Modeling of Creep for Structural Analysis

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Springer Science & Business Media, Apr 6, 2007 - Technology & Engineering - 220 pages

"Creep Modeling for Structural Analysis" develops methods to simulate and analyze the time-dependent changes of stress and strain states in engineering structures up to the critical stage of creep rupture. The principal subjects of creep mechanics are the formulation of constitutive equations for creep in structural materials under multi-axial stress states; the application of structural mechanics models of beams, plates, shells and three-dimensional solids and the utilization of procedures for the solution of non-linear initial-boundary value problems. The objective of this book is to review some of the classical and recently proposed approaches to the modeling of creep for structural analysis applications as well as to extend the collection of available solutions of creep problems by new, more sophisticated examples.

In Chapter 1, the book discusses basic features of the creep behavior in materials and structures and presents an overview of various approaches to the modeling of creep. Chapter 2 collects constitutive models that describe creep and damage processes under multi-axial stress states. Chapter 3 deals with the application of constitutive models to the description of creep for several structural materials. Constitutive and evolution equations, response functions and material constants are presented according to recently published experimental data. In Chapter 4 the authors discuss structural mechanics problems. Governing equations of creep in three-dimensional solids, direct variational methods and time step algorithms are reviewed. Examples are presented to illustrate the application of advanced numerical methods to the structural analysis. An emphasis is placed on the development and verification of creep-damage material subroutines inside the general purpose finite element codes.

 

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Contents

Introduction
1
112 MultiAxial Creep and Stress State Effects
7
12 Creep in Engineering Structures
11
13 Basic Approaches to Creep Modeling
15
Constitutive Models of Creep
17
22 Secondary Creep
22
221 Isotropic Creep
23
2212 Creep Potentials with Three Invariants of the Stress Tensor
25
43 Beams
122
432 Closed Form Solution
124
433 Variational Formulation and the Ritz Method
126
434 Examples
128
4342 Finite Element Solutions
132
435 Stress State Effects and Cross Section Assumptions
138
Refined vs Classical Beam Theory
144
44 Plates and Shells
148

222 Creep of Initially Anisotropic Materials
28
2221 Classical Creep Equations
30
2222 NonClassical Creep Equations
38
223 Functions of Stress and Temperature
44
23 Primary Creep and Creep Transients
48
231 Time and Strain Hardening
50
232 Kinematic Hardening
53
24 Tertiary Creep and Creep Damage
60
241 ScalarValued Damage Variables
62
2412 MicromechanicallyConsistent Models
72
2413 MechanismBased Models
75
2414 Models Based on Dissipation
77
242 DamageInduced Anisotropy
78
Examples of Constitutive Equations for Various Materials
85
31 Models of Isotropic Creep for Several Alloys
86
312 Steel 13CrMo45
87
32 Model for Anisotropic Creep in a MultiPass Weld Metal
92
321 Origins of Anisotropic Creep
93
322 Modeling of Secondary Creep
99
323 Identification of Material Constants
100
Modeling of Creep in Structures
103
42 InitialBoundary Value Problems and General Solution Procedures
106
422 VectorMatrix Representation
108
423 Numerical Solution Techniques
111
4231 Time Integration Methods
113
4232 Solution of Boundary Value Problems
117
4233 Variational Formulations and Procedures
118
442 Examples
151
4422 Long Term Strength Analysis of a Steam Transfer Line From the
161
Basic Operations of Tensor Algebra
167
A1 Polar and Axial Vectors
168
A2 Operations with Vectors
169
A23 Scalar Dot Product of Two Vectors
170
A3 Bases
171
A4 Operations with Second Rank Tensors
172
A42 Multiplication by a Scalar
173
A46 Dot Products of a Second Rank Tensor and a Vector
174
A48 Trace
175
A410 SkewSymmetric Tensors
176
A413 Determinant and Inverse of a Second Rank Tensor
177
A415 CayleyHamilton Theorem
178
A417 Orthogonal Tensors
179
Elements of Tensor Analysis
181
B2 Hamilton Nabla Operator
182
B3 Integral Theorems
184
B4 ScalarValued Functions of Vectors and Second Rank Tensors
185
Orthogonal Transformations and Orthogonal Invariants
187
C2 Invariants for the Full Orthogonal Group
188
C31 Invariants for a Single Second Rank Symmetric Tensor
189
C32 Invariants for a Set of Vectors and Second Rank Tensors
194
C4 Invariants for the Orthotropic Symmetry Group
196
References
199
Index
215
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Creep Mechanics
Josef Betten
Limited preview - 2008

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