Module 4: Fatigue & Creep
note set c:
• High Temperature Deformation.
• Introduction to Creep.
• Creep laws and deformation mechanism maps.
• Failure due to creep.
Low Temperature Deformation
• In module 2 we discussed plastic deformation at low temperatures.• During plastic deformation, dislocations move in the material resulting in permanent strain. The dislocations also multiply, leading to an increase in the yield stress.
• Deformation did not depend on time (or strain-rate). The stress and strain were related by a simple relation of the type:
st
re
ss
strain
st
ra
in
time n
k
Work-hardening
)
(
f
High Temperature Deformation
• At high temperature, the material behaves differently;-The stress-strain curve saturates.
-The saturation stress depends on temperature and strain-rate.
-If a constant stress is applied to the material, the strain will increase with time (it is not constant!!).
st
re
ss
strain
st
ra
in
time
saturation
f
(
,
T
,
,
t
)
High Temperature:
• So, what is a high temperature and what is a low temperature?
• We define high temperature as T/Tm > 0.3, where Tm is the melting point.
• Note how “high temperature” means different absolute temperatures for different materials. e.g. RT is high temperature for ice, Pb and Al, but not for Cu, Ni or Fe.
Material Tm (K) R.T./Tm Tm/3 (K)
W 3680 0.08 1200
SiC 3110 0.10 1000
Al2O3 2400 0.13 800
Fe 1809 0.16 600
Ni 1726 0.17 580
Cu 1084 0.27 360
Al 933 0.45 311
Pb 327 0.91 109
High T deformation:
• What is happening during high temperature deformation? -As before the material is work-hardening.
-At the same time, the high temperature permits the dislocations to recover. Recovery which takes place during deformation is known as
dynamic recovery.
st
re
ss
strain Saturation,
Work-hardening is balanced by dynamic recovery
rdt
hd
d
dt
dt
d
d
d
d
d
T
t
t
r -recovery, softening,
h hardening,
High T deformation:
• As the stress increases, the number of dislocations increases and the rate of dynamic recovery increases.
• Saturation occurs when the rate of dislocation creation by work-hardening is balanced by the rate of dislocation annihilation by dynamic recovery.
• Saturation stress corresponds to a dynamic equilibrium. Dislocations are continually being created and removed and they are continually moving through the material. As a result, the material continues to deform (strain increases).
st
re
ss
strain Saturation, work-hardening is balanced by dynamic recovery
st
ra
in
time
)
,
,
,
(
T
t
f
h r dt
d rdt
hd d
ss
0 0
ss
Introduction to Creep:
• Creep refers to high temperature deformation under a constant stress or constant load.
st
ra
in
time
0
I II
ss
-Initial strain: When the load is
applied an instantaneous deformation,
0, is observed.
-Stage I: During stage I, the strain increases at a decreasing rate (d/dt decreases). Stage I is relatively short.
-Stage II: This stage is known as the steady-state. The hardening and softening are balanced and
microstructure is constant.
-Stage III: Eventually, defects (voids) appear in the material, leading to
accelerated creep and eventual fracture.
Significance:
• Creep can lead to failure for the following applications:
- Displacement limited applications in which small clearances must be maintained (e.g. turbine
engine blade).
- Rupture limited applications: Creep can cause fracture at relatively small stresses (e.g. pressure piping).
- Stress-relaxation applications (e.g. pre-tensioning of cables and bolts).
- Buckling limited applications (e.g. upper wing skin of an aircraft).
need to understand creep fracture
need to understand stress relaxation
We won’t discuss.
understand to
Factors that influence Creep rate:
• Creep rate increases with the appliedstress and temperature.
• The rupture strain decreases with increasing stress and temperature.
• The material spends most of its life time at steady-state. For this reason models have been developed to describe the effects of stress and temperature on the steady-state strain-rate: st ra in time T and increasing
RT
Q
RT
Q
n ss ss n ssexp
exp
0 0 0
Activation energy is found to be that of diffusionConstitutive
Creep Mechanism:
• The stress dependence of the creep rate is determined experimentally bymeasuring the steady-state strain rate as a function of the applied stress.
• Two types of behavior are observed: -Power-law creep: is observed at high stresses. The creep exponent is typically between 3 and 8.
-Diffusional creep: is observed at low stresses. It shows linear
dependence on stress.
• One should be very careful when
Mechanism I: Power Law Creep
• Power law creep is controlled by dislocation motion.
• The dislocations are assumed to glide on the glide plane until they encounter an obstacle.
• Climb allows the dislocation to bypass the obstacle by permitting the dislocation to move to a slip plane which is parallel to the one containing the obstacle.
• The climb step is the rate limiting step. • The climb velocity is:
RT Q Q/RT) ( D D v b b kT D v SS c c exp exp and , , but 3 0 0 0 2
Mechanism II: Diffusional Creep
• At low stresses, a different type of creep mechanism dominates.
