Ellipsoidal Defect Research Articles

Assessment of the Local Mechano-Electrochemical Effect on Pipeline Defects by 2D and 3D Finite Element Models

Local corrosion at a defect on a pipeline was assessed using both 2-dimensional (2D) and 3-dimensional (3D) finite element models under mechano-electrochemical (M-E) interaction. While the M-E interaction increases corrosion activity at the defect, the assessment of M-E interaction would have different results using 2D and 3D models. Compared with the 3D model, the 2D model produces a greater local stress, a higher local plastic strain, a more negative corrosion potential and a higher anodic current density at the defect, and thus, a lower threshold internal pressure causing local yielding. The 3D model is more conservative for corrosion rate prediction of corroded pipelines. A new concept, rAZ (the ratio of the anodic zone length to defect length in the 2D model, or the ratio of the anodic zone area to the defect area in the 3D model), is proposed to define growth mode of the corrosion defect. There is a smaller rAZ produced in 2D model. At specific internal pressures, the 2D model predicts an ellipsoidal defect center area experiencing accelerated corrosion and potentially resulting in pipeline leaking.

Fracture resistance of zirconia-based all-ceramic crowns after bur adjustment.

Intra-oral grinding is often required to optimize occlusion of all-ceramic restorations. The effect of burs of different grit size on the fracture resistance of veneered zirconia crowns was investigated in this study. Forty-eight standardized zirconia copings were produced. The ceramic veneer was designed with a positive ellipsoidal defect on the palatal aspect of the crowns. To simulate adjustment of dental restorations by burs, this palatal defect was removed by use of three different diamond-coated burs with grit sizes 46, 107, or 151μm (fine, medium, or coarse, respectively). Each different grit size of bur was used to grind 16 crowns. All crowns were then polished and surface roughness was measured. Half of the specimens underwent thermomechanical aging (10,000 thermocycles between 6.5°C and 60°C) and 1.2 million cycles of chewing simulation (F=108N). A linear regression model was computed to test the effect of aging and grinding grit size at a level of significance of α=0.05. Fracture loads increased with decreasing grit size. Grit size and aging had a significant effect on the fracture resistance of the crowns. Use of fine and coarse burs for intra-oral adjustments resulted in different fracture resistance of veneered zirconia crowns. Coarse burs should be avoided in the final stage of grinding before polishing.

Fatigue from defect under multiaxial loading: Defect Stress Gradient (DSG) approach using ellipsoidal Equivalent Inclusion Method

The fatigue design of metallic parts depends on the casting process. It requires a compromise between the fatigue resistance of the component and the allowable defect size due to the process. The research team has proposed, in previous work [Leopold G, Nadot Y. J ASTM Int 7:2010], to represent the effect of a defect in the fatigue criterion by means of a stress gradient term. This general methodology called Defect Stress Gradient (DSG) can consider explicitly the type, the morphology and the size of the defect due to the fact that a Finite Element (FE) submodel describes directly the defect at the mesoscopic scale. The DSG approach gives correct results for the defects range from 100 to 1000μm but it is limited for application to full scale components by the use of FE submodel. The aim of this paper is to present an upgraded version of the DSG approach using the Equivalent Inclusion Method (EIM) due to Eshelby [Eshelby JD. Proc Royal Soc Lond Ser A. Math Phys Sci 241:1957; 376–96], [Eshelby JD. Elastic inclusions and inhomogeneities. In: Sneddon IN, Hill R (Eds.), Progress in solid mechanics 2. Amsterdam: North-Holland Publishing Company; 1961. p. 89–140] to compute stresses around the defect. Using this analytical approach, it is possible to compute the stresses around an ellipsoidal defect without FE simulations. Furthermore, the EIM for an ellipsoidal defect is efficient to address the question of the defect size related to loading direction in the case of a non-spherical defect. Although the framework of the original EIM is for internal defect, this paper shows that its application for a surface defect gives fair results in the context of the DSG approach. The new DSG proposal is evaluated on a low carbon steel, containing ellipsoidal defects with different orientations, under tension and torsion fatigue loadings.

Reconstruction of an ellipsoidal defect in anisotropic elastic solid, using results of one static test

A problem of identification of an ellipsoidal defect (a cavity or inclusion) in an infinite anisotropic linear elastic solid is considered in this article. It is assumed that arbitrary constant stresses are applied at the infinity and the loads and displacements are known on some closed surface containing the defect inside. An analytical method for identification of the geometrical parameters of the ellipsoidal defect (coordinates of its centre, the magnitudes and directions of the axes) using the available data is developed. The results, obtained for the case of an infinite solid, are applied to the bounded elastic body. Numerical examples showing the efficiency of the proposed identification method are considered.

