Validation of surface crack stress intensity factors of a tubular K-joint

Tubular K-joints are encountered widely in offshore structures, and the prediction of damaged joints depends very much on the accuracy of stress intensity factor solutions (SIFs). No parametric equations and very few results have been proposed and published in the literature for estimating the SIFs of any K-joints subjected to complex loading conditions. In this paper, a mesh generation method proposed previously for the Y-joint and T-joint has been extended to the K-joint. This method is realized by dividing the K-joint into several sub-zones with each zone consisting of different types of elements and mesh densities. This method has a distinct advantage of controlling the mesh quality, and most importantly the aspect ratio of the elements along the crack front. When the mesh of all the sub-zones has been generated automatically and completely, they are merged to form the complete model. The two most commonly used methods, namely the J-integral and displacement extrapolation, are used to evaluate the SIF values along the crack front of a typical K-joint. To validate the accuracy of these computed SIFs, a full-scale K-joint specimen was tested to failure under fatigue loading conditions. The standard alternating current potential drop (ACPD) technique was used to monitor the rate of crack propagation of the surface crack located at the hot spot stress region. Using the given material parameters C and m, the experimental SIFs were deduced, and they are found to be in good agreement with the computed SIFs obtained from the generated models. Hence, the proposed finite element models are both efficient and reliable.     

Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading

Different from previous two-dimensional thermal weight function (TWF) method, a three-dimensional (3D) TWF method is proposed for solving elliptical interface crack problems in bimaterial structures under a transient thermal loading. The present 3D TWF method based on the Betti's reciprocal theorem is a powerful tool for dealing with the transient thermal loading due to the stress intensity factors (SIFs) of whole transient process obtained through the static finite element computation. Several representative examples demonstrate that the 3D TWF method can be used to predict the SIFs of elliptical interface crack subjected to transient thermal loading with high accuracy. Moreover, numerical results indicate that the computing efficiency can be enhanced when dealing with transient problems, especially for large amount of time instants.     

Finite element based evaluation of stress intensity factors for interactive semi-elliptic surface cracks

A finite thickness plate with two coplanar self-same shallow and deep semi-elliptical surface cracks subjected to remote tensile surface traction is considered for fracture analysis. Based on three-dimensional (3D) finite element solutions, stress intensity factors (SIFs) are evaluated along the entire crack front using a force method. The line spring model has also been used to evaluate crack depth point SIFs using shell finite element analysis. A wide range of geometric dimensions and crack configurations viz. crack shape aspect ratio (0.3≤a/c≤1.2), crack depth ratio (1.25≤t/a≤6), relative crack location (0.33≤2c/d≤0.9) and normalized location on the crack front (0≤2φ/π≤2) are considered for numerical estimation of crack interaction factors. SIFs evaluated at the depth point using the force method from the 3D finite element results are compared with SIFs evaluated using the line spring model. Finally, using finite element results, an empirical relation is proposed for the evaluation of crack interaction factors. For the ranges considered, the proposed empirical relation predicts crack interaction factors at critical locations within ±2% of the 3D finite element solutions.     

A coupled meshless-finite element method for fracture analysis of cracks

This paper presents a coupling technique for integrating the element-free Galerkin method (EFGM) with the traditional finite element method (FEM) for analyzing linear-elastic cracked structures subject to mode-I and mixed-mode loading conditions. The EFGM was used to model material behavior close to cracks and the FEM in areas away from cracks. In the interface region, the resulting shape function, which comprises both EFGM and FEM shape functions, satisfies the consistency condition thus ensuring convergence of the method. The proposed method was applied to calculate mode-I and mode-II stress–intensity factors (SIFs) in a number of two-dimensional cracked structures. The SIFs predicted by this method compare very well with the existing solutions obtained by all-FEM or all-EFGM analyses. A significant saving of computational effort can be achieved due to coupling in the proposed method when compared with the existing meshless methods. Furthermore, the coupled EFGM–FEM method was applied to model crack propagation under mixed-mode loading condition. Since the method is partly meshless, a structured mesh is not required in the vicinity of the cracks. Only a scattered set of nodal points is required in the domain of interest. A growing crack can be modeled by simply extending the free surfaces, which correspond to a crack. By sidestepping remeshing requirements, crack-propagation analysis can be dramatically simplified. A number of mixed-mode problems were studied to simulate crack propagation. The agreement between the predicted crack trajectories with those obtained from existing numerical simulation and experiments are excellent.     

