ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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Wear, Vol 59, 1980, p 191–211
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Waterhouse, Ed., Pergamon, 1988, p 87–98
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I, 1999, p 38–45
Introduction to Creep and Stress-Relaxation Testing
James C. Earthman, University of California at Irvine
Introduction
THE FIELD of materials behavior at elevated temperatures has seen a formidable wealth of advancements over
the last century. These accomplishments were made possible by the work of many scientists and engineers
throughout the world who developed critical technologies necessary to make high-temperature materials
stronger and more reliable (Ref 1, 2, 3). Applications for these materials include jet engines, power generation
facilities, automobile engines, and electronic devices (Ref 4, 5). The potential efficiency of these systems
typically increases with increasing operating temperature. This natural trend provides a strong demand for
materials that can withstand higher temperatures. For aerospace applications, there is also a strong need for
reducing weight, and it is often the high-temperature materials that have the highest densities in the aerospace
structure. Reduced weight has been achieved by reducing component geometry, leading to greater stresses in
high-temperature materials. Naturally, the importance of reliable creep and stress-rupture testing increases with
increasing service stress. Introducing new high-temperature materials that have lower densities is another
means by which weight reduction goals have been met for aerospace structures.
References cited in this section
1. Creep and Fracture of Engineering Materials and Structures: Proc. of the Seventh International Conf.
in honor of Prof. Oleg D. Sherby, (University of California, Irvine), 10–15 Aug 1997, J.C. Earthman
and F.A. Mohamed, Ed., Minerals, Metals and Materials Society/AIME, 1997
2. Creep Behavior of Advanced Materials for the 21st Century, proc. from 1999 TMS annual meeting (San
Diego, CA), 28 Feb to 4 March 1999, R.S. Mishra, A.K. Mukherjee, and K.L. Murty, Ed., Minerals,
Metals and Materials Society/AIME, 1999
3. Advanced Materials for the 21st Century: The 1999 Julia R. Weertman Symposium, proc. from 1999
TMS fall meeting (Cincinnati, OH), 31 Oct to 4 Nov 1999, Y-W. Chung, D.C. Dunand, P.K. Liaw, and
G.B. Olson, Ed., Minerals, Metals and Materials Society/AIME, 1999
4. H.T. Lin, P.F. Becher, M.K. Ferber, and V. Parthasarathy, “Verification of Creep Performance of a
Ceramic Gas Turbine Blade,” paper presented at the Science of Engineering Ceramics II, an
International Symposium, (Osaka, Japan), 1998
5. Frontiers in Electronics: High Temperature and Large Area Applications, proc. of Symposium A on
High Temperature Electronics, Materials, Devices, and Applications, and proc. of Symposium B on
Thin Film Materials for Large Area Electronics of the 1996 E-MRS Spring Conference (Strasbourg,
France), 4–7 June 1996, J. Camassel et al., Ed., Elsevier, Amsterdam, 1997
Introduction to Creep and Stress-Relaxation Testing
James C. Earthman, University of California at Irvine
Trends and New Technologies in Materials Testing
Considerable resources and effort have been spent over the last few decades on developing new methods of
materials synthesis in order to satisfy the demand for better high-temperature materials. For example,
mechanical alloying, sol gel processing, and various spray processing technologies have developed rapidly (Ref
6). These and other processing methods have successfully provided new materials systems that exhibit
significantly higher creep strengths compared to those for conventional alloys. These new materials are
typically tested extensively at elevated service temperatures before they can be approved for use (Ref 3). The
demand for reliable data has led to the advancement of high-temperature testing methodologies that incorporate
computer-based data acquisition and control.
