# Inelasticity Variants of the Theory.

## Description

Problems of reliable functioning and materials consumption decrease for modern technique constructions operating under conditions of high level of power and temperature loadings, and ionizing radiation as well make a problem of mathematical modelling of nonelastic behavior and constructions destruction rather urgent.

The increase in working parameters of modern machines and devices leads to increase of both of the general and local intensity of the constructions. Real loading processes for such constructions lead to nonelastic (viscous-plastic) deformations.

Thus the loading is a complex nonisothermal one, and a mode of its' changes may be one of the most any under conditions of repeated and continuous influence of the thermal power loadings and ionizing radiation. Theories of plasticity, creep and nonelasticity based on the nonisothermal loading now-in-use lead to the authentic results under narrow limited conditions only, when loadings are close to ordinary and stationary.

Separated examination of processes of plasticity, creep and damage accumulation without considering of their mutual influence is practically proper to all theories applied in calculations. Such prominent aspects influencing damage accumulation as brittle behavior and healing are not considered practically.

All it essentially limits areas of applicability of the theories of plasticity, creep and kinetic equations of damage accumulation (criteria of destruction) used in calculations.

The theory of nonelasticity belongs to the class of single-surface theories of flow under the combined loading. Comparisons of calculations under various theories of plasticity, creep and nonelasticity have shown that the results received by the means of the developed theory of nonelasticity are the best to correspond to the experimental data.

On the basis of these researches the conclusion is drawn that the developed theory of nonelasticity can be applied to practical calculations of nonelastic behavior and material damage accumulation of construction material under unrestricted process of complex nonisothermal loading. And authentic forecast for lifetime of high rating construction material under repeated and continuous influence of the thermal power loadings and ionizing radiation can be made on the basis of this theory.

The range of application of the theory of nonelasticity is limited by small strain of homogeneous and initially isotropic metals at temperatures when there is no phase transformation, and deformation rates when dynamic effects can be neglected.

174 pages,
© 2013

## Table of Contents:

CHAPTER 1 THEORY OF STRESSES AND STRAINS

1.1. Stress Tensor and Its Invariants

1.2. Stress Deviator and Its Invariants

1.3. Strain Tensor and Its Invariants

1.4. Strain Deviator and Its Invariants

CHAPTER 2 VECTOR REPRESENTATION OF STRESSES AND STRAINS

2.3. Vector and Scalar Properties

CHAPTER 3 THERMOELASTICITY

3.1. Stress–Strain Relationships

3.2. Matrix Representation of Stress–Strain Relationships

3.3. Stress–Strain Rates Relationships

3.4. Matrix Representation of Stress–Strain Rates Relationships

CHAPTER 1 THEORY OF PLASTIC DEFORMATION

1.1. Basic Principles and Equations

1.3. Relationship between the Plastic Strain Theory and the General Theories of Plasticity

1.4. Matrix Representation of the Equations of the Theory

1.5. Equations of the Theory in the Case of Generalized Plane State

1.6. Equations of the Theory in the Case of Uniaxial Stressed State

1.7. Low-Cycle Fatique Criteria in Uniaxial Stressed State

1.8. Computational-Experimental Method of Determining Material Functions

1.9. Material Functions of Some Structural Steels and Alloys

CHAPTER 2 THEORY OF PLASTIC DEFORMATION OF MATERIALS SENSITIVE TO THE TYPE OF STRESSED STATE

2.1. Basic Principles and Equations of the Theory

2.2. Material Functions and the Method of Determining Them

2.3. Matrix Representation of the Equations of the Theory

2.4. Equations of the Theory in the Case of Generalized Plane State

CHAPTER 3 THEORY OF PLASTIC DEFORMATION OF EXTRA HARDENING MATERIALS

3.1. Basic Principles and Equations of the Theory

3.2. Computational-Experimental Method of Determining Material Functions

3.3. Matrix Representation of the Equations of the Theory

CHAPTER 4 THEORIES OF PLASTIC DEFORMATION UNDER NONISOTHERMAL LOADING AND IONIZING RADIATION CONDITIONS

4.1. Equations of the Variants of the Theories

4.2. Material Functions and the Method of Determining Them

4.3. Material Functions of Some Structural Steels and Alloys

4.4. Matrix Representation of the Equations of the Variants of the Theories

4.5. Equations of the Theory in the Case of Generalized Plane State

CHAPTER 5 THEORY OF PLASTIC DEFORMATION ON CYCLIC LOADINGS

5.1. Basic Principles and Equations of the Theory

5.2. Computational-Experimental Method of Determining Material Functions

CHAPTER 1 THEORY OF INELASTIC DEFORMATION

1.1. Basic Principles and Equations

1.3. Relationship between the Theory of Inelastic Strain and General Theories

1.4. Matrix Representation of the Equations of the Theory

1.5. Equations of the Theory in the Case of Generalized Plane State

1.6. Equations of the Theory in the Case of Uniaxial Stressed State

1.7. Criteria of Long-Term Strength in Uniaxial Stressed State

1.8. Computational-Experimental Method of Determining Material Functions

CHAPTER 2 THEORY OF INELASTIC DEFORMATION OF STRESSED STATE-SENSITIVE MATERIALS

2.1. Basic Principles and Equations

2.2. Material Functions and the Method of Determining Them

CHAPTER 3 THEORIES OF INELASTIC DEFORMATION UNDER THE CONDITIONS OF NONISOTHERMAL LOADING AND IONIZING RADIATION

3.1. Equations of the Variants of the Theories

3.2. Material Functions and the Method of Determining Them

3.3. Material Functions of Some Structural Steels and Alloys

3.4. Matrix Representation of the Equations for the Variants of Theories

3.5. Equations of the Theory of Inelastic Deformation in the Case of Generalized Plane State