Xin Q. Diesel Engine System Design
Подождите немного. Документ загружается.
126 Diesel engine system design
© Woodhead Publishing Limited, 2011
2.8.2 Fundamental concepts of mechanical failures
Stress
When the stress is higher than the yield limit the material works in the plastic
domain. The ratio of the ultimate strength or yield strength to the actual
stress is dened as the factor of safety. In a one-dimensional model where
the effects of the other two dimensions are neglected, the stress tensor is
reduced to only one component and indistinguishable from a scalar stress.
The stress in this case is called a uni-axial stress. In engineering applications
of elastic materials it is usually assumed that the cross-sectional area of the
structural element remains constant during deformation when the element
is elongated or compressed. In fact, the cross-sectional area changes by a
small amount depending on the Poisson’s ratio of the material. The stresses
determined under the assumption of constant cross-sectional area are called
engineering stress or nominal stress. The stress calculated by considering
the cross-sectional area change is called true stress. The true stress in uni-
axial compression is less than the nominal stress. The true stress in uni-axial
tension is greater than the nominal stress.
The loads can create multi-axial stresses in the engine component due to
external loads, residue stresses and the geometry of the structure (Bignonnet
and Thomas, 2001). Although in many cases a calculation of uni-axial
stresses is sufcient for preliminary analysis, FEA is required to calculate
the stresses under multi-axial loads together with the complex geometry of
the component.
Examples of stresses include the residual stresses as a result of material
casting process and heat treatment, residual stresses due to inelastic deformation,
pre-stresses due to press-t and tightening of the bolts (bolt loads), dynamic
mechanical stresses due to gas and inertia loading, compressive stresses
caused by constrained thermal expansion due to different thermal expansion
coefcients of the parts, and temperature gradients in the components, etc.
The residual stresses are those that remain after the original cause of the
stresses has been removed. Uncontrolled residual stresses are undesirable.
Stress relaxation refers to the behavior that the stress in the material
decreases when time increases and the strain is unchanged. Stress relaxation
may affect the loading behavior of fasteners and springs.
Stress or strain concentration is a common problem in component design
resulting in failures even under low loads. Both loads and component geometry
design details determine the location and the level of stress concentration. In
the system-level stress estimation during the system design stage where the
component design details are not available, it is reasonable to assume the
component design will solve any stress concentration problems successfully
so that they will not become the bottleneck for system performance and the
associated required loads.
Diesel-Xin-02.indd 126 5/5/11 11:44:47 AM
127Durability and reliability in diesel engine system design
© Woodhead Publishing Limited, 2011
Strain
Mechanical strain is a geometric measure of deformation representing the
relative displacement between particles in a material body. Strain is caused
by external constraints or loads. There are two types of strain: elastic and
plastic. Stress–strain curves are usually used to characterize the material
structural behavior (e.g., the hysteresis loop, Fig. 2.2) in a load cycle.
The stress–strain curves together with the material properties obtained by
thermal fatigue testing can be used to ensure the accuracy of nite element
structural analysis.
There are two types of models of stress–strain relationship. In the
stress–strain model based on the deformation theory of plasticity, the strain
is expressed as a function of stress, temperature, and time. In the unied
stress–strain model based on the incremental theory of plasticity, the plastic
and creep strain increments are treated as one inelastic strain increment.
Typical models of the above two types are the Robinson model and the
Sehitoglu model, respectively, quoted by Ogarevic et al. (2001). The life
time of the component can be predicted based on the plastic strain amplitude
or the stress amplitude, or both.
Strength
The yield strength is the stress at which the material strain changes from
elastic deformation to permanent plastic deformation. Below the yield strength
all the deformation is recoverable because it is within the elastic range. For
applications where plastic deformation is not acceptable, the yield strength
is used as the design limit. The yield point of some ductile metals is dened
by using the rule of ‘0.2% offset strain’.
The ultimate strength is the maximum stress a material can withstand at
compression, tension or shearing loads before fracture occurs (i.e., the peak
on the engineering stress–strain curve in Fig. 2.2). The ultimate strengths for
compression and tension may be similar or very different in value, depending
on the material. For instance, the ultimate compressive and tensile strengths
of steel (a ductile material) are similar, while the compressive strength of
cast iron (a brittle material) is much greater than its ultimate tensile strength.
Ultimate tensile strength indicates when necking (i.e., reduction in cross-
sectional area due to plastic ow) will occur under a tensile load. Note that
necking is not observed for materials subject to compressive loading. After
the period of necking in tension loading, the material will rupture and the
stored elastic energy will be released as noise and heat. The stress at the time
of material rupture is known as the breaking strength. A typical example
of an engine component subject to both compressive and tensile stresses
periodically is the connecting rod.
Diesel-Xin-02.indd 127 5/5/11 11:44:47 AM
128 Diesel engine system design
© Woodhead Publishing Limited, 2011
Both yield strength and ultimate strength are functions of temperature of
the material. Beyond a certain temperature (e.g., above 375°C for iron), the
ultimate strength starts to decrease. Generally, tensile stress is detrimental
to the component while compressive stress may relieve the fatigue of the
material (Kim et al., 2005).
2.8.3 Damage and damage models
Damage is dened as the ratio of the actual number of cycles (or time) to
the required number of cycles (or time) to reach a pre-dened macroscopic
failure (e.g., crack length due to LCF or HCF; wear amount). The concept of
damage in structural analysis has usually referred to the failures of thermo-
mechanical fatigue, but it can easily be extended to cover the damage caused
by other mechanical failures such as wear and cavitation. Fatigue damage
mainly includes three mechanisms: fatigue, creep, and oxidation. The damage
can be caused by a single type of cyclic loading or multiple types of cyclic
loading. For complex stress time histories of driving/usage proles (e.g.,
obtained from thermo-mechanical simulation or test data), the commonly
used approach to decompose them into a set of simple fatigue cycles is the
‘rainow decomposition’ method (Masuishi and Endo, 1968).
