Advanced Thermal Stress Analysis of Smart Materials and Structures

313 Pages·2020·9.102 MB·English

by  Zengtao Chen, Abdolhamid Akbarzadeh

Structural Integrity 10
Series Editors: José A. F. O. Correia · Abílio M. P. De Jesus
Zengtao Chen
Abdolhamid Akbarzadeh
Advanced
Thermal Stress
Analysis of
Smart Materials
and Structures
Structural Integrity
Volume 10
Series Editors
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Alfonso Fernández-Canteli, Faculty of Engineering, University of Oviedo, Gijón,
Spain
Matthew Hebdon,VirginiaState University,VirginiaTech,Blacksburg,VA,USA
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Adelaide, SA, Australia
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Science and Technology, Wrocław, Poland
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Fukuoka, Japan
Hermes Carvalho, Department of Structural Engineering, Federal University of
Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
Shun-Peng Zhu, School of Mechatronics Engineering, University of Electronic
Science and Technology of China, Chengdu, Sichuan, China
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Zengtao Chen Abdolhamid Akbarzadeh
(cid:129)
Advanced Thermal Stress
Analysis of Smart Materials
and Structures
123
Zengtao Chen AbdolhamidAkbarzadeh
Department ofMechanical Engineering Department ofBioresource Engineering
University of Alberta McGill University
Edmonton, Canada Island of Montreal,QC,Canada
Department ofMechanical Engineering
McGill University
Montreal,QC, Canada
ISSN 2522-560X ISSN 2522-5618 (electronic)
Structural Integrity
ISBN978-3-030-25200-7 ISBN978-3-030-25201-4 (eBook)
https://doi.org/10.1007/978-3-030-25201-4
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Preface
Advanced smart materials and structures are under rapid development to meet
engineeringchallengesformultifunctionality,highreliability,andhighefficiencyin
modern technology. Advanced manufacturing technology calls for high-energy,
non-contact, laser-forming materials in a sophisticated spatial and temporal envi-
ronment. Thermal stress analysis of advanced materials offers a viable tool for
optimized design of advanced, multifunctional devices and for accurate modelling
of advanced manufacturing processes.
In classical thermal analysis, thermal stress is caused by the constrained defor-
mation when a temperature variation occurs in an elastic body. How the material
reaches the final temperature from the initial temperature will not affect the cal-
culation of the steady-state or quasi-static thermal stresses. Classical Fourier heat
conduction theory is widely used in the thermal stress analysis leading to perfect
and trustworthy results. In transient and high-temperature gradient cases, when
materialsexperiencesuddenchangesintemperaturewithinanextremelyshorttime,
the reaction to this ultrafast, temporal temperature changes or heat flux would be
expectedtohaveatimedelaysinceheatpropagationtakestimetooccur.Thisdelay
might not be felt for most metallic materials as relaxation time of metals is in the
rangeof10–8–10–14s,opposedtosoftandorganicmaterialswitharelaxationtime
between1 sand10s,wherethedelayisnotnegligibleandthesubsequentthermal
wave propagation is evident. Non-Fourier, time-related heat conduction models
havebeenproposedtocompensatetheeffectofthisdelayinaheattransferprocess.
Anaturaloutcomeofthenon-Fourierheatconductionmodelsisthewave-likeheat
conductionequation,whereathermalwaveisrequiredtospreadtheheat.Thermal
stress analysis in advanced materials based on the non-Fourier heat conduction
theories has become a popular topic in the past decades. The authors of this book
are among the researchers who initiated and continued working on promoting the
research in the area of thermal stresses in advanced smart materials. Although the
literature in this area is booming in recent years, a single-volume monograph
summarizing the recent progress in implementing non-Fourier heat conduction
theoriestodealwiththemultiphysicalbehaviourofsmartmaterialsandstructuresis
still missing in the literature.
v
vi Preface
This monograph is a collection of the research on advanced thermal stress
analysis of advanced and smart materials and structures mainly written by the
authorsofthisbook,andtheirstudentsandcolleagues.Thisbookisorganizedinto
seven chapters. Chapter 1 provides a brief introduction to the non-Fourier heat
conduction theories, including the Cattaneo–Vernotte (C–V), dual-phase-lag
(DPL), three-phase-lag (TPL) theory, fractional phase-lag, and non-local heat
conduction theories. Chapter 2 introduces the fundamental of thermal wave char-
acteristics by reviewing different methods for solving non-Fourier heat conduction
problems in representative homogenous and heterogeneous advanced materials.
Chapter 3 provides the fundamentals of smart materials and structures, including
the background, application, and governing equations. In particular, functionally
graded smart structures are introduced as they represent the recent development in
the industry; a series of uncoupled thermal stress analyses on one-dimensional
smart structures are also presented. Chapter 4 presents coupled thermal stress
analyses in one-dimensional, homogenous and heterogeneous, smart piezoelectric
structures considering alternative coupled thermopiezoelectric theories. Chapter 5
introduces a generalized method to deal with plane crack problems in smart
materials and structures based on classical Fourier heat conduction. Thermal frac-
tureanalysisofcrackedstructuresbasedonnon-Fourierheatconductiontheoriesis
presented in Chap. 6. Finally, Chap. 7 lists a few perspectives on the future
developments in non-Fourier heat conduction and thermal stress analysis.
We sincerely thank our students, colleagues, and friends for their contributions
in preparation of this book. We are indebted to our families for their sacrifice,
patience, and constant support during the composition of this book.
Edmonton, Canada Zengtao Chen
Montreal, Canada Abdolhamid Akbarzadeh
April 2019
Contents
1 Heat Conduction and Moisture Diffusion Theories . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Heat Conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Fourier Heat Conduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Non-Fourier Heat Conduction. . . . . . . . . . . . . . . . . . . . . 7