Creep deformation and rupture experiments are used to determine the strength and lifetime of materials under
quasi-static conditions at elevated temperatures. This testing typically involves imposing constant stress or
displacement conditions as well as a constant elevated temperature. In addition to simulating service
environments, these quasi-static conditions typically induce a physical behavior that is quite tractable from a
theoretical perspective. Accordingly, there have been a considerable number of advancements in the theory of
creep and creep rupture that can provide a physically based understanding of the microstructural mechanisms
that govern the observed behavior. For the practicing engineer, an understanding of the physics of creep
behavior can be quite useful for determining how a material might be altered microstructurally to perform better
at elevated temperatures. This knowledge can also be used to improve methods of predicting high-temperature
behavior from extrapolations of available laboratory data. With a good fundamental understanding, an engineer
might also exercise more wisdom in selecting the best material for a given application. In light of these benefits,
the following article in this Section, “Creep Deformation of Metals, Polymers, Ceramics, and Composites,”
reviews the current theoretical underpinnings of creep deformation of engineering materials. This article
provides the theoretical background for understanding many of the physical processes relevant to the testing
methods, experimental results, and analytical approaches described in the subsequent articles.
Our best understanding of creep behavior has been developed for constant stress conditions. For relatively small
strains (less than about 1%), constant load conditions suffice as a good approximation of constant stress in a
creep experiment. For larger strains, constant stress conditions must be strictly imposed in order to obtain valid
data. Accordingly, various approaches for imposing constant stress conditions in a creep test are presented in
the article “Creep and Creep-Rupture Testing” in this Section. This article has been updated in the present
volume to include two computer-aided approaches that are emerging as the preferred methods for creep
laboratories.
Creep rupture often presents a severe risk in high-temperature applications when not addressed using
appropriate testing and data interpretation methods. The article “Assessment and Use of Creep-Rupture
Properties” covers methods for accurately assessing creep rupture properties. These methods include
established interpolation and extrapolation procedures and properties-estimation schemes when data is sparse.
The methods presented in this Section are primarily useful for testing under constant stress conditions.
Stress relaxation testing involves imposing a constant displacement under load at elevated temperatures. As
mentioned above, this approach represents another quasi-static loading condition that can provide useful
information about creep properties. The term stress relaxation refers to the time-dependent decrease in stress as
creep deformation reduces elastic strain in the specimen under a fixed displacement. One of the primary
advantages of this approach is that it can often provide an assessment of creep properties in a fraction of the
time it takes using constant stress methods. It is also the most appropriate testing scheme when the target
application, such as high-temperature bolting, undergoes a constant displacement condition. The article “Stress
Relaxation Testing” gives an overview of methods that may be used to rapidly generate creep data over several
orders of magnitude in strain rate.
Creep properties have for the most part been studied under uniaxial stress conditions in which the loading is
applied parallel to the longitudinal axis of a cylindrical or plate specimen. Although uniaxial stress experiments
have led to a good understanding of the physical processes involved, they often do not provide sufficient
information to predict the behavior of high-temperature components. Load bearing parts at elevated
temperatures are often subjected to multiaxial loading conditions that drive the deformation and rupture
mechanisms in a manner that is different from uniaxial loads. Multiaxial conditions are particularly relevant for
pressurized pipe and vessel components subjected to high temperatures. Hence, it is generally necessary to
impose multiaxial stress conditions in creep and creep-rupture testing so that the effects of multiaxial stress
states can be appropriately addressed. Accordingly, an article is also presented in this Section that describes the
current state-of-the-art for testing tubular samples at elevated temperatures under multiaxial conditions.
Superplastic behavior refers to the ability of some fine-grained materials to achieve strains at elevated
temperatures exceeding 300% and, in some cases, in excess of 2000%. From an industrial perspective,
superplastic materials are of great interest because of the ability to produce complex shapes in a single
inexpensive forming operation, eliminating labor-intensive machining costs. Naturally, exceptional testing
methods are generally required for superplastic materials due to the large strains that are realized. A
comprehensive overview entitled “Superplastic Deformation at Elevated Temperatures” is provided in this
Section. Considerations for determining the optimum strain rate and impurity level are also discussed in this
article.
