1. Anandh Subramaniam & Kantesh Balani
CREEP
CREEP
Creep mechanisms (and maps)
Creep resistant materials
MATERIALS SCIENCE
&
ENGINEERING
Anandh Subramaniam & Kantesh Balani
Materials Science and Engineering (MSE)
Indian Institute of Technology, Kanpur
URL: home.iitk.ac.in/~anandh
AN INTRODUCTORY E-BOOK
Part of
A Learner’s Guide
Mechanical Metallurgy
George E Dieter
McGraw-Hill Book Company, London (1988)

2. Mechanisms / Methods by which a can Material can FAIL
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-chemical degradation
Creep
Physical degradation
Fatigue
Plastic
deformation
Fracture
Microstructural changes
Twinning
Wear
Slip
Twinning
Corrosion
Erosion
Phase transformations
Oxidation
Grain growth
Particle coarsening
* Beyond a certain limit

3. Plastic Deformation in Crystalline Materials
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

4. 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.

5. High temperature effects (many of the effects described below are coupled)
Increased vacancy concentration  at high temperatures more vacancies are thermodynamically stabilized.
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.

6. 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 > 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

7. I II III Strain () → 0 t → 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.
Constant load creep curve
Stages of creep I II
Stage-I
Creep rate decreases with time.
Effect of work hardening more than recovery.
III
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 →

8.   Constant Stress creep curve I II Strain () → III t →
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). I II
Strain () →
III  
t →

9. 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).   
Strain () →
Elastic strains
Increasing stress
 →
0 increases
 → t1
t →

10. Effect of temperature Strain () → E↓ as T↑ Increasing T  →  → 0 t1
On increasing the temperature at which the experiment is conducted: (i) the instantaneous strain (elastic) increases (slightly), (ii) for a given time (say t1) the strain is more, (iii) the time to failure (tf) decreases.   
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 →

11. 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 creep: 1 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. Typically these maps overlay descriptors, which are based both on phenomenology and mechanism.

12. Creep Dislocation related Diffusional Grain boundary sliding
Creep Mechanisms of crystalline materials
Cross-slip
Dislocation related
Climb
Glide
Coble creep
Creep
Grain boundary diffusion controlled
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

14. 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.

15. Diffusional creep
Nabarro-Herring creep → high T → lattice diffusion
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 

16. 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 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.

17. Creep resistance 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

18. 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.