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Burgers power-law model
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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
.... 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...
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: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005404
EISBN: 978-1-62708-196-2
... microstructure low temperature creep power-law breakdown diffusional creep twinning deformation mechanism maps power law creep creep-strengthening microstructural modeling FOR MANY ENGINEERING MATERIALS, deformation is highly sensitive to both temperature and strain rate. Under these conditions...
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.
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006277
EISBN: 978-1-62708-169-6
... energies and atomic mobilities are established as functions of temperature, pressure, and composition and serve directly as key inputs of any microstructure modeling. The article presents examples of the integrated computation tool set in simulating microstructural evolution. Burgers orientation...
Abstract
This article describes the integration of thermodynamic modeling, mobility database, and phase-transformation crystallography into phase-field modeling and its combination with transformation texture modeling to predict phase equilibrium, phase transformation, microstructure evolution, and transformation texture development during heat treatment of multicomponent alpha/beta and beta titanium alloys. It includes quantitative description of Burgers orientation relationship and path, discussion of lattice correspondence between the alpha and beta phases, and determination of the total number of Burgers correspondence variants and orientation variants. The article also includes calculation of the transformation strain with contributions from defect structures developed at alpha/beta interfaces as a precipitates grow in size. In the CALculation of PHAse Diagram (CALPHAD) framework, the Gibbs free energies and atomic mobilities are established as functions of temperature, pressure, and composition and serve directly as key inputs of any microstructure modeling. The article presents examples of the integrated computation tool set in simulating microstructural evolution.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005412
EISBN: 978-1-62708-196-2
... is situated at the interfaces ( Ref 5 ). In microsystems technology, interfaces determine the service life and performance of devices ( Ref 6 ). Atomistic modeling is a powerful tool for understanding the structure of defects in a crystalline lattice. However, there is an infinite range of possible...
Abstract
This article summarizes a physical model of an interface structure and shows how the model helps in optimizing atomistic modeling studies. It presents the orientation relationship of the interface structure to define the mutual crystallographic position of adjacent crystals. The article describes the model-informed atomistic modeling of the interface structures for interpolating the results of atomistic modeling to predict the properties of interfaces. Theories to predict low-energy orientation relationships are described. The article discusses the use of the localization parameter, such as shear modulus, bonding energy, and transformations, for prediction of interface structures. It provides information on the application of the atomistic modeling of interface structure to predict interface reaction mechanisms.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005418
EISBN: 978-1-62708-196-2
... a self-consistent model for the hot working of equiaxed α/β Ti-6Al-4V, focusing on the use of power law viscoplasticity where the strengths of each phase are composition dependent, based on the temperature dependence of the volume fractions and compositions from thermodynamic models and experimental...
Abstract
Self-consistent models are a particular class of models in continuum micromechanics, that is, the field concerned with making predictions of the properties and evolution of aggregates whose single-crystal deformation behavior is known. This article provides information on the measurement and representation of textures as well as prediction of texture evolution in single-phase materials and two-phase aggregates.
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: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005403
EISBN: 978-1-62708-196-2
... ) or Stüwe and Hertel ( Ref 28 ), can be employed as well. In contrast to the power law, they lead to a steady-state flow stress at large strains. However, they are unable to model the flow softening usually associated with DRX. Effect of Grain-Boundary Migration on the Dislocation Density A first...
Abstract
Recrystallization is to a large extent responsible for their final mechanical properties. This article commences with a discussion on static recrystallization (SRX) and dynamic recrystallization (DRX). The DRX includes continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static recrystallization. The article reviews the kinetics of DRX with the aid of the Avrami relations. It considers the basic framework of the mesoscale approach for DDRX, including the three basic equations for grain size changes, strain hardening and dynamic recovery, and nucleation. The article explains the mesoscale approach for CDRX to predict microstructural evolutions occurring during hot deformation, along with an illustration of the main features of the CDRX mesoscale model.
Book Chapter
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005169
EISBN: 978-1-62708-186-3
... material modeling length; linear distance; crystal CAD/CAM computer-aided design/ DMZ dead-metal zone A lattice length along the a axis DOE design of experiment A CAE computer-aided manufacturing DP design parameter A area; heat retention factor CAO computer-aided engineering DRCR dynamic...
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.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005433
EISBN: 978-1-62708-196-2
... are noted because the phenomenological equations are abundant in superplasticity literature. There are relations ranging from the standard power-law types, various polynomial models, mechanical models (such as generalized Maxwell and Bingham body problems; mechanical threshold models such as Zehr...
Abstract
This article presents a mechanical description of superplasticity and discusses constitutive equations that are essential for simulating superplastic forming processes, applicable to structural superplasticity. It presents the phenomenological constitutive equations of superplasticity and classical physical constitutive equations. The article also reviews the accommodation mechanisms that are divided into two major groups, namely, diffusional accommodation and accommodation by dislocations.
Book: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002410
EISBN: 978-1-62708-193-1
... but also the fracture toughness of the material ( Ref 75 ): (Eq 5) d a d N = C Δ K n [ ( 2 − R ) K Ic − Δ K ] where K Ic is the fracture toughness of the material. Finally, one of the most widely used and recognized models is the classic Paris law...
