Unified constitutive equations for creep and plasticity

TLDR: In this paper, Hart's Model for Grain Matrix Deformation was extended to a multiaxial loading case and a new state variable theory was proposed to describe the effect of grain boundary sliding.

Abstract: 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.