Plastic Limit Pressure Research Articles

Plastic Limit Pressure and Stress Intensity Factor for Cracked Elbow Containing Axial Semi-Elliptical Part-Through Crack

The aim of this study is to provide a solution for the plastic limit pressure and stress intensity factor of the elbows containing a part-through axial semi-elliptical crack by considering various crack sizes. The supporting system and loading conditions of the pipeline are described. The critical part of the observed pipeline was isolated for analysis and subjected to various sizes of semi-elliptical cracks. By performing numerical analysis, results were obtained for crack dimension ratios of c/a, and depth/thickness ratios of a/t. The obtained results include plastic limit pressure and stress intensity factor. The results were analyzed with a symbolic regression algorithm, and closed-form solutions for the limit pressure and stress intensity factor were proposed. To validate pipeline integrity, the Structural Integrity Assessment Procedure (SINTAP) was applied, and the FAD (Failure Assessment Diagram) was generated for cracks below the FAD function. The failure pressure was calculated by determining the points where the loading paths intersect the FAD function.

Plastic Limit Pressure Solutions for Elbows With Slant Through-Wall Cracks

Abstract For leak-before-break (LBB) assessment, an idealized through-wall crack (TWC) is typically postulated to determine the critical crack length of cracked piping. However, such an idealization in terms of crack shape can lead to underestimations of plastic limit pressure. Although many studies have been performed to obtain accurate limit load solutions for cracked straight pipes by considering realistic crack geometries, there is still a lack of information regarding slant TWC at elbow. Therefore, three-dimensional finite element (FE) models of an elbow considering the effects of slant TWC on plastic limit pressure are developed. The proposed FE model and analysis procedure were verified through comparisons to the existing solutions for idealized TWCs in elbow. On this basis, the effect of slant TWC on the plastic limit pressure is analyzed, and a closed-form solution of the plastic limit pressure is proposed, for an elbow containing a longitudinal or a circumferential through-wall crack.

Plastic limit pressures for cracked tube containing twin collinear axial through-wall cracks

The paper analyzes plastic limit loads for cracked tubes containing twin collinear axial through-wall cracks under internal pressure. Calculations of these loads are based on small strain finite element limit analysis using elastic-perfectly plastic materials. Flow stress as the average value of the yield stress and the ultimate tensile strength was used in the analysis. An effect of crack configurations on plastic limit loads is investigated. The obtained values of plastic limit load present coalescence pressures of twin collinear cracks. The effect of flow stress on coalescence pressure was also investigated. The analysis has been shown that criterion for characterization of the twin collinear axial through-wall cracks into equivalent single crack according to SINTAP procedure is too conservative.

Condition assessment of damaged elbow in subsea pipelines

The evaluation of the performance of aged structures is essential in the oil and gas industry, where inaccurate predictions of structural performance may lead to significant hazardous consequences. Elbows are critical structures subject to continuous corrosion that can lead to a burst or collapse. It is important to be able to predict both burst strength in continually corroding structures and the behaviour of the structures after critical corrosion takes place. Structural failures due to a significant reduction in wall thickness make it very complicated for pipeline operators to maintain pipeline serviceability. This paper discusses the plastic limit pressure of elbows without defects and with several local thinned areas. Finite element analysis (FEA) and the Goodall formula were used to evaluate the new formula. The results of the FEA show that the limit load of elbows under internal pressure differs with position and depth of damage. An empirical formula for the limit load of elbows with local thinned areas is proposed. Eight sizes of elbow were considered in this study, with Rm/t of 5, 6, 7.5, 9, 12, 15, 20 and 25. This range covers most of the piping used in high-pressure environments, such as nuclear and subsea situations. The method of numerical analysis was validated by experiment and with FEA results from the literature. The results of the study can be applied to both the operation and assessment of pipelines. A formula to predict the maximum burst strength of damaged elbows is presented, which will enable more accurate estimates of the time until pipelines need to be replaced or repaired.

Burst strength of tubing and casing based on twin shear unified strength theory.

The internal pressure strength of tubing and casing often cannot satisfy the design requirements in high pressure, high temperature and high H2S gas wells. Also, the practical safety coefficient of some wells is lower than the design standard according to the current API 5C3 standard, which brings some perplexity to the design. The ISO 10400: 2007 provides the model which can calculate the burst strength of tubing and casing better than API 5C3 standard, but the calculation accuracy is not desirable because about 50 percent predictive values are remarkably higher than real burst values. So, for the sake of improving strength design of tubing and casing, this paper deduces the plastic limit pressure of tubing and casing under internal pressure by applying the twin shear unified strength theory. According to the research of the influence rule of yield-to-tensile strength ratio and mechanical properties on the burst strength of tubing and casing, the more precise calculation model of tubing-casing's burst strength has been established with material hardening and intermediate principal stress. Numerical and experimental comparisons show that the new burst strength model is much closer to the real burst values than that of other models. The research results provide an important reference to optimize the tubing and casing design of deep and ultra-deep wells.