1.3 Moisture Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.1 Fickian Moisture Diffusion . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.2 Non-Fickian Moisture Diffusion . . . . . . . . . . . . . . . . . . . 18
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Basic Problems of Non-Fourier Heat Conduction. . . . . . . . . . . . . . . 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Laplace Transform and Laplace Inversion . . . . . . . . . . . . . . . . . . 23
2.2.1 Fast Laplace Inverse Transform . . . . . . . . . . . . . . . . . . . 24
2.2.2 Reimann Sum Approximation. . . . . . . . . . . . . . . . . . . . . 25
2.2.3 Laplace Inversion by Jacobi Polynomial . . . . . . . . . . . . . 25
2.3 Non-Fourier Heat Conduction in a Semi-infinite Strip. . . . . . . . . . 26
2.4 Nonlocal Phase-Lag Heat Conduction in a Finite Strip . . . . . . . . . 31
2.4.1 Molecular Dynamics to Determine Correlating
Nonlocal Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Three-Phase-Lag Heat Conduction in 1D Strips, Cylinders,
and Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.1 Effect of Bonding Imperfection on Thermal Wave
Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5.2 Effect of Material Heterogeneity on Thermal Wave
Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5.3 Thermal Response of a Lightweight Sandwich Circular
Panel with a Porous Core. . . . . . . . . . . . . . . . . . . . . . . . 50
2.6 Dual-Phase-Lag Heat Conduction in Multi-dimensional Media . . . 53
vii
viii Contents
2.6.1 DPL Heat Conduction in Multi-dimensional Cylindrical
Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.6.2 DPL Heat Conduction in Multi-dimensional Spherical
Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3 Multiphysics of Smart Materials and Structures. . . . . . . . . . . . . . . . 65
3.1 Smart Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.1 Piezoelectric Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.1.2 Magnetoelectroelastic Materials. . . . . . . . . . . . . . . . . . . . 69
3.1.3 Advanced Smart Materials . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 Thermal Stress Analysis in Homogenous Smart Materials. . . . . . . 74
3.2.1 Solution for the a Thermomagnetoelastic
FGM Cylinder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2.2 Solution for Thermo-Magnetoelectroelastic
Homogeneous Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2.3 Benchmark Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3 Thermal Stress Analysis of Heterogeneous Smart Materials. . . . . . 90
3.3.1 Solution Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.3.2 Benchmark Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4 Effect of Hygrothermal Excitation on One-Dimensional Smart
Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4.1 Solution Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.4.2 MEE Hollow Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.4.3 MEE Solid Cylinder. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.4.4 Benchmark Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.5 Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4 Coupled Thermal Stresses in Advanced Smart Materials . . . . . . . . . 119
4.1 Functionally Graded Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2 Hyperbolic Coupled Thermopiezoelectricity
in One-Dimensional Rod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2.2 Homogeneous Rod Problem . . . . . . . . . . . . . . . . . . . . . . 122
4.2.3 Solution Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.2.4 Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.3 Hyperbolic Coupled Thermopiezoelectricity in Cylindrical
Smart Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.3.2 Hollow Cylinder Problem. . . . . . . . . . . . . . . . . . . . . . . . 135
4.3.3 Solution Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.3.4 Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.4 Coupled Thermopiezoelectricity in One-Dimensional
Functionally Graded Smart Materials. . . . . . . . . . . . . . . . . . . . . . 146
Contents ix
4.4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.4.2 The Functionally Graded Rod Problem . . . . . . . . . . . . . . 147
4.4.3 Solution Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.4.4 Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.4.5 Introduction of Dual Phase Lag Models . . . . . . . . . . . . . 161
4.4.6 Results of Dual Phase Lag Model Analysis . . . . . . . . . . . 163
4.5 Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5 Thermal Fracture of Advanced Materials Based on Fourier
Heat Conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.2 Extended Displacement Discontinuity Method and Fundamental
Solutions for Thermoelastic Crack Problems . . . . . . . . . . . . . . . . 171
5.2.1 Fundamental Solutions for Unit Point Loading
on a Penny-Shaped Interface Crack. . . . . . . . . . . . . . . . . 174
5.2.2 Boundary Integral-Differential Equations
for Interfacial Cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.2.3 Stress Intensity Factor and Energy Release Rate . . . . . . . 194
5.3 Interface Crack Problems in Thermopiezoelectric Materials. . . . . . 197
5.3.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.3.2 Fundamental Solutions for Unit-Point Extended
Displacement Discontinuities . . . . . . . . . . . . . . . . . . . . . 200
5.3.3 Boundary Integral-Differential Equations for an
Interfacial Crack in Piezothermoelastic Materials . . . . . . . 204
5.3.4 Hyper-Singular Integral-Differential Equations. . . . . . . . . 206
5.3.5 Solution Method of the Integral-Differential
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
5.3.6 Extended Stress Intensity Factors . . . . . . . . . . . . . . . . . . 219
5.4 Fundamental Solutions for Magnetoelectrothermoelastic
Bi-Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
5.5 Fundamental Solutions for Interface Crack Problems
in Quasi-Crystalline Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
5.5.1 Fundamental Solutions for Unit-Point EDDs . . . . . . . . . . 228
5.6 Application of General Solution in the Problem
of an Interface Crack of Arbitrary Shape . . . . . . . . . . . . . . . . . . . 234
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236