Fundamentals of Creep in Metals and Alloys

289 Pages·2009·4.91 MB·English

by  Michael Kassner

Preface
This book on the fundamentals of creep plasticity is a review and analysis of investigations
in a variety of areas relevant to creep plasticity. These areas include fi ve-power-law creep,
which is sometimes referred to as dislocation climb-controlled creep in metals, alloys and
ceramics, viscous glide or Three-Power-Law creep in alloys, diffusional creep, Harper-
Dorn creep, superplasticity, second-phase strengthening, and creep cavitation and fracture.
Many quality reviews and books precede this attempt to write an extensive review of creep
fundamentals and improvement was a challenge. One advantage with this attempt is the
ability to describe the substantial work published subsequent to these earlier reviews. An
attempt was made to cover the basic work discussed in these earlier reviews but especially
to emphasize more recent developments.
This is the second edition of this book, and one aspect of this recent edition is correcting
errors in the fi rst edition. Also, many advances have occurred over the fi ve years since
the fi rst edition and theses are also incorporated. Dr. María-Teresa Pérez-Prado was a
co-author of the fi rst edition. While she did not participate in the formulation of the sec-
ond edition, Chapters 5, 6 and 9 remain largely a contribution by Dr. Pérez-Prado, and her
co-authorship is indicated on these chapters.
List of Symbols and Abbreviations
a cavity radius
a lattice parameter
0
A(cid:1) – A(cid:2)(cid:2) constants
A
A
F
A
C–J solute dislocation interaction parameters
A
APB
A
SN
A
CR
A grain boundary area
gb
A Harper–Dorn equation constant
HD
A constants
PL
A projected area of void
v
A – A constants
0 12
b Burgers vector
B constant
c concentration of vacancies
c* crack growth rate
c concentration of jogs
j
c concentration of vacancies in the vicinity of a jog
p
c* steady-state vacancy concentration near a jog
p
c equilibrium vacancy concentration
v
cD vacancy concentration near a node or dislocation
v
c initial crack length
0
C concentration of solute atoms
C* integral for fracture mechanics of time-dependent plastic materials
C constant
1–2
C Larson–Miller constant
LM
CBED convergent beam electron diffraction
CGBS cooperative grain-boundary sliding
CS crystallographic slip
CSL coincident site lattice
C* constant
0
C–C constants
1 5
d average spacing of dislocations that comprise a subgrain boundary
D general diffusion coeffi cient
D diffusion coeffi cient for climb
c
xii Fundamentals of Creep in Metals and Alloys
D effective diffusion coeffi cient
eff
D diffusion coeffi cient for glide
g
Dgb diffusion coeffi cient along grain boundaries
D interfacial diffuson
i
D surface diffusion coeffi cient
s
D lattice self-diffusion coeffi cient
sd
D diffusion coeffi cient for vacancies
v
D diffusion constant
0
DRX discontinuous dynamic recrystallization
~
D diffusion coeffi cient for the solute atoms
e solute-solvent size difference or misfit parameter
E Young’s modulus
E formation energy for a jog
j
EBSP electron backscatter patterns
f fraction
f fraction of mobile dislocations
m
f chemical dragging force on a jog
p
f fraction of material occupied by subgrains
sub
F total force per unit length on a dislocation
g average grain size (diameter)
g(cid:1) constant
G shear modulus
GBS grain-boundary sliding
GDX geometric dynamic recrystallization
GNB geometrically necessary boundaries
h dipole height
h hardening rate
r
h average separation between slip planes within a subgrain with gliding
m
dislocations
HAB high-angle boundary
HVEM high-voltage transmission electron microscopy
j jog spacing
J J integral for fracture mechanics of plastic material
J vacancy flux along a grain boundary
gb
k Boltzmann constant
k(cid:1) – k˝´ constants
ky Hall–Petch constant
k Monkman–Grant constant
MG
k relaxation factor
R
k – k constants
1 10
List of Symbols and Abbreviations xiii
K constant
K stress intensity factor
