Estimate Stress Concentration Research Articles

Approximation method for arbitrary-shaped stress concentration source; application of physical and mathematical approximations of arbitrary parent–child notch

The degree of stress concentration in structures is of critical importance in safety designs. Many stress concentration factors for various shapes of notches with defined their geometry have been published, and if not published, the stress concentration factors can be obtained by FEM. However, when a complex, non-reproducible, and diverse notch exists on the surface of an actual machine that has undergone processing or is in a corrosive environment, it is usually more rational to use an immediate approximate solution rather than a rigorous but time-consuming analytical solution. There are two methods proposed for obtaining such approximate solutions. Although physical and mathematical approximate methods are separately used to estimate stress concentration factors in a specific-shaped notch, the application limits to arbitrarily sized and shaped notches are not yet clarified. In this study, we first extended the double-notch concept to the “parent–child notch” concept in the mathematical method, and then conducted finite element modelling for typical and complex notches. Further, we introduced the two representative lengths in the stress distribution induced by the parent notch from the mechanical consideration, and we deductively and inductively elucidated the application limits of the physical and mathematical approximations for an arbitrary parent–child notch. It was finally found that the stress concentrations of an arbitrary parent–child notch could be estimated only with the physical or mathematical approximation. Furthermore, a method for predicting fatigue limits of real structures subjected to cyclic loading was also proposed based on the present results.

Estimating Stress Concentration near Grips by the Tension of Polymer Composite Samples

This work aims at the problem of justification of the tensile strength test of flat glass- and carbon-fiber-reinforced plastic samples. Any technique of sample holding causes a concentration of stress and influences negatively on the strength; quantitative estimates of this effect are presented in this work. Based on a simplified equation of shear analysis, the stress distributions in the samples were calculated by different ways of simulation of the diagram of shear stresses applied from the grip side. The advantage of the analytical solution consists in the fact that a clear description of the influence on strength of the following factors is possible, namely, the lengths of the grips and the working part and, particularly, the sample thickness. A similar scale effect is often explained in terms of statistical strength theory, but the analysis shows that the decrease in strength observed with an increase in the sample thickness can be explained by the effect of nonuniformity of the stress field near the grips. The appearance of this edge effect like a Saint-Venant effect is especially pronounced in polymer composites with a low ratio (as compared with metals) of the interlaminar shear modulus to the longitudinal Young’s modulus.

Stress concentration at cruciform welded joints under axial and bending loading modes

The paper is concerned with the problem of stress concentration in cruciform fillet welded joints subjected to axial and bending load. Extended numerical analyses were carried out with the help of the finite element method. It made it possible to estimate stress concentration factors Kt for a variety of geometrical parameters defining the geometry of cruciform welded joints. It has been found that approximate Kt formulas, available in the literature, have two disadvantages, i.e. an unknown accuracy and small range of application with respect to geometrical parameters defining the weld shape. For these reasons, more general and accurate new formulas for stress concentration factors Kt have been derived. Even though the present approach is applicable to all types of welded joints, the analysis presented below has been conducted for a cruciform joint with the weld flank angle of θ = 45°. Final solutions have been given in the form of polynomial expressions, and they can be easily used in computer-aided design procedures.

Numerical analysis and formulae for SCF reduction coefficients of CFRP-strengthened CHS gap K-joints

The focus of this paper is on estimating stress concentration factor (SCF) reduction coefficients (ψ) of circular hollow section (CHS) gap K-joints strengthened with carbon fibre reinforced polymer (CFRP) sheets (CFRP-CHS K-joints), so that the SCFs can be calculated on the basis of the existing formulae for unstrengthened joints. Three-dimensional finite element models are developed for both CFRP-strengthened and unstrengthened CHS gap K-joints to calculate the SCFs, which are verified using previous test data. A parametric study is then carried out to explore the effects of various parameters (11 independent CFRP strengthening parameters and 5 basic geometric parameters describing the steel K-joints) on the efficiency of CFRP strengthening in terms of SCF reduction coefficient ψ. It is found that ψ is primarily affected by the CFRP relative reinforcement rates, the CFRP-to-steel tensile modulus ratios, the adhesive modulus, and non-dimensional geometric parameters. Through regression analyses, parametric formulae are finally developed for estimating ψ at six critical hot spots in CFRP-CHS K-joints under balanced axial loading. The proposed parametric formulae agree well with the experimental data.

Estimation on stress concentration factor of remanufacturing notch for TC4 titanium alloy

Remanufacturing notch would be produced after crack polishing in remanufacturing pre-treatment. In the present study, stress concentration of remanufacturing notch was investigated by a series of semi-elliptical notch models using finite element analysis. Comparing with notch width, notch depth has a critical effect on stress concentration. An equation to estimate stress concentration factor (SCF) has been modified to be suitable for remanufacturing notch. Based on the pre-estimation of stress concentration for remanufacturing notch, references on crack polishing plan can be provided in the remanufacturing field.

