CREEP

1
CREEP

• Review of plastic deformation and failure
• Creep Mechanisms (and Maps)
• Creep Resistant Materials
• Creep in Nanomaterials
• Superplasticity
• Superplascity in Nanomaterials

Mechanical Metallurgy George E Dieter
McGraw-Hill Book Company, London (1988)
2
Review
If failure is considered as change in desired
performance- which could involve changes in
properties and/or shape then failure can occur
by many mechanisms as below.
Mechanisms / Methods by which a can Material can
FAIL
Elastic deformation
Chemical /Electro-chemicaldegradation
Creep
Physicaldegradation
Fatigue
Plastic deformation
Fracture
Microstructuralchanges
Twinning
Wear
Slip
Twinning
Erosion
Corrosion
Phase transformations
Oxidation
Grain growth
Particle coarsening
Beyond a certain limit
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Review
Though plasticity by slip is the most important
mechanism of plastic deformation, there are other
mechanisms as well (plastic deformation here
means permanent deformation in the absence of
external constraints)
Plastic Deformation in Crystalline Materials
Slip(Dislocation motion)
Twinning
Phase Transformation
Creep Mechanisms
Grain boundary sliding
Other Mechanisms
Vacancy diffusion
Grain rotation
Dislocation climb
Note Plastic deformation in amorphous materials
occur by other mechanisms including flow
(viscous fluid) and shear banding
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High-temperature behaviour of materials

• Designing materials for high temperature
  applications is one of the most challenging tasks
  for a material scientist.
• Various thermodynamic and kinetic factors tend to
  deteriorate the desirable microstructure. This is
  because kinetics of underlying processes (like
  diffusion) are an exponential function of
  temperature.? Hence, a small increase in
  temperature can prove to be catastrophic.
• Strength decreases at high temperature and
  material damage (e.g. void formation) tends to
  accumulate.
• Phenomena like creep and accelerated oxidation
  kick-in.
• Cycling between high and low temperature will
  cause thermal fatigue.

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High temperature effects (many of the effects
described below are coupled)

• Increased vacancy concentration ? at high
  temperatures more vacancies are thermodynamically
  stabilized (this will further increase the
  diffusion rate).
• Thermal expansion ? material will expand and in
  multiphase materials/hybrids thermal stresses
  will develop due to differential thermal
  expansion of the components.
• High diffusion rate ? diffusion controlled
  processes become important.
• Phase transformations can occur ? this not only
  can give rise to undesirable microstructure, but
  lead to generation of internal stresses. ?
  Precipitates may dissolve.
• Grain related? Grain boundary weakening ? may
  lead to grain boundary sliding and wedge
  cracking. ? Grain boundary migration ?
  Recrystallization / grain growth ? decrease in
  strength.
• Dislocation related ? these factors will lead to
  decrease in strength ? Climb ? New slip systems
  can become active ? Change of slip system ?
  Decrease in dislocation density.
• Overaging of precipitates and precipitate
  coarsening ? decrease in strength.
• The material may creep (time dependent elongation
  at constant load/stress).
• Enhanced oxidation and intergranular penetration
  of oxygen.

Etc.
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Creep
Creep is phenomenological term, which is
responsible for plastic deformation.

• In some sense creep and superplasticity are
  related phenomena in creep we can think of
  damage accumulation leading to failure of sample
  while in superplasticity extended plastic
  deformation may be achieved (i.e. damage
  accumulation leading to failure is delayed).
• Creep is permanent deformation (plastic
  deformation) of a material under constant load
  (or constant stress) as a function of time.
  (Usually at high temperatures ? lead creeps at
  RT).

• Normally, increased plastic deformation takes
  place with increasing load (or stress)
• In creep plastic strain increases at constant
  load (or stress)
• Usually appreciable only at T gt 0.4 Tm ? High
  temperature phenomenon.
• Mechanisms of creep in crystalline materials is
  different from that in amorphous materials.
  Amorphous materials can creep by flow.
• At temperatures where creep is appreciable
  various other material processes may also active
  (e.g. recrystallization, precipitate coarsening,
  oxidation etc.- as considered before).

• Creep experiments are done either at constant
  load or constant stress and can be classified
  based on Phenomenology or underlying Mechanism.

Phenomenology
Constant load (easier)
Creep can be classified based on
Harper-Dorn creep
Creep tests can be carried out at
Power Law creep
Constant stress
Mechanism
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Constant load creep curve

• In a typical creep test the load and temperature
  are kept constant and the elongation is monitored
  with time. The strain (typically engineering
  strain) computed from the elongation is plotted
  as function of time. The loads employed are
  typically below the elastic limit.
• Three stages may be observed in such a plot (i)
  decreasing rate with time, (ii) approximately
  constant rate, (iii) increasing rate with time.
  These stages have to be understood keeping in
  view underlying mechanisms ( necking in
  stage-III).
• The instantaneous strain seen (?0) is the elastic
  strain, which develops on the application of the
  load.

