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The aim of this paper is to show a new geometrical specimen in fatigue to define the behavior of semi elliptical crack growth in thick-walled pressure vessels. This research emphasize on the importance of the behavior of fatigue crack in test specimen and real conditions in vessels .In other word, there must be more adaptations between stress intensity factor in new specimen and real vessel that includes crack along the wall, so, under Fatigue loadings, as a result, more adaptation will be obtained between growth speed and relative crack lifetime according to loading cycles. By introducing this new specimen we compare the results of fatigue loading on propositional new specimen with results of vessel fatigue loading and standard specimen. We estimate the behavior of fatigue crack growth in specimen and pressure vessel with (FEM) and experimental method. In order to comparing of limit component with experimented results, some piece of with new specimen made of steel (ck45) can be used and all of these must be under fatigue testing and results are obtained in these methods.

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In this paper, the Meshless Local Petrov-Galerkin (MLPG) method is used to analyze the fracture of an isotropic FGM plate. The stress intensity factor of Mode I and Mode II are determined under the influence of various non-homogeneity ratios, crack length and material gradation angle. Both the moving least square (MLS) and the direct method have been applied to estimate the shape function and to impose the essential boundary conditions. The enriched weight function method is used to simulate the displacement and stress field around the crack tip. Normalized stress intensity factors (NDSIF) are calculated using the path independent integral, J*, which is formulated for the non-homogeneous material. The Edge-Cracked FGM plate is considered here and analyzed under the uniform load and uniform fixed grip conditions. To validate results, at first, homogeneous and FGM plate with material gradation along crack length was analyzed and compared with exact solution. Results showed good agreement between MLPG and exact solution.

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Functionally graded materials have been taken into consideration by many researchers in the last two decades. Gradual changes of mechanical properties in FGMs decrease stress concentration, crack initiation and propagation and delamination. Many of the present and potential applications of FGM contain contact loading.This kind of loading causes surface crack initiation which is followed by subcritical crack propagation.Thus, propagation of surface cracks is one of the most important failure mechanisms in FG structures. In this article two dimensional sliding contact of a rigid flat punch on a homogeneous substrate with an FGM coating is studied. Plane strain condition is considered in this problem. The Properties of the substrate and the FGM layer are assumed to be elastic and the Poisson’s ratio is assumed to be constant. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions. The governing equations are solved by Finite Difference method by means of MATLAB software. The influence of different parameters such nonhomogeneity,q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction on the mode I and II stress intensify factors are investigated.

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Extended finite element method (XFEM) is one of the strongest numerical methods that its basis is finite element but regardless of mesh location respect to discountinuty solves the problems. In this method, using of enreaching the nodes and increasing of their degrees of freedom (from 2 to 4 or even upto 10) virtually and without verifying the mesh and geometry of discountinuty, one can model and develop the required governing equations of the system. In this paper, fatigue crack growth of repaired aluminum panels containing a crack is studied. The cracked panels were repaired on one side with glass/epoxy composite patches in the mixed mode condition. The extended finite element method is used to study the effects of patch lay-up configuration on crack front displacement and stress intensity factor and the effect of crack angle on stress intensity factor of the repaired panels. The results show that the plate-fiber-fiber-aluminum configuration has best effect and it could reduce the stress intensity factor (k1) by upto seventy percent.

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In this paper, the eXtended Finite Element Method is implemented to model the effect of the mechanical and thermal shocks on a cracked 2D orthotropic media. The uncoupled thermoelasticity equations are considered. Isoparametric four-node and eight-node rectangular elements are used to discrete governing equations. The dynamical stress intensity factors are computed by the interaction integral method. The Newmark and the Crank–Nicolson time integration schemes are used to numerical solve the spatial-discretized elastodynamic and thermal equations, respectively. A MATLAB code is developed to carry out all stages of the calculations from mesh generation to post-processing. Several elastic and thermoelastic numerical examples are implemented, to check the accuracy of the results and to investigate the effect of the orthotropic direction on the stress intensity factors.

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In this paper, the anti-plane stress analysis in an infinite elastic plane with multiple cracks is carried out by using the distributed dislocation technique. The solution is obtained for an infinite plane containing the screw dislocation via Fourier transform of biharmonic equation for the analysis of infinite plane in gradient elasticity. These solutions are used to perform integral equations for an infinite plane weakened by multiple straight cracks. Integral equations are hypersingular type which are solved numerically for density of dislocation on the cracks surfaces. The numerical method in Chebyshev series form are used to solve the hypersingular integral equations. The solution of integral equations leads to dislocation density functions. The stress intensity factor for cracks tips are formulated in terms of density of dislocation. Employing the definition of dislocation density, stress intensity factors for cracks tips are calculated. The influence of size-effect and crack location on the stress intensity factors are studied. To confirm the validity of formulations, numerical values of stress intensity factors are compared with the results in the literature. The results of the present approach are in excellent agreement with those in the literature. Some new examples with different geometrics of cracks are solved to illustrate the applicability of procedure.

