Part-through Crack Research Articles

Free Vibrations of Plates on Elastic Foundation

In the current study the free vibrations of stepped anisotropic rectangular plates on elastic foundation are considered. The anisotropic stepped plate has a part-through crack at the re-entrant corner of the step. Natural frequencies of the plate are calculated for the given crack length. The influence of physical properties and geometric parameters on the natural frequencies is analyzed.

A New Solution Method for Vibration Analysis of Circular Cylindrical Thin Shells with a Circumferential Surface Crack

In this paper, a new solution method is proposed for determining the natural frequency of a given mode for a finite-length circular cylindrical thin shell with a circumferential part-through crack. The governing equation of the cracked cylindrical shell is derived by integrating the line-spring model with the classical thin shell theory. The proposed method calculates the natural frequency from an initial trial to satisfy both the governing equations and appropriate boundary conditions through an optimization process. The initial trial is proposed to satisfy the governing equations by using the beam modal function to determine the modal wavenumbers and mode shapes of cylindrical shells in the axial direction, assuming the flexural mode shapes of cylindrical shells in the axial direction to be of the same form as that of a flexural vibration beam with the same boundary conditions. Four representative sets of boundary conditions are considered: simply supported (SS-SS), clamped-clamped (C-C), clamped-simply supported (C-SS), and clamped-free (C-F). Compared with the finite element (FE) method, the proposed solution method is verified to provide an accurate and efficient way to calculate the dynamic characteristics of both intact and cracked cylindrical shells.

Dynamic Analysis of Finite-Length Circular Cylindrical Shells with a Circumferential Surface Crack

AbstractIn this paper, a new solution method is proposed for investigation of the vibration characteristics of finite-length circular cylindrical shells with a circumferential part-through crack. Four representative sets of boundary conditions are considered: simply supported, clamped-clamped, clamped-simply supported, and clamped-free. The governing equation of the cracked cylindrical shell is derived by integrating the line-spring model with the classical thin shell theory. A computationally efficient numerical solution method for determining the natural frequency of the system of a given mode is proposed. The algorithm calculates the natural frequency from an initial trial through a one-dimensional optimization process. Two initial trial estimation methods are considered: the beam-function method and Soedel’s expression method. On the basis of the case study results, a recommendation is made on the selection of a suitable initial trial calculation method. The verification of the proposed method is divi...

823 受動型電気ポテンシャルCT法を用いた非貫通三次元き裂の同定(GS-3 き裂検出,固定)

823 受動型電気ポテンシャルCT法を用いた非貫通三次元き裂の同定(GS-3 き裂検出,固定)

Shell of arbitrary curvature with cracks of different type and geometry

The interaction of through, surface, and internal cracks in shells of arbitrary curvature is examined. Crack of the same and different types with various geometry are considered. The curvature of the shell, the length and depth of the cracks, their arrangement and distance between them have a strong effect on the stress intensity factors for part-through cracks and on the force and moment intensity factors for through cracks

Studies on the behavior of part-through circumferential crack at intrados in elbows under in-plane bending moment

This paper presents the behavior of part-through circumferential crack at intrados in elbows under in-plane bending moment. This is based on detailed non-linear (both material and geometric) finite element analysis performed on various sizes of elbows (generally used in piping industry), having different crack sizes. It is observed that some part of the crack always opens and some part gets closed irrespective of the mode of applied bending moment (opening/closing). The fraction of the crack that opens basically decides the weakening effect of the cracked elbow. It is observed that there is a threshold value of crack length and crack depth, before which no crack opening is observed under opening mode. Also as elbow becomes thinner, the threshold value of above two parameters increases. Quite interestingly, the part of crack which closes in opening mode opens under closing mode. The above mentioned study on the behavior of crack will be useful for fracture studies and limit load estimation especially when leak before break concept is to be employed.

