Semi-elliptical Notch Research Articles

Mixed Boundary Value Problem with Two Displacement Boundaries for Thin Plate Bending.

Solution of the mixed boundary value problem for thin plate bending with two external force and two displacement boundaries is derived. General solution is derived using a rational mapping and complex stress functions. A semi-infinite plate with two displacemen constraints within a semi-elliptic notch under uniform bending is considered as an application. Stress distributions, stress intensity of debonding at the tip of the displacement constraint, stress concentration factors at the bottom of the semi-elliptic notch, and stress intensity factors when the semi-elliptic notch is changed into an edge crack are calculated. Besides, a general solution for one external force boundary and one displacement boundary is also derived.

Creep-fatigue crack growth in austenitic stainless steel centre cracked plates at 650°C. Part I: experimental study and interpretation

Experimental data on fatigue or creep-fatigue crack growth on large components at high temperature are of primary importance to validate or develop further existing defect assessment procedures and leak before break methods. This paper addresses in the first part a detailed presentation of a creep-fatigue experiment consisting of a wide plate subjected to cyclic bending loads. The specimen consists of a large 316L(N) austenitic stainless steel plate containing a wide semi-elliptical surface notch, machined in the centre of the specimen. The test is conducted at a temperature of 650°C. Over 3000 cycles with a one hour holdtime at the peak load of the cycle were applied to the plate allowing to obtain a significant amount of crack growth, both on the surface and through the thickness of the plate. In the second part, a first interpretation of the experimental results is proposed. It is based on global fracture mechanics quantities estimated from a linear elastic analysis. The results are compared with those obtained from similar plate specimens but for continuous fatigue loading conditions. A good correlation of the experimental results is obtained with observations made on small scale laboratory specimens.

A Second-Order Perturbation Method for the Stress Analysis of Solids with Slightly Wavy or Irregular Surfaces

Actual shapes of welded plate structures slightly deviate from the designed geometry due to imperfections mainly caused by welding. In order to investigate the stress concentration due to weld geometry, a second-order perturbation method is applied to the two-dimensional elastic problem of a semi-infinite plane, whose surface slightly deviates from a straight line. The accuracy of the method is confirmed by solving the problem of a semi-elliptical notch under combined tensile and in-plane bending conditions. The method is applied to the problem of a slightly wavy surface, which is sometimes observed in actual weld beads. Since it is well known that the fatigue strength of weldment cannot be predicted simply by using the peak stress of highly stress-concentrated regions, the stress gradient and the stress distribution in the neighborhood of the peak point are also presented. The present method is found to be effective for the analyses of geometrical imperfections with arbitrary surface shapes, which may be difficult to analyze by conventional numerical analysis procedures.

Bimaterial plane with elliptic hole under uniform tension normal to the interface

A bimaterial plane subject to uniform tensile traction normal to the interface is analyzed. The plane consists of two dissimilar elastic half-planes each with a semi-elliptic notch. The stress analysis is carried out by using a rational mapping function and complex stress ones. Stress Intensity of Debonding is defined as an index for the stress intensity at the tip of debonding and is investigated. The expression of energy release rate is derived by applying the residue theorem to a contour integral expressed by the complex stress function. Stress distributions around a circular hole and on the interface are shown. Stress concentration factors are studied for various oval shapes, material constants, and debonding lengths. Expressions of stress concentration factor are given.

Stress Analysis of a Slightly Wavy Surface by Using a Perturbation Method

Actual geometries of welded structures are slightly deviated from the designed shapes due to the gas-cut surfaces along plate edges and due to the irregular shapes of weld beads with possible undercuts at weld toes. Although fatigue failures of welded structures may be initiated at these highly stressed regions, conventional finite element structural analyses are usually carried out disregarding these imperfection effects at the design stage. A second order perturbation method is proposed to the two-dimensional elastic problem of a semi-infinite plane, whose surface is slightly deviated from a straight line. The deviation, η, of the actual surface from the straight line is assumed to be small compared with the characteristic length of the problem, and it is taken as the perturbation parameter of the present formulation.The accuracy of the present method is first investigated by solving the problem of semi-elliptical notch in a semi-infinite plane under a combined uniform tension and in-plane bending at infinity. In comparing the present perturbation solution with other results, it is found that the peak stress can be estimated by the first order approximation with satisfactory accuracy, while the second order solution is necessary for the proper determination of the stress gradient at the peak point. The method is then applied to the problem of a slightly wavy surface, which is sometimes observed in actual weld beads. The peak stress and the stress gradient are calculated in closed forms up to the second order in terms of the height and wave length of the wavy surface. It can be seen that the present method is effective for the analyses of geometrical imperfections of arbitrary shapes, which may be difficult to analyze through the conventional structural design procedures of welded structures.