THERMAL STRESSES IN FUNCTIONALLY GRADED MATERIALS

The thermal stress problems of functionally graded materials (FGMs), as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, are discussed. The FGMs consist of the continuously changing composi tion of two different materials. For example, one is an engineering ceramic to resist the severe thermal loading from the high-temperature environment, and the other is a light metal to maintain the structural rigidity. When the FGMs are subjected to extremely severe thermal loading, large thermal stresses are produced in the FGMs. Therefore, one of the most important problems of FGMs is how to decrease thermal stresses and how to increase heat resistance. The optimal composition profile problems of the FGMs in decreasing thermal stresses are discussed in detail. When FGMs are subjected to extremely severe thermal loading, the FGMs are damaged. The crack initiates on the ceramic surface and propagates in the FGMs. It is important to discuss the thermal stresses in the FGMs with various types of cracks. The thermal stress intensity factors in the FGMs with various types of crack are treated analytically and numerically. The optimal composition profile problems of the FGMs in decreasing thermal stress intensity factor are studied. Finally, the crack propagation paths due to thermal shock are discussed.     

Failure assessment of cracked square hollow section T-joints

Three full-scale static strength tests were carried out on pre-cracked square hollow section (SHS) T-joints. In accordance with the experimental results, an accurate crack model for welded SHS joints is proposed in this paper. Based on this numerical model, the load–displacement curves and the stress intensity factors (SIFs) along the crack front are calculated. It is found that the SIF varies greatly along the crack front, and the highest value is located at the brace corner. From Charpy V-notch impact test results, anisotropic fracture toughness was found, and influenced the failure behavior of the damaged joints. Ductile tearing was found to initiate from the crack front parallel to the chord side wall where the fracture toughness was smaller, and not from the crack front at the corner where the SIF value was the highest. Using the plastic collapse load obtained via the twice elastic compliance technique and the fracture toughness obtained from the Crack tip opening displacement (CTOD) tests, the BS7910 Level 2A Failure Assessment Diagrams (FAD) for the three cracked joints are plotted. It is confirmed that the standard BS7910 Level 2A curve gives a conservative assessment for cracked SHS T-joints under brace end axial loads.     

EFFECT OF IMPERFECT INTERFACE ON THERMAL STRESSES-ASSISTED MATRIX CRACKING IN FIBER COMPOSITES

In this article we study the effects of imperfect bonding on stress intensity factors (SIFs) calculated at a radial matrix crack in a fiber (inclusion) composite subjected to thermal loading. We use analytic continuation to extend existing series methods to obtain series representations of deformation and stress fields in both the inclusion and the surrounding matrix in the presence of the crack. The interaction between the crack and the inclusion is demonstrated numerically for different elastic materials, geometries, and varying degrees of bonding (represented by imperfect interface parameters) at the interface. The results show that, generally, SIF decreases monotonically with the interface imperfection at both nearby and distant crack tips. The sliding and nonslipping interfaces have a relatively small effect on the reduction of thermal stresses-induced SIF as compared to a general imperfect interface. Therefore, the pronounced effect of the imperfect fiber-matrix bond on the thermal stresses-assisted SIF at the crack tips should not be ignored.     

Stress intensity factors for a surface crack in a tubular T-joint

This paper describes a systematic modelling of a general cracked tubular Y-joint commonly found in offshore structures. The Y-joint under consideration may contain either a through-thickness or surface crack which can be of any length and located at any position along the brace–chord intersection. This is particularly significant, as it has always been found in practice that the initiation site of a surface crack does not always start from the saddle or crown position when tubular joints are subjected to a complex loading condition. The geometrical model developed in the work described in this paper includes the weld detail which is compatible with the American Welding Society (AWS) standard [1]. Based on this geometry, well-graded finite element (FE) meshes were generated for a T-joint, which is a specific type of Y-Joint, to obtain the stress intensity factors (SIFs) for a surface semi-elliptical crack along the crack tip using quarter-point elements. The numerical analysis indicated that the FE models generated are appropriate to the geometry of the joints since converging values of SIF were obtained as the meshes used were refined. The accuracy of the Mode I, Mode II and Mode III SIFs demonstrates that the proposed model is reliable.     

Analysis of arbitrarily shaped planar cracks in three-dimensional isotropic hygrothermoelastic media

In the present article, a planar crack of arbitrary shape embedded in three-dimensional isotropic hygrothermoelastic media is investigated. Based on the general solutions and Hankel transform technique, the fundamental solutions for unit-point and extended displacement discontinuities (EDD; including the displacement discontinuities, moisture concentration discontinuity, and the temperature discontinuity) are derived. The EDD boundary integral equations for an arbitrarily shaped, planar crack in the hygrothermoelastic medium are established in terms of the EDD. Utilizing the boundary integral equation method, the singularities of near-crack front fields are analyzed, and the stress, moisture flux, and heat flux intensity factors are all derived in terms of the EDD. As a special case, the analytical solution for a penny-shaped crack under uniform combined loadings is presented. The EDD boundary element method is proposed for numerical simulation. The numerical result for a penny-shaped crack subjected to uniform mechanical–moisture–thermal loading is compared with the analytical solution to verify the correctness of the proposed method. Two coplanar elliptical cracks subjected to combined loadings are simulated as an application, and the influences of applied loadings and the ellipticity ratio are discussed.     