Measured as strain rate (note that this strain
rate is not the one imposed as in UTT, but the
one which develops in the material)
Stages of creep
Constant load creep curve

• Stage-I
• Creep rate decreases with time.
• Effect of work hardening more than recovery.

I
II
III
A technical term

• Stage-II
• Stage of minimum creep rate ? constant.
• Work hardening is balanced by recovery.

Strain (?) ?

• The distinguishability of the three stages
  strongly depends on T and ?

• Stage-III
• Absent (/delayed very much) in constant stress
  tests (shown later).
• Necking of specimen starts in this stage.
• Specimen failure processes set in.

?0 ? Initial instantaneous strain
?0
t ?
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Constant Stress creep curve

• In stage-III (due to necking) the engineering
  stress is no longer a correct measure of the
  state of stress. To keep the stress constant, the
  instantaneous area has to be taken into account.
• If this is done, then the increasing strain rate
  part is not observed. Note if load is kept
  constant then in stage-III the stress is actually
  increasing (for the material it is stress which
  matters and not load).

II
I
Strain (?) ?
III
?
?
t ?
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Effect of stress on the creep curve (constant
load)

• On increasing the load at which the experiment is
  conducted (i) the instantaneous strain
  (?elastic) increases, (ii) for a given time (say
  t1) the strain is more, (iii) the time to failure
  (tf) decreases (i.e. as expected, specimens fail
  earlier).

Fracture
?
?
?
Elastic strains
Strain (?) ?
? ?
Increasing stress
With increasing load there is increased initial
elastic strain
? ?
?0 increases
t ?
t1
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Effect of temperature

• On increasing the temperature at which the
  experiment is conducted (i) the instantaneous
  strain (?elastic ?0) increases (slightly),
  (ii) for a given time (say t1) the strain is
  more, (iii) the time to failure (tf) decreases.
• The instantaneous strain ?0 increases with
  increasing T because of the slight decrease in
  the Youngs modulus (E) of the material.

?
?
?
Strain (?) ?
E? as T?
Increasing T
? ?
As decrease in E with temperature is usually
small the ?0 increase is also small
?0 increases
? ?
?0
t1
t ?
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Creep Mechanisms of crystalline materials

• Stress and temperature are the two important
  variables, which not only affect the creep rate,
  but also the mechanism operative. Three kinds of
  mechanisms are operative in creep1? dislocation
  related, 2? diffusional, 3? grain boundary
  sliding. These and their sub-classes are shown
  in the next page.
• At high temperatures the grain boundary becomes
  weaker than the grain interior and two grains can
  slide past one another due to shear stress. The
  temperature at which the grain is as strong as
  the grain boundary is called the equicohesive
  temperature.
• A combination of these mechanisms could also be
  responsible for the creep strain.
• Depending on the stress and temperature other
  mechanisms of plastic deformation or
  microstructural changes may occur concurrently
  with creep. These include plastic deformation by
  slip and dynamic recrystallization.
• Deformation mechanism maps can be drawn with
  homologous temperature (T/Tm) and normalized
  shear stress (?/G) as the axis (other combination
  of variables may also be chosen for these plots
  T/Tm vs shear strain rate, normalized shear
  stress vs shear strain rate, etc.). Typically
  these maps overlay descriptors, which are based
  both on phenomenology and mechanism.

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Creep Mechanisms of crystalline materials
Cross-slip
Climb
Dislocation related
Glide
Coble creep
Grain boundary diffusion controlled
Creep
Diffusional
Nabarro-Herring creep
Lattice diffusion controlled
Dislocation core diffusion creep
Diffusion rate through core of edge dislocation
more
Interface-reaction controlled diffusional flow
Grain boundary sliding
Accompanying mechanisms creep with dynamic
recrystallization
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Creep Mechanisms of crystalline materials
Cross-slip
Harper-Dorn creep
Climb
Dislocation related
Glide
Coble creep
Creep
Grain boundary diffusion controlled
Nabarro-Herring creep
Diffusional
Lattice diffusion controlled
Dislocation core diffusion creep
Diffusion rate through core of edge dislocation
more
Interface-reaction controlled diffusional flow
Grain boundary sliding
Accompanying mechanisms creep with dynamic
recrystallization
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Dislocation related mechanisms

• Two roles can be differentiated with respect to
  of dislocations activity (i) it is the primary
  source of strain, (ii) it plays a secondary role
  to accommodate local strain (while the major
  source of strain is another mechanism (e.g. grain
  boundary sliding).

