Partially Plastic Thick-Walled Cylinder Theory

1952 ◽  
Vol 19 (2) ◽  
pp. 133-140
Author(s):  
M. C. Steele
Keyword(s):  
Internal Pressure ◽  
Experimental Evidence ◽  
Closed Form ◽  
Strain Hardening ◽  
Axial Stress ◽  
Quantitative Comparison ◽  
Stress Strain ◽  
Von Mises ◽  
Walled Cylinder

Abstract Previous theories for partially plastic thick-walled cylinders under internal pressure are reviewed. A quantitative comparison is given for (a) compressibility versus incompressibility of material, and (b) von Mises’ versus Tresca’s theory of failure. The former reveals that deflections at the outside and bore surfaces agree closely, although considerable percentage differences may be found in the axial stresses and strains. Large differences (except for the axial stress) are found in comparing the two theories of failure. Based on the comparison and available experimental evidence, a theory is presented in closed form to include the Hencky stress-strain relations, incompressibility, and Ludwik’s strain-hardening function.

Derivation to Calculate Pipe Collapse Performance using a Combined Loading Equivalent Grade Accounting for Axial Stress, Internal Pressure, Bending and Torsion

2021 ◽  
Author(s):  
Jean-Guillaume Besse
Keyword(s):  
Yield Strength ◽  
Internal Pressure ◽  
Closed Form ◽  
Axial Stress ◽  
Combined Loading ◽  
Collapse Pressure ◽  
Form Equation ◽  
Analytical Derivation ◽  
Von Mises ◽  
Performance Calculation

Abstract This paper proposes a new analytical derivation to incorporate bending and torsion into collapse calculation, further pushing the already existing approach of combined loading equivalent grade proposed in API TR 5C3 (2019) Clause 8.4.6 Eq. (42) for axial stress and internal pressure (identical to ISO TR 10400 Clause 8.4.7) used to calculate a differential collapse pressure. This new derivation is also based on Hencky-von Mises maximum distortion criterion. The interest of developing such combined loading equivalent grade is to enable the use of the four collapse types described in Clause 8 i.e., Yield Strength, Plastic, Transition and Elastic. The formulae are adapted to a closed-form equation similar to current Eq. (42), enabling pipe collapse performance calculation. Newly derived formulae are checked against a size governed by yield strength collapse to verify consistency. The restrictions regarding collapse performance under compression are discussed.

On Thick-Walled Cylinder Under Internal Pressure

2003 ◽  
Vol 125 (3) ◽  
pp. 267-273 ◽  
Author(s):  
W. Zhao ◽  
R. Seshadri ◽  
R. N. Dubey
Keyword(s):  
Internal Pressure ◽  
Strain Curve ◽  
Stress Strain ◽  
Piecewise Linearization ◽  
Elastic Plastic ◽  
Plastic Cylinder ◽  
Parametric Functions ◽  
The Difference ◽  
New Formulation ◽  
Walled Cylinder

A technique for elastic-plastic analysis of a thick-walled elastic-plastic cylinder under internal pressure is proposed. It involves two parametric functions and piecewise linearization of the stress-strain curve. A deformation type of relationship is combined with Hooke’s law in such a way that stress-strain law has the same form in all linear segments, but each segment involves different material parameters. Elastic values are used to describe elastic part of deformation during loading and also during unloading. The technique involves the use of deformed geometry to satisfy the boundary and other relevant conditions. The value of strain energy required for deformation is found to depend on whether initial or final geometry is used to satisfy the boundary conditions. In the case of low work-hardening solid, the difference is significant and cannot be ignored. As well, it is shown that the new formulation is appropriate for elastic-plastic fracture calculations.

Effect of Biaxial Stress on Crack Driving Force

2006 ◽  
Author(s):  
G. Shen ◽  
W. R. Tyson
Keyword(s):  
Internal Pressure ◽  
Driving Force ◽  
Axial Stress ◽  
Axial Strain ◽  
Biaxial Stress ◽  
J Integral ◽  
Longitudinal Stress ◽  
Secondary Stress ◽  
Stress Strain ◽  
Strain Equation

A stress-strain equation of Ramberg-Osgood type is proposed to correlate the longitudinal stress with longitudinal strain of a thin plate when a constant stress is applied transversely. The same approach can be used to correlate the axial stress with axial strain for a thin-walled pipe in axial tension with internal pressure. The proposed stress-strain equation relating the longitudinal stress and strain closely approximates that of deformation theory. The effect of a secondary stress (hoop stress) on the J-integral for a circumferential crack in a pipe under axial load and internal pressure is evaluated by finite element analysis (FEA). The results show that the J-integral decreases with internal pressure at a given axial stress but increases with internal pressure at a given axial strain. It is concluded that while a secondary stress may be safely neglected in a stress-based format because it decreases the driving force at a given applied stress, it should not be neglected in a strain-based format because it significantly increases the driving force at a given applied strain.

