Unified Constitutive Equations For Creep And Plasticity by A.k. MillerUnified Constitutive Equations For Creep And Plasticity by A.k. Miller

Unified Constitutive Equations For Creep And Plasticity

EditorA.k. Miller

Paperback | September 27, 2011

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Constitutive equations refer to 'the equations that constitute the material response' at any point within an object. They are one of the ingredients necessary to predict the deformation and fracture response of solid bodies (among other ingredients such as the equations of equilibrium and compatibility and mathematical descriptions of the configuration and loading history). These ingredients are generally combined together in complicated computer programs, such as finite­ element analyses, which serve to both codify the pertinent knowledge and to provide convenient tools for making predictions of peak stresses, plastic strain ranges, crack growth rates, and other quantities of interest. Such predictions fall largely into two classes: structural analysis and manufacturing analysis. In the first category, the usual purpose is life prediction, for assessment of safety, reliability, durability, and/or operational strategies. Some high-technology systems limited by mechanical behavior, and therefore requiring accurate life assess­ ments, include rocket engines (the space-shuttle main engine being a prominent example), piping and pressure vessels in nuclear and non-nuclear power plants (for example, heat exchanger tubes in solar central receivers and reformer tubes in high-temperature gas-cooled reactors used for process heat applications), and the ubiquitous example of the jet engine turbine blade. In structural analysis, one is sometimes concerned with predicting distortion per se, but more often, one is concerned with predicting fracture; in these cases the informa­ tion about deformation is an intermediate result en route to the final goal of a life prediction.
Title:Unified Constitutive Equations For Creep And PlasticityFormat:PaperbackPublished:September 27, 2011Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401080399

ISBN - 13:9789401080392

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Table of Contents

1 Constitutive Behavior Based on Crystal Plasticity.- 1 Introduction.- 2 Some Important Realities.- 2.1 Uniaxial Monotonic Deformation.- 2.2 Multiaxial Deformation.- 3 Flow Kinetics.- 3.1 Non-uniform Deformation.- 3.2 Uniform Deformation.- 4 Polycrystal Plasticity.- 4.1 Crystal Plasticity.- 4.2 Averaging over a Polycrystal.- 5 Evolution.- 5.1 Texture Evolution.- 5.2 Substructure Evolution.- 6 Internal Stresses.- 6.1 Two-phase Materials.- 6.2 Single-phase Materials.- 7 Application.- 7.1 Diagnostics.- 7.2 Constitutive Relations.- 8 Summary and Recommendations.- 2 State Variable Theories Based on Hart's Formulation.- 1 Introduction.- 2 The Physical and Phenomenological Bases.- 3 A State Variable Description.- 3.1 Hart's Model for Grain Matrix Deformation.- 3.2 An Extension of Hart's Model to a Multiaxial Loading Case.- 3.3 An Extension of Hart's Model to Transient Deformation.- 3.4 An Extension of the State Variable Description to Grain Boundary Sliding.- 4 The Type of Data Utilized in Determining the Material Parameters.- 5 Materials Tested.- 6 Simulative and Predictive Powers of the State Variable Approach.- 6.1 Schematic Description of the Flow Chart.- 6.2 Simulations.- 6.3 Predictions.- 7 Discussion.- 7.1 The Components of the Flow Stress.- 7.2 Work-hardening.- 7.3 Limitations of the Present State Variable Approach.- 7.4 Future Developments.- Appendix 1.- Appendix 2.- 3 The MATMOD Equations.- 1 Introduction.- 2 Development of the Equations.- 2.1 General Relations Between the Phenomena Addressed and the Types of Equations Required.- 2.2 Physical and Phenomenological Bases for the Equations.- 2.3 Phenomenological Development of the Specific Equations.- 3 Simulations and Predictions.- 3.1 Aluminum (emphasizing strain hardening and strain softening behaviors).- 3.2 Austenitic Stainless Steel (emphasizing solute effects).- 3.3 Zircaloy (emphasizing irradiation effects).- 4 Numerical Integration Methods.- 5 Calculation of the Material Constants.- 6 Summary.- 4 The Mechanical Equation of State.- 1 Yield Criteria.- 1.1 Von Mises Yield Criterion.- 1.2 Other Yield Criteria.- 1.3 Yield Criteria Applicable to Polymers.- 1.4 Yield Criteria Applicable to Metals.- 2 Mechanical Equation of State for Dislocation Creep under Multiaxial Stresses.- 2.1 Some Anticipated Features of the MEOS.- 2.2 Anelasticity: the Delayed Elastic Strain Diagram.- 2.3 Non-recoverable Strain.- 2.4 Remobilisation by Stress Reversal.- 2.5 Multiaxial Strain Rates and the Dislocation Velocity.- 2.6 The Strain-Time Equation.- 2.7 Computer Program that Solves the MEOS.- 5 A Physically Based Internal Variable Model for Rate Dependent Plasticity.- 1 Introduction.- 2 The General Problem.- 2.1 Linear Model.- 2.2 Non-Linear Model.- 3 Proposed New Model.- 3.1 The Kinematic Internal Variable.- 3.2 The Isotropic Internal Variable.- 3.3 Final Equations for the Model.- 3.4 Determination of Constants.- 3.5 Problems with Parameter Determination.- 4 Behavior of the Model.- 6 Review of Unified Elastic-Viscoplastic Theory.- 1 Introduction.- 2 Constitutive Equations.- 2.1 Basic Equations.- 2.2 Evolution Equations.- 2.3 Temperature Dependence.- 3 Interpretation and Evaluation of Material Constants.- 4 Modeling of Metals.- 5 Applications.- 5.1 Finite Element Computer Programs.- 5.2 Finite Difference Computer Programs.- 5.3 Special Problems.- 7 Summary and Critique.- 1 Introduction.- 2 Model by Krieg, Swearengen and Jones.- 3 Model by Miller.- 4 Model by Bodner.- 5 Model by Korhonen, Hannula and Li.- 6 Model by Gittus.- 7 Numerical Difficulties with the Models.- 8 Conclusion.- Appendix A.- Appendix B.