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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Saddle supports, for heat exchangers, Safety factors, Safety, of heat exchangers: Salicyl aldehyde: Salts, heat transfer, as heat transfer media, Sand roughness, equivalent, Santotherm, heat transfer media, Sastri and Rao correlation for surface tension, Saturated boiling: Saturated density: Saturated fluids, tables of physical properties, Saturation pressure, Saturation temperature, Saunders, E A D Sauer, H J Jr, Scale formation in heat exchangers, Scaling approximations, in nonisothermal gas radiation, Scattering bed models, for radiative heat transfer from surfaces, Scattering, interaction phenomena with, Scattering coefficient, Schack wide-band model, for gas radiation properties, Schick and Prausnitz method, for critical volume of mixtures, Schlunder, E U Schmidt, F W Schmidt correlation, for heat transfer in in-line banks of high fin tubes, Schmidt number, Schneider, G E, Schrock and Grossman correlations, for forced convective heat transfer in two-phase flow, Schunk, M Schwier, K, Scraped surfaces: Scaling devices, in shell-and-tube heat exchangers, Seawater physical properties, Seider-Tate equation, for heat transfer in heat exchangers, Selection of heat transfer equipment: Semiconductors, thermal conductivity, Separated flow model: Separation, exergy analysis for, Separators, for use in association with evaporators, Series solutions, for one-dimensional transient conduction, Serrated fins, in plate fin heat exchangers, Shah correlation for boiling, Shah correlation, for boiling in horizontal tubes, Shape factor, in radiative heat transfer between diffuse surfaces, Shear flow, of non-Newtonian fluids, Shear free flow, of non-Newtonian fluids, Shear rate, in fluid, Shear stress: Sheffield, J W, Shelf dryer, Shell-and-tube heat exchanger: Shell-to-baffle clearance, in shell-and-tube heat exchangers, Shells, for shell-and-tube heat exchangers: Sherwood number Shipes, K V, Short-tube vertical evaporator, Sigma phase embrittlement, of stainless steels, Silicate scales, in heat exchangers, Silicone oils, as heat transfer media, physical properties of, Silver method, for calculation of multicomponent condensation, Similarity theory, Simonis, V, Single-phase fluid flow: Single stage flash evaporation (SSF): Singularities, two-phase gas-liquid pressure drop across, Sink, in radiation: Skid-mounted units, specification of, Skin friction coefficient, Skrinska, A, Slab: Sleeves, internal, for expansion bellows, Slot: Slug flow: Slugging, in fluidized beds, Smith, A A, Smith, R, Smith, R A Smith, O, Snell's law, in radiation, Software, for code design, Solar absorber, Solar reflector, Soldered fins, in double pipe exchangers, Solid fuels, properties of, Solids circulation, in fluidized beds, Solid-gas flow: Solid-liquid flow: Solidification: Solids: Solids circulation, in fluidized beds, Soot blowing, Sound velocity: Source, in radiation: Spacers, in shell-and-tube heat exchangers, Spalding, D B, Sparging: Specific enthalpy, Specific entropy: Specific heat capacity, Specific internal energy, Specific volume: Specification of heat exchangers, Spectral absorptivity: Spectral emissivity, in gases, Specular surface, Specular-walled passages, radiative heat transfer in, Spheres: Spherical coordinates, for finite difference equations for conduction, Spherical shells: Spheroids (oblate and prolate), free convective heat transfer from, Spine fins: Spiral heat exchanger: Spirally fluted tubes: Sponge rubber balls, in fouling mitigation, Spray dryers, Sprays, in heat exchangers, Square ducts: Stable equilibrium, of vapor and liquid, Staggered tube banks: Stainless steels, Stanton number Startup: State diagram, for fluidized beds, Static mixers, in heat exchangers, Statically stable foams, Steam, dropwise condensation of, Steam tables, Steam turbine exhaust condensers, Steels, as material of construction, Stefan-Boltzmann constant, Stefan's law, for blackbody radiation, Stegmaier, W, Steiner and Taborek correlation, for forced convective boiling, Stephan and Korner correlation, for boiling of binary mixtures, Stiffeners, PD5500 code guidelines for, Stiffeners, against external pressure, EN13445 guidance on, Stirred beds, heat transfer to, Stirred reactor model, for furnaces, Stone's strongly implicit method, Straight fins (longitudinal fins): Stratified gas-liquid flow: Stratified liquid-liquid-gas flow: Steam analysis methods, for shell-side heat transfer and pressure drop in shell-and-tube heat exchangers, Stress, compressive, in heat exchanger tubes, Stress corrosion cracking, of stainless steels, Stress equation models, for turbulent boundary layers, Stress-strain curve, for solids, Stress tensor: Stresses: Strip baffles, in tube bundles with longitudinal flow, Strouhal number, Subchannel analysis, for critical heat flux in rod bundles, Subcooled boiling: Subcooling: Sublayer, viscous, Submerged combustion, Successive over-under relaxation method for solution of implicit equations, Suction: Suction line exchangers in refrigeration, Sulfur: Sulfur compounds (organic): Sulfur dioxide: Sulfur hexafluoride: Sulfur trioxide: Supercritical fluids: Superficial velocity, in multiphase flow, Superheated gases: Superheated liquid, in metastable state, Superheated vapor, condensation of, on vertical surface, Supersaturation, as cause of fogging in condensers: Suppression of nucleate boiling, Surface catalysis, in augmentation of heat transfer, Surface condensers, Surface finish: Surface, hydraulically smooth, Surface material, effect on fouling, Surface models, in radiative heat transfer, Surface modification for drag reduction, Surface temperature, effect on fouling, Surface tension: Surfactants, in drag reduction, Suspension, radiation interaction phenomena in, Sutherland formula, for viscosity variation with temperature, Sutterby fluid (non-Newtonian), free convective heat transfer to, Swirling flow, in augmentation of heat transfer, Synthetic heat transfer media, Synthetic mixture heat transfer media,

