Thermal Ratcheting With Kinematic Hardening in a Two-Bar Assembly With Unequal Areas and Properties

1976 ◽  
Vol 98 (3) ◽  
pp. 256-263 ◽  
Author(s):  
A. R. Brunsvold ◽  
H. U. Ahmed ◽  
C. C. Stone
Keyword(s):  
Kinematic Hardening ◽  
Pressure Vessels ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Thermal Loads ◽  
Strain Behavior ◽  
Thermal Ratcheting ◽  
Cyclic Changes ◽  
Inelastic Strains ◽  
Special Case

An analytical model based on a two-bar assembly with unequal areas and material properties is used to determine inelastic stress-strain behavior under a steady mean load and cyclic thermal loads. The study with the model extends previous study on thermal ratcheting with kinematic hardening. The model exhibits much of the behavior of interest in design of pressure vessels subject to thermal loads: elastic behavior, shakedown, ratcheting, captive plastic behavior (a special case of elastic followup), and plastic cycling. The expressions for cyclic changes in stress and cyclic inelastic strains are developed, and the mean-load and thermal-load bounds for the behavior modes are mapped.

Constitutive Law of Finite Deformation Elastoplasticity With Proportional Loadings

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
H. Darijani ◽  
R. Naghdabadi
Keyword(s):  
Constitutive Equation ◽  
Finite Deformation ◽  
Constitutive Models ◽  
Pressure Vessels ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Proportional Loading ◽  
Von Mises ◽  
Plastic Parts

In this paper, decomposition of the total strain into elastic and plastic parts is investigated for extension of elastic-type constitutive models to finite deformation elastoplasticity. In order to model the elastic behavior, a Hookean-type constitutive equation based on the logarithmic strain is considered. Based on this constitutive equation and assuming the deformation theory of Hencky as well as the yield criteria of von Mises, the elastic-plastic behavior of materials at finite deformation is modeled in the case of the proportional loading. Moreover, this elastoplastic model is applied in order to determine the stress distribution in thick-walled cylindrical pressure vessels at finite deformation elastoplasticity.

Effects of Water on the Mechanical Properties of Paper and their Relationship to the Treatment of Paper

1992 ◽  
Vol 267 ◽  
Author(s):  
Timothy Vitale
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Tap Water ◽  
Water Immersion ◽  
Exchange Process ◽  
Elastic Behavior ◽  
Elastic Fibers ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Behavior

ABSTRACTThrough a series of experiments the mechanical properties of paper are explored. Hydrogen bonding is fundamental to the performance of paper and its disruption results in distinctive stress-strain behavior. Stress-strain curves were generated from which tensile strength, Young's modulus, percent stretch, and work (tensile energy absorption) were obtained.It was found that the contribution of the fiber to the mechanical properties of paper is primarily elastic. Fibers are many times stronger than paper. Only fibers which have been severely deteriorated show measurable changes in stress-strain behavior. Fiber deterioration results in characteristically different stress-strain behavior than that which results from disruption of interfiber bonding.Water immersion results in the disruption of interfiber bonds in paper, leaving only 2-3% of dry tensile strength. Interfiber bonds make a profound contribution to the mechanical properties of the paper. Aqueous treatment is shown to be a radical treatment, altering the original dried-in properties of the sheet. The release of structural bonds and dried-in strains during wetting and the subsequent reformation of interfiber bonds during drying are shown to be independent of water purity, be it ultrapure water, tap water, or water containing washing aids such as Ca(OH)2, NaOH, CaCO3 or Na2CO3.The effects of immersion in organic solvents was explored. Solvents have effects on mechanical properties which are approximately proportional to the degree of swelling caused by the solvent. Water, the liquid which caused the greatest swelling of the liquids evaluated, is shown to be the most disruptive liquid followed by methanol and acetone; toluene caused virtually no change.To explore the behavior of interfiber bonds paper was taken through a solvent exchange process. A sample was immersed in water and then taken through separate ethanol and acetone immersions to toluene, and dried. The result was a sheet with little bonding and decreases in all mechanical properties. To explore the surface tension and capillary action effects of water, the solvent-exchanged sheet was re-immersed in water. Upon drying, interfiber bonding was reintroduced which resulted in the regain of mechanical properties lost.A paradigm for the mechanical behavior of paper is developed. Fibers contribute elastic behavior and interfiber bonds are a principal source of plastic behavior.

