This document discusses creep, which is the time-dependent deformation of materials under sustained stress and elevated temperature. It provides background on creep testing and defines the three stages of creep: primary, secondary, and tertiary. Equations to describe creep behavior and the effect of stress and temperature on creep curves are presented. Creep properties of metals, nonmetals like concrete, and factors that influence concrete creep are examined through examples. The document is authored by Salih Khudair for a class on the theory of elasticity and references additional sources on experimental techniques and mechanics of materials.

1. Theory of Elasticity CE 527
Creep, Time Dependent Deformation
SUBMITTED BY:
SALIH KHUDAIR
PHD STUDENT
201568988
SUBMITTED TO:
Assist. Prof. Dr. Nildem TAYŞİ
UNIVERSITY OF GAZIANTEP
FACULTY of ENGINEERING
DEPARTMENT of CİVİL ENGINEERING
MECHANİC FİELD

2. Introduction
Creep being defined as time-dependent inelastic strain under sustained load and elevated
temperature.
Because creep deformation is significant at elevated temperatures, it is frequently
described as a thermally activated process, that is, temperature plays an important role.
The meaning of elevated temperature must be determined individually for each material
on the basis of its behavior, elevated temperature behavior for various metals occurs over
a wide range of temperature, for example, at 205°C (479 K) for aluminum alloys, 315°C
(588 K) for titanium alloys, 370°C (644 K) for low-alloy steels.
For certain plastics, asphalt, concrete, lead, and lead alloys, elevated temperatures for
creep behavior may lie in the range of "ordinary temperatures," say, from 0°C to 50°C
(274 K to 324 K).

3. 1. Different standards for creep testing specify
the geometric design of test specimens
(ASTM, 1983; BSI, 1987; ISO, 1987).
2. During the test, the tension specimen is
subjected to sufficiently high stress a and
temperature T to produce time-dependent
inelastic strain (creep).
3. The strain in the specimen varies with time.
For an appropriate constant stress and
elevated temperature.
1. A strain-time plot (creep curve)
The Tension Creep Test for Metals

4. Creep curve
1. Creep curve exhibits three
distinct ranges.
2. The primary range of the creep
curve, the strain rate (the slope of
the creep curve), decreases, until
It reaches some minimum rate.
3. The secondary range, this
minimum rate is maintained,
more or less, until a time at
which the strain rate begins to increase.
4. In the tertiary range, the strain rate continues to increase under the sustained stress and
temperature until at time t = tR, the specimen is pulled apart .

5. The creep behavior of materials is usually evaluated in terms of the creep rate, that is, the
change in creep strain with time (dε/dt = ). Since creep rate corresponds to the strain rate
 The creep strain in stage I can be described using the equation:
 Since the creep strain changes linearly with time during the secondary stage, the creep
strain is given by the equation
The value of is most important and is used in evaluating the useful life of engineering
components that are expected to be operated for a long period of time (several years)
 The creep strain during Stage III is expressed by the relation
ε = 𝐴𝑡1/3
𝛆 = 𝜀 𝑜 + t
𝛆 = B + C exp(γt)
.
εs
.
εs
.
ε

6. Effect of Stress and Temperature
 if the material used to generate curve C1 is
subjected to a lower load or temperature, its
response may be given by curve C0, for
which the tertiary range of creep is never
reached.
 If the material of curve C1 is subjected to a
higher stress or temperature, its response may
be given by curve C2. Or curve C3 (for which
both the primary and secondary ranges of creep
are bypassed and for which fracture occurs in
a relatively short time).

7. This Fig. illustrates the change in the creep curve that is produced by increasing the stress
level in steps of approximately 20 MPa from 83 to 164 MPa. Which the same increases in the
creep strain also occur with temperature for constant stress.

8. Since creep is a thermally activated process, the creep rate can be
expressed as:
= C exp−(
𝑸
𝑹𝑻
)
Where C is the preexponential constant, Q is the activation
energy for creep, R is the universal gas constant, and T is the
temperature expressed in degrees Kelvin. By taking natural
logarithms on both sides of the above equation, we get
ln = ln C −(
𝑸
𝑹𝑻
)
The value of the activation energy, Q enables one to predict the
mechanism by which creep occurs.
.
εs
.
εs
Slop = (−Q /R)
Reciprocal temperature (1/T )
lnsteady-statecreeprate(ln)
.
εs

9. The empirical relations have been developed between the steady-state creep rate
and the applied stress and temperature. The stress dependence of the steady-
state creep rate can be expressed as
= 𝐴1σ 𝑛
if both stress and temperature effects are considered together, then the steady-
state creep rate is expressed as
= 𝐴1σ 𝑛 exp(-Qc/RT)
This equation is known as the power-law equation.
.
εs
.
εs
.
εs
.
εs

10. Creep formulas for metals
A number of formulas that have been used to represent creep curves, the
equations separated into time-, temperature-, and stress-dependent parts:-
 The time- dependence formulas are sometimes of the form
ϵ = ϵ0+ ϵ 𝑐
where ϵ 𝑐= ϵ 𝑃𝐶 + ϵ 𝑆𝐶 + ϵ 𝑇𝐶, ϵ is the total strain, ϵ0 is the initial strain, ϵ 𝑐 is
creep strain, and ϵ 𝑃𝐶, ϵ 𝑆𝐶, ϵ 𝑇𝐶denote primary, secondary, and tertiary creep,
respectively.

