least one order compared with the non-repaired structure. Both surface preparations provide equivalent results. The repair lifetime is significantly influenced by the patch geometry, and the longer patch significantly increases the lifetime of the panel. The lifetime of the structure can be increased by ˜40-fold if the patch geometry is a rectangle with 1:1.5 proportions of the sides (length in the crack direction/length perpendicular to the crack propagation). The patch length in the crack direction should be twice that of the initial crack length. Additional patch length extension in the direction that is perpendicular to the crack propagation does not appear to be effective for significantly decreasing the stress intensity factor and patch efficiency. The repair also retards the crack propagation if the crack grows out of the patch. No significant disbonding was detected.

The work described in this paper provides information that is very useful for patch design and verification with relation to different patch geometries and technologies. The designed and verified repair has been successfully applied to an L-39 Czech aircraft structure.

This paper aims to deal with the study of interaction between multiple cracks in an aluminum alloy under static loading. Self-similar as well as non-self-similar crack growth has been observed which depends on the relative crack positions defined by crack offset distance and crack tip distance. On the basis of experimental observations, the conditions for crack coalescence, crack shielding, crack interaction, crack initiation, etc. are discussed with respect to crack position parameters. Considering crack tip distance, crack offset distance, crack size and crack inclination with loading axis as input parameter and crack initiation direction as output parameter, an artificial neural network (ANN) model is developed. The model results were then compared with the experimental results. It was observed that the model predicts the crack initiation direction under monotonic loading within a scatter band of ±0.5°.

The study is based on the experimental observations. Growth studies are made from the growth initiation from two cracks in a rectangular aluminium plate under static loading. The present study is focused on the influence of crack position defined by crack offset distance and crack tip distance on growth direction. In addition to this, ANN has been used to predict crack growth direction in multiple crack geometry under static loading. The predicted results have been compared with the experimental data.

The influence of the interaction between multiple cracks on crack extension angle greatly depends on the relative position of cracks defined by crack tip distance S, crack offset distance H and crack inclinations with respect to loading direction. The intensity of the crack interaction can be described according to degree of crack extension angle and relative crack position factors. It is also observed that the progress of the outer and inner crack tip direction is different which mainly depends on the relative crack position.

It is limited to static loading only. Under fatigue loading findings may differ.

It is important to investigate the growth behaviour under multiple cracks and also to know the effect of crack statistics on the growth behaviour to estimate the component life. The study also focused on the development of a high quality predictive method.

The results show trends that vary with crack geometry condition and the ANN and empirical solution provides a possible solution to assess crack initiation angle under multiple crack geometry.

This paper aims to calculate the mixed‐mode stress intensity factors (SIFs) of a 3D crack meeting the interface in a bimaterial under shear loading by a hypersingular integral equation (HIE) method, And further to assess the accuracy of numerical solutions for the mixed mode SIFs along the crack front.

A 3D crack modeling is reduced to solving a set of HIEs. Based on the analytical solutions of the singular stress field around the crack front, a numerical method for the HIEs is proposed by a finite‐part integral method, where the displacement discontinuities of the crack surface are approximated by the product of basic density functions and polynomials. Using FORTRAN program, numerical solutions of the mixed‐mode SIFs of some examples are presented.

The numerical method is proved to be an effective construction technique. The numerical results show that this numerical technique is successful, and the solution precision is satisfied.

This work takes further steps to improve the fundamental systems of HIE for its application in the fields of arbitrary shape crack problems. Propose several techniques for numerical implementation, which could increase the efficiency and accuracy of computation.

Whenever there is a structure containing the 3D crack, the analysis method described in this paper can be utilized to find the critical configurations under which the structure may be most vulnerable. In such cases, the strength predictions would be safer if the crack could be taken into account.

This paper is the first to apply HIE method to analyzing the mixed‐mode crack meeting the interface in 3D dissimilar materials. Numerical solutions of the mixed‐mode SIFs can give the satisfied solution precision.

Reinforced concrete (R.C.) beams are part of the structure so their design depends on the structural code and its requirements. In this paper, two simply supported R.C. beams were designed in terms of flexural and shear strength design requirements and investigated in terms of deflections and crack widths, when subjected to two asymmetric concentrated loadings, where one load is double the other one. Both beams had dimensions of 3,500 mm length, 200 mm width, and 300 mm height. The first beam (beam B1) was designed according to the combination of the structural requirements of American and Saudi building codes (ACI318-and-SBC304), while the second beam (beam B2) was designed according to the structural requirements of Eurocode (EC2). The paper aims to discuss these issues.

The design of ultimate capacity (section capacity) to design both flexure and shear capacity according to the design provisions in EC2 code deals with the Ultimate Limit State Design Approach, while it deals with the Ultimate Strength Design Approach according to the design provisions in both ACI318 and SBC304 codes. In the serviceability (mid-span deflection and flexural crack width) check, the three codes deal with the Serviceability Limit State Design Approach.

The laboratory behaviour of both test beams was as expected in flexure and failed in shear, but there was more shear cracks in the left shear span for both beams. This refers to the left applied loading and the spacing of shear links, where the failure occurred at the higher loading points. Perhaps, if the number of links was increased in the left side of the beam during the manufacture and reinforcing of the beam, the failure loading will be delayed and the diagonal cracks will be decreased.

From this study, it was concluded that: the ACI318 and SBC304 design approaches are safer than the EC2 design approach. The EC2 design approach is more economic than the ACI318 and SBC304 design approaches. The structural behaviour of both test beams was as expected in flexure but both beams failed in shear. The shear failure was in the left side of both test beams which was referred to a high loading point. Diagonal cracks followed the applied loading until both beams reached to the failure.