Plastic limit loads for cracked large bore branch junction

This paper reports plastic limit loads for a cracked large bore branch junction, based on three-dimensional finite element limit analyses using elastic-perfectly plastic materials. Part-through surface and through-wall cracks are postulated in the intersection. For loading conditions, internal pressure and (in-plane and out-of-plane) bending to the branch pipe and to the run pipe are considered. The effect of the crack on limit loads is found to be significant for internal pressure and bending to the branch pipe, but not for bending to the run pipe. The large geometry change effect for bending to the branch pipe is briefly discussed.

The Local Flexibility of A Pipe with A Part-Through Circumferential Crack

The part-through circumferential crack is a typical crack form in pipe structure, which often lead to the structure failure. Firstly, the local flexibility equations of a pipe with a part-through circumferential crack are derived by using linearly elastic fracture mechanics. Secondly, an adaptive Simpson quadrature-revisted was used to numerically calculate the local flexibility coefficients. Finally, the model test were performed to validate the local flexibility for a part-through circumferentially cracked pipe. The results show that the natural frequencies of cracked pipe obtained by the model test agree well with the theoretical values from the proposed equations of the local flexibility. It is demonstrated the feasibility of the proposed method for vibtaion analysis and damage identification of a cracked pipe.

Crack growth with a part-through process zone in thin plates

A cohesive zone model has been proposed to model crack growth with a part-through process zone in a thin solid. With the solid being modeled in Kirchhoff’s plate theory, the crack with a relatively long, inclined front is modeled as a line discontinuity with a finite cohesive zone within the plate. A cohesive force law is adopted to capture the effect of residual strength and residual rigidity of a plate cross-section gradually cracking through the thickness. It is derived by a plane-strain elasticity analysis of a cross section normal to the part-through crack. It is then applied in the plate formulation of a line crack to simulate its propagation within the plate plane. This model essentially resolves the originally three-dimensional crack problem in two hierarchical steps, i.e., in the thickness and in the in-plane directions. In the present study, the bending case is considered. A boundary element method is applied to numerically derive the cohesive force law and simulate the crack growth in a thin titanium-alloy plate. The computational efficiency of the model is demonstrated. The plate is shown to fracture in a nominally brittle or ductile manner depending on its thickness.

Exact free vibration study of rectangular Mindlin plates with all-over part-through open cracks

Based on Mindlin plate theory (MPT), a set of exact closed-form characteristic equations incorporating shear deformation and rotary inertia are proposed for the first time to analyze free vibration problem of moderately thick rectangular plates with an arbitrary number of all-over part-through cracks. The proposed rectangular plates have two opposite edges simply supported while six possible combinations of free, simply supported and clamped boundary conditions are taken into account for two other edges. The crack is assumed to be open, non-propagating and perpendicular to two opposite simply supported edges. A continuously distributed line-spring model is used to describe the elastic behavior of an all-over part-through crack. The accuracy of the current approach is investigated through comparing the present exact natural frequencies with those of 3D finite element method obtained by ABAQUS software package. A parametric study is undertaken to show the effect of crack depth, crack location, number of cracks and thickness-to-length ratio on natural frequencies of rectangular moderately thick plates with different boundary conditions in tabular and graphical forms. Finally, the effect of shearing and tearing modes on the modeling of cracks located at the nodal line is shown.

Development of a reference strain approach for assessment of fracture response of reeled pipelines

As a result of recent increase in exploitation of hydrocarbon resources in harsher environments and also installation techniques which utilize the materials plastic deformation capacity, accurate assessment of fracture response of pipelines subject to large plastic strains (e.g., typical of reeled pipes) has attracted particular interest nowadays. In this paper, an approach, based on the evaluation of the J-integral, is developed for assessing the integrity of such pipelines, manifested in a model of a pipeline with a circumferential part-through crack subjected to plastic bending. The proposed approach is an extension of the reference strain method developed earlier by other researchers, and takes advantage of the displacement controlled loading nature in such pipes (thus being suitable for Strain Based Design methodologies), and the resulting high strain levels, which often cause fracture response of the material in the plastic regime. The developed formulation relates the fracture response of the pipe (in terms of the non-dimensionalized J-integral) as a linear function of the axial strain in the pipe at its uncracked state. A series of 300 3D nonlinear finite element models using the ABAQUS software were analyzed in preparation of the equation that could assess the fracture response of such pipes with great accuracy. The resulting equation, calibrated by the finite element results, can predict the fracture response of pipes with a maximum error of 2% for a practical uncracked material strain range of 1.5% ⩽ εunc ⩽ 4%.