• This mechanism does not involve the motion of dislocations. It simply involves the motion of vacancies (i.e. diffusion).
• In the example below, the surfaces that are perpendicular to the tensile stress will have a higher vacancy concentration than the parallel surfaces. Vacancies migrate from areas where their concentration is high to areas where the concentration is low.
• Atoms migrate in the opposite direction and a net change in shape occurs.
Mechanism Maps:
• The various creep mechanisms take place simultaneously. The actual creep rate is that sum of all contributing creep mechanisms.
• We often find, however, that one
mechanism dominates under a certain set of conditions. The dominant mechanism is determined by temperature, stress and grain-size.
• Deformation mechanism maps
summarize the experimental data and show the region in temperature-stress space over which a given mechanism will dominate.
• Example shown is for Ni with grain size 100m.
m
T T /
E
0.000001 0.00001 0.0001 0.001 0.01 0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Elastic Creep L.T.
Creep H.T.
Diffusional Flow
1 GPa
100 MPa
10 MPa
1 MPa
0.1 MPa Ideal Strength
Plastic
Mechanism Maps:
m
T T /
10-8/s 10-9/s
10-7/s
Extrapolation of Creep Data:
• Some parts are expected to be in service for decades. It is not practical to test a new material or a new part for 10 or 20 yrs before approving it for service.
• Is there a way of carrying out accelerated creep testing? • The answer is yes. Starting with the equation:
Example:
• An chemical reactor part is required to operate for 20 yrs at 500oC. The
steel from which the part is made was tested at 700oC. Its life at 700oC, was
found to be 11 days. If the activation energy for creep is 210kJ/mole and if the creep mechanism is not expected to change in the temperature range from 500 to 700oC, determine if the above steel can be used in the reactor.
yrs
days
t
t
C
C
C
R
Q
C
t
T
t
f f f f9
.
24
9085
314
.
8
210000
]
6
.
23
)
)[ln(
273
500
(
500
At
ln(days)
6
.
23
314
.
8
210000
]
)
11
)[ln(
273
700
(
]
)
[ln(
days
1
1
C,
700
At
o o
Warning! Make sure theSignificance:
• Creep can lead to failure for the following applications:
- Displacement limited applications in which small clearances must be maintained (e.g. turbine
engine blade).
- Rupture limited applications: Creep can cause fracture at relatively small stresses (e.g. pressure piping).
- Stress-relaxation applications (e.g. pre-tensioning of cables and bolts).
- Buckling limited applications (e.g. upper wing skin of an aircraft).
need to understand creep fracture
need to understand stress relaxation
We won’t discuss.
understand to
High Temperature Failure:
• High temperature fracture resembles low temperature ductile fracture in many way.
• Rupture failure is associated with high-strain rates and high temperatures (hot-working conditions). Void nucleation is suppressed and the material necks down to a point.
• Intergranular and transgranular creep fracture involve the nucleation, growth and coalescence of voids. The nucleation and growth of voids is responsible for accelerated creep during stage III.
rupture
Intergranular creep fracture (ICF)
High Temperature Failure:
• Void nucleation takes place at boundaries and second phase particles due to plastic
incompatibilities.
• Void growth is accelerated by diffusional and power-law creep.
-The formation of vacancies on surfaces perpendicular to the tensile stress and their
migration (diffusional flow) cause the void to grow. This partly accounts for the increase in creep rate during tertiary creep.
-The area between voids is subjected to higher stresses. Since power-law creep is a strong
function of the stress, accelerated creep take place in these regions and this contributes to the
increase in strain rate during tertiary creep.
• When the void boundary area fraction (rh/l)2
reaches a critical value, rapid failure occurs.
High Temperature Failure:
Significance:
• Creep can lead to failure for the following applications:
- Displacement limited applications in which small clearances must be maintained (e.g. turbine
engine blade).
- Rupture limited applications: Creep can cause fracture at relatively small stresses (e.g. pressure piping).
- Stress-relaxation applications (e.g. pre-tensioning of cables and bolts).
- Buckling limited applications (e.g. upper wing skin of an aircraft).
need to understand creep fracture
need to understand stress relaxation
We won’t discuss.
understand to
Stress Relaxation:
• So far we considered the case in which the sample elongates in response to a fixed stress/load.
• Another important case is that in which the total strain is constant and the stress decays with time. To understand this consider the following:
BEt n B dt d E B dt d E B E n i n n n cr el tot tot n cr el cr el tot ) 1 ( 1 1 1 0 1 : constant is since and but, 1
1
1 ) 1 ( 1 1 1 1 BEt n E E n i n i n
Elastic strain at time t
Example:
• In order to counteract stress relaxation, a casting bolt in a large turbo-generator has to be retightened at regular intervals. Assuming that the bolt must be tightened when the elastic stress falls to half its initial value, derive an expression for the time after which the bolt must be retightened.
