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Boltzmann superposition principle
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Book Chapter
Deformation and Viscoelasticity of Polymers
Available to PurchaseSeries: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003024
EISBN: 978-1-62708-200-6
... employed for analytical prediction of deformation characteristics of polymers. Boltzmann superposition principle creep experiments deformation characteristics dynamic mechanical experiments plastics polymers prediction of deformation time-temperature superposition viscoelastic characteristics...
Abstract
This article discusses the deformation and viscoelastic characteristics of plastics as polymeric materials, focusing on the test methods used for the evaluation of their mechanical properties, methods available for analytically predicting the deformation response of polymers, and the effect of viscoelasticity on the test methods used. Two common ways of evaluating viscoelasticity of plastics are by means of creep experiments and dynamic mechanical experiments. Graphic or tabular analysis of test data, time-temperature superposition, and empirical correlation methods are commonly employed for analytical prediction of deformation characteristics of polymers.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006941
EISBN: 978-1-62708-395-9
... often cannot be considered to behave, even at room temperature, as purely elastic materials. Several superposition principles can be used to extrapolate short-term test data to a longer period of material property behavior. These include the Boltzmann superposition principle, the time-temperature...
Abstract
This article describes the viscoelastic behavior of plastics in their solid state only, from the standpoint of the material deforming without fracturing. The consequences of viscoelasticity on the mechanical properties of plastics are described, especially in terms of time-dependencies, as well as the dependence of the viscoelastic character of a plastic on chemical, physical, and compositional variables. By examining the viscoelastic behavior of plastics, the information obtained are then applied in situations in which it may be important to anticipate the long-term properties of a material. This includes assessing the extent of stress decay in materials that are pre-stressed, the noise and vibration transmission characteristics of a material, the amount of heat build-up in a material subjected to cyclic deformation, and the extent a material can recover from any prior deformation. Several qualitative graphs are presented, which highlights the possible differences in the viscoelastic behavior that can exist among plastics.
Book Chapter
Accelerated Life Testing and Aging
Available to PurchaseSeries: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006909
EISBN: 978-1-62708-395-9
... activated process strongly dependent on temperature, diffusivity ( D ) can, in principle, be expressed as a function of absolute temperature, T , according to the Arrhenius expression: (Eq 6) D ( T ) = D 0 e − ( E a / kT ) In this expression, k is the Boltzmann’s...
Abstract
Accelerated life testing and aging methodologies are increasingly being used to generate engineering data for determining material property degradation and service life (or fitness for purpose) of plastic materials for hostile service conditions. This article presents an overview of accelerated life testing and aging of unreinforced and fiber-reinforced plastic materials for assessing long-term material properties and life expectancy in hostile service environments. It considers various environmental factors, such as temperature, humidity, pressure, weathering, liquid chemicals (i.e., alkalis and acids), ionizing radiation, and biological degradation, along with the combined effects of mechanical stress, temperature, and moisture (including environmental stress corrosion). The article also includes information on the use of accelerated testing for predicting material property degradation and long-term performance.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006929
EISBN: 978-1-62708-395-9
... temperatures. Source: Ref 14 There are precautions for using time-temperature superposition for the prediction of long-term behavior. The time-temperature superposition is valid only if linear viscoelastic equations are applicable, which is referred to as the Boltzmann linearity. The application limits...
Abstract
This article provides an overview of the physics and math associated with moisture-related failures in plastic components. It develops key equations, showing how they are used to analyze the causes and effects of water uptake, diffusion, and moisture concentration in polymeric materials and resins. It explains how absorbed moisture affects a wide range of properties, including glass transition temperature, flexural and shear modulus,creep, stress relaxation, swelling, tensile and yield strength, and fatigue cracking. It provides relevant data on common polymers, resins, and fiber-resin composites.