Howland’s isotropic Kts curve for plates with circular holes as a master curve for Kts in orthotropic plates with elliptical holes

The importance of the role played by the so-called stress concentration factors (or symbolically referred to as Kts) in analysis and design in both mechanical and structural engineering is a well-established fact, and accuracy and ease in their estimation result in significant aspects related to engineering costs, and additionally on both the reliability in the design of parts and/or in the analysis of failed members. In this work, rectangular finite width plates of both isotropic and orthotropic materials with circular and elliptical holes are considered. Based on two key observations reported herein, it is shown in a partially heuristic engineering sense, that Howland’s solution curve for the stress concentration factors for finite width plates with circular holes subjected to tension can be viewed as a master curve; accordingly, it can be used as a basis to rather accurately estimate stress concentration factors for isotropic finite width tension rectangular plates with centered elliptical holes and also rather accurately used to estimate stress concentration factors for orthotropic finite width rectangular plates under tension with centered elliptical holes. Two novel concepts are defined and presented to this effect: geometric scaling and material scaling. In all the examined and reported cases, the specific numerical results can be obtained accurately using a hand-held calculator making virtually unnecessary the need to program and/or use other complex programs based on the finite element method, just as an example. The maximum recorded average error for all the considered cases being 2.62% as shown herein.

Lateral displacement of silty clay under cement-fly ash-gravel pile-supported embankments: Analytical consideration and field evidence

Based on back analysis of lateral displacements measured in situ by using the analytical solution, a useful method for estimating stress concentration ratio of geosynthetic-reinforced and pile-supported (GRPS) embankments was proposed. In order to validate the proposed method, a full-scale high-speed railway embankment (HSRE) with four instrumented subsections over medium compressibility silty clay was constructed in three stages. The soil profile, construction procedure and monitoring of settlements and lateral displacements of the four test sections were described. The field deformation analysis results show that 1) the combined reinforcement of CFG piles and geosynthetic layer perform well in terms of reducing lateral displacements; 2) the development of lateral displacements lags behind the increase of fill load, which can be attributed to the vertical load transfer mechanism of the pile foundation; and 3) pile length has a dominant effect on the stress distribution proportion between piles and surrounding soils. The comparison between predicted and experimental results suggests that the proposed analytical solution and the back analysis-based method are capable of reasonably estimating the lateral deformation and the stress concentration ratio, respectively, if the appropriate soil elastic modulus is chosen.

Fatigue life assessment of damaged pipelines under cyclic internal pressure: Pipelines with longitudinal and transverse plain dents

This ongoing work aims to refine a methodology for fatigue life assessment of dented steel pipelines under cyclic internal pressure. A numerical model is developed to obtain stress concentration factors on dented pipes under internal pressure. A comprehensive parametric study is accomplished and analytical expressions to estimate stress concentration factors for spherical, longitudinal and transverse plain dents as a function of selected geometric parameters are developed. The proposed fatigue assessment methodology is validated from fatigue test results. Here, the analytical expressions are refined to include a more complete dent geometry definition for transverse, longitudinal and short longitudinal dents.

Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges

The flexure hinges are the most vulnerable parts in a flexure-based mechanism due to their smaller dimensions and stress concentration characteristics, therefore evaluating the maximum stresses generated in them is crucial for assessing the workspace and the fatigue life of the mechanism. Stress concentration factors characterize the stress concentrations in flexure hinges, providing an analytical and efficient way to evaluate the maximum stress. In this work, by using the ratio of the radius of curvature of the stress-concentrating feature to the minimum thickness as the only fitting variable, generalized equations for both the bending and tension stress concentration factors were obtained for two generalized models, the conic model and the elliptic-arc-fillet model, through fitting the finite element results. The equations are applicable to commonly used flexure hinges including circular, elliptic, parabolic, hyperbolic, and various corner-fillet flexure hinges, with acceptable errors. The empirical equations are tractable and easy to be employed in the design and optimization of flexure-based mechanisms. The case studies of the bridge-type displacement amplifiers demonstrated the effectiveness of the generalized equations for predicting the maximum stresses in flexure-based mechanisms.

Fatigue analysis of damaged steel pipelines under cyclic internal pressure

A methodology for fatigue analysis of damaged steel pipelines under cyclic internal pressure is proposed. This methodology employs stress concentration factors, which are commonly used to modify standard S–N curves of metallic structures under high cycle fatigue loadings. Experiments are accomplished to evaluate the strain behavior of small-scale steel pipes during denting and cyclic internal pressure. A nonlinear finite element model is developed to obtain stress concentration factors induced by plain dents on steel pipes under internal pressure. Afterwards, analytical expressions are developed to estimate stress concentration factors as function of the damaged pipe geometric parameters. Finally, fatigue tests are conducted to evaluate the finite life behavior of small-scale damaged pipes under cyclic internal pressure and to validate the proposed methodology of fatigue analysis.