Studies on Plastic Flow of Anisotropic Metals

1956 ◽  
Vol 23 (3) ◽  
pp. 444-450
Author(s):  
L. W. Hu
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Biaxial Tension ◽  
Plastic Behavior ◽  
Theory Of Plastic Flow ◽  
Walled Cylinder

Abstract This investigation deals with a study of the plastic behavior of anisotropic metals. By extending Hill’s theory of plastic flow of anisotropic metals, plastic stress-strain relations for anisotropic materials with strain hardening are developed. Applications of these relations are also made to plane-stress and plane-strain problems with anisotropy. The effect of anisotropy on the stress distribution and on the pressure to produce yielding in a thick-walled cylinder under internal pressure is discussed. The influence of anisotropy on the interpretation of conventional biaxial tension-tension and tension-torsion tests is also considered in this study.

scholarly journals Numerical Study of The Effect of Wall Thickness and Internal Pressure on Von Mises Stress and Safety Factor of Thin-Walled Cylinder for Rocket Motor Case

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Lasinta Ari Nendra Wibawa
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Internal Pressure ◽  
Wall Thickness ◽  
Axial Stress ◽  
Rocket Motor ◽  
Von Mises Stress ◽  
Element Analysis ◽  
Maximum Hoop Stress ◽  
Von Mises

The rocket motor is an important part of rockets. The rocket motor works using the pressure vessel principle because it works in an environment with high pressure and temperature. This paper investigates the von Mises stress that occurs in thin-walled cylinders and safety factors for rocket motor cases due to the influence of the wall thickness and internal pressure. Dimensions of the cylinder length are 500 mm, outer diameter is 200 mm, and cap thickness is 30 mm. The wall thickness is varied 6, 7, 8, and 9 mm, while the internal pressure is varied 8, 9, and 10 MPa. Stress analysis is performed using the finite element method with Ansys Workbench 2019 R3 software. The simulation results show that the maximum von Mises stress decreases with increasing wall thickness. The maximum von Mises stress increases with increasing internal pressure. The material has a safety factor higher than 1.25 for all variations in wall thickness and internal pressure. It means that the material can withstand static loads. The verification process is done by comparing the results of finite element analysis with analytical calculations for maximum hoop stress and maximum axial stress with a fixed boundary condition. The results of maximum hoop stress and maximum axial stress using finite element analysis and analytical calculations are not significantly different. The percentage of errors between analytical calculations and finite element analysis is less than 6 percent.

A Comparison of Flow and Deformation Theories in a Radially Stressed Annular Plate

1973 ◽  
Vol 40 (1) ◽  
pp. 283-287 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Internal Pressure ◽  
Closed Form ◽  
Deformation Theory ◽  
Annular Plate ◽  
Yield Condition ◽  
Flow Theory ◽  
Quantitative Comparison ◽  
The Other ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Two mathematically consistent solutions to the strains and displacement in a partly plastic, annular plate stressed by internal pressure are obtained according to the deformation theory of Hencky and to the flow theory of Prandtl-Reuss. In both cases, the material is assumed to be elastic, perfectly plastic and obeying the Mises yield condition. It is shown that one solution is expressed in closed form and the other, in terms of simple integrals. A quantitative comparison of two theories is given and the effect of compressibility is discussed.

Plastic Collapse Assessment of Thick Vessels Under Internal Pressure According to Various Hardening Rules

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
A. Chaaba
Keyword(s):  
Internal Pressure ◽  
Strain Hardening ◽  
Limit Analysis ◽  
Limit State ◽  
Plastic Behavior ◽  
Plastic Collapse ◽  
Perfectly Plastic ◽  
Von Mises ◽  
Hardening Rules ◽  
Collapse Assessment

This paper aims to deal with plastic collapse assessment for thick vessels under internal pressure, thick tubes in plane strain conditions, and thick spheres, taking into consideration various strain hardening effects and large deformation aspect. In the framework of von Mises’ criterion, strain hardening manifestation is described by various rules such as isotropic and/or kinematic laws. To predict plastic collapse, sequential limit analysis, which is based on the upper bound formulation, is used. The sequential limit analysis consists in solving sequentially the problem of the plastic collapse, step by step. In the first sequence, the plastic collapse of the vessel corresponds to the classical limit state of the rigid perfectly plastic behavior. At the end of each sequence, the yield stress and/or back-stresses are updated with or without geometry updating via displacement velocity and strain rates. The updating of all these quantities (geometry and strain hardening variables) is adopted to conduct the next sequence. As a result of this proposal, we get the limit pressure evolution, which could cause the plastic collapse of the device for different levels of hardening and also hardening variables such as back-stresses with respect to the geometry change.