Direct Methods of Plasticity in Aluminium Frames Accounting for Eurocode 9 Failure Criteria

2016 ◽  
Vol 710 ◽  
pp. 415-420
Author(s):  
Alexios T. Ampatzis ◽  
Vasileios G. Psomiadis ◽  
Evangelos Efthymiou
Keyword(s):  
Kinematic Hardening ◽  
Load Capacity ◽  
Limit State ◽  
Direct Methods ◽  
Failure Criteria ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Plastic Collapse ◽  
Shakedown Analysis ◽  
Stress Resultant

Metal structures, given their broad plastic deformation capacity, have been often at the core of research for the evaluation of the post elastic behavior via the direct methods of plasticity. Limit and shakedown analysis were often exploited to determine the plastic collapse load capacity, as they provide advantages in terms of computational robustness in comparison with incremental non-linear analysis. The aforementioned approach has been widely and effectively applied for steel structures, characterized by rigid-plastic behavior. Υet in the case of aluminium structures, there are special parameters to be considered, as they exhibit a relationship of round-house type, whose trend cannot be interpreted through the classic elastic-perfectly plastic material law idealization.The present paper aims to develop a limit and shakedown analysis formulation suitable for the safety assessment of 3D aluminium frame structures against plastic collapse. Research yielded the proposed two-surface methodology in the framework of stress resultant plasticity, which is capable of estimating the plastic collapse limit state of real-life aluminium frames, incorporating Eurocode 9 codified failure criteria and limited kinematic hardening. A numerical example of a 3D frame is realized utilizing the finite element method and the 3-node Timoshenko column-beam element, in order to showcase the proposed methodology and validate the influence of hardening effect.

Thermo-Elasto-Plastic Analysis of Thick-Walled Spherical Pressure Vessels Made of Functionally Graded Materials

2016 ◽  
Vol 08 (04) ◽  
pp. 1650054 ◽  
Author(s):  
Zeinab Mazarei ◽  
Mohammad Zamani Nejad ◽  
Amin Hadi
Keyword(s):  
Heat Flux ◽  
Functionally Graded Materials ◽  
Poisson’S Ratio ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Material Behavior ◽  
Poisson's Ratio ◽  
Uniform Heat Flux ◽  
Plastic Behavior ◽  
Graded Materials

An exact closed-form analytical solution is presented to solve the thermo-elasto-plastic problem of thick-walled spherical vessels made of functionally graded materials (FGMs). Assuming that the inner surface is exposed to a uniform heat flux, and that the outer surface is exposed to an airstream. The heat conduction equation for the one-dimensional problem in spherical coordinates is used to obtain temperature distribution in the sphere. Material properties are graded in the thickness direction according to a power law distribution, whereas the Poisson’s ratio is kept constant. The Poisson’s ratio due to slight variations in engineering materials is assumed constant. The plastic model is based on von Mises yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit heat flux, displacement and stresses versus the radial direction. Moreover, the effect of increasing the heat flux and pressure on the propagation of the plastic zone are investigated. Furthermore, the effect of change in Poisson’s ratio on the value of the critical material parameter is demonstrated. The present study is also validated by comparing the numerical results for thick elasto-plastic spherical shells available in the literature. To the best of the authors’ knowledge, in previous studies, exact thermo-elasto-plastic behavior of FGM thick-walled sphrical pressure vessels has not investigated.

Using Thermoplastic (HDPE) Liners and Glass Fiber Reinforced Thermosetting and Thermoplastic Structural Wall Matrices to Produce Filament Wound Pressure Vessels

2010 ◽  
Author(s):  
Joao F. Silva ◽  
Joao P. Nunes ◽  
Joao C. Velosa
Keyword(s):  
Glass Fiber ◽  
Composite Laminates ◽  
Large Scale ◽  
Service Condition ◽  
Pressure Vessels ◽  
Filament Winding ◽  
Plastic Behavior ◽  
Fiber Reinforced ◽  
Structural Wall ◽  
Glass Fiber Reinforced