Plastic Limit Loads for Slanted Through-Wall Cracks in Cylinder and Plate Based on Finite Element Limit Analyses

The plastic limit load solutions for cylinder and plate with slanted through-wall cracks (TWCs) are developed based on the systematic three-dimensional (3D) finite element (FE) limit analyses. As for loading conditions, axial tension, global bending, and internal pressure are considered for a cylinder with slanted circumferential TWC, whereas, axial tension and internal pressure are considered for a plate and a cylinder with slanted axial TWC. Then, the verification of FE model and analysis procedure employed in the present numerical work was confirmed by employing the existing solutions for both cylinder and plate with idealized TWC. Also, the geometric variables of slanted TWC which can affect plastic limit loads were considered. Based on the systematic FE limit analysis results, the slant correction factors which represent the effect of slanted TWC on plastic limit load were provided as tabulated solutions. By adopting these slant correction factors, the plastic limit loads of slanted TWC can be directly estimated from existing solutions for idealized TWC. Furthermore, the modified engineering estimations of plastic limit loads for slanted TWC are proposed based on equilibrium equation and von Mises yield criterion. The present results can be applied either to diverse structural integrity assessments or for accurate estimation of fracture mechanics parameters such as J-integral, plastic crack opening displacement (COD) and C*-integral for slanted TWC based on the reference stress concept (Kim, et al., 2002, “Plastic Limit Pressure for Cracked Pipes Using Finite Element Limit Analyse,” Int. J. Pressure Vessels Piping, 79, pp. 321–330; Kim, et al., 2001, “Enhanced Reference Stress-Based J and Crack Opening Displacement Estimation Method for Leak-Before-Break Analysis and Comparison With GE/EPRI Method,” Fatigue Fract. Eng. Mater. Struct., 24, pp. 243–254; Kim, et al., 2002, “Non-Linear Fracture Mechanics Analyses of Part Circumferential Surface Cracked Pipes,” Int. J. Fract., 116, pp. 347–375.)

Plastic limit pressure of spherical vessels with combined hardening involving large deformation

The paper aims to investigate plastic limit pressure of spherical vessels of nonlinear combined isotropic/kinematic hardening materials. The Armstrong-Frederick kinematic hardening model is adopted and the Voce hardening law is incorporated for isotropic hardening behavior. Analytically, we extend sequential limit analysis to deal with combined isotropic/kinematic hardening materials. Further, exact solutions of plastic limit pressure were developed analytically by conducting both static and kinematic limit analysis. The onset of instability was also derived and solved iteratively by Newton's method. Numerically, elastic–plastic analysis is also performed by the commercial finite-element code ABAQUS incorporated with the user subroutine UMAT implemented with user materials of combined hardening. Finally, the problem formulation and the solution derivations presented here are validated by a very good agreement between the numerical results of exact solutions and the results of elastic–plastic finite-element analysis by ABAQUS.

Plastic limit load of ellipsoidal pressure vessel head with nozzle under internal pressure loading

A new method and numerical procedure for determining the plastic limit load in an ellipsoid-cylinder intersection using the elastic-plastic finite element analysis are presented. The proposed method is based on the maximum criterion of the rate of change of the relative plastic work. For the elastic-plastic analysis of the nozzle connections the 2D finite element method and plasticity theory with strain hardening are used. The results of the comparison of the plastic limit pressure obtained on the basis of different known criteria and the proposed criterion are presented. A parametric study of ellipsoidal heads with a nozzle under internal pressure loading was performed. The effects of nondimensional geometric parameters of shell intersection on the plastic limit pressure are discussed.

New Criterion for the Definition of Plastic Limit Load in Nozzle Connections of Pressure Vessels

In this research, a new criterion for determining the plastic limit load in shell intersections using elastic-plastic finite element analysis is presented. Using the proposed maximum criterion of the rate of the change of the relative plastic work (PW), a numerical procedure is described to define the plastic pressure. Also, a specific plastic work criterion is presented using a local deformation parameter. Results of comparisons with different criteria were considered for experimental models of cylindrical vessels with radial and nonradial (lateral) nozzles. A parametric study of the radial intersections of cylindrical shells under the internal pressure loading was performed to examine the influence of the diameter ratio on the plastic limit pressure on the basis of the proposed criteria.