References cited in this section
3. Advanced Materials for the 21st Century: The 1999 Julia R. Weertman Symposium, proc. from 1999
TMS fall meeting (Cincinnati, OH), 31 Oct to 4 Nov 1999, Y-W. Chung, D.C. Dunand, P.K. Liaw, and
G.B. Olson, Ed., Minerals, Metals and Materials Society/AIME, 1999
6. Non-Equilibrium Processing of Materials, C. Suryanarayana, Ed, Pergamon Materials Series, Vol 2,
Pergamon, 1998
Introduction to Creep and Stress-Relaxation Testing
James C. Earthman, University of California at Irvine
References
1. Creep and Fracture of Engineering Materials and Structures: Proc. of the Seventh International Conf.
in honor of Prof. Oleg D. Sherby, (University of California, Irvine), 10–15 Aug 1997, J.C. Earthman
and F.A. Mohamed, Ed., Minerals, Metals and Materials Society/AIME, 1997
2. Creep Behavior of Advanced Materials for the 21st Century, proc. from 1999 TMS annual meeting (San
Diego, CA), 28 Feb to 4 March 1999, R.S. Mishra, A.K. Mukherjee, and K.L. Murty, Ed., Minerals,
Metals and Materials Society/AIME, 1999
3. Advanced Materials for the 21st Century: The 1999 Julia R. Weertman Symposium, proc. from 1999
TMS fall meeting (Cincinnati, OH), 31 Oct to 4 Nov 1999, Y-W. Chung, D.C. Dunand, P.K. Liaw, and
G.B. Olson, Ed., Minerals, Metals and Materials Society/AIME, 1999
4. H.T. Lin, P.F. Becher, M.K. Ferber, and V. Parthasarathy, “Verification of Creep Performance of a
Ceramic Gas Turbine Blade,” paper presented at the Science of Engineering Ceramics II, an
International Symposium, (Osaka, Japan), 1998
5. Frontiers in Electronics: High Temperature and Large Area Applications, proc. of Symposium A on
High Temperature Electronics, Materials, Devices, and Applications, and proc. of Symposium B on
Thin Film Materials for Large Area Electronics of the 1996 E-MRS Spring Conference (Strasbourg,
France), 4–7 June 1996, J. Camassel et al., Ed., Elsevier, Amsterdam, 1997
6. Non-Equilibrium Processing of Materials, C. Suryanarayana, Ed, Pergamon Materials Series, Vol 2,
Pergamon, 1998
Creep Deformation of Metals, Polymers, Ceramics,
and Composites
Jeffery C. Gibeling, University of California, Davis
Introduction
CREEP DEFORMATION is any permanent inelastic strain that occurs when a material is subjected to a
sustained stress. The rate at which this deformation occurs depends not only on the magnitude of the applied
stress, but also on time and temperature. Thus, it is appropriate to consider creep to be a kinetic process and to
write an appropriate rate law. In addition, the rate at which a material creeps depends on the size, spacing, and
distribution of relevant microstructural features. As a consequence, it is also necessary to write equations that
describe how the internal structure changes with respect to time or strain (Ref 1, 2).
Creep is considered to be a high-temperature phenomenon, although it is important to recognize that
temperature is a relative quantity for any material. In crystalline solids such as metals and ceramics, creep is of
concern when the service temperature is greater than or equal to approximately 0.5 T
m
, where T
m
is the absolute
melting temperature, commonly expressed on the Kelvin scale (Ref 3, 4). In the creep literature, it is common
to refer to the ratio of T/T
m
as the homologous temperature.. Because homologous rather than absolute
temperature is the relevant quantity, nickel-base superalloys undergo creep in gas turbine engine blades and
vanes at 900 to 1400 K (1160–2060 °F), whereas the solder used to attach integrated circuits to their packages
can deform at a service temperature of 400 K (260 °F). In both cases, the service temperature is high with
respect to the melting point of the material. However, some crystalline materials exhibit measurable creep
strains at temperatures as low as 0.25 T
m
. In noncrystalline materials such as polymers and glasses, the relevant
reference is the glass transition temperature, T
g
, above which creep occurs at measurable rates.
These observations suggest that a material with a sufficiently high melting temperature be chosen to achieve the
creep resistance needed in a particular application. To do so, however, is rarely practical because of a variety of
other design requirements including cost, density, and environmental stability. For this reason, the goal of
materials engineers is to identify compositions and microstructures that will lead to improved creep strength at
a given service temperature. To do so requires an understanding of the mechanisms by which creep deformation
occurs.