I
K – K constants
0 7
l link length of a Frank dislocation network
l critical link length to unstably bow a pinned dislocation
c
l maximum link length
m
l migration distance for a dislocation in Harper–Dorn creep
L particle separation distance
LAB low-angle boundary
LM Larson–Miller parameter
m strain-rate sensitivity exponent (= 1/N)
m(cid:1) transient creep time exponent
m(cid:2) strain-rate exponent in the Monkman–Grant equation
m constant
–c
(cid:3) average Taylor factor for a polycrystal
M dislocation multiplication constant
(cid:4)
n steady-state creep exponent
n* equilibrium concentration of critical-sized nuclei
n steady-state stress exponent of the matrix in a multi-phase material
m
N constant structure stress exponent, and dislocation link length per unit volume
N nucleation rate, and rate of release of dislocation loops
p steady-state dislocation density stress exponent
p(cid:1) inverse grain size stress exponent for superplasticity
PLB power law breakdown
POM polarized light optical microscopy
PSB persistent slip band
q dislocation spacing, d, stress exponent
Q activation energy for creep (with E or G compensation)
c
Q(cid:1) apparent activation energy for creep (no E or G compensation)
c
Q activation energy for dislocation pipe diffusion
p
Q activation energy for lattice self-diffusion
sd
Q formation energy for a vacancy
v
Q* effective activation energies in composites where load transfer occurs
r recovery rate
r
R diffusion distance
0
R radius of solvent atoms
s
s structure
SAED selected area electron diffraction
t time
t time for cavity coalescence on a grain-boundary facet
c
xiv Fundamentals of Creep in Metals and Alloys
t time to fracture (rupture)
f
t time to the onset of steady-state
s
T temperature
T dislocation line tension
d
T melting temperature
m
T temperature of the peak yield strength
p
TEM transmission electron microscopy
(cid:5) dislocation glide velocity
(cid:5) dislocation climb velocity
c
(cid:5) critical dislocation velocity at breakaway
cr
(cid:5) Debye frequency
D
(cid:5) jog climb velocity
p
(cid:5) average dislocation velocity
(cid:5) climb velocity of dislocation links of a Frank network
l
w width of a grain boundary
average dislocation climb distance
c
average dislocation slip length due to glide
g
XRD x-ray diffraction
(cid:6) Taylor equation constant
(cid:6)(cid:1) climb resistance parameter
(cid:6) constants
1–3
(cid:7) constants
1–3
(cid:8) shear straing
(cid:8) anelastic unbowing strain
A
(cid:8) interfacial energy of a grain boundary
gb
(cid:8) surface energy of a metal
(cid:9)m
(cid:8) shear creep-rate
(cid:9)
(cid:8) steady-state shear creep-rate
ss
(cid:10) grain boundary thickness
(cid:1)a activation area
(cid:1)G Gibbs free energy
(cid:1)V activation volume for creep
C
(cid:1)V activation volume for lattice self-diffusion
L
(cid:11) uniaxial strain
(cid:11) instantaneous strain
(cid:11)(cid:9) 0 strain rate
(cid:11)(cid:9) minimum creep-rate
(cid:11)(cid:9)m in steady-state uniaxial strain-rate
(cid:11)–s s effective uniaxial or von Mises strain
(cid:12) misorientation angle across high-angle grain boundaries
List of Symbols and Abbreviations xv
(cid:12) misorientation angle across (low-angle) subgrain boundaries
(cid:13)
(cid:12) average misorientation angle across (low-angle) subgrain boundaries
(cid:13)ave
(cid:13) average subgrain size (usually measured as an average intercept)
(cid:13) cavity spacing
s
(cid:13) average steady-state subgrain size
ss
ν Poisson’s ratio
(cid:4) density of dislocations not associated with subgrain boundaries
(cid:4) mobile dislocation density
m
(cid:4) mobile screw dislocation density
ms
(cid:4) steady-state dislocation density not associated with subgrain wall
ss
(cid:14) applied uniaxial stress
(cid:14) internal stress
i
(cid:14) single crystal yield strength
0
(cid:14)(cid:1) annealed polycrystal yield strength
0
(cid:14)(cid:2) sintering stress for a cavity
0
(cid:14) Peierls stress
p
(cid:14) uniaxial steady-state stress