Identification of Defects in an Elastic Body by Means of the Boundary Measurements

A problem of identification of a single defect (a crack, a cavity or an inclusion) in an anisotropic, linear elastic body using boundary measurements is considered. An analytical solution of the problem of ellipsoidal defect identification in an infinite elastic solid is presented in the conditions when arbitrary constant stresses are applied at the infinity and the loads and displacements are known on a closed surface, containing the defect inside. The problem is solved using reciprocity gap functional method. The obtained analytical solution is used for solving the problem of ellipsoidal defect identification in a bounded elastic body by means of the results of one static test. It is assumed that the loads and displacements are measured on the external boundary of the body. Numerical examples illustrating efficiency of the developed method are considered. Stability of the results relative to the noise in the data and variation of the defect shape is studied.

Identification of parameters of a plane elliptic crack in an isotropic linearly elastic body from the results of a single uniaxial tension test

The method earlier developed by one of the authors for identifying ellipsoidal defects is numerically tested for the applicability to the problem of identification of a degenerate ellipsoidal defect, i.e., an elliptic crack. The method is based on the reciprocity functional and the assumption that the displacements are measured in a uniaxial tension test of an isotropic linearly elastic body. Calculations show that the earlier developed method is also efficient for identification of an elliptic crack and its parameters (the center coordinates, the normal to the crack plane, and the directions and lengths of the semiaxes) can be determined with high accuracy. Some examples where the crack has a non-elliptic shape are also considered. It is discovered that, in many cases, the ellipsoids that were constructed by formulas reconstructing the ellipsoidal crack from the data on the external boundary of the body that correspond to a nonelliptic crack, approximate the actual defect with sufficient accuracy. The method stability was investigated with respect to noise in the initial data.

Identification of an ellipsoidal defect in an elastic solid using boundary measurements

Elastostatic problem of identification of an ellipsoidal cavity or inclusion (rigid or linear elastic) in an isotropic, linear elastic solid is considered. The reciprocity gap functional method is used for solving the problem. It is shown that the parameters of the ellipsoidal defect (coordinates of its center, the directions and magnitudes of the semiaxes and elastic moduli in the case of isotropic, linear elastic inclusion), located in an infinite elastic solid are expressed by means of the values of the reciprocity gap functional. The values of the reciprocity gap functional can be calculated if the loads and displacements corresponding to uniaxial tension (compression) of an infinite solid are known on the closed surface containing the defect inside. Applications of the results to the problem of ellipsoidal defect identification in a bounded body are discussed. A number of numerical examples showing the efficiency of the developed identification method are considered.

Ellipsoidal defect identification in an elastic body from the results of a uniaxial tension (compression) test

We consider the problem of identification of an ellipsoidal cavity or ellipsoidal inclusion (rigid or elastic) in an isotropic linearly elastic body. We solve the problem by a method based on the use of a reciprocity functional. We propose a constructive procedure which allows us to express the defect geometric parameters in terms of the values of the reciprocity functional. These values can be calculated by measuring the displacements on the external surface of the body in a static uniaxial tension (compression) test. The proposed procedure permits exact identification of the parameters of the ellipsoidal defect if it is located in an infinite space. In the case of a bounded elastic body, it can be considered as an approximate procedure.

Combined shape-material sensitivity approach for elastic-wave identification of penetrable obstacles

This study deals with elastic-wave identification of heterogeneities (inclusions) in an otherwise homogeneous "reference" solid from limited-aperture measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion defined through its boundary, elastic moduli, and mass density. Expressions for the shape and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIE's, respectively. A constrained nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian is implemented. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component.

Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

This study deals with elastic-wave identification of discrete heterogeneities (inclusions) in an otherwise homogeneous “reference” solid from limited-aperture waveform measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary, elastic moduli, and mass density. For an optimal performance of the gradient-based search methods suited to solve the problem, explicit expressions for the shape (i.e. boundary) and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIEs. Making use of the message-passing interface, the proposed sensitivity formulas are implemented in a data-parallel code and integrated into a nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible (or overly distorted) trial inclusion configurations. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component of the defect identification algorithm.

