A General Solution for the Pressurized Elastoplastic Tube

1992 ◽  
Vol 59 (1) ◽  
pp. 20-26 ◽  
Author(s):  
David Durban ◽  
Michael Kubi
Keyword(s):  
General Solution ◽  
Finite Strain ◽  
Cylindrical Tube ◽  
Yield Function ◽  
Material Behavior ◽  
Deformation Pattern ◽  
Perfectly Plastic ◽  
Plastic Phase ◽  
Thin Walled ◽  
Elastic Perfectly Plastic

The problem of a thick-walled cylindrical tube subjected to internal pressure is investigated within the framework of continuum plasticity. Material behavior is modeled by a finite strain elastoplastic flow theory based on the Tresca yield function. The deformation pattern is restricted by the plane-strain condition but arbitrary hardening and elastic compressibility are accounted for. A general solution is given in terms of quadratures. The analysis also includes treatment of a second plastic phase, characterized by corner relations, that may develop at the inner boundary. It is shown that the interface between the two plastic regions moves initially outwards and then, beyond a certain strain level, it moves back inwards. Some useful and simple results are given for thin-walled tubes of hardening materials and for thick-walled elastic/perfectly plastic tubes.

scholarly journals Investigation of natural frequencies of axially loaded thin-walled columns

2018 ◽  
Vol 219 ◽  
pp. 02018
Author(s):  
Łukasz Żmuda-Trzebiatowski
Keyword(s):  
Applied Load ◽  
Natural Frequencies ◽  
Elastic Buckling ◽  
Correlation Technique ◽  
Buckling Loads ◽  
Perfectly Plastic ◽  
Linear Buckling ◽  
Thin Walled ◽  
Elastic Perfectly Plastic ◽  
Flexural Torsional Buckling

The paper deals with correlation between natural frequencies of two steel thin-walled columns and the corresponding applied load. The structures are made of cold-formed lipped channel sections. The columns lengths were assumed to follow two buckling patterns – global flexural and flexural-torsional buckling. In the thicker structure two material models were considered – linearly-elastic and elastic-perfectly plastic. Numerical computations cover dynamic eigenvalue problem, linear buckling and geometrically (and materially) non-linear analysis. The correlation between squares of natural frequencies and the applied load is linear in both columns. The first natural frequencies drop to zero due to structural buckling. This method, called the Vibration Correlation Technique, allows to predict buckling loads on the basis of measured vibration frequencies of the structures. Plasticity does not affect the corresponding curves – the use of the presented technique is limited to the structures exhibiting elastic buckling behaviour.

scholarly journals Thermo-Mechanical Modeling of Distortions Promoted during Cooling of Ti-6Al-4V Part Produced by Superplastic Forming

2016 ◽  
Vol 838-839 ◽  
pp. 196-201
Author(s):  
Maxime Rollin ◽  
Vincent Velay ◽  
Luc Penazzi ◽  
Thomas Pottier ◽  
Thierry Sentenac ◽  
...  
Keyword(s):  
Finite Element ◽  
Thermal Stresses ◽  
Superplastic Forming ◽  
Model Material ◽  
Material Behavior ◽  
Mechanical Modeling ◽  
Temperature Dependent ◽  
Finite Element Software ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

In AIRBUS, most of the complex shaped titanium fairing parts of pylon and air inlets are produced by superplastic forming (SPF). These parts are cooled down after forming to ease their extraction and increase the production rate, but AIRBUS wastes a lot of time to go back over the geometric defects generated by the cooling step. This paper investigates the simulations of the SPF, cooling and clipping operations of a part on Abaqus® Finite element software. The different steps of the global process impact the final distortions. SPF impacts the thickness and the microstructure/behavior of material, cooling impacts also the microstructure/behavior of material and promotes distortions through thermal stresses and finally, clipping relaxes the residual stresses of the cut part. An elastic-viscoplastic power law is used to model material behavior during SPF and a temperature dependent elastic perfectly plastic model for the cooling and clipping operations.

