fatigue life prediction of thermo-mechanically loaded engine
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FATIGUE LIFE PREDICTION OF THERMO-MECHANICALLY LOADED
Csaba Halszi, Christian Gaier, Helmut Dannbauer
MAGNA Powertrain, Engineering Center Steyr GmbH & Co. KG
Steyrer str. 32, A-4300 St.Valentin, Austria
Keywords: thermo-mechanical fatigue, engine, Sehitoglu
Nowadays engine components are subjected to higher loads at elevated temperatures than before,
due to the increasing requirements regarding weight, performance and exhaust gas emission. Thus,
fatigue due to simultaneous thermal and mechanical loading became determinant among the
At the same time, there is the need to reduce development times and costs to handle the growing
number of model variants. Therefore, the development of suitable simulation tools, which reduce
the number of necessary component tests, seems to be very rewarding.
The problem of thermo-mechanical fatigue (TMF) life prediction has received considerable
attention in recent years, with efforts principally concentrated on the prediction of TMF under
uniformly repeated loading conditions. Several researchers have developed models to treat this
problem, generally based on isothermal (IT) considerations. However, isothermal tests do not
capture all damage mechanisms that operate under variable strain-temperature conditions. As
Sehitoglu emphasizes, a deeper understanding of the different micro mechanisms affecting the
behavior of materials under isothermal and thermo-mechanical loading conditions is needed.
Thermo-mechanical fatigue (TMF) is the case of fatigue failure due to simultaneous thermal and
mechanical loading. The life prediction of TMF loading cases has received considerable attention in
recent years mainly in engine and gas turbine development. The fluctuation of complex thermal and
mechanical strains is usually determinant for fatigue life of machine parts. The mechanical strain
arises either from external constraints or externally applied loadings.
Thermo-mechanical and low cycle fatigue (LCF) can show a lot of similarity, mainly because of
the presence of cyclic plastic strain. The cyclic thermal load occurs by nature in a small number of
cycles, but the stresses generated by the restrained thermal expansion may be far beyond the elastic
limit. In engine parts the superposition of a LCF/TMF effect due to start-stop cycles and a HCF
effect due to the combustion cycle is to be observed.
Throughout a thermo-mechanical cycle, one crosses different temperatures. The temperature
dependent processes that occur during a common TMF cycle are plastic deformation, cyclic aging,
creep and oxidation effects, coarsening of the microstructure and crack initiation and propagation.
The main damage mechanisms are fatigue (mechanical) damage, environmental (oxidation) damage
and creep damage. These may act independently or can interact depending on various material
characteristics like thermal conductivity, thermal strain coefficient, Youngs modulus, mechanical
properties and operating conditions, as maximum and minimum temperatures, mechanical strain
range, strain rate, phasing of temperature and mechanical strain, dwell time, environmental factor.
TMF testing methodology
In TMF tests a specimen is subjected to a desired thermal and mechanical strain with different
phasings. Two baselines of TMF tests are conducted in the laboratory with proportional phasings:
in-phase (IP), where the maximum strain (the strain is signed: tension has a positive, and
compression has a negative sign) occurs at maximum temperature, and out-of-phase (OP), with
maximum strain at the minimum temperature. The variations of thermal, mechanical and total strain
components with time as well as schematics of stress-strain behavior corresponding to OP and IP
cases are illustrated in Figure 1 and Figure 2.
Figure 1 Out-of-phase loading
Figure 2 In-phase loading
The two types of phasing reproduce many of the mechanisms that develop under TMF. The
mechanical strain ( mech ) is the sum of the elastic ( el ) and inelastic ( in ) strain components, while
the total strain ( tot or t ) is the sum of thermal ( th ) and mechanical ( mech ) strain components,
( ) inelmechthtot TT ++=+= 0 (1)
where , 0T is the reference temperature where the test was begun, T is the test temperature, and
is the coefficient of thermal expansion.
SEHITOGLUS TMF LIFE PREDICTION MODEL
Prof. Huseyin Sehitoglu and his colleagues at the University of Illinois, Urbana-Champaign
developed a method for life prediction of thermo-mechanically loaded components. This method
includes a unified constitutive visco-plastic material model to describe the material behavior at
different temperatures and strain rates in the stress-strain analysis, and a damage model.
The damage model is based on three separate damage mechanisms (fatigue, environmental
attack, creep) that are acting simultaneously. Depending on the strain rate, strain amplitude,
temperature and phasing these damage mechanisms can have different parts in the total damage,
which is the sum of these components. Formally:
creepoxfattot DDDD ++= or creepoxfattot
where totD , fatD , oxD and creepD are total damage, fatigue (mechanical) damage, environmental
(oxidation) and creep damage, respectively, and totN , fatN , oxN , creepN are total cycles to failure,
cycles to failure due to mechanical fatigue, oxidation and creep damage, respectively.
Fatigue (mechanical) damage
Fatigue damage is represented by the classical fatigue mechanisms, which normally occur at
ambient temperature. These include crack nucleation and propagation due to the strain amplitude.
Since the cyclic plastic strain is remarkable, strain-life approach is used to describe the fatigue
behavior. The fatigue life term, fatN , is estimated with the Manson-Coffin-Basquin relationship:
( ) ( )cfatfbfatf
Tests performed with steel and aluminum showed that the room temperature (RT) strain-life curve
can be considered as an upper bound of all strain-life curves. Thus, the constants ( cbE ff ,,,, ) are
determined from isothermal room-temperature fatigue tests. As the temperature increases, the
damage increases due to oxidation and creep.
Environmental (oxidation) damage
Oxidation damage mechanism includes crack nucleation in surface oxides and oxide-induced crack
growth. Crack nucleation is defined as the rupture of the first oxide layer. Oxide-induced crack
growth is described as the repeated formation of an oxide layer at the crack tip and its rupture,
exposing fresh metallic surface to the environment.
Upon the examination of oxide-induced crack growth two major growth types can be differrenti-
ated. These crack initiation types are shown on Figure 3 and denoted as Type I and Type II crack
Figure 3 left: Type I growth, right: Type II growth
All oxide-induced crack growth process starts with an initial oxide layer formed on the surface of
the specimen. When this layer reaches a critical thickness, the oxide ruptures, and the crack
nucleation has occurred. Then a fresh metallic surface is exposed to the environment, which rapidly
oxidizes. When the thickness of this newly formed oxide reaches its own critical thickness, the
oxide ruptures again. The process continues as shown in Figure 3.
Type I growth is characterized by a continuous oxide layer. This layer results in oxide
intrusion without any visible stratification. Therefore, it will be distinguished from Type II, which is
characterized by multilayered or stratificated oxide growth. It is important to note, that the
progression of both growth types is similar until the layer reaches its critical thickness. The
difference comes up with the first rupture, as in Type II growth the oxide layer detaches from the
surface of the substrate. This results in exposition of a larger fresh surface area to the environment,
accounting for a wider intrusion,
The oxidation damage is calculated using following equation:
( )( )( )
where hcr, 0, , and B are material parameters. mech& is the mechanical strain rate and eff
pK is the
effective oxidation constant,
where D0 is a constant, Q is the activation energy for oxidation and R is the universal gas constant.
The Oxidation Phasing Factor
where ox measures the relative amount of damage associated with different phasing. th& is the
thermal strain rate.
The form of ox is chosen to represent the behavior of the oxidation damage observed in the tests. The most detrimental TMF loading case is the fully const