Plastic Work Curvature Research Articles

Generation of interaction diagrams of pad-reinforced and non-padded vessel/nozzle structures via employing various plastic collapse techniques

The present research investigates the effect of pad reinforcement on the load-carrying capacities of a thin-walled pressurized cylindrical vessel with a radial nozzle structure. The main objective is to generate the plastic collapse moment boundaries versus a spectrum of steady internal pressures employing various criteria, namely the Plastic Work Curvature (PWC) and the Plastic Work (PW) criteria in addition to the Twice-Elastic-Slope (TES) Method. Initially, a validation study is conducted utilizing the finite element method to determine the out-of-plane (OP) plastic collapse moments utilizing the TES Method concerning two experimentally tested pad-reinforced vessel/nozzle structures. The validation study revealed very good outcomes. A non-padded vessel/nozzle is also analyzed for comparison purposes. The pad reinforcement enormously enhanced both the in-plane and the OP load-carrying capacities. The TES Method displayed a noticeable deficiency in determining the plastic collapse moments for the non-padded structure concerning the late medium to the high internal pressure spectra.

Generation of Plastic Collapse Load Boundaries of a Pressurized Cylindrical Vessel/Radial Nozzle Structure Subjected to Nozzle Bending Loadings Utilizing Various Plastic Collapse Load Techniques

This research focuses on generating the plastic collapse load boundaries of a cylindrical vessel with a radial nozzle via employing three different plastic collapse load techniques. The three plastic collapse load techniques employed are the plastic work curvature (PWC) criterion, the plastic work (PW) criterion, and the twice-elastic-slope (TES) method. Mathematical based determination of plastic collapse loads is presented and employed concerning both the PWC and the PW criteria. A validation study is initially conducted on a pressurized 90-degree pipe bend structure subjected to in-plane closing bending via finite element analyses along with an elaborate explanation of the mathematical approaches for determining the plastic collapse loads via the PWC and the PW criteria. Outcomes of the validation study revealed very good outcomes for the three techniques. Accordingly, the aforementioned three techniques are utilized to determine the plastic collapse load boundaries of a pressurized cylindrical vessel/nozzle structure subjected to in-plane (IP) and out-of-plane (OP) bending loadings applied on the nozzle one at a time. The TES method revealed considerate limitations when applied within the medium to the high internal pressure spectra. It is shown that both the PWC and the PW criteria outperform the TES method in computing the plastic collapse loads. The vessel/nozzle structure revealed relatively higher plastic collapse moment boundaries under IP bending as compared to OP bending. Conclusively, methodical steps are devised for determining the plastic collapse loads via the PWC and the PW criteria for the ease of systematic application on pressurized structures in general.

Development of new ηpl, β and limit load equations to evaluate fracture parameters of pre-cracked small punch test specimens

The small punch test (SPT) is an alternative method for determination of the mechanical properties when enough material is not available for conventional testing. Recently SPT specimen configuration is changed to have a crack (known as pre-cracked SPT) for more accurate determination of material fracture properties. Use of p-SPT specimens needs limit and maximum load values and geometric parameters, β and ηpl for evaluation of Stress Intensity Factor (SIF) and plastic J-integral respectively. However, general equations for these parameters are not available in the open literature. The present paper is an attempt to address this aspect of p-SPT specimens. Finite element analysis has been employed to evaluate the above parameters. Square pre-cracked specimens with crack parallel and perpendicular to the thickness direction are considered in this paper. The range of crack size a/W = 0.40–0.60 is considered for the present analysis. The load–displacement curves are extracted for both specimens using 3-D elastic–plastic FE analysis assuming elastic perfectly plastic material behaviour. Maximum load is directly obtained from the FEA load–deflection curves. The maximum load helps to assess the machine capacity to perform the SPT. Using the elastic–plastic J-integral and load–displacement data from FEA, ηpl values are calculated. Limit analysis using Plastic Work Curvature (PWC) criterion is carried out to obtain the limit loads. The geometric factor (β) is found out using elastic FE analysis for SIF calculation. Based on these FEA results, new equations have been proposed for limit load, maximum load, geometry factor (β) and ηpl for both types of p-SPT specimen configurations.

