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2.8 Fundamentals of thermo-mechanical failures .1 Overview of thermo-mechanical structural
2.8.5 Fatigue
Oxidation
Oxidation damage is caused by repeated formation of an oxidation layer at the crack tip and its rupture. The rate of growth of oxidation layer thickness is proportional to the square root of time in the absence of cyclic loading;
and the rate of growth is much higher in cyclic loading conditions where the oxidation layer repeatedly breaks and the fresh surface is exposed to the environment (Ogarevic et al., 2001). The details of the modeling of oxidation damage and creep damage were provided by Su et al. (2002) in their investigation of cylinder head failures.
magnitude since crack initiation requires a larger stress than crack propagation.
The fatigue life of the component can be determined by the strain, stress, or energy approach. Fatigue is a very complex process affected by many factors. It is usually more effective to use a macro phenomenological method to model the effects of fatigue mechanisms on fatigue life rather than using a microscopic approach.
Fatigue strength and fatigue limit
Fatigue strength is defined as the stress value at which fatigue failure occurs after a given fatigue life. Fatigue limit is defined as the stress value below which fatigue failure occurs when the fatigue life is sufficiently high (e.g., 10–500 million cycles). Ferrous alloys and titanium alloys have a fatigue limit below which the material can have infinite life without failure. However, other materials (e.g., aluminum and copper) do not have such a fatigue limit for infinite life and will eventually fail even with small stresses. For these materials, a number of loading cycles is chosen as a design target of fatigue life.
Thermal fatigue
Thermal fatigue is a fatigue failure with macroscopic cracks resulting from cyclic thermal stresses and strains due to temperature changes, spatial temperature gradients, and high temperatures under constrained thermal deformation. Thermal fatigue may occur without mechanical loads. The constraints include external ones (e.g., bolting load) and internal ones (e.g., temperature gradient, different thermal expansion due to different materials connected). Compressive stresses are produced by the bolting load at high temperatures, or generated in the material having high coefficient of thermal expansion. Tensile stresses are produced when the component cools, or generated in the material having low coefficient of thermal expansion.
Thermal stresses are produced by cyclic material expansion and contraction when temperature changes under geometric constraints. A crack may develop after many cycles of heating and cooling. The failure indicator or criterion of thermal fatigue is usually strain rather than stress. Thermal fatigue life is determined mainly by material ductility rather than material strength.
Thermal fatigue can be HCF or LCF, depending on the magnitude of thermal stress compared to the yield strength of the material. Thermal fatigue life can be predicted by using either stress (for HCF) or plastic strain (for LCF) as a criterion. The thermal fatigue in engine applications usually refers to the thermo-mechanical fatigue problems where thermal fatigue plays a dominant role.
Anisothermal fatigue can sometimes be more damaging than isothermal fatigue. Isothermal fatigue occurs when tension or compression cycles are imposed at a constant temperature. Anisothermal fatigue occurs when the component temperature and strain vary simultaneously. An engine may operate at isothermal conditions in steady state for a long period of time (e.g., in stationary power application or durability testing). Automotive engines often encounter anisothermal fatigue during largely varying thermal cycles.
Anisothermal fatigue is more complex to model than isothermal fatigue because of the varying temperatures within the cycle.
The mechanical properties of the material deteriorate with time when the material is exposed above certain level of temperature. The ultimate strength of the material decreases due to the aging of mechanical properties at high temperatures. This aggravates the occurrence of plastic deformation in thermal fatigue. Experimental work has confirmed that the maximum component temperature in a thermal cycle (e.g., cycling from high engine speed-load modes to low speed-load modes) has a much greater influence on thermal fatigue life than the minimum or cycle-average component temperatures.
The maximum temperature is also more important than the temperature range of the cycle for the reason that the fatigue-resistance property of the material deteriorates quickly at high temperatures. This means in engine system design the maximum gas temperature and heat flux should be used as design constraints in most cases.
Thermal fatigue life can be improved by reducing the temperature and temperature gradient or alleviate the geometric constraints. For example, reducing metal wall thickness can reduce the gas-side surface temperature and thermal expansion hence increase fatigue life. Using slots or grooves in the component may eliminate the constraints for thermal expansion.
Thermo-mechanical fatigue
The thermal fatigue in engines is usually accompanied by both thermal and mechanical stresses. The compressive and tensile stresses often exceed the yield strength of the material in much thermo-mechanical fatigue. Three typical engine components subjected to thermo-mechanical fatigue failures are the cylinder head, the piston, and the exhaust manifold.
Thermo-mechanical fatigue (either HCF or LCF) failures consist of the accumulated damage due to three major mechanisms: mechanical or thermal fatigue; oxidation and degradation; and creep. Oxidation is caused by environmental changes. Degradation refers to chemical decomposition and the deterioration of material strength due to temperature change or mechanical fatigue. Material aging also affects damage but as a secondary effect.
