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power law creep
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Image
Published: 01 January 2002
Fig. 9 Power-law dependence of creep crack growth with K in less ductile materials. Source: Ref 11
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Image
Published: 15 January 2021
Fig. 10 Power-law dependence of creep crack growth with K in less ductile materials. Source: Ref 19
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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005404
EISBN: 978-1-62708-196-2
... materials using expressions known as constitutive equations that relate the dependence of stress, temperature, and microstructure on deformation. The article reviews the characteristics of creep deformation and mechanisms of creep, such as power-law creep, low temperature creep, power-law breakdown...
Abstract
This article, to develop an understanding of the underlying mechanisms governing deformation at elevated temperatures, discusses the phenomenological effects resulting from temperature-induced thermodynamic and kinetic changes. It describes the deformation behavior of engineering materials using expressions known as constitutive equations that relate the dependence of stress, temperature, and microstructure on deformation. The article reviews the characteristics of creep deformation and mechanisms of creep, such as power-law creep, low temperature creep, power-law breakdown, diffusional creep, twinning during creep deformation, and deformation mechanism maps. It discusses the creep-strengthening mechanisms for most structural engineering components. The article provides a description of the microstructural modeling of creep in engineering alloys.
Image
Published: 01 November 2010
Fig. 4 Stress distributions in a rectangular beam for various exponents ( n ) of the power-law creep model obtained using the reference stress method
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Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003287
EISBN: 978-1-62708-176-4
... as that for lattice self-diffusion. This evidence supports the concept that power law creep is diffusion controlled. Diffusion is needed to enable dislocations to climb past obstacles to their continued glide. Thus, creep occurs by the sequential processes of dislocation glide and climb. As the climb step is slower...
Abstract
Creep deformation is normally studied by applying either a constant load or a constant true stress to a material at a sufficiently high homologous temperature so that a measurable amount of creep strain occurs in a reasonable time. This article provides the phenomenological descriptions of creep and explains the testing and mechanism of creep in crystalline solids. It also presents information on the creep response of crystalline and amorphous solids.
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006934
EISBN: 978-1-62708-395-9
... method, one of the most common to describe the material deformation and rupture time, is also discussed. Burgers power-law model creep failure Findley power-law model Larson-Miller parametric method material deformation polymers rupture time service life stress relaxation time-stress...
Abstract
This article describes the general aspects of creep, stress relaxation, and yielding for homogeneous polymers. It then presents creep failure mechanisms in polymers. The article discusses extrapolative methods for the prediction of long-term creep failure in polymer materials. Then, the widely used models to simulate the service life of polymers are highlighted. These include the Burgers power-law model, the Findley power-law model, the time-temperature superposition (or equivalence) principle (TTSP), and the time-stress superposition principle (TSSP). The Larson-Miller parametric method, one of the most common to describe the material deformation and rupture time, is also discussed.
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005506
EISBN: 978-1-62708-197-9
... = ∫ A σ y d A Finally, the third equation is the constitutive equation, which takes the form of a power-law creep model relating creep strain rate ( ε ˙ c ) to stress through: (Eq 4) ε ˙ c = B σ n where B and n are fitting parameters describing the creep...
Abstract
This article summarizes many approaches that are used to simulate relaxation of bulk residual stresses in components. It presents analytical examples to highlight the complexity of residual stress and strain distributions observed in simple geometries, with ideal material behavior and trivial loading and boundary conditions. The article discusses approximate and advanced solution techniques that can be employed in practice for simulation of residual stress relief: finite-difference method and finite-element method. It also describes advanced techniques applicable to transient creep, advanced constitutive models, and complicated stress and temperature loading histories.
Book Chapter
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003288
EISBN: 978-1-62708-176-4
... the activation energy for lattice self-diffusion and the activation energy for creep deformation. Power Law Model of Steady State Creep Rates In the intermediate temperature regime (0.4 T m < T < 0.6 T m ), the creep rate varies nonlinearly with stress, as either a power function...
Abstract
This article reviews the basic equipment and methods for creep and creep rupture testing. It begins with a discussion on the creep properties, including stress and temperature dependence, as well as of the extrapolation techniques that permit estimation of the long-term creep and rupture strengths of materials. The article describes the different types of equipment for determination of creep characteristics, including test stands, furnaces, and extensometers. It also discusses the different testing methods for creep rupture: constant-load testing and constant-stress testing. The article presents other testing considerations and concludes with information on stress relaxation testing.
