Table Of ContentDeformation and Evolution
of Life in Crystalline Materials
An Integrated Creep-Fatigue Theory
Xijia Wu
National Research Council Canada
Ottawa, Ontario, Canada
p,
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Aerospace Engineering, Delft University of Technology, Delft, The
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Preface
Ever since fatigue and creep were first studied more than one hundred years
ago, life prediction for materials in service has been mostly an experimental
science. The phenomena that mask the underlying physics and mechanisms
are so complicated, especially at high temperatures, that it requires a multi-
disciplinary understanding of materials science, solid mechanics, and
fracture mechanics. This book attempts to give a holistic treatment of all the
material deformation behaviours observed from mechanical testing to date,
using a mechanism-delineated approach—the integrated creep-fatigue theory
(ICFT)—for the first time in the literature.
To obtain this holistic view, we start with the understanding of
basic material physical nature—crystalline structures and imperfections
(dislocations and vacancies), and the kinetics of their movements in a
microstructure strengthened by mechanisms involving interactions of
dislocations with various point defects (solute atoms), line defects (dislocation
themselves), planar defects (grain boundaries and interfacial discontinuities)
and volume defects (precipitates and inclusions), in Chapter 1. Because
of the nature of crystalline materials, the theory of anisotropic elasticity is
introduced with the Stroh formalism. Indeed, crystals only deform elastically,
except the movements of crystalline defects leading to permanent shape
change, i.e. inelastic deformation. In Chapter 2, the fundamental deformation
mechanisms involving various types of dislocation and vacancy movements
are summarized, and their constitutive equations are given to describe both
the transient and steady states. In Chapter 3, physical damage processes
are discussed in relation to the responsible deformation mechanisms. It
classifies damage into either intragranular damage such as dislocation pile-
ups and persistent slip band, which tend to cause surface or subsurface crack
nucleation; or intergranular damage such as creep cavities and microcracks,
which are regarded as internally distributed damage. The integrated creep-
fatigue theory framework is introduced in Chapter 4, where constitutive laws
are formulated based on physical decomposition of mechanism strains, and
a holistic damage accumulation equation is derived, considering nucleation
and propagation of surface/subsurface cracks in coalescence with internally
distributed damage. The process can also be assisted by environmental
iv Deformation and Evolution of Life in Crystalline Materials
effects such as oxidation. In the next four chapters, Chapter 5 to Chapter
8, the ICFT is consistently applied to creep, low-cycle fatigue (LCF),
thermomechanical fatigue (TMF) and high-cycle fatigue (HCF) processes
and life prediction. Detailed mechanism-delineated treatments are given to
the above deformation and damage processes, which include: for example, a
mechanism-based true-stress model of the three-stage creep behaviour and
long-term creep life prediction with oxidation effect, a dislocation-based
mechanical fatigue life model and its extension to high-temperature LCF
and TMF, and HCF with foreign object damage, dwell damage and prior
creep damage. Such descriptions are not provided in any other books. To
describe crack nucleation and microscopic crack growth, Chapter 9 presents
a mathematical theory to treat continuously distributed dislocation pile-
ups in two basic forms—the Zener-Stroh-Koehler (ZSK) type and Bilby-
Cottrel-Swinden (BCS) type—in anisotropic crystalline materials with due
considerations for dislocation-microstructure interactions. The short crack
growth phenomenon is shown as an example. In Chapter 10, the processes
of macroscopic crack growth, or phenomenologically long crack growth,
under fatigue and creep conditions are treated with the consideration of the
average effect of the aforementioned dislocation mechanisms in the crack-
tip plastic/creep zone. The emphasis is on explanation of the relationships
between the crack growth rate and the crack-tip field controlling parameters
such as the stress intensity factor, and the microstructure and environment
dependence of such relationships. The crack closure concept is challenged
with an energy approach for the K-similitude, and the existence of fatigue
crack growth threshold is interrogated. The above deformation and crack
growth processes are actually integral parts of the holistic structural integrity
process (HOLSIP) that are divided into phases of 1) crack nucleation, 2) small
crack growth, 3) long crack growth, and 4) unstable fracture. In line with
material development for advanced gas turbine engines, Chapter 11 treats
single crystal Ni-base superalloys with consideration of anisotropy in creep,
fatigue and fatigue crack growth. In Chapter 12, microstructural evolution
and failure mechanisms in thermal barrier coatings are discussed, and a crack
number density theory description is given to the crack evolution process. In
Chapter 13, constitutive and life prediction models are developed for tensile,
creep and fatigue behaviors of ceramics matrix composites, which emerge as
advanced gas turbine materials to endure the hottest operating conditions.