Hybrid formulation solution for stress analysis of curved pipes with welded bending joints

A method is presented for evaluating the stress intensity factor of part-through cracks in a thin pipe elbow. A hybrid formulation solution is used to evaluate the stress field close to the crack area. The stress field values are then inputted into a previously developed method published in the literature to evaluate the stress intensity factor in cylindrical shells. Results from cylindrical shells with part-through cracks are extended to double-curvature pipe configurations that contain the same kind of flaw.

Effect of Cladding on Biaxially Loaded Underclad Part-Through Cracks

Abstract Fracture toughness testing on standard specimens in the ductile to brittle transition regime is well established and standardized by the ASTM since 1997. However, its applicability to structural components and its potential conservatism remain a subject of concern. In structural integrity assessment of reactor pressure vessels submitted to an accidental loading condition called pressurized thermal shock, the cladding is generally considered not to play any role and is neglected. However, cladding has the ability to restrain the crack from opening due to its good ductility. To investigate the potential safety margin, a semielliptical crack introduced by fatigue is covered by a stainless steel cladding and specimens are tested under biaxial conditions in the ductile to brittle transition regime. Test results shows that cladding plays a significant role and contributes to an additional safety margin. In addition, cladding increases the potential for crack arrest.

Fatigue crack paths for inclined cracks and surface flaws under biaxial loading

Two approaches are developed for geometrical modeling of crack growth trajectories for the inclined through thickness central cracks and the part-through surface flaw respectively. The principal feature of such modeling is the determination of crack growth direction and the definition of crack length increment in this direction. The damage process zone size concept is employed for calculations of mixed-mode crack growth trajectories and surface flaw shape and positions. Crack front behavior for a straight-fronted edge crack in an elastic bar of circular cross-section is studied through experiments and computations under axial tension loading. The elaborated theoretical model is applied for fatigue crack shape simulation of part-through cracks in a hollow thick- and thin-walled cylinders under different biaxial loading conditions. Suggested approach of crack paths modeling is used for an analysis and prevention of operation failures of existing in-service aircraft gas-turbine engine rotating components.

The wave propagation and vibrational energy flow characteristics of a plate with a part-through surface crack

In the view of structure-borne sound, vibrational wave and energy flow characteristics of infinite thin plate of finite width with a part-through surface crack are investigated. The case of an all-over part-through crack parallel to the finite side of the plate is considered. The crack is modeled as a line spring and the flexibility of the spring is deduced from the relationship between the strain energy and stress intensity factor in fracture mechanics. The responses of both intact plate and cracked plate under the excitation of harmonic force are reduced with wave propagation approach, then the input energy flow and transmitted energy flow of intact and cracked plates are calculated. The results show that the vibrational energy flow of cracked plate is highly related to the depth and location of the part-through crack. The location and the depth of the crack can be identified by the contour lines of normalized input energy flow with different driving frequencies. The research provides theoretical basis for the crack detection by measuring the vibrational energy flow in cracked plate structures.

Dynamic Stability of Cracked Viscoelastic Rectangular Plate Subjected to Tangential Follower Force

Based on the thin plate theory and the two-dimensional viscoelastic differential type constitutive relation, the differential equation of motion of a viscoelastic plate containing an all-over part-through crack and subjected to uniformly distributed tangential follower force is established in Laplace domain. Then, by performing the Laplace inverse transformation, the differential equation of motion of the plate in the time domain is obtained. The expression of the additional rotation induced by the crack is given. The complex eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are obtained by the differential quadrature method, and the δ method is adopted at the crack continuity conditions. The general eigenvalue equations of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force under the different boundary conditions are calculated. The transverse vibration characteristics, type of instability, and corresponding critical loads of the cracked viscoelastic plate subjected to uniformly distributed tangential follower force are analyzed.