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The autofrettaged thick-walled tube containing semi-elliptical crack is investigated. To study the variation of stress intensity factor on crack front, at first, two dimensional weight function is extracted. Stress intensity factor of all points on crack front can be calculate using proposed weight function, also, the complicated loading on crack faces including the loads due to axial gradient pressure in short cylinder and open-end tubes can be considered. Results show that, opposite of the cylinder subjected to uniform pressure, in pipes under gradient pressure, the maximum stress intensity factor are not necessarily on deepest point and surface points. The maximum stress intensity factor occurs on non-surface points in autofrettaged tubes. The results obtained from two dimensional weight function method have a good accuracy with the results obtained from finite element method. Prediction of fatigue crack configuration using two dimensional weight function can be more accurate than those obtained from one dimensional weight function.

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In this study, the first mode of stress intensity factor of semi-elliptical circumferential crack in the outer surface of a cylinder with radius to thickness ratio of 30, is investigated. The cylinder is applied in semi-submersible drilling platforms. First, the stress field of the cylinder under thermal and mechanical loads is extracted based on semi couple thermo-elastic equations. Then, the weight functions are derived for deepest and surface points using three reference loads results. Explicit expressions of stress intensity factors for surface and deepest points are presented using thermo-elastic stress field and the weight functions of the cracked cylinder. The results obtained by proposed weight functions and those obtained by finite element method and those presented in the literatures have a good accuracy. The interaction effects of thermal and mechanical loads on the stress intensity factors are studied. The results show that with increasing load ratio, the dimensionless stress intensity factors of deepest and surface points, decrease and increase, respectively.

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The use of stop drill holes is one of the most convenient methods for reducing the stress intensity factors and crack growth rate. The efficiency of stop drill holes on the crack growth retardation depends on the amount of reduction in stress intensity factors. The curved plates are frequently used in engineering structures. Therefore, in this paper, by using the finite element method, the effects of configurations and diameters of crack flank holes on the variations of stress intensity factor are studied for a curved plate. The numerical results indicate that the location and the size of stop drill holes affect the stress intensity factors which is mainly due to their interaction with the crack tip stresses. Closer distances to the crack tip and larger diameters of the flank holes provide more reduction in the stress intensity factors. Also, the finite element results show that the use of stop drill hole method for the curved plates has the same efficiency as that of the flat plates.

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To investigate, understanding and predicting dynamic fracture behavior of a cracked body, dynamic stress intensity factors (DSIFs) are important parameters. In the present work interaction integral method is presented to compute static and dynamic stress intensity factors for three-dimensional cracks contained in the functionally graded materials (FGMs), and is implemented in conjunction with the finite element method (FEM). By a suitable definition of the auxiliary fields, the interaction integral method which is not related to derivatives of material properties can be obtained. For the sake of comparison, center, edge and elliptical cracks in homogeneous and functionally graded materials under static and dynamic loading are considered. Then material gradation is introduced in an exponential form in the two directions in and normal to the crack plane. Then the influence of the graded modulus of elasticity on static and dynamic stress intensity factors is investigated. It has been shown that, material gradation has considerable reduce influence on DSIFs of functionally graded material in comparison with homogenous material. While, static stress intensity factors can decrease or increase, depend on the direction of gradation material property.

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In this paper, the stress intensity factor for a longitudinal semi-elliptical crack in the internal surface of a thick-walled cylinder is derived analytically and numerically. The cylinder is assumed enough long and subjected to the axisymmetric cooling thermal shock on the internal surface. The uncoupled thermoelasticity governing equations for an uncracked cylinder are solved analytically. The non-dimensional hyperbolic heat equation is solved using separation of variables method. The weight function method is implemented to obtain the stress intensity factor for the deepest and surface points of the crack. Results show the different behavior of the crack under hyperbolic thermal shock. At a short time after the thermal shock, the stress intensity factor at the deepest point –especially for shallow cracks- for hyperbolic model is significantly greater than Fourier one. The stress intensity factor at the deepest point is greater as the crack is narrower for both models. Unlike mechanical loading, the greatest stress intensity factor may occur at the surface point. According to the results, assumption of adequate heat conduction model for structure design under transient thermal loading is critical.