Human factor—Factor human

The fatigue design of metallic parts depends on the casting process. It requires a compromise between the fatigue resistance of the component and the allowable defect size due to the process. The research team has proposed, in previous work [Leopold G, Nadot Y. J ASTM Int 7:2010], to represent the effect of a defect in the fatigue criterion by means of a stress gradient term. This general methodology called Defect Stress Gradient (DSG) can consider explicitly the type, the morphology and the size of the defect due to the fact that a Finite Element (FE) submodel describes directly the defect at the mesoscopic scale. The DSG approach gives correct results for the defects range from 100 to 1000 μm but it is limited for application to full scale components by the use of FE submodel. The aim of this paper is to present an upgraded version of the DSG approach using the Equivalent Inclusion Method (EIM) due to Eshelby [Eshelby JD. Proc Royal Soc Lond Ser A. Math Phys Sci 241:1957; 376–96], [Eshelby JD. Elastic inclusions and inhomogeneities. In: Sneddon IN, Hill R (Eds.), Progress in solid mechanics 2. Amsterdam: North-Holland Publishing Company; 1961. p. 89–140] to compute stresses around the defect. Using this analytical approach, it is possible to compute the stresses around an ellipsoidal defect without FE simulations. Furthermore, the EIM for an ellipsoidal defect is efficient to address the question of the defect size related to loading direction in the case of a non-spherical defect. Although the framework of the original EIM is for internal defect, this paper shows that its application for a surface defect gives fair results in the context of the DSG approach. The new DSG proposal is evaluated on a low carbon steel, containing ellipsoidal defects with different orientations, under tension and torsion fatigue loadings.

Surgical treatment of an unusual atrial septal defect: the vestibular defect

A 14-year-old female patient underwent surgical treatment of multiple atrial septal defects associated with unroofed coronary sinus and pulmonary valvar stenosis. One of the defects was that of the superior oval fossa and the other a large ellipsoidal defect positioned inferior to the inferior rim of the oval fossa. The patient underwent primary closure of the defects with a favorable result. To the best of our knowledge, this is the first surgical experience of an unusual atrial septal defect or the vestibular defect.

Modeling of transient point defect dynamics in Czochralski silicon crystals

Intrinsic point defects control the formation of grown-in defects in silicon crystals. Under steady state conditions, the type of the prevailing point defect species is exclusively determined by the ratio of pull rate and temperature gradient in the crystal at the interface. In this study, simulations have been performed for transient growing processes where the pulling rate has been abruptly changed. Large reservoirs of interstitials are formed in fast-grown, vacancy-rich crystals near the interface after abruptly reducing the pulling rate for 30 min. During further growth at high pull rate, these interstitial reservoirs are transformed into large ellipsoidal defect patterns. Experimental results are excellently reproduced if equilibrium concentrations are used as boundary conditions for interstitials and vacancies at all crystal surfaces.

Boundary elements and fracture stress analysis

In this paper we concentrate on the application of the boundary element method to problems of fracture mechanics and the particular difficulties which are germane to this field. As summarised in Atkinson I these occur because a crack is usually modelled as having a planform of zero thickness (e.g. a line crack in two dimensions) and this leads to two distinct kinds of difficulty. These are:(a) The indeterminacy when (in plane strain or stress), the direct BIE formulation of a thin ellipse is used to represent a crack when the ellipse degenerates to a line. The corresponding feature for three-dimensional problems is the BIE formulation of an ellipsoidal defect degenerating to a flat crack with elliptical planform. In Ref. 1 it was suggested that the natural way to treat crack problems of arbitrary planform was to model the crack profile by means of infinitesimal Somigliana dislocations. These dislocations are elementary solutions of the equilibrium elasticity equations where there is a specified jump in the displacement components across an infinitesimal domain. Such a formulation leads to integral equations which are more singular than the standard forms so some care is required in the implementation of this method. Attempts at implementing this approach to stationary crack problems will be reviewed in Section 2. It is noted, however, that the indeterminacy difficulty can be avoided either by subdividing the body into regions or by using special Green's functions which take the crack into account. The first method increases the size of the problem and the second works only for special cases since it requires quite a lot of preliminary analytic work to find the necessary Green's functions. (b) The second distinct feature which arises in fracture mechanics stress analysis is the occurrence of stress singularities. The most common of these being the square root stress singularity associated with a crack in a homogeneous elastic body. In this case special procedures have been developed to take into account the known character of the displacement variation along the crack faces (usually accompanying a simplifying symmetry assumption so difficulty (a) above is avoided). These include the use of special elements, the subtraction of singularities and the application of various path independent integrals which enable information about the near crack tip stress and displacement fields to be

Elastic interaction between surface anisotropic defects and steps or kinks

We study the elastic interaction energy between an anisotropic ellipsoidal defect and a step on the surface of an elastic medium. The defect is represented by three mutually perpendicular double forces along three principal axes. Two of these principal axes are assumed to be equivalent, so the orientation of the defect with respect to the step is entirely defined by two Euler angles. The interaction energy is inversely proportional to the distance between the defect and the step. It presents three extrema which are obtained when one of the principal axes of the defect is perpendicular to the surface and another parallel to the edge of the step. For one of these particular orientations of the defect we discuss the effect induced by the presence of a kink.