Approximate Formula for Estimating Stress Concentration Factors for V-Notched Cylindrical Specimens

Approximate Formula for Estimating Stress Concentration Factors for V-Notched Cylindrical Specimens

Prediction of stress concentrations and degrees of bending in axially loaded tubular K-joints

An extensive database of stress concentrations and degree of bending in tubular K-joints under balanced axial loading, generated recently in a finite element parametric study, has been used to develop parametric equations. The study covers a comprehensive range of geometric joint parameters which are commonly found in offshore structures. This database of thin shell finite element results was used to develop parametric equations for estimating stress concentration factors and the degree of bending at key locations on both the chord and brace. Formulae for the stress distributions around the intersection of K-joints were also derived using the parametric equations at key locations as input parameters, thus allowing the stress distributions to be predicted from the geometric joint parameters. Fracture mechanics fatigue calculations were performed to demonstrate that the information provided from the proposed equations could be used to obtain safe estimates of fatigue lives of tubular K-joints.

New parametric equations for stress concentration factors in tubular K-joints under balanced axial loading

An extensive parametric study is presented on stress concentrations in tubular K-joints calculated using thin shell finite elements. This study covers a comprehensive range of geometric joint parameters under balanced axial loading. The results of this investigation were used to assess the existing parametric equations of Efthymiou ( Proc. Conf. Recent Dev. Tubular Joints Technol., Surrey, 1988, p. 2-1) and Lloyds Register ( Proc. 1st Int. Soc. Offshore Polar Eng. Conf., 1991, Edinburgh). These equations predict stress concentration factors on the chord and the brace at selected locations as a function of the joint geometry, and are based upon databases which cover relatively narrow ranges of geometric parameters. The new database of thin shell finite element results was used to develop new parametric equations for estimating stress concentration factors on the chord and on the brace. The reliability of the proposed parametric equations was then assessed using the database of steel and acrylic joints published recently by the Department of Energy (Draft Background to New Fatigue Design Guidance for Steel Joints and Connections in Offshore Structures, 1995).

Stacking faults in fatigued titanium single crystals: Tan, X.-L. and Gu, H.-C. Scr. Metall. Mater. (1995) 33 (12), 1977–1980

An extensive parametric study is presented on stress concentrations in tubular K-joints calculated using thin shell finite elements. This study covers a comprehensive range of geometric joint parameters under balanced axial loading. The results of this investigation were used to assess the existing parametric equations of Efthymiou (Proc. Conf. Recent Dev. Tubular Joints Technol., Surrey, 1988, p. 2-1) and Lloyds Register (Proc. 1st Int. Soc. Offshore Polar Eng. Conf., 1991, Edinburgh). These equations predict stress concentration factors on the chord and the brace at selected locations as a function of the joint geometry, and are based upon databases which cover relatively narrow ranges of geometric parameters. The new database of thin shell finite element results was used to develop new parametric equations for estimating stress concentration factors on the chord and on the brace. The reliability of the proposed parametric equations was then assessed using the database of steel and acrylic joints published recently by the Department of Energy (Draft Background to New Fatigue Design Guidance for Steel Joints and Connections in Offshore Structures, 1995).

Design formula for grooved shafts under torsion

A design formula has been derived to estimate stress concentration factors of grooved shafts with several kinds of groove shapes. This formula was based on the analytical result for infinitesimal grooves and for finite grooves the experimental values found by the author and others, with the numerical values found by other investigators. Over a wide range of groove sizes, the formula agrees fairly well with the numerical values of Nishitani et al. Comparison with Neuber's formula shows that his formula gives much lower values than the present one, especially for deep grooves.

A simple estimation method of stress intensity factors for through-cracks in angle-ply laminates

In the present paper a simple method of estimation of stress intensity factors for through-cracks in angle-ply laminates is developed. In this procedure, Savin's elasticity solution for an elliptical hole in two-dimensional infinite plate is used as a basic solution for the stress distribution in each ply of laminate. The present method is applied to the problems of through cracks in a ( 0° 90 ) s laminate and a ( −45° + 45° ) s laminate. Comparison with existing numerical solutions obtained by three-dimensional finite element analysis shows good agreement. The simplicity of the present method gives the design engineer a useful tool for estimating stress concentration due to the presence of a hole or a crack.

Photoelastic study of stress concentration in specimens with surface defects

1. The stress concentration factor for a plate in tension with a triangular notch withl≥ 1.67h does not depend on distance between notches. 2. Under plane and volumetric stress state conditions K depends linearly on defect depth and nonlinearly on tip radius. 3. The level of the effect of defect geometry on stress concentration factor for volumetric problems is considerably less than for plane ones. 4. Theoretical evaluation of the plane problem gives satisfactory results with notch tip radii ϱ≥ 0.35 mm, and in this case errors do not exceed 27%. 5. The results obtained may be used to estimate stress concentration at defects in structural elements such as plates, box girders, and shells operating under conditions close to a moment-free stress state .