ss
(cid:14) transition stress between five-power-law and Harper–Dorn creep
T
(cid:14) threshold stress for superplastic deformation
THs
(cid:14)(cid:14)– y|T,(cid:11)(cid:9) yefifeeldct oivre fl uonwia sxtiraels, so ar tv ao nre Mferiesensc,e s tteremssperature and strain-rate
(cid:15) shear stress
(cid:15) breakaway stress of the dislocations from solute atmospheres
b
(cid:15) critical stress for climb over a second-phase particle
c
(cid:15) detachment stress from a second-phase particle
d
(cid:15) stress to move screw dislocations with jogs
j
(cid:15) Orowan bowing stress
or
(cid:15) shear stress necessary to eject dislocation from a subgrain boundary
B
(cid:15) maximum stress from a simple tilt boundary
BD
(cid:15) stress to move a dislocation through a boundary resulting from jog creation
L
(cid:15) shear strength of a Frank network
N
((cid:15)/G) normalized transition stress
t
(cid:16)(P) Frank network frequency distribution function
χ stacking fault energy
χ(cid:1) primary creep constant
(cid:17) angle between cavity surface and projected grain-boundary surface
ω maximum interaction energy between a solute atom and an edge dislocation
m
Ω atomic volume
ω fraction of grain-boundary area cavitated
Chapter 1
Introduction
M.E. Kassner
1.1 DescriptionofCreep 3
1.2 Objectives 8

Chapter 1
Introduction
1.1 DESCRIPTIONOFCREEP
Creep of materials is classically associated with time-dependent plasticity under a fixed
stress at an elevated temperature, often greater than roughly 0.5 T , where T is the
m m
absolute melting temperature. The plasticity under these conditions is described in
Figure1forconstantstress(a)andconstantstrain-rate(b)conditions.Severalaspectsof
the curve in Figure 1 require explanation. First, three regions are delineated: Stage I, or
primarycreep,whichdenotesthatportionwhere[in(a)]thecreep-rate(plasticstrain-rate),
e_ ¼de=dt is changing with increasing plastic strain or time. In Figure 1(a) the primary-
creep-rate decreases with increasing strain, but with some types of creep, such as solute
drag with “3-power creep,” an “inverted” primary occurs where the strain-rate increases
withstrain.Analogously,in(b),underconstantstrain-rateconditions,themetalhardens,
resultinginincreasingflowstresses.Often,inpuremetals,thestrain-ratedecreasesorthe
stressincreasestoavaluethatisconstantoverarangeofstrain.Thephenomenonistermed
StageII,secondary,orsteady-statecreep.Eventually,cavitationand/orcrackingincrease
the apparent strain-rate or decrease the flow stress. This regime is termed Stage III, or
tertiarycreep,andleadstofracture.Sometimes,StageIleadsdirectlytoStageIIIandan
“inflection”isobserved.Thus,caremustsometimesbeexercisedinconcludingamechan-
icalsteady-state(ss).
Theterm“creep”asappliedtoplasticityofmaterialslikelyarosefromtheobservation
thatat modestand constantstress, at or even belowthe macroscopicyield stress ofthe
metal(ata“conventional”strain-rate),plasticdeformationoccursovertimeasdescribed
in Figure 1(a). This is in contrast with the general observation, such as at ambient
temperature, where, a material deformed at, for example, 0.1–0.3T , shows very little
m
plasticity under constant stress at or below the yield stress, again, at “conventional” or
typical tensile testing strain-rates (e.g., 10(cid:2)4–10(cid:2)3s(cid:2)1). {The latter observation is not
always true as it has been observed that some primary creep is observed (e.g., a few
percentstrain, orso) over relatively shortperiodsoftime at stresses lessthan theyield
stressinsome“rate-sensitive”andrelativelylowstrain-hardeningalloyssuchastitani-
um [1] and steels [2].}
WeobserveinFigure2thatatthe“typical”testingstrainrateofabout10(cid:2)4s(cid:2)1,theyield
stressiss .However,ifwedecreasethetestingstrain-rateto,forexample,10(cid:2)7s(cid:2)1,the
y1
yield stress decreases significantly, aswill be showniscommon for metals and alloysat
high temperatures. To a “first approximation,” we might consider the microstructure
3