Creep Mechanics (eBook)

Josef Betten (Autor)

eBook Download: PDF

2008 | 3rd ed. 2008
XVI, 367 Seiten
Springer Berlin (Verlag)
978-3-540-85051-9 (ISBN)

Infos

The simplest way to formulate the basic equations of continuum mech- ics and the constitutive or evolutional equations of various materials is to restrict ourselves to rectangular cartesian coordinates. However, solving p- ticular problems, for instance in Chapter 5, it may be preferable to work in terms of more suitable coordinate systems and their associated bases. The- fore, Chapter 2 is also concerned with the standard techniques of tensor an- ysis in general coordinate systems. Creep mechanics is a part of continuum mechanics, like elasticity or pl- ticity. Therefore, some basic equations of continuum mechanics are put - gether in Chapter 3. These equations can apply equally to all materials and they are insuf?cient to describe the mechanical behavior of any particular material. Thus, we need additional equations characterizing the individual material and its reaction under creep condition according to Chapter 4, which is subdivided into three parts: the primary, the secondary, and the tertiary creep behavior of isotropic and anisotropic materials. The creep behavior of a thick-walled tube subjected to internal pressure is discussed in Chapter 5. The tube is partly plastic and partly elastic at time zero. The investigation is based upon the usual assumptions of incompre- ibility and zero axial creep. The creep deformations are considered to be of such magnitude that the use of ?nite-strain theory is necessary. The inner and outer radius, the stress distributions as functions of time, and the cre- failure time are calculated.

Inhalt

Preface to the Third Edition 5
Preface to the Second Edition 6
Preface to the First Edition 8
Contents 13
1 Introduction 17
2 Tensor Notation 25
2.1 Cartesian Tensors 25
2.2 General Bases 32
3 Some Basic Equations of Continuum Mechanics 47
3.1 Analysis of Deformation and Strain 47
3.2 Analysis of Stress 56
4 Creep Behavior of Isotropic and Anisotropic Materials Constitutive Equations
4.1 Primary Creep 68
4.2 Secondary Creep 77
4.3 Tertiary Creep 93
5 Creep Behavior of Thick-Walled Tubes 101
5.1 Method to discribe the Kinematics 101
5.2 Isochoric Creep Behavior 106
5.3 Stress Field 109
5.4 Expansion and Failure Time 113
5.5 Numerical Computation and Examples 116
6 The Creep Potential Hypothesis in Comparison with the Tensor Function Theory 125
6.1 Isotropy 125
6.2 Oriented Solids 127
6.3 Modi.cation of the Normality Rule 131
6.4 Anisotropy expressed through a Fourth-Rank Tensor 134
7 Damage Mechanics 155
7.1 Damage Tensors and Tensors of Continuity 155
7.2 Stresses in a Damaged Continuum 164
7.3 Damage Effective Stress Concepts 171
8 Tensorial Generalization of Uniaxial Creep Laws to Multiaxial States of Stress 175
8.1 Polynomial Representation of Tensor Functions 175
8.2 Interpolation Methods for Tensor Functions 176
8.3 Tensoral Generalization of NORTON-BAILEY’s Creep Law 178
8.4 Tensorial Generalization of a Creep Law including Damage 181
9 Viscous Fluids 187
9.1 Linear Viscous Fluids 187
9.2 Nonlinear Viscous Fluids 195
10 Memory Fluids 205
10.1 MAXWELL Fluid 205
10.2 General Principle 206
10.3 Effects of Normal Stresses 209
11 Viscoelastic Materials 211
11.1 Linear Theory of Viscoelasticity 211
11.2 Nonlinear Theory of Viscoelasticity 217
11.3 Special Visoelastic Models 218
12 Viscoplastic Materials 261
12.1 Linear Theory of Viscoplasticity 262
12.2 Nonlinear Theory of Viscoplasticity 265
12.3 Viscoplastic Behavior of Metals 266
13 Creep and Damage Experiments 269
14 Creep Curve 295
A The HEAVISIDE and DIRAC Functions 301
B The LAPLACE Transformation 311
References 361
Index 377

Produkt-Details

• Erscheint lt. Verlag: 17.8.2008
• Zusatzinfo: XVI, 367 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Behavior • Concrete • Continuum Mechanics • creep • damage • Evolution • fluid- and aerodynamics • Glas • Glass • Mechanics • Memory • metals • Modeling • Polymers • rheology • solids • Tensors • viscoelasticity • viscoplasticity
• ISBN-10: 3-540-85051-1 / 3540850511
• ISBN-13: 978-3-540-85051-9 / 9783540850519