Design for Displacement Strains

2021 ◽  
pp. 65-73
Author(s):  
Charles Becht, IV
Keyword(s):  
Thermal Expansion ◽  
Allowable Stress ◽  
Controlled Conditions ◽  
Sustained Loads ◽  
Induced Stresses ◽  
The Difference

The allowable stress for thermal expansion and other deformation-induced stresses is substantially higher than for sustained loads. This is due to the difference between load-controlled conditions, such as weight and pressure, and deformation-controlled conditions, such as thermal expansion or end displacements (e.g., due to thermal expansion of attached equipment).

Algorithms for Density, Potential Temperature, Conservative Temperature, and the Freezing Temperature of Seawater

2006 ◽  
Vol 23 (12) ◽  
pp. 1709-1728 ◽  
Author(s):  
David R. Jackett ◽  
Trevor J. McDougall ◽  
Rainer Feistel ◽  
Daniel G. Wright ◽  
Stephen M. Griffies
Keyword(s):  
Thermal Expansion ◽  
Equation Of State ◽  
Thermodynamic Potential ◽  
Potential Temperature ◽  
Inverse Function ◽  
Freezing Temperature ◽  
Ocean Models ◽  
The Difference ◽  
New Equation ◽  
Density Equation

Abstract Algorithms are presented for density, potential temperature, conservative temperature, and the freezing temperature of seawater. The algorithms for potential temperature and density (in terms of potential temperature) are updates to routines recently published by McDougall et al., while the algorithms involving conservative temperature and the freezing temperatures of seawater are new. The McDougall et al. algorithms were based on the thermodynamic potential of Feistel and Hagen; the algorithms in this study are all based on the “new extended Gibbs thermodynamic potential of seawater” of Feistel. The algorithm for the computation of density in terms of salinity, pressure, and conservative temperature produces errors in density and in the corresponding thermal expansion coefficient of the same order as errors for the density equation using potential temperature, both being twice as accurate as the International Equation of State when compared with Feistel’s new equation of state. An inverse function relating potential temperature to conservative temperature is also provided. The difference between practical salinity and absolute salinity is discussed, and it is shown that the present practice of essentially ignoring the difference between these two different salinities is unlikely to cause significant errors in ocean models.

Pressureless Co-Sintering of Al2O/ZrO2 Multilayers and Bilayers

1996 ◽  
Vol 434 ◽  
Author(s):  
Peter Z. Cai ◽  
David J. Green ◽  
Gary L. Messing
Keyword(s):  
Thermal Expansion ◽  
Cyclic Loading ◽  
Microscopic Observation ◽  
Surface Defects ◽  
Tape Casting ◽  
Thermal Expansion Mismatch ◽  
Heating Rates ◽  
The Difference ◽  
Extent Of Damage ◽  
Transverse Damage

AbstractVarious types of damage were observed in pressureless-sintered Al2O3/ZrO2 symmetric laminates (multilayers) and asymmetric laminates (bilayers) fabricated by tape casting and lamination. These defects included channel defects in ZrO2-containing layers, Al2O3 surface defects parallel to the layers, decohesion between the layers, and transverse damage within the Al2O3 layer in the bilayers. Detailed microscopic observation attributed the defects to a combined effect of mismatch in both sintering rate and thermal expansion coefficient between the layers. Crack-like defects were formed in the early stages of densification, and these defects acted as pre-existing flaws for thermal expansion mismatch cracks. Curling of the bilayers during sintering was monitored and the measured rate of curvature change, along with the layer viscosities obtained by cyclic loading dilatometry, was used to estimate the sintering mismatch stresses. The extent of damage could be reduced or even eliminated by decreasing the difference in layer sintering rate. This was accomplished by reducing the heating rates or by adding Al2O3 in the ZrO2 layers.

Synthesis, structure and thermal expansion of the phosphates M0.5+x M′x Zr2−x (PO4)3 (M, M′–metals in oxidation state +2)

2017 ◽  
Vol 89 (4) ◽  
pp. 523-533 ◽  
Author(s):  
Elena Asabina ◽  
Vladimir Pet’kov ◽  
Pavel Mayorov ◽  
Dmitriy Lavrenov ◽  
Igor Schelokov ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Thermal Treatment ◽  
Ir Spectroscopy ◽  
Microprobe Analysis ◽  
Electron Microprobe Analysis ◽  
Sol Gel ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structural Types ◽  
The Difference

AbstractThe phosphates M0.5+x M′x Zr2−x (PO4)3 (M–Ca, Mn, Co, Sr, Cd, Ba, Pb; M′–Mg, Mn, Co) were synthesized by sol-gel method with the following thermal treatment of reaction mixtures. X-ray diffraction, IR spectroscopy and electron microprobe analysis showed that the obtained phosphates crystallized in Sc2(WO4)3 (SW) and NaZr2(PO4)3 (NZP) structural types. Both types of crystal structures are based on a framework comprised of octahedra and tetrahedra, the difference between them is fragments orientation. Thermal expansion of the phosphates was studied in the temperature range 20–800°C. Some compounds were found to belong to low-expanding materials (αav ~2·10−6°C−1).

