Expressions For Stress Concentration Factors Research Articles

Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads

Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads

A generalized empirical expression for the collapse of worn tubulars with a crescent-shaped wear groove under combined loads

As a large proportion of easily recoverable global hydrocarbon reserves is extracted and fields in operation are maturing, the oil and gas industry requires new methods of ensuring well integrity. Production of the remaining reserves may involve, for instance, extended-reach wells, multilateral wellbores, long horizontal sections and highly deviated trajectories. Moreover, wells in mature fields are being used to increase recovery through side-tracking. Casing wear has a significant influence on the well integrity in such operations and the ability to assess its effects is crucial, both in terms of its impact on health, safety and environment, and in terms of enabling cost-efficiency. This article utilizes the Finite Element Method (FEM) to analyze the stress distribution in worn tubulars with a crescent-shaped wear groove under external pressure. A model for tubular collapse is proposed using generalized empirical expressions for stress concentration factors in worn tubulars. The generalized expressions are based on 640 finite element analyses of different geometries designed to represent typical dimensions used in the oil and gas industry. Comparisons with experimental data and existing models demonstrate improvement in both accuracy and precision using the developed approach. • The influence of wear on elastic and yield collapse is significantly different. • A method for automated finite element analysis is demonstrated. • Results from finite element analysis are generalized using the Buckingham PI theorem. • The new proposed model for collapse of worn tubulars shows excellent performance.

Stress Concentration Factors at Welded Connections Between Tubular Sections and a Transverse Plate

Abstract Welded connections between tubulars and transverse plates are used to build together part structures such as support of flare towers and wind turbines and deck structures on foundation structures. They are used in traditional jacket structures for oil and gas production and in support structures for wind turbines. These welded connections are typically made from the outside resulting in a weld root on the inside and a weld toe on the outside. Different S–N curves apply to these positions; therefore, stresses both on the inside and the outside are needed for fatigue assessment. From the actual design, it is noted that the thicknesses of the tubulars being connected can be different. Also, the diameters of the tubulars can be different. In addition, the fabrication is associated with some fabrication tolerances that provide local eccentricity moments to be transferred through these connections. In this paper, analytical expressions for stress concentration factors for these connections are presented based on classical shell theory. The stress concentration is dependent on the radial restraint from the transverse plate and the eccentricity of the neutral axes in the tubular thickness of one tubular relative to the other tubular. The superposition principle is used to derive resulting stress concentration factors for the inside weld root and the outside weld toe.

Numerical investigation of stress concentration factor induced by multiple scenarios of adjacent corrosion pits

This paper simulates the stress concentration caused by adjacent corrosion pits using experimental and numerical method. A detailed three-dimensional finite element solid model is established and validated by individual notched specimen. The shape factor and shape transformation factor are proposed to represent the relationship between the stress concentration factor induced by individual ellipse and triangular notch. A distance factor and an angle factor are integrated to represent the stress concentration factor resulted from adjacent notches. Quantitative expressions for stress concentration factors in multiple scenarios are obtained. The results show that the adjacent notches distributed along the longitudinal direction of rebar with a relative angle of 0° induced stress concentration factor is close to that the individual ellipse notch when the notch spacing exceeds a critical distance (6 mm), and using the latter scenario instead of the former scenario for simplified modelling process has an insignificant effect on stress concentration. For the adjacent notches distributed along the cross-section direction of rebar with a relative angle of 90°, the maximum stress is approximately 40% higher than that of an individual notch in the analyzed range of depth. Several suggestions are also provided based on the present study.

Generalized expressions for stress concentration factors of pipeline plain dents under cyclic internal pressure

The present work follows a previous study devoted to developing a new methodology for fatigue life assessment of steel pipelines with plain dents, under cyclic internal pressure, based on the estimation of SCFs to modify appropriate S–N curves. SCFs were estimated from a non-linear finite element model and the methodology was validated according to experimental results. A comprehensive parametric study was then carried out for spherical, longitudinal and transverse plain dents, with varying pipe and dent dimensions, and analytical expressions to provide SCFs were developed for each dent type. The aim of this work is to simplify these expressions, which have the disadvantage of being related to particular dent types (geometries). Here, a new analytical formulation is developed and simpler expressions are obtained to estimate SCFs. The proposed methodology becomes then more practical and easy to be used in the fatigue life assessment of steel pipelines with plain dents of different types, based only on measurements of dent dimensions without the need of classifying them according to their types.

Analytical solution with validity analysis for an elliptical void and a rigid inclusion under uniform or nonuniform anti-plane loading

An elliptical inclusion (covering both void and rigid inclusions) embedded in an infinite and finite elastic plane subject to uniform or nonuniform (m-th order polynomial) anti-plane loading conditions is analyzed. An analytical solution in terms of the stress field for an infinite plane is developed through the method of analytic function and conformal mapping. Closed-form complex potentials and analytical expressions for Stress Concentration Factors (SCFs) are obtained. The results show that (i.) the SCF value decreases with an increasing loading order, so that the influence of the non-uniformity of the anti-plane loads on the SCF is revealed to be beneficial from the failure point of view; (ii.) decrease in the SCF value for an infinite plane is monotonic, which does not hold true for a finite plane. The results for an infinite plane are confirmed and extended for finite planes by exploiting the well-known heat–stress analogy and the finite element method. It is worth mentioning that the comparison between the analytical solution for an infinite plane and the numerical solution for finite plane is provided, showing that the analytical solution of an infinite plane can be used as an accurate approximation to the case of a finite plane. Moreover, the proposed heat–stress analogy can be exploited to study the crack–inclusion interaction or multiply connected bodies. The computational efficiency of the proposed methodology makes it an attractive analysis tool for anti-plane problems with respect to the full scale three-dimensional analysis.