Engine system design, component design and durability testing are three
closely related areas to achieve successful design and prediction of thermo- mechanical fatigue life of the engine. Complete thermo-mechanical fatigue analysis includes both stress–strain and life predictions. The key elements in the analysis include the following (Fig. 2.5):
∑ dynamic thermal loading
∑ dynamic mechanical loading
∑ transient component temperature distribution
∑ material constitutive law (behavior) under both low and high tempera- tures
∑ stress and strain
∑ fatigue criteria and damage indicator
∑ component lifetime prediction
∑ statistical probabilistic prediction to account for the variations in the population.
The temperature field calculation is dependent on the thermal history and thermal inertia of the engine as well as the gas temperature and mass flow rate during the transient cycles. The effects of three-dimensional stresses and anisothermal cycle may be important in damage indicator calculation for detailed component-level design analysis.
A comprehensive review of engine thermo-mechanical fatigue was provided by Ogarevic et al. (2001). The simulation methodologies of thermo-mechanical fatigue life prediction were presented by Swanger et al. (1986), Lowe and Morel (1992), Zhuang and Swansson (1998), and Ahdad and Soare (2002).
A discussion of diesel engine cumulative fatigue damage was provided by Junior et al. (2005). Deformation and stress analysis was reviewed by Fessler (1984).
Thermal load/Heat transfer (cycle simulation, or CFD+FEA)
Metal temperature distribution (cycle simulation, or CFD+FEA)
Stress and strain analysis (structural analysis)
Damage parameter model
Fatigue life prediction
Design
Material properties model
Mechanical loading (cycle simulation)
2.5 Thermo-mechanical fatigue analysis process.
HCF
High cycle fatigue is a type of fatigue caused by small elastic strains under a high number of load cycles before failure occurs. The stress comes from a combination of mean and alternating stresses. The mean stress is caused by the residual stress, the assembly load, or the strongly non-uniform temperature distribution. The alternating stress is a mechanical or thermal stress at any frequency. A typical loading parameter in engine HCF is the cyclic cylinder pressure load or component inertia load.
HCF requires a high number of loading cycles to reach fatigue failure mainly due to elastic deformation. It has lower stresses than LCF, and the stresses are also lower than the yield strength of the material. HCF usually does not have macroscopic plastic deformation as large as that in LCF. The dominant strain in HCF is mainly elastic. In contrast, the dominant strain in LCF is plastic. Typical HCF examples are the cracks at the tangential intake ports connected to the fl ame deck on the water side of the cylinder head, the valve seat area, the piston, the crankshaft, and the connecting rod.
Because HCF is governed by elastic deformation, stress is usually a more convenient parameter than strain to be used as the failure criterion. The HCF life of the component is usually characterized by a stress–life curve (i.e., the s–Nf curve, Fig. 2.3b), where the magnitude of a cyclic stress is plotted versus the logarithmic scale of the number of cycles to failure. For constant cyclic loading, an empirical formula of the HCF s–Nf curve is usually expressed as
s Ns Ns Ns Ns NCC1 f =C2 2.5
where C1 and C2 are constants, s is the maximum stress in the load cycle, Nf is the HCF life in terms of the number of cycles to failure. Higher stress results in a shorter life. Higher material strength can improve the HCF life.
LCF
LCF is a type of fatigue caused by large plastic strains under a low number of load cycles before failure occurs. High stresses greater than the material yield strength are developed in LCF due to mechanical or thermal loading.
For instance, high tensile stresses are developed after the hot compressed area has cooled down during one loading cycle. The stresses may exceed the yield strength and cause large plastic deformation. Like other failures the crack due to LCF is usually initiated in the small areas having stress–strain concentration. The failure criterion of LCF can be a macroscopic crack with certain length or depth or a complete fracture of the component. Typical examples of LCF failure are the cracks at the inter-valve bridge area in the cylinder head and in the exhaust manifold after thermal cycles.
The lifetime of the component in LCF can be predicted by either plastic strain amplitude or stress amplitude, with the former being more appropriate and commonly used. In fact, both maximum tensile stress and the strain amplitude are useful in LCF life prediction. In general, larger plastic strains cause a shorter life. Better material ductility can improve the LCF life. Higher material strength may actually reduce the component life if it is subject to LCF failure since higher material strength usually reduces ductility.
Under a single type of cyclic loading (i.e., the plastic strain range remains constant in every cycle of the loading) the plastic strain deformation is usually predicted by the Manson–Coffi n relation developed in the 1950s.
The formula characterizes the relationship between the plastic strain range and LCF life as follows:
DepNNNNNNNNNfff–CCC33 =CCCCCCCCC4
i.e.,
Dep =C NC NC N44 Cf3 2.6 where Dep is the plastic strain range, Nf is the number of load cycles to reach fatigue failure. Note that 2Nf is the number of reversals to failure in the stress–strain hysteresis loop. C3 and C4 are empirical material constants.
C3 is known as the fatigue ductility exponent, usually ranging from –0.5 to –0.7. Higher temperature gives a more negative value of C3. C4 is an empirical constant known as the fatigue ductility coeffi cient, which is closely related to the fracture ductility of the material. It is observed from equation 2.6 that a larger plastic strain range leads to a lower number of cycles of the fatigue life.