Index

HEDH
A B C D E F G H I J K L M N O P Q R S
Saddle supports, for heat exchangers, Safety factors, Safety, of heat exchangers: Salicyl aldehyde: Salts, heat transfer, as heat transfer media, Sand roughness, equivalent, Santotherm, heat transfer media, Sastri and Rao correlation for surface tension, Saturated boiling: Saturated density: Saturated fluids, tables of physical properties, Saturation pressure, Saturation temperature, Saunders, E A D Sauer, H J Jr, Scale formation in heat exchangers, Scaling approximations, in nonisothermal gas radiation, Scattering bed models, for radiative heat transfer from surfaces, Scattering, interaction phenomena with, Scattering coefficient, Schack wide-band model, for gas radiation properties, Schick and Prausnitz method, for critical volume of mixtures, Schlunder, E U Schmidt, F W Schmidt correlation, for heat transfer in in-line banks of high fin tubes, Schmidt number, Schneider, G E, Schrock and Grossman correlations, for forced convective heat transfer in two-phase flow, Schunk, M Schwier, K, Scraped surfaces: Scaling devices, in shell-and-tube heat exchangers, Seawater physical properties, Seider-Tate equation, for heat transfer in heat exchangers, Selection of heat transfer equipment: Semiconductors, thermal conductivity, Separated flow model: Separation, exergy analysis for, Separators, for use in association with evaporators, Series solutions, for one-dimensional transient conduction, Serrated fins, in plate fin heat exchangers, Shah correlation for boiling, Shah correlation, for boiling in horizontal tubes, Shape factor, in radiative heat transfer between diffuse surfaces, Shear flow, of non-Newtonian fluids, Shear free flow, of non-Newtonian fluids, Shear rate, in fluid, Shear stress: Sheffield, J W, Shelf dryer, Shell-and-tube heat exchanger: Shell-to-baffle clearance, in shell-and-tube heat exchangers, Shells, for shell-and-tube heat exchangers: Sherwood number Shipes, K V, Short-tube vertical evaporator, Sigma phase embrittlement, of stainless steels, Silicate scales, in heat exchangers, Silicone oils, as heat transfer media, physical properties of, Silver method, for calculation of multicomponent condensation, Similarity theory, Simonis, V, Single-phase fluid flow: Single stage flash evaporation (SSF): Singularities, two-phase gas-liquid pressure drop across, Sink, in radiation: Skid-mounted units, specification of, Skin friction coefficient, Skrinska, A, Slab: Sleeves, internal, for expansion bellows, Slot: Slug flow: Slugging, in fluidized beds, Smith, A A, Smith, R, Smith, R A Smith, O, Snell's law, in radiation, Software, for code design, Solar absorber, Solar reflector, Soldered fins, in double pipe exchangers, Solid fuels, properties of, Solids circulation, in fluidized beds, Solid-gas flow: Solid-liquid flow: Solidification: Solids: Solids circulation, in fluidized beds, Soot blowing, Sound velocity: Source, in radiation: Spacers, in shell-and-tube heat exchangers, Spalding, D B, Sparging: Specific enthalpy, Specific entropy: Specific heat capacity, Specific internal energy, Specific volume: Specification of heat exchangers, Spectral absorptivity: Spectral emissivity, in gases, Specular surface, Specular-walled passages, radiative heat transfer in, Spheres: Spherical coordinates, for finite difference equations for conduction, Spherical shells: Spheroids (oblate and prolate), free convective heat transfer from, Spine fins: Spiral heat exchanger: Spirally fluted tubes: Sponge rubber balls, in fouling mitigation, Spray dryers, Sprays, in heat exchangers, Square ducts: Stable equilibrium, of vapor and liquid, Staggered tube banks: Stainless steels, Stanton number Startup: State diagram, for fluidized beds, Static mixers, in heat exchangers, Statically stable foams, Steam, dropwise condensation of, Steam tables, Steam turbine exhaust condensers, Steels, as material of construction, Stefan-Boltzmann constant, Stefan's law, for blackbody radiation, Stegmaier, W, Steiner and Taborek correlation, for forced convective boiling, Stephan and Korner correlation, for boiling of binary mixtures, Stiffeners, PD5500 code guidelines for, Stiffeners, against external pressure, EN13445 guidance on, Stirred beds, heat transfer to, Stirred reactor model, for furnaces, Stone's strongly implicit method, Straight fins (longitudinal fins): Stratified gas-liquid flow: Stratified liquid-liquid-gas flow: Steam analysis methods, for shell-side heat transfer and pressure drop in shell-and-tube heat exchangers, Stress, compressive, in heat exchanger tubes, Stress corrosion cracking, of stainless steels, Stress equation models, for turbulent boundary layers, Stress-strain curve, for solids, Stress tensor: Stresses: Strip baffles, in tube bundles with longitudinal flow, Strouhal number, Subchannel analysis, for critical heat flux in rod bundles, Subcooled boiling: Subcooling: Sublayer, viscous, Submerged combustion, Successive over-under relaxation method for solution of implicit equations, Suction: Suction line exchangers in refrigeration, Sulfur: Sulfur compounds (organic): Sulfur dioxide: Sulfur hexafluoride: Sulfur trioxide: Supercritical fluids: Superficial velocity, in multiphase flow, Superheated gases: Superheated liquid, in metastable state, Superheated vapor, condensation of, on vertical surface, Supersaturation, as cause of fogging in condensers: Suppression of nucleate boiling, Surface catalysis, in augmentation of heat transfer, Surface condensers, Surface finish: Surface, hydraulically smooth, Surface material, effect on fouling, Surface models, in radiative heat transfer, Surface modification for drag reduction, Surface temperature, effect on fouling, Surface tension: Surfactants, in drag reduction, Suspension, radiation interaction phenomena in, Sutherland formula, for viscosity variation with temperature, Sutterby fluid (non-Newtonian), free convective heat transfer to, Swirling flow, in augmentation of heat transfer, Synthetic heat transfer media, Synthetic mixture heat transfer media,
T U V W X Y Z