Polymer composites are an excellent alternative to replace more traditional materials in the fabrication of pressure cylinders for common applications. They minimize the weight and improve the mechanical, impact and corrosion behavior, which are relevant characteristics for almost all current and future large scale pressure cylinder applications, such as liquid filters and accumulators, hydrogen cell storage vessels, oxygen bottles, etc. A new generation of composite pressure vessels has been studied in this work. The vessels consist on a thermoplastic liner wrapped with a filament winding glass fiber reinforced polymer matrix structure. A conventional 6-axis CNC controlled filament winding equipment was used to manufacture the thermosetting matrix composite vessels and adapted for production of thermoplastic matrix based composite vessels. The Abaqus 6.4.2 FEM package was used to predict the mechanical behavior of pressure vessels with capacity of approximately of 0.068 m3 (68 liters) for a 0.6 MPa (6 bar) pressure service condition according to the requirements of the EN 13923 standard, namely, the minimum internal burst pressure. The Tsai-Wu and von-Mises criteria were used to predict composite laminate and thermoplastic liner failures, respectively, considering the elasto-plastic behavior of the HDPE liner and the lamina properties deducted from the micromechanical models for composite laminates. Finally, the results obtained from the simulations were compared with those obtained from the experimental pressure tests made on the thermoplastic liners and final composite vessels.

Analysis of the Influence of the Cooling Patterns and the Shape of the Bulges on the Levels of Stress in the Cylindrical Section of Delayed Coke Drums

2018 ◽  
Author(s):  
Gabriel A. Vivas ◽  
Armando J. Moret ◽  
Roberto E. Bello ◽  
Luis M. Melian ◽  
Julian J. Bedoya
Keyword(s):  
Laser Scanning ◽  
Thermal Loading ◽  
Low Cycle Fatigue ◽  
Pressure Vessels ◽  
Transient Temperature ◽  
Thermal Gradients ◽  
Cooling Rates ◽  
Area Of Interest ◽  
Stress Levels ◽  
Cyclic Changes

Coke drums are thin-walled pressure vessels that experience low cycle fatigue due to thermal loadings. The delayed coking process is comprised by three major stages: heating, coking and cooling, which repeat at intervals between 20 and 48 hours. The cyclic changes of temperature increase the growth of bulges and cracks which with the passing of time, propagate and eventually cause failures due to the loss of containment. A better understanding of the phenomena of the thermal gradients and their influence on the generated stresses would reduce the effects of the damage mechanisms afflicting coke drums, for example; a continuous monitoring system could be implemented in order to control the cooling ramp to obtain a more homogeneous quenching around the cylinder of the coke drum and consequently increase its lifetime. It is been widely accepted that there is a relationship between high cooling rates in isolated zones and high axial stresses. However, this relationship has not been fully validated, since there are also been reported events of low cooling rates and high stresses. This study shows a predictable behavior (trend) that relates the spatial thermal gradients and the axial and circumferential stresses generated. A coke drum in an upgrader facility was instrumented with two arrays or grids, each of them having 24 thermocouples and 2 strain gauges in zones with distinct bulges. One arrangement was located at an inward bulge while the other was located at an outward bulge. Computational models were carried out to reproduce the behavior of the instrumented zones with their actual deformations obtained from laser scanning. Finite element models were developed using a sequentially coupled thermo-mechanical analysis to determine the transient temperature and stress distributions. The effect of the circumferential thermal gradients on the stress levels in the instrumented cylindrical sections were analyzed, considering two cases; the first of them a perfect cylinder (without deformation) and the second one considering the presence of bulges in the area of interest. The results indicate that there is a relationship between the circumferential thermal gradients [°C/m] or [°F/ft] and the axial stress levels, i.e., cold zones generate axial tensile stresses, and hot zones produce compressive axial stresses. This relationship is affected — exacerbated or counteracted — by the presence of the bulges. Additionally, the results obtained in this paper confirm those of previous investigations showing that outward bulges subject to pressure and thermal loading generate high stresses on its internal surface and low stresses on its external face whereas inward bulges produce the opposite effect.

Elastic-Plastic Analysis of Fretting Contacts

2015 ◽  
Vol 642 ◽  
pp. 248-252
Author(s):  
Chang Hung Kuo
Keyword(s):  
Kinematic Hardening ◽  
Carbon Steels ◽  
Plastic Behavior ◽  
Rule Based ◽  
Elastic Plastic ◽  
Hardening Rule ◽  
Chaboche Model ◽  
Plastic Analysis ◽  
Finite Element Procedure ◽  
Elastic Shakedown

A finite element procedure is implemented for the elastic-plastic analysis of carbon steels subjected to reciprocating fretting contacts. The nonlinear kinematic hardening rule based on Chaboche model is used to model the cyclic plastic behavior in fretting contacts. The results show that accumulation of plastic strains, i.e. ratchetting, may occur near the contact edge while elastic shakedown is likely to take place in substrate.