Book Chapter
Electron Spin Resonance
Available to PurchaseSeries: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001750
EISBN: 978-1-62708-178-8
...) n 1 n 2 = e − h ν / k T where h is Planck's constant, ν is frequency, k is the Boltzmann constant, and T is temperature. Therefore, use of a high applied frequency improves the sensitivity of this technique. In practice, the frequencies in the well-developed radar...
Abstract
Electron spin resonance (ESR), or electron paramagnetic resonance (EPR), is an analytical technique that can extract a great deal of information from any material containing unpaired electrons. This article explains how ESR works and where it applies in materials characterization. It describes a typical ESR spectrometer and explains how to tune it to optimize critical electromagnetic interactions in the test sample. It also identifies compounds and elements most suited for ESR analysis and explains how to extract supplementary information from test samples based on the time it takes electrons to return to equilibrium from their resonant state. Two of the most common methods for measuring this relaxation time are presented as are several application examples.
Book Chapter
In-Process Thermography of Metal Additive Manufacturing Processes
Available to PurchaseSeries: ASM Handbook
Volume: 24A
Publisher: ASM International
Published: 30 June 2023
DOI: 10.31399/asm.hb.v24A.a0006954
EISBN: 978-1-62708-439-0
... convenient to use c 1 L = 1.191,042,972 × 10 8 W · μm 4 · m −2 · sr −1 and c 2 = 1.438,776,877 × 10 4 μm · K ( Ref 34 ). These constants are based on c 1 L = 2 hc 2 and c 2 = hc / k B , where h is the Planck’s constant, c is the speed of light, and k B is the Boltzmann constant...
Abstract
This article provides readers with a brief review of the applications of thermography in additive manufacturing (AM), which still is largely a research and development (R&D) effort. There is a particular focus on metals-based laser powder-bed fusion (L-PBF), although applications in directed-energy deposition (DED) and electron beam PBF (E-PBF) also are mentioned. The metrological basis of thermography is discussed in the article. Background information on radiation thermometry is provided, including how the various equations are applied. Finally, specific examples and lessons learned from various AM thermographic studies at the National Institute of Standards and Technology (NIST) are provided.
Book Chapter
Internal-State Variable Modeling of Plastic Flow
Available to PurchaseSeries: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005413
EISBN: 978-1-62708-196-2
... temperature changes). As a consequence, the activation enthalpy, Q = kTm / m *, is constant as well during a stress-strain test, where k is the Boltzmann factor. The usual interpretation of these interdependencies is that the thermal and the athermal parts of the flow stress stay in a fixed relation...
Abstract
This article focuses on the analyzing and modeling of stress-strain behavior of polycrystals of pure face-centered cubic (fcc) metals in the range of temperatures and strain rates where diffusion is not important. It presents a phenomenological description of stress-strain behavior and provides information on the physical background, alternative interpretations, and directions of research. The quantitative description of strain hardening of fcc polycrystals is provided. The article also discusses the modeling of stress-strain behavior in body-centered cubic metals, hexagonal metals, stage IV work hardening, and the various classes of single-phase alloys.
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.a0001333
EISBN: 978-1-62708-173-3
... where ∈ is emissivity, σ is the Stefan-Boltzmann constant, θ w is the surface temperature, θ ∞ , is the environmental temperature, and B is the characteristic surface dimension. Natural convection is dominant at a temperature below 550 °C (1020 °F), whereas radiation becomes more important...
Abstract
During fusion welding, the thermal cycles produced by the moving heat source cause physical state changes, metallurgical phase transformation, and transient thermal stress and metal movement. This article presents an analysis of heat flow in the fusion welding process. The primary objective of welding heat flow modeling is to provide a mathematical tool for thermal data analysis, design iterations, or the systematic investigation of the thermal characteristics of any welding parameters. The article addresses analytical heat-flow solutions and their practical applications. It describes the effects of material property and welding condition on the temperature distribution of weldments. The thermal properties of selected engineering materials are provided in a table.
