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constitutive model
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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
... 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. constitutive model superplastic flow superplasticity phenomenological constitutive equation...
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.
Image
Published: 01 January 2006
Fig. 26 The role of numerical procedures and constitutive modeling in springback accuracy as represented by standard error of fit,<σ>, to measurement. Springback angles (Δθ): (1) Plane stress, 5 integration points ( N IP ), 600 elements along length ( N EL ), von Mises yield
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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
... creep in terms of a constitutive model, and then using the constitutive model in a process model or finite element analysis to predict the final part shape. age-forming finite element analysis low-temperature creep mechanical test stress AGE FORMING is a shaping process for heat treatable...
Abstract
Compared to cold-formed parts, age-formed parts have lower residual stresses and consequently better stress corrosion resistance. This article addresses the technical issues that arise in the investigations of creep in precipitate-strengthened materials. The issues addressed help in developing alloys and tempers particularly suited for the age-forming process. The different steps involved in the program for predicting the final part shape are discussed. These basic steps involve developing mechanical tests to study creep at low temperatures and low stresses, describing low-temperature creep in terms of a constitutive model, and then using the constitutive model in a process model or finite element analysis to predict the final part shape.
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
..., 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...
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
... 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...
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: 24A
Publisher: ASM International
Published: 30 June 2023
DOI: 10.31399/asm.hb.v24A.a0006988
EISBN: 978-1-62708-439-0
... manufacturing (AM). Two of the primary ingredients needed to predict structure-property relationships via material modeling include a geometrical representation of the microstructural features of interest (e.g., grain structure and void defects) and a suitable constitutive model describing the material behavior...
Abstract
This article focuses specifically on material modeling applied to structure-property predictions. It provides general guidelines and considerations in terms of modeling the salient material features that ultimately impact the mechanical performance of parts produced by additive manufacturing (AM). Two of the primary ingredients needed to predict structure-property relationships via material modeling include a geometrical representation of the microstructural features of interest (e.g., grain structure and void defects) and a suitable constitutive model describing the material behavior, both of which can be scale and resource dependent. The article also presents modeling challenges to predict various aspects of (process-) structure-property relationships in AM.
Book: Powder Metallurgy
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
... where these data help in the development of a constitutive model for sintering simulation. Finally, the article provides information on the simulation approaches used to optimize die compaction and sintering. compaction continuum modeling continuum plasticity models deformation densification...
Abstract
This article discusses continuum modeling, which is the most relevant approach in modeling grain growth, densification, and deformation during sintering. Continuum plasticity models are frequently used to describe the mechanical response of metal powders during compaction. The article illustrates the typical procedure for computer simulation for press and sinter process. It describes the procedure to obtain the material properties based on the generalized Shima-Oyane model. The article presents a wide variety of tests, accounting for data on the grain growth, densification, and distortion where these data help in the development of a constitutive model for sintering simulation. Finally, the article provides information on the simulation approaches used to optimize die compaction and sintering.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003322
EISBN: 978-1-62708-176-4
... Abstract Forming processes can be divided into three major categories: bulk forming, sheet-metal forming, and semisolid forming and polymer extrusion. This article introduces each process category with a description of the constitutive models. It outlines the required properties for process...
Abstract
Forming processes can be divided into three major categories: bulk forming, sheet-metal forming, and semisolid forming and polymer extrusion. This article introduces each process category with a description of the constitutive models. It outlines the required properties for process modeling and describes the test methods for determining these properties. The article discusses several compression tests used to determine stress-strain curves for bulk forming and tensile tests used to obtain stress-strain curves for sheet-metal forming. The article concludes with information on the measurement of viscosity of semisolid alloy materials by using three types of viscometers: the coaxial cylinder viscometer, the cone-and-plate viscometer, and the capillary viscometer.
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006807
EISBN: 978-1-62708-329-4
... temperatures. The article describes the stages of the creep curve, discusses processes involved in the extrapolation of creep data, and summarizes notable creep constitutive models and continuum damage mechanics models. It demonstrates the effects of stress relaxation and redistribution on the remaining life...
Abstract
This article provides some new developments in elevated-temperature and life assessments. It is aimed at providing an overview of the damage mechanisms of concern, with a focus on creep, and the methodologies for design and in-service assessment of components operating at elevated temperatures. The article describes the stages of the creep curve, discusses processes involved in the extrapolation of creep data, and summarizes notable creep constitutive models and continuum damage mechanics models. It demonstrates the effects of stress relaxation and redistribution on the remaining life and discusses the Monkman-Grant relationship and multiaxiality. The article further provides information on high-temperature metallurgical changes and high-temperature hydrogen attack and the steps involved in the remaining-life prediction of high-temperature components. It presents case studies on heater tube creep testing and remaining-life assessment, and pressure vessel time-dependent stress analysis showing the effect of stress relaxation at hot spots.
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
..., advanced constitutive models, and complicated stress and temperature loading histories. finite-difference method finite-element method residual strain residual stress stress relaxation testing THE ADVANCES IN PROCESSING OF METALLIC MATERIALS for improved physical, thermal, and mechanical...
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.
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...
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 discusses the experimental determination of material properties and simulation verification for compaction and sintering. It reviews the use of modeling and simulation of press and sinter powder metallurgy, including gravitational distorting in sintering, compaction optimization, sintering optimization, and coupled press and sinter optimization.
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005519
EISBN: 978-1-62708-197-9
... coefficients to an equation that will result in analytical prediction of similar forces under similar cutting conditions. Constitutive Models The typical approach is to adjust the coefficients of a constitutive equation until predicted forces match the experimental results. Johnson and Cook ( Ref 24...