Bilayer graded Al/B4C/rice husk ash composite: Wettability behavior, thermo-mechanical, and electrical properties

2018 ◽  
Vol 52 (27) ◽  
pp. 3745-3758 ◽  
Author(s):  
Amin Bahrami ◽  
Niloofar Soltani ◽  
Martin I Pech-Canul ◽  
Shaghayegh Soltani ◽  
Luis A González ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Thermal Expansion ◽  
Aluminum Alloys ◽  
Rice Husk ◽  
Rice Husk Ash ◽  
Material Selection ◽  
Coefficient Of Thermal Expansion ◽  
Thermal Expansion Coefficients ◽  
One Step ◽  
The Difference

In this study, wettability behavior of B4C substrate as well as B4C/crystalline rice husk ash and B4C/amorphous rice husk ash substrates with two aluminum alloys were studied. The electrical resistivity, thermal expansion coefficients, and thermal diffusivity of bilayer Al/B4C/rice husk ash composite fabricated by one-step pressureless infiltration were measured and the obtained data were systemically analyzed using the Taguchi method and analysis of variance. Boron carbide substrates after addition of amorphous or crystalline rice husk ash display good wettability with molten aluminum alloys. The results show that, electrical resistivity of Al/B4C/rice husk ash composites is mainly influenced by initial preform porosity, while the coefficient of thermal expansion of composites is determined by the chemical composition of infiltrated alloys. The measured values for coefficient of thermal expansion (10.5 × 10−6/℃) and electrical resistivity (0.60 × 10−5 Ω.m) of Al/B4C/rice husk ash composites, fabricated according to analysis of variance's optimal conditions are in good agreement with those of the projected values (11.02 × 10−6/℃ and 0.65 × 10−5 Ω.m, respectively). The difference between the corresponding values obtained from verification tests and projected values, for electrical resistivity and coefficient of thermal expansion are less than 5%. Finally, as a material selection approach, the strengths and weaknesses of the composites have been graphed in the form of radar diagrams.

Effect of Annealing Temperature and External Tensile Stress on Negative Thermal Expansion to Cold Rolled Ti–23Nb–0.7Ta–2Zr Alloy

2020 ◽  
Vol 12 (9) ◽  
pp. 1409-1412
Author(s):  
Jeong-Tae Moon ◽  
Tae-Hyun Nam
Keyword(s):  
Thermal Expansion ◽  
Annealing Temperature ◽  
Negative Thermal Expansion ◽  
Constant Load ◽  
External Stress ◽  
Expansion Rate ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cold Rolled ◽  
The Difference

The effect of annealing temperature and external stress on the thermal expansion of a Ti–23Nb–0.7Ta–2Zr alloy were investigated by means of thermal expansion tests under constant load and X-ray diffraction (XRD). Negative thermal expansion (NTE), which is a shrinkage during heating, was observed in both a cold rolled and annealed specimens. The intensity of (200)β peak decreased while that of (211)β peak increased as the annealing temperature increased. The difference in expansion rate between 50 °C and 250 °C is found to decrease with an increasing annealing temperature from 600 °C to 800 °C, above which it kept almost constant. The expansion rate decreased as the applied stress increased.

scholarly journals High-temperature axial stress evolution mechanism of polyacrylonitrile-based carbon fiber

2020 ◽  
Vol 15 ◽  
pp. 155892502094885
Author(s):  
Yu Wang ◽  
Lian-Wei Ye ◽  
Ru-yu Ruan ◽  
Ai-Jun Gao ◽  
Yuan-Jian Tong
Keyword(s):  
Thermal Expansion ◽  
High Temperature ◽  
Carbon Fiber ◽  
Graphite Furnace ◽  
Axial Stress ◽  
Temperature Treatment ◽  
High Temperature Treatment ◽  
Stress Evolution ◽  
Carbon Structure ◽  
The Difference

Temperature and stretching are important factors in the high-temperature treatment of carbon fiber. The axial stress during carbon-fiber high-temperature treatment affects its ability to stretch. The high-temperature axial stress evolution mechanism of polyacrylonitrile-based carbon fiber was studied through in situ tension tests, Raman spectroscopy, X-ray diffractometry, elemental analysis, X-ray photoelectron spectroscopy, high-resolution transmission electron microscopy, thermal expansion coefficient tests, and density methods. The high-temperature axial stress evolution of polyacrylonitrile-based carbon fiber involved three stages: rapid increase, rapid decrease, and relaxation. The highest stress and relaxation temperatures of the polyacrylonitrile-based carbon fiber were 1600°C and 1950°C, respectively. The main factors that affected the fiber axial stress included carbon-structure rearrangement and the effect of thermal expansion and cold shrinkage on fiber length. During the first stage ( T < 1600°C), carbon-structure rearrangement after nitrogen atom removal increased the fiber axial stress. In the second stage (1600 ⩽  T ⩽ 1950°C), the difference in the thermal expansion of fibers that entered the graphite furnace and the cold shrinkage of fibers that exited the graphite furnace increased gradually, which resulted in a decrease in fiber axial stress by up to 1950°C, where the fiber relaxed and the third stage ( T > 1950°C) began. The difference between expansion and shrinkage increased significantly, which increased fiber relaxation. Carbon fibers with fewer nitrogen atoms and more regular structures had a lower axial stress during high-temperature treatment, but the trend and characteristic temperature remained unchanged. The corresponding fiber high-temperature maximum stretching ratio and axial stress showed opposite trends below 1950°C. The ability to stretch the carbon fiber increased above 1950°C, which differed from the axial stress relaxation.