Reliability assessment by analytical calculation of the plastic collapse load of thin pressure vessels with strain hardening and large deformation

The paper investigates the assessment of the capacity loading in terms of internal limit pressure of thin metallic vessels such as thin tubes and thin spheres. This assessment is dealt with, taking into consideration large deformations of the geometry as well as the most common rules for strain hardening modeling such as isotropic, kinematic or isotropic and kinematic combined. Analytical solutions are established for predicting plastic limit pressure evolution together with hardening variables.

Exact solutions of sequential limit analysis of pressurized cylinders with combined hardening based on a generalized Hölder inequality: Formulation and validation

The paper aims to investigate nonlinear combined isotropic/kinematic hardening cylinders under internal proportional pressure by sequential limit analysis. The Armstrong–Frederick kinematic hardening model is adopted and the Voce hardening law is incorporated for isotropic hardening behavior. In particular, we establish the kinematic formulation of sequential limit analysis from the corresponding static formulation by a generalized Hölder inequality. Especially, it is found that the derived kinematic formulation involving combined isotropic/kinematic hardening is equivalent to that by the bipotential concept. Further, exact solutions of plastic limit pressure were developed analytically by performing both static and kinematic limit analysis. Finally, the problem formulation and the solution derivations presented here are validated by a very good agreement between the numerical result of exact solutions of the present work and the upper bounds from the kinematic formulation available in literature.

Research on the Plastic Limit Pressure of the Plate-fin Heat Exchanger Header with Lateral Nozzle

To investigate the strength design of the plate-fin heat exchanger header with lateral nozzle,the calculation procedure of limit load for plastic work curvature(PWC) criterion by using ANSYS and Solidworks is presented,the limit pressure results of the header with 30 degree-lateral are compared for three limit pressure criteria,which are the PWC criterion,the twice elastic slope(TES) criterion and the American Society of Mechanical Engineers(ASME) limit load criterion of perfect plastic material,and the three dimensional parameters affecting the limit pressure,which are the lateral oblique angle β,the ratio of header diameter/header thickness iDδ,and the opening ratio idD,are studied.The comparison of limit pressure results for the header with 30 degree-lateral shows that the PWC limit pressure is characterized by reflecting the structural strengthening effect of the material strain-hardening on the header by using the plastic work and the plastic work curvature as the global indicators of plastic collapse mechanism,which is objective other than the arbitrary deformation parameter and the twice elastic slope failure line of TES criterion;the relationship study of limit pressure and the three dimensional parameters shows that the limit pressure is decreased with the smaller lateral oblique angle,larger opening ratio and larger header diameter/header thickness ratio.The research results can provide beneficial guideline for calculating the plastic limit pressure and selecting geometrical dimensional parameters in designing the plate-fin heat exchanger with lateral nozzle.

Strength Behavior of Hot-Tapped Pipeline Under Internal Pressure Load

The objective of this study is to investigate the strength behavior and plastic limit pressure of hot-tapped pipelines under an internal pressure load. Two full scale test models were fabricated for the experiment. A three-dimensional nonlinear finite element analysis was also carried out. The plastic limit pressure was determined approximately by use of the twice the elastic-slope criterion. The results indicate that plastic limit pressures obtained by experiment and finite element analysis are in good agreement. On the basis of the above results, a parametric analysis of the plastic limit pressure was carried out and resulted in the development of formulas useful for the design of hot-tapped pipelines.

Mechanical formula for the plastic limit pressure of stent during expansion

The mechanics of cardiovascular stents during the process of expansion are very important for stent function and safety. In general, finite element method (FEM) or experiments are major methods used to ascertain mechanical properties of the stent. In this paper, we develop a theoretical model of the tubular stent, derive formulas for the axial forces and moments on the stent end, and propose formulas for the plastic limit pressure vs. the stent’s radius during expansion. Examples covering different geometrical parameters and material parameters are provided, and the plastic limit pressures calculated by FEM and the present method are compared, proving that the present formulas are acceptable and meaningful for the design and innovation of the stent.

Static and kinematic limit analysis of orthotropic strain-hardening pressure vessels involving large deformation

This paper analytically investigates plastic limit pressure of orthotropic strain-hardening cylindrical vessels under internal pressure. It is an interesting problem to illustrate the interaction between strengthening and weakening behavior during the deformation process. The Voce hardening law and Hill's yield criterion were adopted in the paper. A sequence of static and kinematic limit analysis problems were performed by updating the yield criterion and the deformed configuration. The equality relation between the greatest lower bound and the least upper bound was confirmed explicitly. Accordingly, exact solutions of plastic limit pressure were developed with an integral term. Particularly, exact closed-form solutions were obtained for certain values of the hardening exponent of the Voce hardening law. Finally, numerical efforts were also made for rigorous validations.