Stress intensity factors of a semi-infinite plate having a semi-elliptical notch with a crack under tension.

The problems of the tension of a semi-infinite plate having a semi-elliptical notch with a crack are analyzed by the body force doublet method. Quite accurate values of the stress intensity factor for a crack of arbitary size can be obtained by using the stress field due to a pair of point forces (doublet) in an infinite plate with an elliptical hole. Furthermore, the error due to the use of equivalent crack length, which is the sum of notch depth and crack length, is discussed.

Response of a semielliptical notch against plastic deformation.

In order to clarify the response of a surface notch for plastic deformation, the influenced stress fields, i.e., the elastic stress distributions at the bottom of a notch due to a pair of point forces were investigated. According to the results, the response of a semielliptical notch for the plastic deformation is almost fully determined by the notch root radius ρ alone. Therefore, the severities of structures or specimens having a notch with a definite plastic deformation almost fully determined by the notch root radius ρ and the maximum elastic stress σe<max> alone.

Eddy-current signal analysis and inversion for semielliptical surface cracks

A scalar potential formulation of the δZ formula for the change in impedance of an eddy-current probe caused by a surface-breaking flaw is developed. The resulting formula is evaluated using a finite-difference method, which permits calculation of δZ for semielliptical flaws. The numerical results are checked by comparing calculations for rectangular-shaped flaws to previous calculations using an analytical solution for this geometry. Theoretical results are then verified by comparison with measurements on semielliptical fatigue cracks and EDM notches in aluminum alloy specimens using air-core eddy-current probes. An inversion method that compares features of the flaw profile, obtained by scanning the eddy-current probe along the length of the flaw, to a theoretical inversion chart (McFetridge chart) is demonstrated using the experimental data.

Thermal Stress Concentrations in the Transient Two-dimensional Temperature Field : 2nd Report, Plate with a Semi-elliptic Notch

The transient thermal stress concentration of a notched semi-infinite plate is analysed numerically. The plate which is initially in a uniform temperature state is assumed to be heated along the straight and notched boundaries through a fluid touching directly on it. The notch shapes are semi-elliptic with various radius ratios. A finite-difference method is used both for temperature and stress analyses. The finite-difference mesh is formed on basis of the equi-potential and flow lines in the potential flow around an elliptic cylinder. It is found by this method that the thermal stress concentration increases with time and the Biot number of heat convection. An approximate method, by which the stress concentration factor of a semi-elliptically notched strip with finite width can be estimated, is proposed.

Thermal Stress Concentrations in the Transient Two-Dimensional Temperature Field : 2nd Report, Plate with a Semi-Elliptic Notch

前報(半円切欠きをもつ平板)の解法を拡張して,初め一様温度に保持された半だ円切欠きをもつ半無限板が,切欠きの側よりこれと接する流体によって非定常加熱を受けるものとして,温度場および応力場について,だ円柱周りのポテンシャル流れの等ポテンシャル線と流線で構成される差分格子を適用して数値解析を行い,3種の切欠き形状に対して熱応力集中係数とフーリエ数およびビオ数の関係を明らかにした.

Bending of Strip with Semielliptic Notches or Cracks

Strips with semi-elliptical notches or edge cracks on both sides are analyzed as a thin plate bending problem. The rational mapping functions of a sum of fractional expressions are used for the analysis. The closed solutions are obtained. Stress distributions, stress intensity factors and stress concentration factors under transverse bending and torsion are investigated. The expressions for stress intensity factor and stress concentration factor are obtained with accuracy. It is also shown that stress intensity factor can be obtained from the expression of stress concentration factor.

Stress analysis for a strip with semi-elliptical notches or cracks on both sides by means of rational mapping function

Strips with semi-elliptical notches or edge cracks on both sides are analyzed as a plane elastic problem. The rational mapping functions of a sum of fractional expressions are used for the analysis. The closed solutions are obtained. Stress distributions, stress intensity factors and stress concentration factors under tension and bending in the plane are investigated. The expression of stress intensity factor is presented. The expression of stress concentration factor is also presented using formula which generally holds for stress concentration factor. It is also shown that stress intensity factor can be obtained from the expression of stress concentration factor.