A comparison of various plastic work curvature methods

The use of plastic work as a means of determining the plastic collapse load of a structure is a promising new approach. Several methods of assessing the plastic limit have been proposed in recent publications but there is, as yet, no clear consensus as to the best approach to take. This article compares the various methods proposed and recommends a new approach which is not subjective and which is considered to be more reliable than the twice elastic slope load.The recommended method plots normalised work versus normalised load, and uses a curve fitting method to estimate the plastic load. It is illustrated by application to several pressure vessels.

A Simplified Strength Checking Approach for a Header–Nozzle Intersection Under Combined Piping Loads

To investigate the strength checking methods for a semi-cylindrical header–nozzle intersection under combined piping loads, the simplified strength checking formulae for two piping load combinations, which are typical in engineering practice, are suggested based on the combined limit piping load interactions of the header. Furthermore, three methods for determining the allowable piping load parameters of the proposed formulae, namely the plastic work curvature (PWC) method of inelastic analysis route for design by analysis (DBA), the twice elastic slope (TES) method of inelastic analysis route for DBA, and the elastic finite element analysis (FEA) method of elastic analysis route for DBA, are presented and compared. Based on the theoretical analyses and the parametric comparison study results of the three methods, it can be concluded that the PWC method, which can take the hardening material effect on the plastic load results into account well and use the engineers' experience independent plastic work as the global indicator of gross collapse, is the most reliable one among the three methods, while the elastic FEA method is of great value for engineers to estimate the allowable piping loads quickly and conveniently.

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.

The Plastic Work Curvature Criterion in Evaluating Gross Plastic Deformation for Pressure Vessels with Conical Heads

Conical shells are often joined to cylindrical shells and under internal pressure, the intersection between the large end of a cone and a cylinder is subjected to a large circumferential compressive stresses which can lead to its failure by whether axi-symmetric gross plastic deformation involving excessive inward deformations or non-symmetric buckling which accompanies by circumferential waves around the intersection. In Pressure Vessel Design by Analysis, the designer is required to address both these behavior modes when specifying the allowable static load. In this paper, plastic collapse or gross plastic deformation load is evaluated for a typical pressure vessel with conical head using plastic work curvature criterion and the results are compared with other criteria suggested by international standards such as ASME. The plastic work curvature criterion is based on the plastic work dissipated in the structure as loading progresses and may be used for structures subject to a single load or a combination of multiple loads. The results of analyzing using this new criterion show that the plastic collapse load given by the plastic work curvature criterion is robust and consistent and is in the close agreement with the results from international codes. The most significant aspect of the proposed method in which plastic work curvature criterion has been used is that the plastic collapse loads are determined purely by the inelastic response of the structure and therefore they are not influenced by the initial elastic response: a problem with some other established plastic criteria. The results also show that the design load is mostly limited by the formation of an axi-symmetric gross plastic deformation in the intersection of the vessel prior to the formation of non-symmetric buckling modes

Design by analysis of ductile failure and buckling in torispherical pressure vessel heads

Thin shell torispherical pressure vessel heads are known to exhibit complex elastic–plastic deformation and buckling behaviour under static pressure. In pressure vessel Design by Analysis, the designer is required to assess both of these behaviour modes when specifying the allowable static load. The EN and ASME boiler and pressure vessel codes permit the use of inelastic analysis in design by analysis, known as the direct route in the EN Code. In this paper, plastic collapse or gross plastic deformation loads are evaluated for two sample torispherical heads by 2D and 3D FEA based on an elastic-perfectly plastic material model. Small and large deformation effects are considered in the 2D analyses and the effect of geometry and load perturbation are considered in the 3D analysis. The plastic load is determined by applying the ASME twice elastic slope criterion of plastic collapse and an alternative plastic criterion, the Plastic Work Curvature criterion. The formation of the gross plastic deformation mechanism in the models is considered in relation to the elastic–plastic buckling response of the vessels. It is concluded that in both cases, design is limited by formation of an axisymmetric gross plastic deformation in the knuckle of the vessels prior to formation of non-axisymmetric buckling modes.