Transverse vibration of viscoelastic rectangular plate with linearly varying thickness and multiple cracks

Based on the thin-plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equations of motion of the viscoelastic plate with linearly varying thickness and an arbitrary number of all-over part-through cracks are established, and the expressions of the additional rotation angle induced by the cracks are deduced. We assume that it is elastic in dilatation, but postulate the Kelvin–Voigt laws for distortion, the complex eigenvalue equations of the viscoelastic plate with linearly varying thickness and multiple cracks are derived by the differential quadrature method. The general eigenvalue equations of the viscoelastic plate with multiple cracks under different boundary conditions are calculated. The effects of various geometric parameters, dimensionless delay time and dimensionless crack parameters on the transverse vibration characteristics of a viscoelastic plate containing multiple all-over part-through cracks are analyzed.

Transverse vibration characteristics of viscoelastic rectangular plate with crack

Based on the two-dimensional viscoelastic differential constitutive relation and the thin plate theory,the differential equations of motion of the viscoelastic plate with an all-over part-through crack are established and the expression of additional rotation induced by the crack is derived.The complex eigenvalua equations of the viscoelastic plate with crack are derived by the differential quadrature method,and theδmethod is used at the crack continuity conditions.Dimensionless complex frequencies of a crack viscoelastic plate with four edges simply supported,two opposite edges simply supported and other two edges clamped are calculated.The effects of the crack parameter,the aspect ratio and dimensionless delay time of the material on the transverse vibration of the viscoelastic plate are analyzed.

Mismatch limit loads and approximate J estimates for tensile plates with constant-depth surface cracks in the center of welds

The present work provides mismatch limit loads and approximate J estimates for tensile plates with constant-depth, part-through surface cracks in the center of the weld metal. Based on systematic three-dimensional FE limit analyses, effects of strength mismatch related variables on limit loads are firstly quantified by the strength mismatch ratio and one geometry-related parameter. Mismatch limit loads for part-through surface cracks are then correlated to those for two-dimensional, through-wall crack problems. Based on the proposed limit load solutions, the applicability of the reference stress based J estimates is also investigated. When the reference stress is defined by the mismatch limit load, predicted J values agree overall well with FE results.

Nonlinear dynamics analysis of cracked rectangular viscoelastic plates

The effects of cracks and materials on nonlinear dynamics behaviors of cracked viscoelastic plates were investigated. Based on the nonlinear plate theory and the isotropic viscoelastic constitutive relation, the nonlinear dynamic equations of the viscoelastic thin plates with an all-over part-through surface crack were derived, and the corresponding boundary conditions and the crack continuity conditions were also introduced. In order to satisfy the boundary conditions and the crack continuity conditions, the suitable expressions of stress functions and deflection shape functions were put forward. In the example calculations, the materials of the plate were assumed to be standard linear solid, and the movable simple supports on four edges of the plates were adopted as the boundary conditions, moreover, in the crack continuity conditions, the Rice crack model was applied. Under the action of transversely distributed simple harmonic loads, and with the use of the Galerkin procedure, the numerical results of the bifurcations and chaos of the cracked rectangular viscoelastic plates were obtained and then expressed by the Poincare maps. According to the numerical results and the Poincare maps, the effects of the crack-depth and the crack-location, as well as the viscoelastic parameters, on the bifurcations and chaos of the plates were discussed. And some significant conclusions were obtained: 1) when the crack-depth increases or when the crack-location approaches the center of the plates, the motions of the plates are changed from single period to periodic bifurcations and then to chaos; 2) when the viscoelastic material parameter increases, the motions of the plates are changed contrarily from chaos to periodic bifurcations and then to single period states.