Calculation of stress intensity factors for straight cracks in grooved and ungrooved shafts

Stress intensity factors have been calculated by finite element methods for a straight edged crack in a plane normal to the axis of rotation of a circular cylinder under tension and bending, and for a similar crack at the base of a symmetric groove in a shaft under tension and bending and under compressive stresses on the cylindrical surface. Satisfactory agreement with results of simplified approximations was found in most cases. A simple formula for determining the effect of the crack on the stiffness of the shaft in bending has also been derived. For the crack in an ungrooved cylinder, the stress intensity factor due to tensile or bending loads was highest at the centre, and lower than that due to a semi-elliptical notch in a slab of the same thickness under the same load. For bending loads on cracks of depths up to a tenth of the cylinder diameter, the stress intensity factor is approx. 1 1 2 σ√l (where l is the maximum crack depth and σ the maximum stress in the absence of the crack). For cracks in shallow grooves, the maximum stress intensity under tensile and bending loads is also at the centre but that for cracks in deep grooves is at the surface. The maximum stress intensity factor due to shrink fit is near the surface for both types of groove.

Stress intensity factors of cracks emanating from semi-elliptical side notches in plates

Stress intensity factors of cracks emanating from semi-elliptical side notches in plates

Stress-concentration factors in u-shaped and semi-elliptical edge notches

Stress-concentration factors are analytically determined for relatively deep U-shaped edge notches of constant radii in a semi-infinite sheet with uniaxial tension applied parallel to the sheet edge. Because a strong geometric similarity exists between a U-notch and a semi-elliptical notch of the same tip radius, a comparison of such analytical data is effected. Stress-concentration factors for U-notches in a semi-infinite sheet are also compared with other comparable analytical and experimental data available in the literature. Finite-width correction factors are applied to the results of the semi-infinite-sheet analysis to provide practical design data. These data are compared with experimental results provided by a number of investigators.

Stress-concentration factors for multiple semielliptical notches in beams under pure bending

Stress-concentration factors for multiple semielliptical notches in beams under pure bending

Effect of Notch Size on Brittle Fracture Initiation (Second Report)

In this paper the brittle fracture initiation characteristics of base metal for a mild steel plate with a semi-elliptical surface notch, which was produced mechanically, were investigated. The notch depth varied systematically. The brittle crack initiated at the tip of semi-elliptical notch, and propagated initially in the direction of plate thickness even when the notch depth varied widely. The phenomenon was different from that for welded joint as mentioned in the previous paper, since the brittle crack propagated in the direction of specimen width for t1/t≤0.6 in the latter case.In this case the theoretical formula for semi-elliptical notch on the plate surface was proposed by Irwin can be applied for t1/t=0.10.9.Next, the phenomenon of brittle crack initiation for internal notch specimen with welded joint which were deposited by using two kinds of electrode for mild steel and stainless steel was investigated.It was concluded that Irwin's formula could be applied only for the case where the brittle crack propagated initially into the direction of plate thickness, and, on the other hand, the fracture stress was approximately constant for the case where the brittle crack propagated initially into the direction of plate width.

Analysis of Edge Notches in a Semi‐Infinite Region

Abstract : A procedure for solving the plane elastic problem for edge notches in a semi-infinite region is presented. A modification of the conventional Muskhelishvili technique is made by utilizing a mapping function which describes both the physical region and its reflection with respect to the straight edges. An effective power series development in the parameter plane is then described and illustrated by the numerical solution for semi-elliptical notches in a semi- infinite sheet in tension at infinity parallel to the edge.

Stress-concentration factors for semielliptical notches in beams under pure bending

Elliptical notches in rectangular beams under pure bending are examined photoelastically. Stress-concentration factors due to a single elliptical notch are obtained for wide ranges of 2a/h andd/h, where 2a, d, andh are the width of notch, depth of notch, and depth of beam, respectively. In particular, the geometries of the optimum elliptical notches producing the least stress concentrations are obtained. Almost the whole elliptical boundary of these notches are stressed to the same peak, which indicates that these notches will probably produce the least stress concentrations among all notches, elliptical or nonelliptical.