In situ strengths of matrix in a composite

A major obstacle to achieving reasonable strength prediction of a composite only from its constituent information is in the determination of in situ strengths of the matrix. One can measure only the original strengths of the pure matrix, on the basis of which the predicted transverse strengths of a unidirectional (UD) composite are far from reality. It is impossible to reliably measure matrix in situ strengths. This paper focuses on the correlation between in situ and original strengths. Stress concentrations in a matrix owing to the introduction of fibers are attributed to the strength variation. Once stress concentration factors (SCFs) are obtained, the matrix in situ strengths are assigned as the original counterparts divided by them. Such an SCF cannot be defined following a classical approach. All of the relevant issues associated with determining it are systematically addressed in this paper. Analytical expressions for SCFs under transverse tension, transverse compression, and transverse shear are derived. Closed-form and compact formulas for all of the uniaxial strengths of a UD composite are first presented in this paper. Their application to strength predictions of a number of typical UD composites demonstrates the correctness of these formulas.

Practical expressions for the notch stress concentration factors of round bars under torsion

Stress concentration factors and generalised stress intensity factors of round bars weakened by different kind of notches are analysed under torsion loading. An exact, closed-form relationship correlating the generalised stress intensity factors of classic notches (parabolic, semi-elliptic and hyperbolic), characterized by an exact mathematical profile, and pointed V-notches is obtained by using in combination the analytical expressions already available in the literature and some new equations developed in the present contribution. Afterwards this link is discussed with reference to U- and blunt V-shaped notches. This allows us to provide a new analytical relationship between the generalised notch stress intensity factor (NSIF) and the maximum shear stress at the notch tip. By taking advantage of the new developed frame, simple but accurate expressions for the stress concentration factors, valid for a large bulk of different configurations changing the notch acuity, from shallow to deep, are developed. For some opening angles an explicit comparison between the new expressions and those proposed by Noda and Takase (Int J Fatigue, 2006;28:151–163) has been carried out, considering deep and shallow notches.

An expression of stress concentration factor for a circular hole eccentrically located in a tensile finite-width strip of orthotropic material

An explicit expression of stress concentration factor (SCF) for a circular hole eccentrically located in a finite-width strip of orthotropic material subjected to remote tension is derived using an approximate and analytical method. The eccentricity of the hole and the ratio of the diameter to strip width are two governing geometric parameters, and their effect to the SCF is shown clearly in the expression. The formulation for the expression is consisted of two steps, first, the derivation is based on section method using balance of force and moment, respectively, second, improvement is done by empirical modification of the related coefficients based on asymptotic matching of good results obtained for some special cases. The accuracy of the final SCF expressions is adequate except the extreme case where the eccentricity of the circular hole is very large, i.e. when the hole is located very near to one side of the strip. On the other hand, when the eccentricity is taken as zero, i.e. for the simplified case of a central circular hole in a finite-width strip, the corresponding SCF expression has good accuracy. The present work is an extension of previous work for central circular hole of orthotropic material and an eccentric circular hole for isotropic material.

Stress concentration factors at welds in pipelines and tanks subjected to internal pressure and axial force

In this paper, analytical expressions for stress concentration factors in pipes subjected to internal pressure and axial force are derived for a number of design cases based on classical shell theory. The effect of fabrication tolerances in simple butt welds is assessed. Analyses based on classical mechanics are compared with results from axisymmetric finite element analyses for verification of the presented methodology. Stress concentration factors are presented for circumferential butt welds in pipes welded together from pipes with different thicknesses, welds at buckling arrestors, welds at flanged connections in pipelines, and welds at ring stiffeners on the inside and the outside of the pipes. It also includes stress concentration factors at end closures in pipes for gas storage. Larger pipes are fabricated from plates with a longitudinal weld. This fabrication process introduces out-of-roundness in the pipes. The actual out-of-roundness is a function of internal pressure. An analytical expression for the bending stress in the pipe wall due to this out-of-roundness is presented. The derived stress concentration factors can be used together with a hot spot stress S– N curve for calculation of fatigue damage.

Stress concentration factors for an eccentric circular hole in a finite-width strip or in a semi-infinite plate in tension

An explicit expression for the largest stress concentration factor (SCF) for an eccentric circular hole in a finite-width strip under remote uniform tension is formulated by approximate stress analysis and asymptotic matching with two exact limit SCF values, which are given by Kirsch and Koiter for very small and large ratios of hole radius to strip half width respectively. The explicit expression of the largest SCF for the tension semi-infinite plate with a circular hole near the free straight boundary is obtained as a special case of the first problem. The accuracy of the proposed expressions is measured by (a) comparison with data of the SCF handbook and (b) comparison with the results from finite element analysis. Corrections for the values given by Jeffery and confirmation of Koiter's exact limit value when the circular hole is very near the free straight boundary are also obtained.

Stress concentration factors at circumferential welds in tubulars

In this paper analytical expressions for stress concentration factors due to fabrication tolerances are derived for a number of design cases based on classical shell theory. These cases include butt welds in tubulars, welds at ring stiffeners and bulkheads in shell structures, welds at conical transitions without and with ring stiffeners and tubulars with colinearity subjected to axial tension in risers and tethers of tension leg platforms.

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 factor from stress concentration factor

Using the general formulas of stress concentration factor, methods for calculating stress intensity factor are mentioned. These methods make use of the several known values of stress concentration and radius of curvature at the point of stress concentration to form expression of stress concentration factor. Values of stress concentration from handbooks or experiments and others can be used. This paper deals with plane elastic, longitudinal shearing and thin plate bending problem.