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phenomenological constitutive equation

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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
... 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...
Book Chapter

By Sammy Tin
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...
Series: ASM Handbook
Volume: 24A
Publisher: ASM International
Published: 30 June 2023
DOI: 10.31399/asm.hb.v24A.a0006988
EISBN: 978-1-62708-439-0
... is treated as a homogeneous material, and the process-induced microstructural features that contribute to the overall material response are accounted for implicitly within a phenomenological constitutive model. Typically, the phenomenological constitutive model comprises an anisotropic yield criterion...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005425
EISBN: 978-1-62708-196-2
... of: Deformation and strain hardening, such as Schmid's law and the Hollomon equation Kinetics of recrystallization (such as the Avrami equation), grain growth (such as the Beck equation), and precipitation/phase transformation Ductility for solid-state processes Similarly, phenomenological models...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005133
EISBN: 978-1-62708-186-3
..., and hence, one needs evolution equations for them to complete the constitutive equation. In the event that explicit evolution equations for microstructural parameters cannot be determined, approximate phenomenological constitutive relations can be obtained by scaling experimentally determined stress-versus...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003402
EISBN: 978-1-62708-195-5
... are the permeabilities of fiber network in thickness and in-plane directions, respectively. Experimental Validation Almost all process models that are developed involve one or more assumptions, and many of them use constitutive or phenomenological equations to represent material behavior. Thus, it is important...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005502
EISBN: 978-1-62708-197-9
... Abstract This article presents the governing equations and methodologies to model the press and sinter powder metallurgy, including continuum, micromechanical, multiparticle, and molecular dynamics approaches. It describes the constitutive relation for compaction and sintering. The article...
Series: ASM Handbook
Volume: 7
Publisher: ASM International
Published: 30 September 2015
DOI: 10.31399/asm.hb.v07.a0006033
EISBN: 978-1-62708-175-7
... and constitutive relations, a system of partial differential equations is created that includes the initial and boundary conditions. These must be integrated with structure and property models so that final compact properties can be predicted. Because the constitutive relations for compaction and sintering...
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
.... A systematic search for other algebraic approximations to the data (for many materials) has led to the conclusion that the phenomenological equation for the reduced activation energy Δ G /μ b 3 ≡ g : (Eq 16) ( Δ G μ b 3 ) 1 / 2 ≡ g 1 / 2 ∝ 1 − ( σ / μ...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... on steady-state equations of mechanical equilibrium and constitutive equations for mechanical flow. The complete set of equations serves as the foundation for continuum mechanics models of bulk working processes. A model for each case is developed by imposing appropriate boundary conditions and initial...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003558
EISBN: 978-1-62708-180-1
... and to assess the significance of various parameters, including materials, which can be changed to resolve the wear problem. Modeling is an essential element in resolving wear failures. The characterizations of the tribosystem and the wear situation provide the basis for models. Simple phenomenological...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005415
EISBN: 978-1-62708-196-2
... microstructure activation energy critical nucleus configuration phase-field kinetic equations chemical free energy kinetic coefficients Fundamentals The collection of a hierarchy of structural and chemical nonuniformities (imperfections or defects) in solids constitutes materials crostructure...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009002
EISBN: 978-1-62708-185-6
... ). In this technique, each grain is divided into a number of elements. Each of the elements has its own constitutive equation depending on its prior history (e.g., level of hardening or softening) and instantaneous crystallographic orientation. With these local constitutive equations, the FEM analysis...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005619
EISBN: 978-1-62708-174-0
... matrix, ü is the nodal acceleration vector, u is the nodal velocity vector, { u } is the nodal displacement vector, and { L } is the applied load vector. The basic constitutive equations between stress (σ) and strain (ε) are as follows: (Eq 2) { σ } = [ D ] { ε el...
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
... on formulating the basic equations for system reliability.) After the following discussion the reader should be cognizant that the expression given in Eq 11 represents the probability of failure for a specified set of boundary conditions. If the boundary conditions are modified in any way, Eq 11 is no longer...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005168
EISBN: 978-1-62708-186-3
... Abstract This article discusses the numerical simulation of the forming of aluminum alloy sheet metals. The macroscopic and microscopic aspects of the plastic behavior of aluminum alloys are reviewed. The article presents constitutive equations suitable for the description of aluminum alloy...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002482
EISBN: 978-1-62708-194-8
... the process under consideration Mathematical equations describing the physical process Data needed to solve the equations Numerical algorithm to solve the equations given the boundary conditions and the constitutive behavior Availability of the software to provide answers One of the most...
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
... 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...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005409
EISBN: 978-1-62708-196-2
... alloys, with their corresponding equations. Microstructure modeling thermomechanical processing titanium alloys beta titanium alloys spheroidization coarsening particle growth phase decomposition heat treatment alpha-beta titanium alloys TITANIUM AND TITANIUM ALLOYS are widely used...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005509
EISBN: 978-1-62708-197-9
... deformations, approximately 15 to 20% linear. The initial density is approximately 60 to 65% of the theoretical density, which is usually reached by the end of the process. From a mathematical point of view, it means that the constitutive equations describing the material flow will be nonlinear...