Mechanical and Thermodynamic Considerations of an Assemblage of Homogeneous Elastic-Plastic States

1968 ◽  
Vol 35 (3) ◽  
pp. 596-603 ◽  
Author(s):  
David Rubin
Keyword(s):  
Plastic Deformation ◽  
Mechanical Behavior ◽  
Strain Energy ◽  
Material Behavior ◽  
Free State ◽  
Elastic Plastic ◽  
Elastic Range ◽  
Perfectly Plastic ◽  
Stress Free State ◽  
Elastic Perfectly Plastic

The mechanics and the thermodynamics of plastic deformation are considered in terms of a general assemblage or continuum of elastic, perfectly plastic elements or states. Such models not only match the external mechanical behavior of real materials structures and continua, but they also afford a simple thermodynamic definability. A consideration of the internal behavior shows that the stress-free state has the maximum elastic range. Hardening in the sense of an increasing macroscopic elastic range is accompanied by a release of stored strain energy; the stress-free state always is restorable. This behavior is appropriate for real structures and continua. However, it is precisely these continuum characteristics which make the assemblages inappropriate models of material behavior. Barriers to continuing plastic deformation are required which do exist on the microscale, but lie outside of the scope of the most complex of these thermodynamically well-defined assemblages.

Nonlinear Analysis of Steel Frames Using Element with Trilinear Model

2013 ◽  
Vol 838-841 ◽  
pp. 519-524
Author(s):  
Shu Jun Hu ◽  
Zhan Wang ◽  
Jian Rong Pan
Keyword(s):  
Nonlinear Analysis ◽  
Degrees Of Freedom ◽  
Steel Frames ◽  
Yield Function ◽  
Constitutive Relationship ◽  
Perfectly Plastic ◽  
Trilinear Model ◽  
Plastic Stage ◽  
Elastic Perfectly Plastic ◽  
Column Element

Considering the elastic-plastic stage of steel constitutive relationship, the assumption that element is elastic perfectly-plastic is no longer valid. The yield function that considers the effect of trilinear model is derived by using section assemblage concept. Element with two subsprings at each end is presented to consider the effect of section stiffness and yielding. Based on the proposed yield function and element, an efficient nonlinear analysis method for steel frame with trilinear model is proposed. The proposed element has the same nodal degrees of freedom as conventional beam-column element by condensing the non-nodal degrees of freedom. Other factors influence the capacity of steel frames, such as shear deformation, residual stress, geometric and material nonlinearity are explicated. The efficiency and accuracy of the proposed approach are demonstrated through the numerical example.

Overcoming Limitations of the Conventional Strain-Life Fatigue Damage Model

1996 ◽  
Vol 118 (1) ◽  
pp. 103-108 ◽  
Author(s):  
T. E. Langlais ◽  
J. H. Vogel
Keyword(s):  
Damage Model ◽  
Strain Curve ◽  
Cyclic Stress ◽  
Material Behavior ◽  
Perfectly Plastic ◽  
Linear Relationships ◽  
Elastic Perfectly Plastic ◽  
Plastic Components ◽  
Log Linear ◽  
Very High

The strain-based approach to fatigue life prediction usually relies on the conventional strain-life equation which correlates the elastic and plastic strain to the life. The correlation is based on separate log-linear curve fits of the elastic and plastic components of the strain data versus the life. It is well known, however, that these linear relationships may be valid only within a specific interval of stress or strain. When material behavior approaches elastic-perfectly plastic, for instance, it is not uncommon for the test data to deviate from linearity at both very high and very low strains. For such materials a separate fit of each curve is likely to give material constants significantly inconsistent with the fit of the cyclic stress-strain curve, especially if a good local fit over a restricted interval is obtained. In this work, some of the errors that arise as a result of this inconsistency are described, and recommended methods are developed for treating these errors. Numerical concerns are also addressed, and sample results are included.