On Thermal Expansion Induced Stresses in U-Bends of Shell-and-Tube Heat Exchangers

1979 ◽  
Vol 101 (4) ◽  
pp. 634-639 ◽  
Author(s):  
Krishna P. Singh ◽  
Maurice Holtz
Keyword(s):  
Thermal Expansion ◽  
Heat Exchangers ◽  
Structural Characteristics ◽  
Design Tool ◽  
Design Variables ◽  
Depth Study ◽  
Shell And Tube ◽  
Induced Stresses ◽  
Critical Regions ◽  
Effective Design

An analytical method is herein developed to evaluate the stress field in the critical regions of a U-tube subject to differential thermal expansion. The solution is intended to be used as a design tool to conveniently study the variation of geometric parameters on the U-tube stress distribution. Those design variables which have significant effects on the structural characteristics of the U-tube are identified by an in-depth study of a typical example problem. Some effective design remedies are also discussed.

Thermo-Viscoelastic Analysis for Warpage in CSP With Different Viscoelastic Properties for Several Layers

2007 ◽  
Author(s):  
Hideo Koguchi ◽  
Atsushi Ueno
Keyword(s):  
Thermal Expansion ◽  
Theoretical Analysis ◽  
Manufacturing Process ◽  
Viscoelastic Properties ◽  
Layered Material ◽  
Viscoelastic Analysis ◽  
Chip Size ◽  
The Difference ◽  
On Chip ◽  
Layered Body

In this study, a simple theory for estimating the warpage of chip size packaging (CSP) during a manufacturing process is presented. A single-sided CSP which is composed of IC, a resin and a substrate is modeled for an analysis as a three-layered material. Especially, the resin and the substrate have different thermo-viscoelastic properties. When the layered body is perfectly bonded, its warpage is caused by the difference of the thermal expansion coefficient in each layer when temperature varies. The warpage of CSP for a various thicknesses of the IC and the substrate is investigated. Finally, the warpage calculated using the theory is compared with the result in experiment, and both results are well agreed with each other. Then, it is shown that the simple theoretical analysis is valid. After that, this program is extended to be able to analyze the warpage in a CoC (Chip on Chip), and the result of the analysis is then presented.

A Chemical Bonding Approach to Ionic Conduction and Thermal Expansion in Oxide Ion Conductors

2010 ◽  
Vol 72 ◽  
pp. 343-347 ◽  
Author(s):  
Sachi Taniguchi ◽  
Masaru Aniya
Keyword(s):  
Thermal Expansion ◽  
Ionic Conductivity ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Ionic Conduction ◽  
Point Of View ◽  
Semiempirical Methods ◽  
Oxygen Ionic Conductivity ◽  
The Difference ◽  
The Individual

In complex perovskite-type oxides which have been studied as cathode materials, the thermal expansion coefficient increases with the increase in the oxygen ionic conductivity. In the present study, with the aim to explain such a behavior, a research has been carried out from a chemical bond point of view. For oxides A1-xA′xB1-yB′yO with perovskite structure, the ionicity of the individual bond, A-O and B-O, and the thermal expansion coefficient of mixed compounds were estimated by using semiempirical methods. It has been shown that the thermal expansion coefficient and the oxygen ionic conductivity decrease with the increase in the difference of the ionicity between A-O and B-O bonds. It is also found that the tolerance factor and the specific free volume are linearly correlated with the difference of ionicity.

2010 Edition of B31.3 Process Piping Code: A First Equation for Stress Due to Sustained Loads

2010 ◽  
Author(s):  
Don R. Edwards
Keyword(s):  
Operating Temperature ◽  
Allowable Stress ◽  
Stress Range ◽  
Explicit Equation ◽  
Process Piping ◽  
Sustained Loads ◽  
History Of ◽  
First Time

For the first time in the history of the ASA [1], ANSI/ASME, ASME/ANSI, to the 2008 edition of ASME B31.3 Process Piping Code (hereafter referred to as “the Code”) [2], an equation for the Stress Due To Sustained Loads, SL, has been introduced into the Code. From its inception to the current edition, the Code has remained ambiguous in several areas. Even though the displacement stress range, SE, has been explicitly defined by both text and equation, the stress due to sustained loads, SL, is mentioned not with an explicit equation but with a statement that SL shall be limited by the allowable stress at the corresponding operating temperature, Sh. This paper describes the equation in detail and the background, the events, and the effort involved that led to the insertion of this equation into the Code.

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