References cited in this section
1. W.D. Nix and J.C. Gibeling, Mechanisms of Time-Dependent Flow and Fracture of Metals, Flow and
Fracture at Elevated Temperatures, R. Raj, Ed., American Society for Metals, 1985, p 1–63
2. B. Ilschner and W.D. Nix, Mechanisms Controlling Creep of Single Phase Metals and Alloys, Strength
of Metals and Alloys, Vol 3, P. Haasen et al., Ed., Pergamon Press, New York, 1980, p 1503–1530
3. O.D. Sherby and P.M. Burke, Mechanical Behavior of Crystalline Solids at Elevated Temperature,
Prog. Mater. Sci., Vol 13 (No. 7), 1967, p 325–390
4. A.K. Mukherjee, J.E. Bird, and D.E. Dorn, Experimental Correlations for High Temperature Creep,
ASM Trans. Quart., Vol 62, 1969, p 155–179
Creep Deformation of Metals, Polymers, Ceramics, and Composites
Jeffery C. Gibeling, University of California, Davis
Creep Testing
Creep deformation is normally studied by applying either a constant load (equivalent to a constant engineering
stress) or a constant true stress to a material at a sufficiently high homologous temperature that a measurable
amount of creep strain occurs in a reasonable time. Constant load testing is normally employed for engineering
purposes, because this situation most accurately represents service loading conditions. In contrast, constant true
stress testing is used to study deformation mechanisms. At small strains, the two methods give essentially the
same results. However, since the focus of this article is on creep mechanisms, primary consideration is given to
the outcome of constant true stress experiments. The basic record of such a test is a plot of creep strain, ε,
versus time, t, as illustrated schematically in Fig. 1(a) for loading in tension. It is often useful to numerically
differentiate these data to determine the creep rate, dε/dt, or , as shown in Fig. 1(b). Normally, a small
permanent loading strain, ε
o
, is observed when the creep stress is first applied. This strain occurs so rapidly that
it is generally treated as instantaneous. With increasing strain, the creep rate gradually decreases. This
hardening transient is called primary creep. Eventually, however, the creep rate reaches a constant value,
known as the steady state creep rate,
ss
, or minimum creep rate in the secondary region. This value is
commonly used to characterize the creep resistance of materials and to identify the mechanism that control the
creep process. In addition, the steady state region often represents the largest fraction of time during the creep
test because the strain rate is the lowest. As strain continues to occur, however, microstructural damage also
begins to accumulate, and the creep rate increases. This final stage, known as tertiary creep, immediately
precedes failure or creep rupture of the test specimen. The tertiary creep strains may be quite large in some
materials, especially at high stresses.
Fig. 1 Schematic illustration of the dependence for pure materials of (a) creep strain on time and (b)
creep rate on creep strain
A variety of empirical relations have been proposed to describe the shape of the creep curve shown in Fig. 1(a).
At low temperatures (T < 0.3T
m
), the primary creep transient is often logarithmic with time, and steady state
may not be reached. The resulting creep response can be represented by a logarithmic dependence of strain on
time. At higher temperatures, the transition from primary to secondary creep can be described by an equation of
the form:
ε = ε
o
+ βt
m
+
ss
t
(Eq 1)
where m is typically equal to and β is a constant. A more recent approach is based on an empirical fitting
procedure to describe all three regions given by:
ε = θ
1
(1 - ) + θ
3
( − 1)
(Eq 2)
where the θ parameters include both the stress and temperature dependence of the creep process (Ref 5). It
should be noted that this approach is based on the inherent assumption that the minimum creep rate represents a
transition from primary to tertiary creep without the presence of any true steady state creep rate. This approach
is especially relevant for many high-strength metals, intermetallic compounds, and ceramics for which the
steady state region does not persist over large strains or long times.
As noted earlier, this discussion of creep mechanisms is based on data obtained primarily from constant true
stress testing. However, the form of the creep curve is very similar under constant load testing. Since creep
deformation occurs under conditions of constant volume (until internal voids begin to form during tertiary
creep), the cross-sectional area must decrease as the sample length increases for deformation in tension. If the
load is held constant, then the true stress must increase with increasing strain. As a consequence, a steady state
is not expected under constant load conditions, and the tertiary region includes the effects of both
microstructural and geometric softening. It is important to note, however, that this distinction between the two
loading modes is only apparent at large strains.
