Creep MechanicsThe 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. |
Contents
1 | |
Tensor Notation | 9 |
Some Basic Equations of Continuum Mechanics | 31 |
Creep Behavior of Isotropic and Anisotropic Materials | 49 |
Creep Behavior of ThickWalled Tubes 85 | 84 |
The Creep Potential Hypothesis in Comparison with the Tensor | 109 |
Damage Mechanics | 139 |
Tensorial Generalization of Uniaxial Creep Laws to Multiaxial | 159 |
Viscoelastic Materials | 195 |
Viscoplastic Materials | 245 |
Creep and Damage Experiments | 253 |
Creep Curve | 279 |
A The HEAVISIDE and DIRAC Functions | 285 |
B The LAPLACE Transformation | 295 |
344 | |
361 | |
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Common terms and phrases
according Aijkl alias H=Heaviside alloy anisotropic anisotropic damage arrive base vectors BETTEN bivectors cartesian CAUCHY stress characterized co-black coefficients components considered constant constitutive equation continuum mechanics contravariant convolution convolution theorem coordinates covariant creep behavior creep curve creep function creep mechanics creep potential hypothesis damage tensor defined deformation gradient delta derivative differential elastic epsilon example experimental data expressed fluids formulate fourth-order tensor HEAVISIDE function ijkl illustrated in Fig instance integrity basis inverse irreducible invariants isotropic KELVIN LAPLACE transform laplace(y(t linear loading material MAXWELL metric tensor net-stress non-NEWTONian fluids nonlinear parameters plastic plot2 plots display relation relaxation function representation respectively scalar shear specimens strain rate strain tensor stress tensor symmetric symmetric tensor temperature tensor functions tensor of continuity tensor-valued function theorem theory tion uniaxial variables viscoelastic viscosity zero лл ллл