Book Chapter
Neutron Diffraction
Available to PurchaseSeries: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006667
EISBN: 978-1-62708-213-6
... energy ( E , in meV) and a temperature ( T , in Kelvin), associated with the corresponding Maxwell-Boltzmann distribution (because moderated neutron beams can be approximated as ideal gases) . Such characteristics can be inferred from knowledge of the neutron velocity (υ, in m/s) obtained from...
Abstract
This article provides a brief introduction to neutron diffraction as well as its state-of-the-art capabilities. The discussion covers the general principles of the neutron, neutron-scattering theory, generation of neutrons, types of incident radiation, and purposes of single-crystal neutron diffraction, powder diffraction, and pair distribution function analysis. The relationship between detector space and reciprocal space are presented. Various factors involved in sample preparation, calibration, and techniques used for analyzing diffraction data are described. The article also presents application examples and possible future developments in neutron diffraction.
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005588
EISBN: 978-1-62708-174-0
... for an oxidized steel surface), σ is the Stefan-Boltzmann constant (5.6704 × 10 −14 J/s · mm 2 · K 4 , where K is the absolute temperature in °C), θ w is the surface temperature (°C), and θ ∞ is the environmental temperature (°C). The natural convection heat-loss coefficient in air is in the range...
Abstract
The finished product, after fusion welding, may contain physical discontinuities due to excessively rapid solidification, adverse microstructures due to inappropriate cooling, or residual stress and distortion due to the existence of incompatible plastic strains. To analyze these problems, this article presents an analysis of the welding heat flow, with focus on the fusion welding process. It discusses the analytical heat-flow solutions and their practical applications. The article concludes with a description of the effects of material property and welding condition on the temperature distribution of weldments.
Book Chapter
Electromagnetic Acoustic Transducers for Nondestructive Evaluation
Available to PurchaseSeries: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006458
EISBN: 978-1-62708-190-0
... in nonmagnetic and magnetic metals using inductive coupling and, specifically, without the use of a mechanical coupling medium between the transducer and the adjacent metal. The most common coupling mechanisms are the Lorentz force on induced currents (various first-principle methods of deriving Lorentz force...
Abstract
This article describes the basic features of electromagnetic acoustic transducers (EMATs) and discusses their existing and some potential uses within the field of ultrasonic nondestructive evaluation (UNDE). It provides sufficient basic and practical information to make an informed choice when considering the transducer to be used for any particular UNDE application. The article describes how different types of EMATs operate and presents their fundamental and some practical limitations. It summarizes the representative literature for electromagnetic acoustic transducer UNDE applications. Some successful uses of EMATs are mentioned to illustrate the depth, range, and potential of commercial EMAT applications. The article concludes with information on the commercial sources for EMAT systems and components.
Book Chapter
Modeling and Simulation of Cavitation during Hot Working
Available to PurchaseSeries: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005421
EISBN: 978-1-62708-196-2
... , individual cavity-growth rate parameter in complex stress state η i , cavity-growth rate along principal direction “ i ” k , Boltzmann constant K , strength coefficient k D, constant dependent on the geometry of the deformation L i , cavity length along principal direction “ i ” λ, cavity spacing...
Abstract
This article focuses on the modeling and simulation of cavitation phenomena. It summarizes the experimental observations of cavitation and reviews the modeling of cavity nucleation and growth. The article discusses the modeling of the cavity growth based on mesoscale and microscale under uniaxial versus multiaxial tensile-stress conditions. Mesoscale models incorporate the influence of local microstructure and texture on cavitation. The article outlines the descriptions of cavity coalescence and shrinkage. It also describes the simulation of the tension test to predict tensile ductility and to construct failure-mechanism maps.
Book
Series: ASM Handbook
Volume: 24A
Publisher: ASM International
Published: 30 June 2023
DOI: 10.31399/asm.hb.v24A.9781627084390
EISBN: 978-1-62708-439-0
Book
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.9781627081788
EISBN: 978-1-62708-178-8
Book
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.9781627082136
EISBN: 978-1-62708-213-6