Material strain hardening in pressure vessel design by analysis

The effect of including material strain hardening on the gross plastic deformation (GPD) load of four sample problems from the EPERC Design by Analysis manual is investigated. The models considered are two axisymmetric vessels with flat heads under pressure, a nozzle/knuckle intersection under pressure, and a cylinder-cylinder intersection under combined pressure and moment loading. The results of limit analysis, large deformation elastic-perfectly plastic analysis, and small and large deformation bilinear hardening analysis are presented. Plastic loads are calculated using the ASME twice elastic slope (TES) criterion and the plastic work curvature (PWC) criterion. It is found that the plastic pressures given by the ASME TES criterion are inconsistent with respect to the limit load. The PWC criterion is found to represent strain hardening more consistently and lead to enhanced plastic loads. Von Mises equivalent plastic strain plots show that the form and extent of plastic deformation at the limit load in a perfectly plastic analysis and at the plastic load in a strain hardening analysis are similar, indicating a common definition of GPD.

Gross Plastic Deformation of Axisymmetric Pressure Vessel Heads

The gross plastic deformation and associated plastic loads of four axisymmetric torispherical pressure vessels are determined by two criteria of plastic collapse: the ASME twice elastic slope (TES) criterion and the recently proposed plastic work curvature (PWC) criterion. Finite element analysis was performed assuming small and large deformation theory and elastic-perfectly plastic and bilinear kinematic hardening material models. Two plastic collapse modes are identified: bending-dominated plastic collapse of the knuckle region in small deformation models and membrane-dominated plastic collapse of the cylinder or domed end in large deformation models. In both circumstances, the PWC criterion indicates that a plastic hinge bending mechanism leads to gross plastic deformation and is used as a parameter to identify the respective plastic loads. The results of the analyses also show that the PWC criterion leads to higher design loads for strain hardening structures than the TES criterion, as it takes account of the effect of strain hardening on the evolution of the gross plastic deformation mechanism.

Characterising plastic collapse of pipe bend structures

Two recently proposed design by analysis criteria of plastic collapse based on plastic work concepts, the plastic work (PW) criterion and the plastic work curvature (PWC) criterion, are applied to a strain hardening pipe bend arrangement subject to combined pressure and in-plane moment loading. Calculated plastic pressure–moment interaction surfaces are compared with limit surfaces, large deformation analysis instability surfaces and plastic load surfaces given by the ASME Twice Elastic Slope criterion and the tangent intersection criterion. The results show that both large deformation theory and material strain hardening have a significant effect on the elastic–plastic response and calculated static strength of the component. The PW criterion is relatively simple to apply in practice and gives plastic load values similar to the tangent intersection criterion. The PWC criterion is more subjective to apply in practice but it allows the designer to follow the development of the gross plastic deformation mechanism in more detail. The PWC criterion indicates a more significant strain hardening strength enhancement effect than the other criteria considered, leading to a higher calculated plastic load.

A Plastic Load Criterion for Inelastic Design by Analysis

The allowable plastic load in pressure vessel design by analysis is determined by applying a graphical construction to a characteristic load-deformation plot of the collapse behavior of the vessel. This paper presents an alternative approach to the problem. The plastic response is characterized by considering the curvature of a plot of plastic work dissipated in the vessel against the applied load. It is proposed that salient points of curvature correspond to critical stages in the evolution of the gross plastic deformation mechanism. In the proposed plastic work curvature (PWC) criterion of plastic collapse, the plastic load is defined as the load corresponding to zero or minimal plastic work curvature after yielding and the formation of plastic mechanisms have occurred. Application of the proposed criterion is illustrated by considering the elastic-plastic response of a simple cantilever beam in bending and a complex three-dimensional finite element analysis of a nozzle intersection. The results show that the proposed approach gives higher values of plastic load than alternative criteria when the material exhibits strain hardening. It is proposed that this is because the PWC criterion more fully represents the constraining effect of material strain hardening on the spread of plastic deformation.

Characterising gross plastic deformation in design by analysis

An investigation of three simple structures is conducted to identify and characterise the condition of gross plastic deformation in pressure vessel design by analysis. Limit analysis and bilinear hardening plastic analysis is performed for three simple example problems. It is found that previously proposed plastic criteria do not fully represent the effect of the hardening material model on the development of the plastic failure mechanism. A new criterion of plastic collapse based on the curvature of the load–plastic work history is therefore proposed. This is referred to as the Plastic Work Curvature or PWC criterion. It is shown that salient points of curvature correspond to critical stages in the physical evolution of the gross plastic deformation mechanism. The PWC criterion accounts for the effect of the bilinear hardening model on the development of the plastic mechanism and gives an enhanced plastic load when compared to the limit load.