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In the present study, in order to evaluate the elastic displacement field and subsequently the fracture parameters within the isotropic homogeneous elastic solids with the edge or interior cracks, the extended finite element method with level set technique was used to avoid the disadvantages associated with the standard finite element method. An overdeterministic least squares method was utilized to determine the crack stress intensity factors as well as the coefficients of the higher order terms in the Williams' asymptotic series solution for structures containing crack in various modes of failure by fitting the series solution of displacement fields around the crack tip to a large number of nodal displacements obtained from the extended finite element method. For validating the results, several cracked specimens subjected to pure mode I, pure mode II, and mixed modes I/II loading were performed. Comparisons with results available from the literature obtained by the other formulations reveal the efficiency and the simplicity of the proposed method and demonstrate the capability of it to capture accurately the crack stress intensity factors and the coefficients of higher order terms.

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Human bones experience different modes of loading including tension, compression, bending, and torsion. The modes of loading depend on the activities done by the body. Regarding the crack shape and loading modes, by the time only the first mode of fracture has been studied in order to analyze the fracture toughness. However, it is necessary to analyze different modes of fracture in order to find more reliable results. In this research, finite element analysis and calculations for geometric coefficients were done to obtain the toughness of bone. Hence, first, second, and combined modes of fracture in cortical samples having cracks were studied numerically and experimentally. To this end, bovine tibia was used to make standard tensile samples for implementation in Arkan’s device. Some optimizations were made on the Arcan’s device. These were included of bone fixation in the device and ability of performing tests in different angels. Stress intensity factor (Kc) was obtained for different fracture modes. Results showed a decrease in KIc respect to change in loading angle while KIIc acted vice versa. Performing some extra optimizations, the device can be used for tortional fracture mode in a torsional test device.

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In this paper, the variations of the stress intensity factor and energy release rate have been investigated based on the displacement correlation and modified crack closure integral methods for external surface cracks in the autofrettaged functionally graded cylinder (FGC). Mechanical properties vary in the radial direction according to the desired function. Isotropic material behavior and bilinear elastoplastic stress-strain relationship are considered for the FGC. Autofrettage process induces the tensile residual stresses in the outer parts of the cylinder wall, which causing the undesirable effects on the external surface cracks. Many variables affect the distribution of tensile residual stresses. Effects of autofrettage ratio, volume fraction of material and cylinder thickness on the residual stress changes and addition, changes in the size and direction of surface cracks on the stress intensity factor and energy release rate are studied. The results show that the volume fraction has the greatest effects on both crack parameters. The axial cracks are critical in compared with circumferential and angled cracks. The principle of superposition can be used to determine the combinational effects of the residual stresses and applied loads on the behavior of cracks in the graded materials.

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In a structural analysis, dynamic response of a crack is of significant importance as well as the impacts of elastic waves on stress intensity factors (SIF). In this paper, dynamic analyses of multiple cracks on a half-plane subjected to anti-plane shear stresses are presented. Stress intensity factors are calculated and the interaction of elastic waves with the boundary of plane and the cracks' tips is investigated at different locations. The distribution discontinuous displacement techniques are used, enabling us to solve the crack problems in dynamic fracture mechanics. Integral transformations (Laplace and Fourier) are applied to elastodynamics equations and by using a set of appropriate boundary conditions solved discontinuous displacement and the crack problem is solved through discontinuous displacement method. As a result, the stress equations with hypersingularity terms are obtained. Using Chebyshev series expansion and collocation points in Laplace domain, the crack solution is achieved. Finally, different algorithms of numerical Laplace inversion are presented and the stress intensity factors (SIF) are obtained. The presented results are compared with published data and a good agreement is observed. Moreover, it is also demonstrated that the present theoretical study is capable of modelling multiple cracks with different arrangements.

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This paper concerns the effect of auxiliary fields and distance of contours from the crack tip on the accuracy of stress intensity factors of Functionally Graded Materials (FGMs), using the interaction integral method. In the first step, defining auxiliary fields of displacement, strain, and stress appropriately, the interaction integral is derived which is independent of derivatives of properties of the materials. Actual and auxiliary fields of displacement, strain and stress are used to compute the interaction integral. Actual fields are obtained by isoparametric finite element method, while auxiliary fields are constructed by use of the crack tip properties on the basis of William’s solution. These auxiliary fields are not appropriate, except near the crack tip. Therefore, different non-equilibrium and incompatibility formulations are used to consider the changes in non-homogeneous material. Considering the changes in FGMs as an exponential function, the results will be obtained from these formulations and are compared with others recorded in the literature. Furthermore, considering different contours, the effect of distance of contours from the crack tip on the stress intensity factors of FGMs is examined. The results confirm that the solutions using the incompatibility and constant constitutive tensor are more accurate. In contrast the non-equilibrium method is not proper for contours which are placed far away from the crack tip and presents less accuracy.