Stress-Strain Equations for Some Near-Eutectic Tin-Lead Solders

1991 ◽  
Vol 113 (4) ◽  
pp. 475-484 ◽  
Author(s):  
K. P. Jen ◽  
J. N. Majerus
Keyword(s):  
Strain Rate ◽  
Printed Circuit Boards ◽  
Volume Fraction ◽  
Total Error ◽  
Tensile Tests ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Strain Rates ◽  
Stress Strain ◽  
Engineering Strain

This paper presents the evaluation of the stress-strain behavior, as a function of strain-rate, for three tin-lead solders at room temperature. This behavior is critically needed for reliability analysis of printed circuit boards (PCB) since handbooks list minimal mechanical properties for the eutectic solder used in PCBs. Furthermore, most handbook data are for stable eutectic microstructure whereas PCB solder has a metastable microstructure. All three materials were purchased as “eutectics.” However, chemical analysis, volume fraction determination, and microhardness tests show some major variations between the three materials. Two of the materials have a eutectic composition, and one does not. The true stress-strain equations of one eutectic and the one noneutectic material are determined from compressive tests at engineering strain-rates between 0.0002/s and 0.2/s. The second eutectic material is evaluated using tensile tests with strain-rates between 0.00017/s and 0.042/s. The materials appear to exhibit linear elastic behavior only at extremely small strains, i.e., less than 0.0005. However, this “elastic” behavior showed considerable variation, and depended upon the strain rate. In both tension and compression the eutectic alloy exhibits nonlinear plastic behavior, i.e., strain-softening followed by strain-hardening, which depends upon the strain rate. A quadratic equation σy = σy(ε˚/ε˚0) + A(ε˚/ε˚0)ε + B(ε˚/ε˚0)ε2 fit to the data gives correlation coefficients R2 > 0.91. The coefficients σy(ε˚/ε˚0), A(ε˚/ε˚0), B(ε˚/ε˚0) are fitted functions of the normalized engineering strain rate ε˚/ε˚0. Replicated experiments are used at each strain-rate so that a measure of the statistical variation could be estimated. Measures of error associated with the regression analysis are also obtained so that an estimate of the total error in the stress-strain relations can be made.

Direct Analysis of Post-Shakedown Quantities With the STPZ Considering Multi-Parameter Loading

2019 ◽  
Author(s):  
Bastian Vollrath ◽  
Hartwig Hübel
Keyword(s):  
Direct Method ◽  
Kinematic Hardening ◽  
Direct Analysis ◽  
Load Cycle ◽  
Material Behavior ◽  
Plastic Behavior ◽  
Method Effects ◽  
Plastic Shakedown ◽  
Initial Strains ◽  
Incremental Step

Abstract If a structure is subjected to cyclic loading, strain, displacements etc. may accumulate cycle by cycle due to a ratcheting mechanism. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. Usually, this is requested to be done considering all load sets pairwise. However, this leads to the fact that ratcheting cannot be detected, if it occurs only because of multi-parameter loading. Ordinary incremental step-by-step calculations can easily exceed time and hardware resources. This is particularly true for travelling loads, where many load steps are required for one load cycle. As an alternative, the Simplified Theory of Plastic Zones (STPZ) is used in the present paper. Being a direct method, effects from load history are disregarded. The elastic-plastic behavior in the state of either elastic or plastic shakedown is estimated on the basis of purely elastic analyses. Two kinds of linear elastic analyses are to be performed, fictitious elastic analyses for each set of loading, and a number of modified elastic analyses. Few of these analyses are usually sufficient to obtain reasonable estimates of the post-shakedown quantities. Trilinear material behavior is adopted along with kinematic hardening, a Mises yield surface and an associated flow law. The modified elastic analyses are performed making use of modified elastic parameters (Young’s modulus and Poisson’s ratio) in the plastic zone and applying suitably defined initial strains. The results obtained can be improved iteratively. The theory of the method is briefly explained and its application is shown using an example with multi-parameter loading.

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