Cross-slip

• This kind of creep is observed at relatively low
  temperatures. Herein screw dislocations
  cross-slip by thermal activation and give rise to
  plastic strain as a function of time.

Dislocation climb

• Edge dislocations piled up against an obstacle
  can climb to another slip plane and cause plastic
  deformation. In response to stress this gives
  rise to strain as a function of time. It is to be
  noted that at low temperatures these dislocations
  (being pinned) are sessile and become glissile
  only at high temperatures.
• Rate controlling step is the diffusion of
  vacancies.

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Nabarro-Herring creep ? high T ? lattice diffusion
Diffusional creep
Coble creep ? low T ? Due to GB diffusion
?

• In response to the applied stress vacancies
  preferentially move from surfaces/interfaces (GB)
  of specimen transverse to the stress axis to
  surfaces/interfaces parallel to the stress axis?
  thus causing elongation.
• Diffusion of vacancies in one direction can be
  thought of as flow of matter in the opposite
  direction.
• This process like dislocation creep (involving
  climb) is controlled by the diffusion of
  vacancies (but diffusional creep does not require
  dislocations to operate).
• The diffusion could occur predominantly via the
  lattice (at high temperatures) or via grain
  boundaries (at low temperatures). The former is
  known as Nabarro-Herring creep, while the later
  is known as Coble creep.
• Diffusion through edge dislocation cores (pipe
  diffusion) could play an important role in creep.

Flow of vacancies
?
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Grain boundary sliding

• At low temperatures the grain boundaries are
  stronger than the crystal interior and impede
  the motion of dislocations.
• Being a higher energy region, the grain
  boundaries may pre-melt before the crystal
  interior.
• Above the equicohesive temperature, due to shear
  stress at the local scale, grain boundaries
  slide past one another to cause plastic
  deformation.
• The relative motion of grain boundaries can lead
  to wedge cracks at triple lines (junction of
  three grains). If these wedge cracks are not
  healed by diffusion (or slip), microstructural
  damage will accumulate and will lead to failure
  of the specimen.

Grains
Wedge crack due to grain boundary sliding
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Phenomenological descriptions of creep

• One of the important descriptions of creep is
  using the power-law formula. The shear strain
  rate is a power function of the shear stress.
  Clearly this formula is not based on a mechanism
  operative, but a fit of data.

• Power-law behaviour can arise from
• Only glide at low temperatures (0.3TM). Here the
  exponent n 3.
• Glide climb (referred to as climb controlled
  creep) occurs at higher temperatures. Above
  0.6TM climb is lattice-diffusion controlled. At
  lower temperatures than this pipe diffusion may
  play an important role in creep.
• At high stresses (gt 10?3G) the power law breaks
  down. At high stresses the mechanism changes from
  climb controlled (creep) to glide controlled
  (slip). This is bordering on normal plastic
  deformation.

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Deformation Mechanism Maps

• Time and temperature are coupled when it comes to
  processes like diffusion.
• At large values of stresses and at low T, the
  time available is less (as material
  immediately begins to deform plastically) and
  creep mechanisms do not have time (/activation)
  to operate.
• Usually contours of constant strain rate are
  superimposed on these diagrams (not shown here).
  Stress or strain rate can be used as axes
  (variable). In components (e.g. truss in a
  structure, pressure vessel, etc.) stress is
  prescribed, while in processing (e.g.
  extrusion, forging, etc.), strain rate is
  prescribed.

At high stresses plastic flow will take place
The dominant mechanism is shown in the diagram
Dynamic recrystallization gives rise to
strain-free grains.
At high temperature and low stress Diffusional
creep dominates
From Deformation Mechanism Maps The plasticity
and creep of Metals and Ceramics by H.J. Frost
and M.F.Ashby, Pergamon Press, Oxford, 1982.
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From Deformation Mechanism Maps The plasticity
and creep of Metals and Ceramics by H.J. Frost
and M.F.Ashby, Pergamon Press, Oxford, 1982.
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Creep Resistant Materials

• The is a growing need for materials to operate at
  high temperatures (and in some applications for
  long times). For example, higher operating
  temperatures gives better efficiency for a heat
  engine. Hence, there is a need to design
  materials which can withstand high temperatures.
• It is to be noted that material should also be
  good in other properties for high temperature
  applications (like it should possess good
  oxidation resistance). Factors like cost, ease of
  fabrication, density, etc. play an important role
  in determining the final choice of a material.
• Some of the material design strategies, which
  work at low temperature are not useful at high
  temperatures (e.g. work hardening, precipitation
  hardening with precipitates which coarsen, grain
  size reduction, etc.).
• Some strategies which work are (i) having grain
  boundaries aligned along the primary loading
  axis, (ii) produce single crystal components
  (like turbine blades), (iii) use precipitates
  with low interfacial energy for strengthen (which
  will not coarsen easily), (iv) use dispersoids
  for strengthening.