MODELING OF THE STRESS-STRAIN STATE OF A TRANSPORT TUNNEL UNDER LOAD AS A MEASURE TO REDUCE OPERATIONAL RISKS TO TRANSPORTATION FACILITIES

2020 ◽  
Vol 3 (8) ◽  
pp. 28-34
Author(s):  
N. V. IVANITSKAYA ◽  
◽  
A. K. BAYBULOV ◽  
M. V. SAFRONCHUK ◽  
◽  
...  
Keyword(s):  
Strain State ◽  
Moving Load ◽  
Element Model ◽  
Transport Infrastructure ◽  
Design Stage ◽  
Surface Load ◽  
Stress Strain ◽  
Stress Strain State ◽  
Operational Risks ◽  
Von Mises

In many countries economic policy has been paying increasing attention to the modernization and development of transport infrastructure as a measure of macroeconomic stimulation. Tunnels as an important component of transport infrastructure save a lot of logistical costs. It stimulates increasing freight and passenger traffic as well as the risks of the consequences of unforeseen overloads. The objective of the paper is to suggest the way to reduce operational risks of unforeseen moving load by modeling of the stress-strain state of a transport tunnel under growing load for different conditions and geophysical parameters. The article presents the results of a study of the stress-strain state (SSS) of a transport tunnel exposed to a mobile surface load. Numerical experiments carried out in the ANSYS software package made it possible to obtain diagrams showing the distribution of equivalent stresses (von Mises – stresses) according to the finite element model of the tunnel. The research results give grounds to assert that from external factors the stress state of the tunnel is mainly influenced by the distance to the moving load. The results obtained make it possible to predict in advance the parameters of the stress-strain state in the near-contour area of the tunnel and use the results in the subsequent design of underground facilities, as well as to increase their reliability and operational safety. This investigation gives an opportunity not only to reduce operational risks at the design stage, but to choose an optimal balance between investigation costs and benefits of safety usage period prolongation.

scholarly journals Axial Stress-Strain Performance of Recycled Aggregate Concrete Reinforced with Macro-Polypropylene Fibres

2021 ◽  
Vol 13 (10) ◽  
pp. 5741
Author(s):  
Muhammad Junaid Munir ◽  
Syed Minhaj Saleem Kazmi ◽  
Yu-Fei Wu ◽  
Xiaoshan Lin ◽  
Muhammad Riaz Ahmad
Keyword(s):  
Axial Stress ◽  
Peak Stress ◽  
Polypropylene Fibre ◽  
Recycled Aggregate Concrete ◽  
Recycled Aggregate ◽  
Recycled Aggregates ◽  
Peak Strain ◽  
Stress Strain ◽  
Polypropylene Fibres ◽  
Aggregate Concrete

The addition of macro-polypropylene fibres improves the stress-strain performance of natural aggregate concrete (NAC). However, limited studies focus on the stress-strain performance of macro-polypropylene fibre-reinforced recycled aggregate concrete (RAC). Considering the variability of coarse recycled aggregates (CRA), more studies are needed to investigate the stress-strain performance of macro-polypropylene fibre-reinforced RAC. In this study, a new type of 48 mm long BarChip macro-polypropylene fibre with a continuously embossed surface texture is used to produce BarChip fibre-reinforced NAC (BFNAC) and RAC (BFRAC). The stress-strain performance of BFNAC and BFRAC is studied for varying dosages of BarChip fibres. Results show that the increase in energy dissipation capacity (i.e., area under the curve), peak stress, and peak strain of samples is observed with an increase in fibre dosage, indicating the positive effect of fibre addition on the stress-strain performance of concrete. The strength enhancement due to the addition of fibres is higher for BFRAC samples than BFNAC samples. The reduction in peak stress, ultimate strain, toughness and specific toughness of concrete samples due to the utilisation of CRA also reduces with the addition of fibres. Hence, the negative effect of CRA on the properties of concrete samples can be minimised by adding BarChip macro-polypropylene fibres. The applicability of the stress-strain model previously developed for macro-synthetic and steel fibre-reinforced NAC and RAC to BFNAC and BFRAC is also examined.

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