While the characteristic creep response shown in Fig. 1 represents the behavior of a large number of materials,
there are other important cases in which the creep response is quite different. For example, some solid solution
strengthened alloys exhibit an inverted primary transient when the interaction between the solute atoms and the
gliding dislocations is rate controlling. This observation is illustrated schematically in Fig. 2(a). Other materials
may exhibit a behavior that combines a normal transient with an inverted transient, resulting in a sigmoidal
primary region. This behavior is shown in Fig. 2(b).
Fig. 2 Schematic illustrations of the variation of creep strain with time. (a) Behavior exhibited by some
solid solution strengthened materials characterized by an inverted primary transient. (b) Behavior of
some other materials that combines a normal transient with an inverted transient
Reference cited in this section
5. R.W. Evans and B. Wilshire, A New Theoretical and Practical Approach to Creep and Creep Fracture,
Proc. Seventh International Conf. Strength of Metals and Alloys, H.J. McQueen, J.-P. Bailon, J.I.
Dickson, J.J. Jonas, and M.G. Akben, Ed., Pergamon Press, Oxford, 1986, p 1807–1830
Creep Deformation of Metals, Polymers, Ceramics, and Composites
Jeffery C. Gibeling, University of California, Davis
Phenomenological Descriptions of Creep
Current knowledge of the mechanisms that control creep deformation is based on a combination of empirical
correlations of results and micromechanical models (Ref 1, 2, 3, 4). Although a number of significant
theoretical descriptions of creep have been presented, current understanding is based primarily on a correlation
of the results from hundreds of independent investigations. In simplest form, creep of a variety of materials
exhibiting a variety of mechanisms can be described by a phenomenological rate equation of the form:
(Eq 3)
where A is approximately constant for a given material, n is the stress exponent, G is the elastic shear modulus,
and Q
c
is the activation energy for creep. This equation describes the dependence of the creep rate on the two
key external variables, temperature and stress. Specific values of n and Q
c
are associated with specific creep
mechanisms. Thus, by characterizing the stress and temperature dependence of the creep rate, it is often
possible to identify the rate-controlling mechanism for a particular material. Commonly, it is observed that the
activation energy for creep is the same as that for diffusion; hence, the term exp -Q
c
/kT is replaced by the
relevant diffusivity, D (Ref 3, 4).
In the following sections, the creep behavior of crystalline and amorphous materials are considered separately.
The emphasis in all cases is on correlating the macroscopic behavior with the underlying microscopic
mechanisms. This requires that a variety of internal variables that describe the microstructural features that
control the rate of deformation be considered.
References cited in this section
1. W.D. Nix and J.C. Gibeling, Mechanisms of Time-Dependent Flow and Fracture of Metals, Flow and
Fracture at Elevated Temperatures, R. Raj, Ed., American Society for Metals, 1985, p 1–63
2. B. Ilschner and W.D. Nix, Mechanisms Controlling Creep of Single Phase Metals and Alloys, Strength
of Metals and Alloys, Vol 3, P. Haasen et al., Ed., Pergamon Press, New York, 1980, p 1503–1530
3. O.D. Sherby and P.M. Burke, Mechanical Behavior of Crystalline Solids at Elevated Temperature,
Prog. Mater. Sci., Vol 13 (No. 7), 1967, p 325–390
4. A.K. Mukherjee, J.E. Bird, and D.E. Dorn, Experimental Correlations for High Temperature Creep,
ASM Trans. Quart., Vol 62, 1969, p 155–179
Creep Deformation of Metals, Polymers, Ceramics, and Composites
Jeffery C. Gibeling, University of California, Davis
Creep Behavior of Crystalline Solids
The mechanisms of creep in crystalline solids primarily include dislocation motion and atomic diffusion. Each
process dominates in certain regimes of stress and temperature for a given material. Accordingly, the stress and
temperature dependencies of the creep rate can be used to identify the relevant creep mechanisms.