Abstract
This article discusses fracture, fatigue, and creep of nickel-base superalloys with additional emphasis on directionally solidified and single-crystal applications. It analyzes the physical metallurgy of these alloys. The effects of grain boundary and grain size on failure are summarized. The article also discusses the effects of microstructure and extrinsic parameters on fatigue crack propagation (FCP). It details the modeling of FCP rates and creep and creep-fatigue crack growth rates.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005413
EISBN: 978-1-62708-196-2
... 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...
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: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003742
EISBN: 978-1-62708-177-1
... is revealed more clearly in Fig. 16 for different materials and monotonic deformation processes, in which a power-law relationship is found between the strain and the dislocation boundary area per unit volume ( S v ) of GNBs. The evolution of the misorientation angle, illustrated Fig. 17 , also yields...
Abstract
Microstructure and crystallographic texture are the key material features used in the continuous endeavor to relate the processing of a metal with its final properties. This article emphasizes several aspects of deformation microstructures, namely, microstructural evolution, dislocation boundaries, and macroscopic properties. It discusses three different microstructural types: cell blocks, TL blocks, and equiaxed subgrains. The article also emphasizes the behavior of metals and single-phase alloys processed under plastic deformation (dislocation slip) conditions. It provides information on the microstructural parameters, measurement techniques, and microstructural relationships, which assist in predicting the mechanical properties and recrystallization behavior of materials. The article concludes with an analysis of the general relationship between the microstructural parameters and properties.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005401
EISBN: 978-1-62708-196-2
... Abstract The modeling and simulation of texture evolution for titanium alloys is often tightly coupled to microstructure evolution. This article focuses on a number of problems for titanium alloys in which such coupling is critical in the development of quantitative models. It discusses...
Abstract
The modeling and simulation of texture evolution for titanium alloys is often tightly coupled to microstructure evolution. This article focuses on a number of problems for titanium alloys in which such coupling is critical in the development of quantitative models. It discusses the phase equilibria, crystallography, and deformation behavior of titanium and titanium alloys. The article describes the modeling and simulation of recrystallization and grain growth of single-phase beta and single-phase alpha titanium. The deformation- and transformation-texture evolution of two-phase (alpha/beta) titanium alloys are also discussed.
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.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004028
EISBN: 978-1-62708-185-6
... ) propose a rate-sensitive viscoplastic response that removes the ambiguity and facilitates the numerical implementation of slip in polycrystal models. The shear rate in a given system is given by a power of the resolved shear stress: (Eq 6) γ ˙ s = γ ˙ o | τ res τ s...
Abstract
This article outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used in technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the homogeneous effective medium (HEM). The article analyzes the anisotropy predictions of rolled face-centered-cubic and body centered-cubic sheets and presents simulations of the axial deformation of hexagonal-close-packed zirconium. The applications of polycrystal constitutive models to the simulation of complex forming operations, through the use of the finite element method, are also presented.
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
... with Eq 5 and explains the often-observed breakdown in the power-law strain-rate dependence at low temperatures and high strain rates. Isothermal Constitutive Model <xref rid="a0004020-ref12" ref-type="bibr">(Ref 12)</xref><xref rid="a0004020-fn3" ref-type="fn">[3]</xref> The temperature...
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: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005599
EISBN: 978-1-62708-174-0
... Abstract This article focuses on the general internal state variable method, and its simplification, for single-parameter models, in which the microstructure evolution may be treated as an isokinetic reaction. It explains that isokinetic microstructure models are applied to diffusional...
Abstract
This article focuses on the general internal state variable method, and its simplification, for single-parameter models, in which the microstructure evolution may be treated as an isokinetic reaction. It explains that isokinetic microstructure models are applied to diffusional transformations in fusion welding, covering particle dissolution, growth, and coarsening of precipitates in the heat-affected zone. The article discusses the versatility of the internal state variable approach in modeling of nonisothermal transformations for various materials and processes. It describes the process models applied to predict the microstructure evolution in Al-Mg-Si alloys during multistage thermal processing involving heat treatment and welding. The article also provides information on the microstructure models exploited in engineering design to optimize the load-bearing capacity of welded aluminum components.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.9781627081962
EISBN: 978-1-62708-196-2
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005435
EISBN: 978-1-62708-196-2
... model for (a) linear elastic material and (b) nonlinear material at onset of martensite mechanical stability. Length scale in units of lattice dislocation Burgers vector, b. Source: Ref 27 A central concept of quantitative martensite kinetic theory ( Ref 40 ) is a potency distribution...
Abstract
This article assesses the evolution of martensite modeling in the changing materials engineering environment. It describes the physics of displacive transformations using Ginzburg-Landau theory, microstructure representation, dynamics and simulations, density functional theory, and shuffle transitions. The article reviews the application of the Ginzburg-Landau approach to rigorous solutions for issues in the structure of a martensitic nucleus based on the martensitic nucleation theory. The three basic behavior modes of martensitic growth, such as elastic, elastic/plastic, and fully plastic are discussed. The article also reviews the overall kinetics of martensitic transformations.
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