Image
Published: 01 January 2000
Fig. 4 Creep data for several fcc metals plotted as a function of normalized shear stress (σ s / G ) compared with a power-law stress exponent of n = 4. Because the activation for creep ( Q in Eq 2 ) is the same as that for diffusion, the term exp (− Q / RT ) in Eq 2 is replaced here
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Book Chapter
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005606
EISBN: 978-1-62708-174-0
.../0025-5416(88)90249-2 • Wallach E.R. , Solid-State Diffusion Bonding of Metals , Trans. JWRI , Vol 17.1 , 1988 , p 135 – 148 • Wilkinson D.S. and Ashby M.F. , Pressure Sintering by Power Law Creep , Acta Metall. , Vol 23 , 1975 , p 1277 – 1285 10.1016/0001-6160...
Abstract
This article provides a qualitative summary of the theory of diffusion bonding, as distinguished from the mechanisms of other solid-state welding processes. Diffusion bonding can be achieved for materials with adherent surface oxides, but the resultant interface strengths of these materials are considerably less than that measured for the parent material. The article describes three stages of diffusion bonding: microasperity deformation, diffusion-controlled mass transport, and interface migration. It concludes with information on diffusion bonding with interface aids.
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.a0001350
EISBN: 978-1-62708-173-3
... Power-law creep Fig. 5 Schematic of numerous paths of material transfer generated during diffusion bonding process. (a) Surface source mechanisms. (b) Interface source mechanisms. (c) Bulk deformation mechanisms. See text for specific mechanisms indicated by numbers shown in schematic...
Abstract
Diffusion bonding is only one of many solid-state joining processes wherein joining is accomplished without the need for a liquid interface (brazing) or the creation of a cast product via melting and resolidification. This article offers a qualitative summary of the theory of diffusion bonding. It discusses factors that affect the relative difficulty of diffusion bonding oxide-bearing surfaces. These include surface roughness prior to welding, mechanical properties of the oxide, relative hardness of the metal and its oxide film, and prestraining or work hardening of the material. The article describes the mechanism of diffusion bonding in terms of microasperity deformation, diffusion-controlled mass transport, and interface migration. It concludes with a discussion on diffusion bonding with interface aids.
Image
Published: 01 January 2000
Fig. 5 Creep data for several bcc metals plotted as a function of normalized shear stress (σ s / G ) compared with a power-law stress exponent of n = 3. Source: Ref 5 with data largely from Ref 19
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Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003307
EISBN: 978-1-62708-176-4
... from the material power-law creep constants, A 2 and n , from Eq 3 . When under plane strain conditions, the equation for a compact-type (CT) specimen is given by: (Eq 5) C * = A 2 ( W − a ) n h 1 ( a W , n ) ( P 1.445 ζ B ) n + 1...
Abstract
Predicting the service life of structural components involves creep-fatigue crack growth (CFCG) testing under pure creep conditions. This article provides a discussion on the loading condition and the type of ductile and brittle material showing creep behavior. It focuses on a description of the experimental method that should be followed in conducting tests of CFCG with various hold times. The article describes the testing conditions, definitions, and the necessary calculations of various crack-tip parameters considered during static and cyclic loading in time-dependent fracture mechanics. The parameters considered for static loading are C*, C(t), C*(t), C*h, Ct, and Cst(t). For cyclic loading, the parameters are delta Jc and (Ct)avg. An overview of life-prediction models is also provided.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005293
EISBN: 978-1-62708-187-0
... 247, René 125) 1185 2165 175 25 4 Mechanisms of Pore Closure during HIP There are four main mechanisms by which pores are eliminated during HIP: Plastic flow Power law creep Coble (grain-boundary) creep Nabarro-Herring (lattice) creep Given appropriate temperature...
Abstract
Hot isostatic pressing (HIP) is used to eliminate porosity in castings. This article provides a history and an overview of the HIP system. It illustrates the reasons for using HIP and discusses the criteria for selecting HIP process parameters. The main mechanisms by which pores are eliminated during HIP are reviewed. The article describes the effect of HIP on the mechanical properties, shape, and structure of castings as well as the effect of inclusions on as-HIPed properties. It examines the problems encountered in HIP and their solution. The article concludes with information on the economics of HIP processing.