Diffusional Creep. Mechanistically, diffusional creep leads to deformation of grains when the transport of
atomic vacancies (opposite to the direction of atom transport) is biased by an applied stress. As a consequence,
it is necessary to include a grain-size dependence in the phenomenological creep equation, resulting in an
expression of the form:
(Eq 4)
where d is the grain size and b is the Burgers vector. This grain size dependence is introduced because the grain
boundaries serve as sources and sinks for the diffusing vacancies. Equation 4 reflects a linear dependence of
creep rate on stress; hence, n = 1. When diffusion through the grain interiors provides the most rapid path, then
the diffusivity, D, is equal to the lattice or bulk self-diffusion coefficient. This process is known as Nabarro-
Herring creep. Alternatively, diffusion may be more rapid through the grain boundaries, in which case D in Eq
4 is replaced by δD
gb
/d, where δ is the grain boundary width and D
gb
is the grain boundary diffusivity. As a
consequence, the creep rate varies as d
-3
when diffusion occurs via grain boundaries; this mechanism is known
as Coble creep. Thus, the grain size exponent can be used to distinguish between mechanisms that exhibit the
same stress exponent.
Diffusional creep is favored at high temperatures, low stresses, and fine grain sizes. As a consequence, this
mechanism is especially important in ceramic materials, where dislocation motion may be restricted by the
strong lattice friction associated with ionic and covalent bonding. Small, stable grains result from common
processing methods. Conversely, resistance to diffusional creep can be improved by increasing the grain size or
developing an elongated grain structure through directional solidification.
Dislocation Creep. When many crystalline metals and ceramics are tested at intermediate temperatures and
stresses, the predominant deformation mechanism involves the motion of dislocations. Upon initial application
of a stress to a well-annealed material, dislocations move rapidly, as there are few obstacles to their motion.
However, they also multiply rapidly, and the subsequent strain hardening causes the creep rate to decrease
dramatically during the primary transient as represented in Fig. 1. This strain hardening arises as the number of
dislocations increases and they begin to serve as barriers to glide motion of other dislocations. During the
primary creep transient, the dislocation structure gradually becomes organized into low-angle boundaries that
define subgrains within the grains. This substructure becomes more stable as deformation approaches steady
state. Through careful study of deformed materials, it is possible to demonstrate that the size of several key
microstructural features scales with the applied stress in the steady state regime. Specifically, the subgrain size,
the spacing of dislocations in the subgrain interiors, and the dislocation spacing within subgrain walls all vary
as σ
-1
. These microstructural features remain in dynamic equilibrium during steady state deformation as
dislocations are continuously generated and annihilated (Ref 2, 6).
One of the most influential and compelling observations regarding creep of single-phase materials is that the
temperature dependence is the same as that for lattice self-diffusion. This evidence supports the concept that
power law creep is diffusion controlled. Diffusion is needed to enable dislocations to climb past obstacles to
their continued glide. Thus, creep occurs by the sequential processes of dislocation glide and climb. As the
climb step is slower than glide, it is rate controlling. A compilation of creep activation energy data (Q
c
) for a
wide variety of metals and ceramics shows that it is inevitably equal to the activation energy for self diffusion
Q
L
(Fig. 3). It should be noted that both species must diffuse to enable dislocation creep to occur in ceramics,
but the creep rate is controlled by the rate of diffusion of the slower moving ions. While there are a few notable
exceptions to the rule that Q
c
= Q
L
, the preponderance of evidence supports the concept that the rate of power
law creep is controlled by lattice self-diffusion at homologous temperatures greater than 0.5. At lower
temperatures, the activation energy falls to lower values, as shown in Fig. 4. The lower plateau (in the range
0.25< T
H
< 0.5) generally corresponds to the activation energy for vacancy diffusion along dislocation cores. In
this temperature range, the creep rate also depends on the density of dislocations to serve as diffusion paths.
Since dislocation density varies inversely with stress, this leads to an effective diffusivity, D
eff
, given by:
(Eq 5)
where D
c
is the self-diffusion coefficient in the dislocation core and β is a constant about equal to 10. As a
consequence of this additional stress dependence, the expected stress exponent is n = 7 in this temperature
range.