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Cracks in composite structures are the most common damages. For example, cracks in thickness direction (translaminar fracture) would be due to inadvertent impact of the projectile with the aerospace structures. Most of studies, so far, aimed at studying the interlaminar crack propagation and emergence of the delamination phenomenon. In this paper, in an attempt to study the translaminar crack propagation of composites, test specimens were prepared in the form of butterfly from a woven glass-epoxy composite by hand layup and the autoclave process. Experimental fracture tests were performed in the first mode, mixed-mode and the pure second mode by changing the loading angle, using a specially developed fixture, based on Arcan. Load versus displacement curves were obtained. Using critical loads of the tests and the dimensionless stress intensity factors, obtained from the finite element analysis by ABAQUS software, translaminar fracture toughness of the composite was determined. As the result, it can be seen that the opening mode translaminar fracture toughness is larger than the shearing mode toughness. This means that translaminar cracked specimen is tougher in tensile loading condition and weaker in shear. Finite element analysis was performed using effective elastic properties of the glass epoxy composite obtained from a homogenized woven composite model based on micromechanics. The effect of laminate thickness on the translaminar fracture toughness behavior of the glass epoxy composite has been studied.

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In this paper, the effect of nonhomogeneous parameter in orthotropic Functionally Graded Material(FGM) in a cracked layer is investigated. It is assumed that the mechanical and thermal properties of material are dependent on x-coordinate (collinear with crack surfaces) in exponential form. The problem is solved for internal and edge crack in two way, integral equations and generalized differential quadrature method. Thermal loading is in a way that temperature distribution in the layer is uniform. Because of variation in mechanical and thermal properties, stress distribution due to this loading is not uniform. In the solution of problem with integral equations method, first, thermo-elasticity problem with no cracks and then isothermal crack problem are separately solved. Afterward with these solutions, the main problem will be solved. In order to solve isothermal crack problem, after conversion and simplifying the equations in orthotropic material, Navier's equations will be solved with the Fourier. Numerical solution of the problem is the generalized differential quadrature element method that is being presented for verification of the results of the integral equations for a specific state in the diagram format. Also the effect of temperature on intensity factor with various values of nonhomogeneous parameter is investigated.

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A family of rotating disks used in Iranian turbine and compressor industry is investigated. Mechanical and thermal loads due to working condition would lead to the crack initiation in the inner surface of the disk. The aim of this paper is the development of the two-dimensional weight function for the rotating disks containing semi-elliptical longitudinal cracks. The general form of the two-dimensional weight function is related to the proposed weight functions for embedded cracked domain in literature. In order to determine the unknown coefficient of the weight function, the reference stress intensity factors for cracked geometry subjected to reference loads are calculated. The analysis indicated that the results are independent of the number of terms in proposed weight function expansion. Extracting the weight function for disks with from 90 to 420 mm thickness enables one to predict the stress intensity factor for cracks in the structure subjected to arbitrary loading. The stress intensity factor for each point on the crack front subjecting to one or two dimensional loads would be calculated using the derived weight function. The results reveal that the increasing of the height to thickness ratio in rotating disks leads to the increase of the stress intensity factor for high depth ratio crack ones. Results show that the configuration of the disk sections affects the stress intensity factors of the same aspect ratio cracks in the structures. The comparison of the results obtained from the weight function method and those obtained with FEM are in good agreement.

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Static and dynamic stress intensity factors are important parameters in the fracture behavior of the cracked bodies. In the present study the displacement correlation technique (DCT) is presented to calculate static and dynamic stress intensity factors of functionally graded materials (FGMs). The displacement field is obtained using finite element method (FEM) and ABAQUS software. To consider the variation of material properties, a subroutine is prepared in the UMAT subroutine of the software. Eight-node singularity elements are used in the FEM. As ABAQUS software is not able to calculate stress intensity factors of FGMs, so a MATLAB code is developed to obtain these factors. By analyzing an example under dynamic load, dynamic fracture behavior of orthotropic FGMs and effect of non-homogeneity parameter are investigated for two cases of material properties variation directions which are perpendicular to each other. To verify presented method, a center crack in a plate of homogeneous and FGM materials are analyzed under static and dynamic loads, the results are compared with data of literatures. The results show that, if the material properties vary parallel to the crack direction, the mode I dynamic stress intensity factor at the crack tip located in the stiffer part increases with increasing of non-homogeneity parameter, while for variation in the normal direction to the crack, this factor first increases and then decreases.