An Embedded Crack in a Graded Coating Bonded to a Homogeneous Substrate Under Thermo-Mechanical Loading

ABSTRACT

The problem of an embedded partially insulated crack in a graded coating bonded to a homogeneous substrate under thermal and mechanical loading is considered. The heat conduction and the plane elasticity equations are converted into singular integral equations which are solved to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm is applied to avoid interpenetration. The main objective of the paper is to study the effect of the coating nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings.     

THERMOELASTIC PROBLEM OF CURVILINEAR CRACK WITH A POINT HEAT SOURCE

Boundary value problems for a circular-arc crack embedded in an infinite medium due to a point heat source are formulated and solved in closed form. Based on the Hilbert problem formulation and a special technique of contour integration, exact solutions of a semicircular crack are obtained in an explicit form. It is found that the thermal stresses or temperature giadient near the tips of a curved crack always possess the characteristic inverse square-root singularity in terms of the radial distance away from the crack tip under the application of a heat source. The simultaneous existence of mode-I and mode-II stress intensity factors are shown in this article to be dependent on the strength of a heat source, heat conductivity, as well as thermal and elastic isotropy. The nonnegative mode-I stress intensity factor is found to be present in this article for the application of the heat sink, which validates the fully open crack assumption.     

THERMAL STRESS ANALYSIS OF A RECTANGULAR PLATE AND ITS THERMAL STRESS INTENSITY FACTOR FOR COMPRESSIVE STRESS FIELD

Abstract

In this study, a transient thermal stress problem of a rectangular plate due to a nonuniform heat supply is treated theoretically and, thereafter, fracture behaviors of the plate with a crack are examined for compressive stress states. Assuming that a crack located on an arbitrary position, with an arbitrary direction, is sufficiently small and is closed because of the compressive stress field, a temperature field, in a transient state, is analyzed by taking into account the effect of relative heat transfer on both surfaces of the plate. Thereafter, the corresponding thermal stress analysis is developed on the basis of the two-dimensional plane stress problem using Airy's stress function method, and the stress intensity factor is analyzed for the biaxial stress state. As an analytical model, we consider mechanical boundary conditions of prescribed displacement and estimate the stress intensity factor of a crack tip using parameters of the crack configuration such as the location, direction, length, and coefficient of friction. These numerical results are shown in graphical form.     

Stress Analysis of a Penny-Shaped Crack in a Magneto-Electro-Thermo-Elastic Layer Under Uniform Heat Flow and Shear Loads

This article analyzes the mechanical behavior induced by a penny-shaped crack in a magneto-electro-thermal-elastic layer that is subjected to a heat flow. The surfaces of the magneto-electro-thermal-elastic layer are subjected to radial shear loads, and the crack is assumed to be thermally insulated. The Hankel transform technique is employed to reduce the problem to a Fredholm integral equation, which is then solved numerically. Shear stress intensity factors (SIFs) are obtained and discussed in detail. Numerical results reveals that in the case of only applied shear loads, the layer height has insignificant effects on the SIF when the ratio of the half-layer height h to crack radius a is larger than 2, and that in the case of only applied heat flow, the layer height also has insignificant effects on the crack extension force when h/a > 8. It is further interesting to note that for the magneto-electro-thermo-elastic layer under only applied heat flow, there exists a critical height as far as the stability of the crack is concerned.     

Thermal Stress Analysis of an Embedded Crack in a Graded Orthotropic Coating-Substrate Structure

An analysis of a coupled plane thermoelastic problem for a graded orthotropic coating-substrate structure is performed under thermomechanical loading conditions. The crack direction is parallel to the free surface. Applying the superposition principle and Fourier integral transform, the heat conduction and plane elasticity equations lends themselves to the derivation of two sets of Cauchy-type singular integral equations. The thermal stress intensity factors are defined and evaluated. In the numerical results, the effects of the orthotropy parameters, thermoelastic non-homogeneity parameters, and dimensionless thermal resistance on the temperature distribution and the thermal stress intensity factors (TSIFs) are studied. The obtained results can be used to design graded orthotropic coating-substrate structures under thermomechanical loading.     

Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory

In this paper, a thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory. The moduli of functionally graded materials (FGMs) are assumed to vary exponentially with the coordinates. By employing the Fourier transform and Laplace transform, coupled with singular integral equations, the governing partial differential equations under mixed, thermo-mechanical boundary conditions are solved numerically. For both the temperature distribution and transient stress intensity factors (SIFs) in FGMs, the results of hyperbolic heat conduction model are significantly different than those of Fourier’s Law, which should be considered carefully in designing FGMs.     

动力作用下硬颗粒诱发裂缝弯曲和分叉机理研究

脆性材料在动荷载作用下的裂缝弯曲和分叉行为,对深入了解材料的抗拉特性和破坏模式有着重要意义。基于损伤演化原理的有限元方法,针对脆性材料中颗粒物诱发裂缝分叉的机理展开研究,通过比较无颗粒与有颗粒两种裂缝扩展模式,分析了硬颗粒对裂缝扩展模式的影响。结果显示,当颗粒物刚度较大物性较好、裂缝扩展遭遇颗粒时裂隙将沿着交界面绕行,易发生弯曲分叉,两者具有迥异的扩展模式。     

The Influence of Graded Coatings on the Thermal Stress Intensity Factors of an Oblique Crack in a Semi-Infinite Substrate Subjected to Local Heating on the Boundary

Thermally induced singular behavior of an arbitrarily oriented crack in a homogeneous substrate overlaid with a functionally graded coating is considered, within the framework of linear plane thermoelasticity. It is assumed that the graded coating/substrate system is subjected to steady-state thermal loading applied over a finite region at the coating surface and the crack in the substrate is thermally insulated, disturbing the prescribed heat flow. Based on the method of Fourier integral transform and the coordinate transformations of basic field variables in thermoelasticity equations, formulation of the crack problem is reduced to two sets of Cauchy-type singular integral equations for temperature and thermal stresses in the coated medium. In the numerical results, the main emphasis is placed on the investigation of influences of loading, geometric, and material parameters of the coated system on the variations of mixed-mode thermal stress intensity factors. Further addressed are the probable cleavage angles for the incipient growth of the original crack and the corresponding values of effective tensile-mode stress intensity factors.     

Analysis of crack arrest event in NESC-1 spinning cylinder experiment

In the NESC-1 spinning cylinder test, a large surface-breaking flaw in a thick steel cylinder component was subjected to high primary and secondary stresses produced by combined rotation and thermal shock loading. The crack was arrested after relatively small amounts of ductile tearing and cleavage crack extension. Finite element analyses have been carried out to obtain static elastic stress intensity factors for the initial and arrested crack under constant load and constant displacement boundary conditions. Applied static elastic stress intensity factors for the arrested crack have been compared with the plane strain crack arrest toughness values measured using small-scale compact crack arrest (CCA) specimens. The present analyses of the crack arrest event in the NESC-1 spinning cylinder test have concluded: (1) Applied static elastic stress intensity factors are reduced significantly for the lobe-shaped arrested crack which developed from the initial semi-elliptical surface crack as a result of the localised cleavage crack propagation. This reduction in crack driving force is likely to be the main reason for crack arrest. (2) The analysis carried out and comparison with the full-scale experiment confirm the prevailing approach to the assessment of crack arrest that brittle propagation will stop if the applied crack driving force falls below the crack arrest toughness. (3) The results justify the use of the static elastic stress intensity factor as the crack propagation driving force parameter and the static plane strain crack arrest toughness as the resistance parameter for crack arrest evaluation for small relative crack jump dimensions. (4) The small-scale CCA tests can be employed to evaluate crack arrest in a large cylinder of the same material.     

Thermal fracture of cracked cylinders associated with nonclassical heat conduction: The effect of material property

The thermoelastic problem of a transversely isotropic hollow cylinder containing a circumferential crack is investigated in the present article based on the non-Fourier heat conduction theory. The temperature and stress fields are obtained by solving the coupled partial differential equations in the Laplace domain, and corresponding thermal axial stress with minus sign is then applied to the crack surface to form a mode I crack problem. Three different kinds of crack are considered, and the singular integral equation method is adopted to solve the fracture problem. Finally, with the definition of stress intensity factor, the effect of material properties, coupling parameter, and crack geometry on the hyperbolic thermal fracture responses of a transversely isotropic hollow cylinder excited by a thermal loading is visualized.     

Transient thermal fracture analysis of a penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder

The problem of penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder is investigated under thermal shock load. The problem is reduced to solve three coupled Fredholm integral equations. The field intensity factors are derived. Numerical results of crack opening displacement intensity factors are presented, and the effects of thermal shock time, crack configuration, and magnetoelectrical crack surface conditions on crack propagation and growth are evaluated. Among others, the larger cylinder's radius, the easier to propagate the crack is. For a fixed crack configuration, magnetoelectrical crack surface conditions have different effects on crack propagation as well.