Last but not the least, Chapter 14 reviews the current and trending component
lifing philosophies and provides a few case studies of component analyses
using ICFT. Particularly, a new paradigm—the holistic structural integrity
process concept—is introduced, which is better suited to the industrial trend
of prognosis health management schemes.
The ICFT is developed from the author’s work at the National Research
Council Canada, in collaboration with colleagues, as governmental research
for various industrial clients. The background phenomena and theories have
Preface v
been well documented in numerous publications in the literature. The author
can only give a brief summarization with a few references, given the limited
space of the book. The readers are encouraged to consult other books on
special topics such as theories of elasticity, plasticity and fracture mechanics
for further details.
Finally, the author is grateful to Bill Wallace, David Simpson and Jerzy
Komorowski, who supported the author’s research endeavour when they
acted as Director Generals of NRC Aerospace (research institute/portfolio/
center) and now are retired. The author also would like to thank several
colleagues, Drs. Rick Kearsey, Scott Yandt, and Zhong Zhang, who provided
constructive inputs into the book. Part of the analysis work of Chapter 5
was performed by Dr. Xiaozhou Zhang, as part of his Ph.D. thesis under the
supervision of the author and Prof. R. Liu from Carleton University.
Xijia Wu
Contents
Preface iii
1. Crystal Structure and Dislocation Kinetics 1
2. Deformation Mechanisms 34
3. Physics of Material Damage 60
4. The Integrated Creep-Fatigue Theory 75
5. Creep 91
6. Low Cycle Fatigue 139
7. Thermomechanical Fatigue 189
8. High Cycle Fatigue 212
9. Microscopic Crack Nucleation and Growth 229
10. Macroscopic Crack Growth 258
11. Single Crystal Ni-Base Superalloys 300
12. Thermal Barrier Coatings 313
13. Ceramics Matrix Composites 335
14. Component—Level Life Cycle Management 345
Appendix A: Solving Dislocation Distributions for a ZSK Crack 372
Appendix B: Solving Dislocation Distributions for a BCS Crack 375
References 378
Index 399
Color Plate Section 405
CHAPTER
1
Crystal Structure and Dislocation
Kinetics
1.1 Introduction
About 13.5 billion years ago, matter, energy, time and space came into
being in what is known as the Big Bang (from Sapiens—A Brief History of
Humankind by Y.N. Harari 2014). About 4.5 billion years ago, planet Earth
formed. About 10,000 years ago, when humans on planet Earth started to
use copper, the time is called the Copper Age. About 5,000 years ago, people
started to use bronze, an alloy of copper and tin, and the time is called the
Bronze Age. About 3,000 years ago, people started to use iron, and the time
is called the Iron Age. Only over the last 300 years, people started to make
more complicated alloys, from steels to superalloys, more recently.
Modern civilization is sustained by the use of advanced engineering
materials ranging from semiconductors to nickel-base superalloys. The
building blocks of all these materials are crystals. When an engineering
device, be it as small as a cell phone or as big as a gas turbine engine, enters
into service, the clock of its life starts to tick. Design engineers are constantly
striving for a better design of high efficiency and durable products. End-
users always want to maximize the performance with low-cost product life
cycle management. Both need advanced life prediction, which requires the
engineers to understand the material behaviour and damage mechanisms
operating under service load-environment (static, cyclic, thermal and fluid
dynamic) conditions.
Physical insights into the material behaviour begin with understanding
of the basic crystalline structures, their defects and the kinetics of defect
motion. The interactions between motion of defects and microstructure
result in various deformation and strengthening mechanisms. Material
designers often utilize these mechanisms to strengthen materials for various
applications. For description of deformation of a crystalline solid, one first
needs to understand solid mechanics concerning stress and strain distribution
within the solid. Usually, stress is generated via external stimuli, and strain
