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.

Unified constitutive equations for creep and plasticity

This paper presents and experimental technique for determining compressive stress-strain curves well into the plastic range of relatively soft metals at strain rates from 300 to 2000 sec−1 at six temperatures from 30 to 550° C. More than 100 curves were obtained on annealed 1100° F aluminum. The strain-rate dependence in these tests could be fitted quite well either by a power function (log-log plot) or by a semilogarithmic plot, but the power function gave a better correlation of the present data with that obtained at lower strain rates by Alder and Phillips.1

Compression-impact testing of aluminum at elevated temperatures

Elastic and damping properties from room temperature to 673 K in an AZ31 magnesium alloy

The influence of pipe diffusion on the creep of fine-grained materials

Specimens of 304 stainless steel subjected to different thermomechanical histories develop different internal stresses, σi, and different substructures. Creep rate is uniquely related not to the applied stress, σA, but to the effective stress, σ*=(σA−σi). Values of σ* are determined from experimental results and σi calculated from σi=(σA−σ*). Results show σi increases with the applied stress according to σi∝σA1.7. Transmission electron microscopic observations show that the density of dislocations within subgrains, ϱD, and the subgrain diameter,D, vary with applied stress according to: ϱD∝σAK,D ∝ σA−0.8, whereK=1.4 to 2.0. Subgrain misorientation is independent of creep stress, strain, or temperature. The contributions of these structural variables to the internal stress are discussed.

Internal stresses and structures developed during creep

Design of Apparatus for Constant-Stress or Constant-Load Creep Tests

Paper 30: Strain-Time, Rate-Stress and Rate-Temperature Relations during Large Deformations in Creep

Testing techniques employed in determining the elastic moduli, i.e., Young's modulus, shear modulus, and Poisson's ratio, at room and elevated temperatures are described. The techniques depend on static or dynamic measurements. A comparison and an analysis of test results determined by the methods are presented. The effect of composition, grain size, and various transformations on the elastic moduli or their temperature dependence is discussed. A review of techniques and experimental data on the effect of high strain rates on plastic and rupture behavior of metals and alloys at elevated temperatures is presented. It is shown that recovery effects explain qualitatively the results obtained. A brief description of the various stages of recovery is presented. The variation of hardness with temperature is discussed for pure metals and alloys, including a description of a typical hot-hardness tester. The relationship between hardness and tensile strength, creep, and creep- rupture behavior is summarized. The use of the hot-hardness tester as a research tool for following solid-state reactions at elevated temperatures is discussed. The reactions may depend on temperature, time, or plastic strain, or a combination of these. (auth)

F. Garofalo

Papers

Design of Apparatus for Constant-Stress or Constant-Load Creep Tests

Paper 30: Strain-Time, Rate-Stress and Rate-Temperature Relations during Large Deformations in Creep

Survey of Various Special Tests Used to Determine Elastic, Plastic, and Rupture Properties of Metals at Elevated Temperatures