Effect of local wall thinning on limit loads for piping branch junctions. Part 1: Internal pressure

This paper presents plastic limit pressures of piping branch junctions with local wall thinning, based on systematic three-dimensional finite element (FE) limit analyses using elastic—perfectly plastic materials. An ideal branch junction is considered, where no weld or reinforcement around the intersection is considered. Two locations of wall thinning are considered: one is in the run pipe (opposite to the intersection) and the other is in the branch pipe (next to the intersection). Based on the assumption of possible plastic collapse modes, approximate plastic limit pressure solutions for piping branch junctions with local wall thinning are proposed using two limit pressure solutions: plastic limit loads for straight pipes with local wall thinning and those for branch junctions without wall thinning. Comparison with FE results shows overall good agreement.

Influence of flow stress choice on the plastic collapse estimation of axially cracked steam generator tubes

The influence of the choice of flow stress on the plastic collapse estimation of axially cracked steam generator (SG) tubes is considered. The plastic limit and collapse loads of thick-walled tubes with external axial semi-elliptical surface cracks are investigated by three-dimensional non-linear finite element (FE) analyses. The limit pressure solution as a function of the crack depth, length and tube geometry has been developed on the basis of extensive FE limit load analyses employing the elastic–perfectly plastic material behaviour and small strain theory. Unlike the existing solutions, the newly developed analytical approximation of the plastic limit pressure for thick-walled tubes is applicable to a wide range of crack dimensions. Further, the plastic collapse analysis with a real strain-hardening material model and a large deformation theory is performed and an analytical approximation for the estimation of the flow stress is proposed. Numerical results show that the flow stress, defined by some failure assessment diagram (FAD) methods, depends not only on the tube material, but also on the crack geometry. It is shown that the plastic collapse pressure results, in the case of deeper cracks obtained by using the flow stress as the average of the yield stress and the ultimate tensile strength, can become unsafe.

Analysis and experiments on the plastic limit pressure of elbows

This paper discusses the plastic limit pressure of elbows without defects and with local thinned area in the extrados. Finite element analysis (FEA) and experiments have been used. The results of FEA show that the limit load of elbows under internal pressure increases with increasing wall thickness and bend radius of the elbow. The results are consistent with the calculated results by the Goodall formula, the maximum error is 6.58%. By data fitting of FEA, an empirical formula for the limit load of elbows with local thinned area in the extrados has been proposed, which is validated by experiments.

Strain gradient plasticity solution for an internally pressurized thick-walled cylinder of an elastic linear-hardening material

An elastic-plastic solution is presented for an internally pressurized thick-walled plane strain cylinder of an elastic linear-hardening plastic material. The solution is derived in a closed form using a strain gradient plasticity theory. The inner radius of the cylinder enters the solution not only in non-dimensional forms but also with its own dimensional identity, which differs from that in classical plasticity based solutions and makes it possible to capture the size effect at the micron scale. The classical plasticity solution of the same problem is recovered as a special case of the current solution. To further illustrate the newly derived solution, formulas and numerical results for the plastic limit pressure are provided. These results reveal that the load-carrying capacity of the cylinder increases with decreasing inner radius at the micron scale. It is also seen that the macroscopic behavior of the pressurized cylinder can be well described by using classical plasticity based solutions.

Strain Gradient Plasticity Solution for an Internally Pressurized Thick-Walled Spherical Shell of an Elastic Linear-Hardening Material

An elastic-plastic analytical solution is derived for an internally pressurized thick-walled spherical shell of an elastic linear-hardening material using a strain gradient plasticity theory. Closed-form expressions are obtained for the stress, strain and displacement components. The inner radius of the shell enters the solution with its own dimensional identity as well as in non-dimensional forms, unlike that in classical plasticity-based solutions. As a result, the current solution can capture the size effect at the micron scale. The classical plasticity-based solution of the same problem is shown to be a special case of the present solution. To further illustrate the capability of the newly derived solution, formulas and numerical results for the plastic limit pressure are provided. These results reveal that the load-carrying capacity of the shell indeed increases with decreasing inner radius at the micron scale. The current solution can be employed to construct improved expanding cavity models in indentation mechanics that incorporate both the strain-hardening and indentation size effects.