Elastic Properties

DOI 10.1615/hedhme.a.000522

5.4 PROPERTIES OF SOLIDS
5.4.5 Elastic properties

A. Introduction

Solids deform when subjected to stresses. The strain is defined as the degree of distortion per unit length, e.g., the change in length per unit length of a wire when subjected to a tensile stress. The stress is defined as the applied force per unit area. A material is said to show perfectly elastic behavior when the stress-strain relationship is perfectly reversible. Furthermore if the strain is proportional to the applied stress then the behavior is known as linear elastic. Most engineering materials show approximately linear clastic behavior up to the onset of plastic deformation. Such behavior was originally described by Hooke and is therefore sometimes known as Hookean.

An important part of mechanical engineering design involves the computation of the distribution of strains in a structure when subject to the stresses imposed in service. Stresses may be imposed by fluid pressure or by fluid motion and also by nonuniform thermal expansion during changes in temperature. Elastic properties are traditionally regarded as being non-structure sensitive but there is one important aspect in which this is not true. The individual grains or crystals of metals are elastically anisotropic. Thus the elastic constants are a function of the orientation of the grain with respect to the orientation of the imposed stresses. The process of manufacture of components tends to introduce a certain degree of preferred orientation of the individual grains composing the structure and thus to introduce elastic anisotropy. It is probable that the existence of various degrees of preferred orientation in test specimens has led to the rather wide scatter in data for the clastic properties of metals and alloys. Because this scatter can introduce errors of as much as 20% in some cases in computing strains, the subject is dealt with in depth in this section. Table 531.3 should be regarded only as an example of the type of information in the literature. There is no reason to suppose, for example, that steels with 5-9% chromium should differ significantly in Young’s modulus from those containing slightly smaller or larger amounts of chromium as shown in that table.

Design codes require that stresses are less than the yield stress in a range in which structural materials are assumed to show linear elastic behavior. The behavior of real materials, however, is only approximately elastic so that on loading and unloading below the yield stress a narrow hysteresis loop is generated. For this reason materials have a nonzero damping capacity. The extent of the departure from elastic behavior becomes greater as the stress increases. Increases in the duration of loading and rise in temperature usually cause increased departure from elastic behavior. For many design purposes, perfect linear elastic behavior is assumed. The finer points of stress-strain behavior are included in this section since they could become very important. For example, the damping capacity of a heat exchanger tube might increase by an order of magnitude when the tube is pressurized. Similarly the elastic constants and damping capacity show significant changes when the temperature is increased in service, causing discrepancies between the behavior during testing cold and unpressurized and in service.

The present section therefore not only describes and defines the various ideal linear elastic moduli that are used in elementary engineering design but also indicates the major sources of error that can arise when the elastic behavior of real materials is not understood. The application of elastic properties in design and analytical procedures is discussed in Part 4 and includes calculation of stress-strain distributions in complex structures, linear elastic fracture mechanics, and vibration studies.

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