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002476
EISBN: 978-1-62708-194-8
Abstract
Brittle materials, such as ceramics, intermetallics, and graphites, are increasingly being used in the fabrication of lightweight components. This article focuses on the design methodologies and characterization of certain material properties. It describes the fundamental concepts and models associated with performing time-independent and time-dependent reliability analyses for brittle materials exhibiting scatter in ultimate strength. The article discusses the two-parameter and three-parameter Weibull distribution for representing the underlying probability density function for tensile strength. It reviews life prediction reliability models used for predicting the life of a component with complex geometry and loading. The article outlines reliability algorithms and presents several applications to illustrate the utilization of these reliability algorithms in structural applications.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004020
EISBN: 978-1-62708-185-6
... or (Eq 14) σ = A ′ ε ˙ m exp ( m Q / R T ) σ = A ′ Z m which is consistent with both the Zener-Hollomon development, Eq 11 , and the power-law expression, Eq 1 . Because sinh( x )→ e x /2 for x »1, at low temperatures and high...
Abstract
The constitutive relations for metalworking include elements of behavior at ambient temperature as well as high-temperature response. This article presents equations for strain hardening and strain-rate-sensitive flow, with alternate sections on empirically determined properties, followed by the models of constitutive behavior. It provides a discussion on creep mechanisms involving dislocation and diffusional flow, such as the Nabarro-Herring creep and the Coble creep. The equations for the several creep rates are also presented. Research on the mechanism of the superplastic flow in fine-grain metals has encompassed many ideas, such as the diffusional creep, dislocation creep with diffusional accommodation at grain boundaries, and concepts of grain-mantle deformation. The article concludes with information on the kinetics of superplastic deformation processes, including low stress behavior, concurrent grain growth, and high stress behavior.
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005183
EISBN: 978-1-62708-186-3
... the Zener-Hollomon development, Eq 11 , and the power-law expression, Eq 1 . Because sinh( x )→ e x /2 for x ≫1, at low temperatures and high stresses, Eq 13 reduces to: (Eq 15) ε ˙ = C exp ( α ′ σ − Q / R T ) but now strain hardening becomes important, so C...
Abstract
Constitutive relations for metal-working include elements of behavior at ambient temperature as well as high-temperature response. This article presents the equations for the strain hardening and strain-rate-sensitive flow, with alternate sections on empirically determined properties, followed by models of constitutive behavior. These models include the isothermal constitutive model and the physical model for superplastic flow. A formal description of the superposition of the operative mechanisms for dynamic recovery at hot-working strain rates is also provided. The article describes creep mechanisms that are useful for illustrating the strong stress dependence of dislocation and diffusional flow.
Book: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002389
EISBN: 978-1-62708-193-1
... C ∗ For times less than the calculated value of t T , stress redistribution in the crack-tip region cannot be ignored. Thus Eq 2 must be modified to include the elastic term in addition to the power-law creep term. Under these circumstances, C ∗ is path-dependent and it no longer...
Abstract
This article describes the concepts for characterizing and predicting elevated-temperature crack growth in structural materials. It discusses both creep and creep-fatigue crack growth and focuses mainly on creep crack growth tests that are carried out in accordance with ASTM E 1457. The article provides information on typical test procedures and equipment used for these tests. It concludes with information on crack growth correlations.
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005512
EISBN: 978-1-62708-197-9
... Power-law creep Given an initial geometry (i.e., wavelength and height of voids, based on measurement of the original surface roughness), rate equations for each of the seven mechanisms operating independently are summed to give an overall void shrinkage rate and hence to predict the small extent...
Abstract
The goals of modeling diffusion bonding can be regarded as twofold: to optimize the selection of the process variables for a given material and to provide an understanding of the mechanisms by which bonding is achieved. This article describes the existing models of diffusion bonding with an assumption that the surfaces to be joined are free of contaminants and oxide, that bonding occurs between similar materials, and that the materials are single-phase metals. It discusses the mechanisms considered for diffusion bonding and limitations of existing models.
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002472
EISBN: 978-1-62708-194-8
... to as beta creep and followed a time to the one-third law, the viscous region (later to be called steady-state creep) was proportional to time, and the accelerating strain region leading to fracture, which was not specifically treated by Andrade, later became known as tertiary creep. Much later...
Abstract
This article reviews the basic mechanisms of elevated-temperature behavior and associated design considerations, with an emphasis on metals. It discusses the key concepts of elevated-temperature design. These include plastic instability at elevated temperatures; deformation mechanisms and strain components associated with creep processes; stress and temperature dependence; fracture at elevated temperatures; and environmental effects. The article describes the basic presentation and analysis methods for creep rupture. It provides information on the application of these methods to materials selection and the setting of basic design rules. The article examines the limitations of high-temperature components as well as the alternative design approaches and tests for most high-temperature components.
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