Nonlinear Analysis of Anchored Tanks Subject to Equivalent Seismic Loading

2002 ◽  
Author(s):  
D. Redekop ◽  
P. Mirfakhraei ◽  
T. Muhammad
Keyword(s):  
Nonlinear Behavior ◽  
Seismic Loading ◽  
Material Behavior ◽  
Seismic Action ◽  
The Finite Element Method ◽  
Perfectly Plastic ◽  
Liquid Storage ◽  
Failure Loads ◽  
Elastic Perfectly Plastic ◽  
Hydrodynamic Effects

The finite element method is applied to the problem of the nonlinear behavior of anchored cylindrical liquid-storage tanks subject to horizontal seismic loading. The tank alone is modelled with assumptions of fixed conditions at the base and free conditions at the top. Geometric nonlinearity is considered and the material behavior is taken as elastic-perfectly plastic. The loading consists of a constant hydrostatic pressure to which is added an equivalent static pressure representing hydrodynamic effects arising from seismic action. The latter loading is increased until failure occurs. As an indication of the validity of the approach a comparison with a test result is given. A parametric study is then conducted. Nonlinear failure loads are calculated in each case, and these are compared with previously determined elastic buckling loads.

On an Extremum Principle for Mode Form Solutions in Plastic Structural Dynamics

1975 ◽  
Vol 42 (3) ◽  
pp. 630-640 ◽  
Author(s):  
P. S. Symonds ◽  
T. Wierzbicki
Keyword(s):  
Structural Dynamics ◽  
Yield Function ◽  
Velocity Fields ◽  
Extremum Principle ◽  
Material Behavior ◽  
Structure Model ◽  
Discrete Structure ◽  
First Variation ◽  
Admissible Velocity ◽  
Perfectly Plastic

An extremum principle of Lee and Martin [2], for mode form solutions of a structure deforming plastically as result of dynamic loading, is discussed with special reference to conditions for the extrema to be stationary, with vanishing first variation of a functional of kinematically admissible velocity fields. Three classes of material behavior are treated: rigid-perfectly plastic, rigid-viscoplastic, and viscous, the last having no yield function. We illustrate various forms of these which are realistic as well as convenient in problems of plastic dynamics of structures. For all three classes of material, we show that stationary extrema occur under certain conditions, but may be regarded as exceptional. The properties of the extrema for structures are illustrated by means of a simple discrete structure model with two masses.

On the Material Modeling of the Autofrettaged Pressure Vessel Steels

2008 ◽  
Author(s):  
G. H. Farrahi ◽  
E. Hosseinian ◽  
A. Assempour
Keyword(s):  
Uniaxial Tension ◽  
High Strength Steels ◽  
High Strength ◽  
Test Methods ◽  
Material Behavior ◽  
Material Modeling ◽  
Chemical Compositions ◽  
Accurate Analysis ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Material modeling of the high strength steels plays an important role in accurate analysis of autofrettaged tubes. Although, the loading behavior of such materials is nearly elastic-perfectly plastic, their unloading behavior due to Bauschinger effect is very complicated. DIN1.6959 steel is frequently used for construction of autofrettaged tubes in some countries such as Germany and Switzerland. In spite of similarity between chemical compositions of this steel with A723 steel, due to different material processing, two steels have unlikely behavior. In this paper material behavior of DIN1.6959 has been accurately modeled by uniaxial tension-compression test results. Both 6 mm and 12.5 mm diameter specimens were used and compared. Also various functions for modeling of autofrettaged steels were investigated and new function was introduced for accurate modeling. Moreover, two test methods, i.e. uniaxial tension-compression and torsion tests, which used for modeling of autofrettage steels, were analyzed. As well, material models of three important autofrettage steels, i.e. A723, HB7 and Din1.6959 were compared.

On Plane Stress Solution of an Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (3) ◽  
pp. 407-410
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Stress ◽  
Yield Surface ◽  
Complete Solution ◽  
Yield Function ◽  
The State ◽  
Perfectly Plastic ◽  
State Of Stress ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic ◽  
Flow Laws

Abstract With the use of Tresca’s yield function and its associated flow laws, the complete solution is obtained for an isotropic elastic, perfectly plastic wedge (with an included angle β < π/2) subjected to a uniform traction in the state of plane stress. Unlike its corresponding plane strain solution, the state of stress in a portion of the plastic domain of the wedge is at a corner of Tresca’s yield hexagon where, in general, the normal to the yield surface is not defined uniquely.

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