A more general relationship was later proposed by Mason by using the total strain, including both elastic and plastic strains, as the indicator of LCF failure:
DDDDDDDDDDDeeeeeeeeeetotatotatotalll DDDDDDDDDDDeeeeeeeeeeppp Dee Cf
Cf
C N C N
De De D =D De De
D D
De De
D l D p
De De D =D De De
D l D p
De De Deeee llll Deeeepppp
De De
D l D p
De De
D D
De De
D l D p
De De
D D + = C NC NC NC NC NC NC NC N44444444 ffffff3333 + + + + + C NC NC NC N66666666 CC5555 2.7 where Dee is the elastic strain range which is equal to the elastic stress range divided by the Young’s modulus, Dep is the plastic strain range, C6 is a coeffi cient related to the fatigue strength, C3 and C5 are material constants. Equation 2.7 can be used to construct the strain–life diagram for the component on a logarithmic scale (Fig. 2.3c).
The LCF in diesel engines is usually caused by large thermal stresses at high component temperatures which are higher than the creep temperature.
The creep temperature is usually equal to 30–50% of the melting temperature of the metal in Kelvin. Many factors such as creep, relaxation, oxidation, and material degradation start to play important roles at high temperatures.
At low temperatures the fatigue mechanism is predominant, while at high temperatures creep may become more important. The life of high temperature LCF is usually signifi cantly lower than the life at lower temperatures (Fig.
2.3d). Ductility is a major factor to determine the LCF life. The material ductility is affected by temperature. Moreover, if the frequency of the loading cycle becomes slower, high temperature LCF life will reduce since creep and oxidation play more prominent roles at lower cycle frequencies. When the creep effect is considered, equation 2.6 is modifi ed as below, and such a modifi cation has been widely used to estimate the LCF life:
Depc = C N fC NC NC NC NC NC N444(((((( f qlfqlqlC7–1)C3 2.8 where Depc is the inelastic strain range including the plastic strain range and the creep strain range, C7 is a material constant, fql is the cyclic loading frequency which accounts for the time-related effects of creep (e.g., the creep hold time) and relaxation, and so on. The elastic strain term in equation 2.7 can be modifi ed similarly.
Barlas et al. (2006) provided an analysis to calculate the number of cycles to failure due to pure creep as an integral over a time period of t1–t2 for the cylinder head:
1 = 1 + 1 dd
8 + 1 9
8 + 1 1 9
8 1 9
8 9
2 d
2 10 d
N =C
N =C s
s d
f dt Nf C
N C88 tt 99
t C
Ú
dÚ
d8
Ú
98
Ú
tt 98 t 9
8
Ú
98 t 9
8 9
Ê d
Ê d
Ë d
Ë d
8 Ë 9
8 ÁÊ 9 dd
ÁÊ d
Ê d
Á d
Ê d
ËÁË d
Ë d
Á d
Ë d
8 Ë 9
8 Á 9
8 Ë 9
8 9
ˆ d
ˆ d
¯ d
¯ dd
˜ d
ˆ˜
ˆ d
ˆ d
˜ d
ˆ d
¯˜¯ d
¯ d
˜ d
¯ d
C d
C d
8 C9
8 9 2.9
where C8, C9 and C10 are material coeffi cients for pure creep, and s is an equivalent stress as a linear combination of the Von Mises stress, the principal maximum stress and the trace of the stress tensor.
Strictly speaking, the classical LCF laws (e.g., the Manson–Coffi n relation) based on the isothermal and uni-axial conditions are not valid for the anisothermal and multi-axial problems in reality. Therefore, the available prevailing analysis method is more or less a simplifi ed approximation for the real world durability problems encountered in engines. Predicting the LCF life in the anisothermal and multi-axial conditions is very challenging, especially for the concept-level structural/life analysis in engine system design.
Lederer et al. (2000) provided an in-depth discussion on the limitations of the classical CLF theories for fatigue life prediction. Lederer et al. (2000) also showed that, using a reasonably simple anisothermal LCF criterion, their simulation produced good agreement between the predicted and the tested critical zones of failure.
Thermal shock
Thermal shock refers to the process that the component experiences suddenly changed thermal stresses and strains of large magnitude when the heat fl ux and component temperature gradient change abruptly. Thermal shock produces cracks as a result of rapid component temperature change. The stresses generated in thermal shock are much greater than those in normal
loading cycles, and even greater than the ultimate strength of the material.
Thermal shock can be regarded as a severe type of LCF although it has its unique characteristics. The criterion used to analyze thermal shock failures can be strain or stress, with strain being more appropriate.
Thermal shock can make the material lose ductility and shorten the normal LCF life and the thermal fatigue life of the component accordingly. It may also cause brittle fracture which has a much shorter life than the normal LCF life. The materials having low thermal conductivity and high thermal expansion coefficient are vulnerable to thermal shock. Thermal shock can be prevented by reducing the thermal gradient through changing the temperature more slowly, or by improving the robustness of a material against thermal shock through increasing a ‘thermal shock parameter’. The parameter is an indicator of the capability to resist thermal shock, and is proportional to the thermal conductivity and the maximum tension that the material can resist, and inversely proportional to the thermal expansion coefficient and the Young’s modulus.