Abstract
This article begins with information on the fundamentals of chip formation process and general considerations for the modeling and simulation of machining processes. It focuses on smaller-scale models that seek to characterize the workpiece/tool/chip interface and behaviors closely associated with that. The article describes the advantages and disadvantages of various finite-element modeling approaches, namely, transient models, continuous cutting model, steady-state model, hybrid model, two-dimensional models, and three-dimensional models. It discusses flow stress measurements using constitutive and inverse testing methods and reviews tool design for chip removal. The article explains the effect of tool geometry on burr formation and the effect of coatings on tool temperatures. It concludes with information on tool wear, which is an unavoidable effect of metal cutting.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003298
EISBN: 978-1-62708-176-4
... THE HIGH-STRAIN-RATE, STRESS-STRAIN RESPONSE of polymers and polymeric-composite materials has received increased scientific and industrial attention in recent years. This interest is driven by the need for predictive constitutive model descriptions to support large-scale finite-element simulations...
Abstract
This article addresses the specialized aspects required to accurately quantify the behavior of soft materials, including polymers and polymeric composites, using the split-Hopkinson pressure bar (SHPB). It details some of the specialized SHPB techniques that facilitate testing soft materials. These techniques include the data-reduction techniques and assumptions required to use polymer pressure bars, the importance of sample-size considerations to polymer testing, and temperature-control methodologies to measure the high-strain-rate uniaxial stress response of polymers and other soft materials.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005238
EISBN: 978-1-62708-187-0
... to solve them, and a few examples of recent applications in shape castings and continuous casting. Governing Equations The modeling of mechanical behavior requires solution of 1) the equilibrium or momentum equations relating force and stress, 2) the constitutive equations relating stress and strain...
Abstract
This article summarizes some issues and approaches in performing computational analyses of mechanical behavior, distortion, and hot tearing during solidification. It presents the governing equations and describes the methods used to solve them. The article reviews the finite element formulation, multidomain approaches, and arbitrary Lagrangian Eulerian method in solidification modeling. It illustrates the sand casting of braking disks and continuous casting of steel slabs.
Book: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002391
EISBN: 978-1-62708-193-1
... been considered in TF and TMF research. Life prediction models and constitutive equations suited for TF and TMF are covered. The structural materials discussed include carbon steels, low-alloy steels, stainless steels, aluminum alloys, and nickel-base high-temperature alloys. The article explains crack...
Abstract
Structural alloys are commonly subjected to a variety of thermal and thermomechanical loads. This article provides an overview of the experimental methods in thermal fatigue (TF) and thermomechanical fatigue (TMF) and presents experimental results on the structural materials that have been considered in TF and TMF research. Life prediction models and constitutive equations suited for TF and TMF are covered. The structural materials discussed include carbon steels, low-alloy steels, stainless steels, aluminum alloys, and nickel-base high-temperature alloys. The article explains crack initiation and crack propagation in TF and TMF. It describes thermal ratcheting and thermal shock behavior of structural metallic materials. The article concludes with information on life prediction of structural materials under TF and TMF.
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
..., 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...
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: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005513
EISBN: 978-1-62708-197-9
... conduction, convection, and phase change; and elastic-plastic deformation. It provides a description of four sets of data used for modeling and simulation of additive manufacturing processes, namely, material constitutive data, solid model, initial and boundary conditions, and laser deposition process...
Abstract
Additive manufacturing produces a change in the shape of a substrate by adding material progressively. This article discusses the simulation of laser deposition and three principal thermomechanical phenomena during the laser deposition process: absorption of laser radiation; heat conduction, convection, and phase change; and elastic-plastic deformation. It provides a description of four sets of data used for modeling and simulation of additive manufacturing processes, namely, material constitutive data, solid model, initial and boundary conditions, and laser deposition process parameters. The article considers three aspects of simulation of additive manufacturing: simulation for initial selection of process parameter setup, simulation for in situ process control, and simulation for ex situ process optimization. It also presents some examples of computational mechanics solutions for automating various components of additive manufacturing simulation.
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
... is often used for predicting the material flow behavior during hot working operations, while the Sherby-Dorn is a general creep parameter that is used in a similar manner as the Larson-Miller parameter. Creep Mechanisms Power Law Creep Although effective, many of the constitutive models developed...
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: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005424
EISBN: 978-1-62708-196-2
... aspects of a process that are strongly influenced by anisotropy, the properties inherited from the crystal structure must appear explicitly in the model formulation. Such aspects include the evolving state of the material during processing as well as its condition subsequent to processing. Constitutive...
Abstract
This article provides an explanation on how crystal plasticity is implemented within finite element formulations by the use of physical length scales: crystal scale and continuum scale. It provides theoretical formulations for kinematic framework for deforming crystals and polycrystals, elastic and plastic behaviors of single crystals, refinements to the single-crystal constitutive, and crystal-scale finite-element. The article also presents examples that illustrate the capabilities of the formulations at the length scales.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005420
EISBN: 978-1-62708-196-2
... and segregation. The modeling of mechanical behavior requires solution of the equilibrium or momentum equations relating force and stress, the compatibility equations relating strain and displacement, and the constitutive equations relating stress and strain. This is because the boundary conditions specify either...
Abstract
This article focuses on the concepts involved in heat-transfer modeling, thermomechanical modeling, and microsegregation modeling of hot tearing. It discusses the modeling of solidification defects, namely, inclusion entrapment, segregation, shrinkage cavities, gas porosity, mold-wall erosion, and hot-tear cracks.
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