High melting point ? E.g. Ceramics
Creep resistance
Dispersion hardening ? ThO2 dispersed Ni (0.9 Tm)
Solid solution strengthening
Single crystal / aligned (oriented) grains
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Creep Resistant Materials, cotd..

• Commonly used materials ? Fe, Ni (including
  superalloys), Co base alloys.
• Precipitation hardening involving usual
  precipitates is not a good method as
  precipitates coarsen (smaller particles dissolve
  and larger particles grow ? interparticle
  separation ? thus lowering the strength)
• Ni-base superalloys have Ni3(Ti,Al) precipitates,
  which form a low energy interface with the
  matrix. This reduces the driving force for
  coarsening. (Note other phenomena like rafting
  may lead to the deterioration of the properties
  of such materials).
• Cold work cannot be used for increasing creep
  resistance, as recrystallization can occur which
  will produced strain free crystals.
• Fine grain size is not desirable for creep
  resistance (this is contrary to what is usually
  practiced for increasing the low temperature
  strength)? grain boundary sliding can cause creep
  elongation/cavitation. Hence, the following two
  strategies can be used? Use single crystals
  (single crystal Ti turbine blades in gas turbine
  engine have been used? though they are very
  costly).? Aligned/oriented polycrystals ? as all
  the grain boundaries are aligned along the
  primary tensile axis, they experience no shear
  stress and creep is negated.

Which coarsen at high temperatures due to high
interfacial energy.
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Creep in Nanomaterials

• Due to fine grain size nanostructured materials
  (grain size in the nanoscale regime) are expected
  to (i) show creep at relatively lower
  temperatures, (ii) display higher creep rates for
  a give temperature, (iii) experience predominance
  of mechanisms like grain boundary diffusion and
  grain boundary sliding. We now see what is
  actually seen in experiments.
• In nanocrystalline Pd (40 nm) and Cu (20 nm),
  there seemed to be no increase in creep rate as
  compared to micron grain sized materials (in some
  temperature regimes even a lower creep rate was
  observed for Pd). This is in direct contradiction
  with the expectation that nanocrystalline
  materials will experience a higher creep rate.
• ? Studies on Cu (10-25 nm GS), Pd (35-55 nm GS)
  (TEM showed porocity in sample) 1 ? creep in
  the low T regime (0.24-0.33 Tm) ? low creep
  rate, low grain growth ? creep in the medium T
  regime (0.33-0.48 Tm) ? creep rate decreasing
  even after long testing time, grain growth (25 nm
  ? 100s of nm)

• Cu creep rates of nc sample was comparable to
  micron GS sample
• Pd nc sample exhibited lower creep rates

1 P.G. Sanders, M. Rittner, E. Kiedaisch, J.R.
Weertman, H.Kung, Y.C. Lu, Nanostruct. Mater. 9
(1997) 433. 2 D.L. Wang, Q.P. Kong, J.P. Shui,
Scr. Metall. Mater. 31 (1994) 47.
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• In some cases the creep rate increased with a
  decrease in grain size in the nanoscale regime of
  grain sizes (e.g. in Ni-P nanocrystalline
  material the creep rate of 30 nm grain sized
  material was higher than that of 250 nm material
  2).
• In cases where high creep rate expected for
  nanocrystalline materials (e.g. Pd, Cu) was not
  observed, the reason attributed are (i)
  presence of low angle grain boundaries and twin
  boundaries (which are not prone to sliding and
  have low diffusivity for vacancies), (ii)
  reduced dislocation activity in nanocrystalline
  samples.

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• Creep of nc-Ni at RT (GS 6, 20, 40 nm) 1?
  Smaller grain size (6nm) showed faster creep
  rate.? Behaviour consistent with Grain boundary
  sliding controlled by grain boundary diffusion
  mechanism.? At high stresses and larger GS (20,
  40 nm), dislocation creep was observed.