13. ϵ denotes total strain, ϵ 𝑐 creep strain, σ stress, T temperature, t time, ln the natural logarithm,
exp the exponential e, and a, b, c,..., A, B, C,... parameters that may be functions of σ, t, T or
they may be constants. Time derivative is denoted by a dot over a symbol (e.g., ). The notation
f(x) denotes a function of x.
.
ε

14. Creep of nonmetals
• The mechanical behavior of many nonmetallic materials during creep is somewhat
simpler than that of metals like glass, polymers, and cements.
• The creep behavior of other nonmetals, such as concrete, asphalt, and wood, is very
complex.
• Concrete is a material that undergoes an aging process, such that under sustained load
the modulus of elasticity changes with time.
• Aging is a phenomenon which changes creep of concrete. It is caused mainly by cement
hydration, a process that continues for a long time after the initial hardening period.
Aging changes the rate of creep and, hence, must be accounted for. This fact increases the
difficulty of predicting the creep behavior of concrete.

15. The creep of concrete
• The creep of concrete is affected by a large number of factors. For example,
water-reducing admixtures tend to increase creep rates.
• Many other experimental variables affect the creep of concrete, for example, paste
parameters (porosity, age, etc.), concrete parameters (aggregate stiffness,
aggregate/cement content, volume to surface ratio), and environmental parameters
(applied stress, duration of load, humidity, etc.).
• Usually, the creep of concrete is influenced more by paste properties, since the
aggregate tends to retard creep rate.

16. The creep strain-stress relation in concrete is usually taken to be:-
ϵ 𝑐= ɸσ
Where ɸ is called the specific creep. The concept of specific creep is useful for
comparing the creep of different concrete specimens at different stress levels.
A typical value of ɸ is approximately 150 μ /MPa, μ = 10−6m
Calculating creep of concrete

17. The American Concrete Institute (ACI, 1991) has developed a simplified creep
equation of the form :
Where t denotes time, В is a constant that depends on the age of the concrete
before loading (B is taken to be 10 when the concrete is more than 7 days old
before loading), and Cult is the ultimate creep coefficient. The value of Cult is
difficult to determine, as it may vary considerably (for 40% relative humidity)
Cult may range between (1.30 and 4.5).
ACI recommends a value of Cult = 2.35.

18. Example 1:
A specimen has been subjected to creep. If the strain measured in stage ‫׀׀‬ is 0.003 at 600h and 0.002 at 200h,
calculate the steady state creep rate of the specimen.
Solution:
Since the steady-state creep rate is the slope of the strain versus time straight line the steady-state creep rate can
be calculated as:
Steady-state creep rate =
Δ𝜖
Δ𝑡
=
0.003−0.002
600ℎ−200ℎ
=
0.001
400ℎ
= 0.0000025 h-1
Or = 2.5 × 10-6 h-1
Example 2:
A metallic alloy exhibits a steady-state creep rate of 2.5 × 10-4 h-1 at a temperature of 550 ºC and 3.2 × 10-3 h-1
at 650 ºC. Calculate the activation energy for creep.
Solution:
Since the steady-state creep rate is given at two different temperatures, and we wish to calculate the activation
energy
.
εs

19. The temperature need to be expressed in degrees K. therefore 550ºC =550+273=823K and
650ºC =650+273=923K. Substituting the appropriate values into this equation at those temperature, we obtain
= C exp(-Q/RT)…… (Mott, 1953)
3.2 ×10-3 h-1 = C exp(- 𝑄
8.314 j mol−1 K−1×(923𝐾)
)
2.5 ×10-3 h-1 = C exp(- 𝑄
8.314 j mol−1 K−1 ×(823𝐾)
)
Dividing the above equations with each other, we get :
3.2 ×10−3 h−1
2.5 ×10−3 h−1 = exp[ -
𝑄
8.314 j mol−1 K−1 (
1
923
-
1
823
)]
1.28 ×10 h-1 = exp[ -
𝑄
8.314 j mol−1 K−1 ( −1.316 10-4 )]
Taking natural logarithms on both sides
Ln(1.28 ×10) = [(-
𝑄
8.314
)(−1.316 ×10-4 )]
2.55= Q ×1.583 ×10-5
Q =1.611 ×105 J mol−1, that is , 161 kJ mol−1
.
εs

20. Reference
 Challapalli Suryanarayana, Experimental Techniques in Materials and Mechanics, CRC
Press (2011).
 Arthur P. Boresi, Richard J. Schmidt, 6th ed. Advanced mechanics of materials, Wiley
(2003).