1 N. Wang, Z. Wang, K.T. Aust, U. Erb, Mater.
Sci. Eng., A 237 (1997) 150.
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Superplasticity
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Superplasticity

• The phenomenon of extensive plastic deformation
  without necking is termed as structural
  superplasticity. Superplastic deformation in
  tension can be gt300 (up to even 2000).
• Typically superplastic deformation occurs when
  (i) T gt 0.5Tm(ii) grain size is lt 10 ?m(iii)
  grains are equiaxed (which usually remain so
  after deformation)(iv) grain boundaries are
  glissile (with a large fraction of high angle
  grain boundaries).
• Presence of a second phase (of similar strength
  to the matrix- reduces cavitation during
  deformation), which can inhibit grain growth at
  elevated temperatures helps (e.g. Al-33Cu,
  Zn-22 Al)).
• Many superplastic alloys have compositions are
  close to eutectic or eutectoid points.
• Superplastic flow is diffusion controlled (can be
  grain boundary or lattice diffusion controlled).

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• A plot of stress versus strain rate is often
  sigmoidal and shows three regions
• Region-I- low stress, low strain rate regime (
  lt10?5 /s) ? m ? (0.2,0.33) Sensitive to the
  purity of the sample. Lower ductility and grain
  boundary diffusion.
• Region-II- intermediate stress strain rate
  regime ? (105, 102) ? m ? (0.4,0.67)Exten
  ded region covering several orders of magnitude
  in strain rate. Region of maximum ductility.
  Strain rate insensitive to grain size and
  insensitive to purity. Often referred to as the
  superplastic region.Mechanism? predominantly
  grain boundary sliding accommodated by
  dislocation activity (Activation energy (Q)
  corresponding to grain boundary diffusion (Qgb)).
• Region-III- high stress strain rate regime (
  gt 10?2 /s) ? m gt 0.33Creep rates sensitive to
  grain size. Mechanism? intragranular dislocation
  process (interacting with grain boundaries).

Note low m in region I and III
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Superplasticity in Nanomaterials

• In most cases the superplasticity has not
  fulfilled the initial expectations.
• In many cases superplasticity is only observed in
  nanocrystalline samples, where it is already
  observed in their microcrystalline counterparts.
• Superplasticity was observed in nanocrystalline
  Ni (20 nm grain size) at 0.36Tm (more than 450?C
  lower than that for the bulk material) 1.
• Nanocrystalline Ni3Al (grain size 50 nm) also
  became superplastic about 450?C below its
  microcrystalline counterparts. Ni3Al had a
  ductility of 350 at 650?C (strain rate of
  103 /s).
• 1420-Al alloy showed superplasticity at a high
  strain rate of 101 /s. High amount work
  hardening and higher flow stress for superplastic
  deformation as compared to micron grain sized
  material is observed in these cases.
• Superplasticity was observed in 40 nm grain size
  Zn-Al alloy at 373 K, tested at a strain rate of
  104 /s 2. Microcrystalline samples showed no
  superplasticity!

Ni3Al (cP4, Pm-3m)
1 S. X. McFadden, R. S. Mishra, R. Z. Valiev,
A. P. Zhilyaev and A. K. Mukherjee, Nature 398
(1999) 684. 2 R.S. Mishra, R.Z. Valiev, A.K.
Mukherjee, Nanostruct. Mater. 9 (1997) 4732.
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• Superplasticity at low temperature (or
  equivalently Superplasticity at high strain rates
  (gt 102 /s) at a given temperature in the
  superplastic regime) is caused by ? increased
  diffusion, grain boundary sliding and dislocation
  activity.
• Grain growth is a serious issue during
  superplasticity experiments. In the case of nc-Ni
  it was seen that the grain size could increase to
  micron sizes, from the starting grain size of the
  order of 20 nm. In other materials the grain
  growth could be less. Grain growth is expected to
  be less is two phase mixtures (2nd phase as a
  precipitate preferred) and intermetallic
  compounds. In two phase mixtures the 2nd phase
  has a pinning effect on the grain boundaries
  while in intermetallics (like Ni3Al) order (with
  respect to the sublattices) has to be maintained
  during grain growth, which restrains the process.
  
• In cases where grain boundary sliding is the
  predominant mechanism for superplasticity (e.g.
  in some Mg alloys), it is seen that
  non-equilibrium grain boundaries give lower
  elongation as compared to equilibrium grain
  boundaries (due to the long range stress fields
  associated with non-equilibrium grain boundaries,
  which is expected to hamper grain boundary
  sliding).
• In Ni3Al the high flow stresses and extensive
  strain hardening during superplastic deformation
  has been attributed to depletion of dislocations
  and high stresses required for the nucleation of
  new ones 1.

1 R.S. Mishra, R.Z. Valiev, S.X. McFadden,
A.K. Mukherjee, Mater. Sci. Eng., A 252 (1998)
174.