The simplest way to estimate the fatigue damage under a combination
of multiple types of loading cycle is to assume a linear accumulation of the
2.2 Stress–strain property of steel.
Stress
Breaking strength
Ultimate strength
Breaking strength
Yield strength
Yield strength
s
e
The hysteresis loop
Strain hardening region
Engineering (nominal)
stress–strain curve
Necking
region
Strain
Rupture
Rupture
True stress–strain curve
Ultimate strength
Diesel-Xin-02.indd 128 5/5/11 11:44:47 AM
129Durability and reliability in diesel engine system design
© Woodhead Publishing Limited, 2011
fatigue damage due to the contributions from each type of cyclic loading
as
D
n
N
i
m
li
fi
=
= 1
=1
S
2.1
where D is the total accumulated damage over the entire stress–strain history,
N
fi
is the number of cycles required to reach the pre-de ned failure criterion
under the loading of the ith type of decomposed simple fatigue cycles, n
li
is the actual number of loading cycles under the ith type of loading, and m
is the number of types of the loading cycle. When the damage D = 1, it is
assumed that fatigue failure occurs. In fact, D can be greater than or less
than 1 in reality.
The above damage model can be extended to include the independent
superposition of various damage mechanisms in order to account for the
combined effect of fatigue, creep, oxidation, etc. The following model has
been widely used:
D = D
1
+ D
2
+ D
3
+ … + D
1
D
2
+ …
=
+
=1
,1
,1
=1
,2
,2
=1
12
,1
12
,1
SS
SS
+ SS+
,1
SS
,1
S
i
m
li
12
li
12
SS
li
SS
fi
i
m
12
m
12
li
fi
i
m
n
12
n
12
SS
n
SS
N
N
SS
N
SS
t
T
T
fi
T
fi
333
,3
,3
t
T
li
fi
T
fi
T
+ … +
1,
1,
2
2
=1
,1
,1
=1
,2
,2
12
,1
12
,1
C
C
n
12
n
12
N
t
T
i
m
li
12
li
12
fi
i
m
12
m
12
li
fi
T
fi
T
SS
SS
· SS ·
,1
SS
,1
n
SS
n
N
SS
N
li
SS
li
ÊÊÊ
Ë
Ë
Á
ÊÊÊ
Á
ÊÊÊ
Ë
Á
Ë
Ë
Á
Ë
ˆ
¯
˜
ˆ
˜
ˆ
¯
˜
¯
+ …
2.2
where D is the total damage, D
1
is the damage due to fatigue, D
2
is the
damage due to creep, D
3
is the damage due to oxidation or degradation,
etc. D
1
D
2
is the interaction term of damage between the two mechanisms.
C
1,2
is a constant characterizing the importance of the interaction effect
(e.g., C
1,2
= –0.5 ~ 0.5). T
fi
is the required time to reach creep failure for
the ith type of temperature or mechanical loading for creep, t
i
is the actual
time of creep under the ith type of loading for creep. The value of D can be
calculated by using equation 2.2 based on experimental data or numerical
simulation models. When C
1,2
= 0 and D = 1, it means the accumulation of
the damages due to different failure mechanisms follow the simplest model
of linear accumulation of damage. Experimental evidence showed that the
total damage due to the combined effects of fatigue, creep, and oxidation
does not always give D = 1. Instead, the actual measured data of D uctuate
around the line of D = 1 (Fig. 2.3a).
The stress–strength model has traditionally been used in the probabilistic
reliability evaluation for structural durability. Since many thermo-mechanical
fatigue problems require using plastic strain (e.g., for low cycle fatigue
problems) instead of stress as an evaluation criterion, the damage parameter
Diesel-Xin-02.indd 129 5/5/11 11:44:48 AM
130 Diesel engine system design
© Woodhead Publishing Limited, 2011
has been commonly used to replace the stress in the stress–strength model
in this scenario. For each material, component design and a usage loading
prole at a given vehicle mileage or engine hours, one damage indicator
can be calculated. Such a damage calculation can be repeated with the
Monte Carlo simulation for the entire production population including all
the variabilities in order to construct the stress–strength curve.
The damage models for life prediction (i.e., to determine the total required
number of cycles to failure) are either stress-based (e.g., the Chaboche
method) or strain-based (e.g., the Sehitoglu method, and the total strain–train
range partitioning method or also known as the TS–SRP method). Ogarevic
et al. (2001) concluded in their review article of thermo-mechanical fatigue
that the three most widely accepted life prediction methods are the TS–SRP
method developed by Manson and Halford, the Sehitoglu method, and the
Chaboche method.
Damage model
50% reliability
99% reliability
Linear
accumulation
damage model
Reliability
probabilistic
distribution
1
0 1
n
l
/N
f
for fatigue
t
l
/T
f
for creep
(a)
N
f
(b)
Log (N)
(c)
Log (N)
(d)
S
P–S–N
f
curve
Log (De)
Log (De
p
)
Total strain range (De) vs. life (N)
Strain range vs. life curve
Elastic strain
range vs. life
Plastic strain
range vs. life
High temperature
Low temperature
Temperature effect on LCF life
2.3 Damage model and durability life analysis.
Diesel-Xin-02.indd 130 5/5/11 11:44:48 AM
131Durability and reliability in diesel engine system design
© Woodhead Publishing Limited, 2011
The TS–SRP method is one of the earliest methods capable of predicting
thermo-mechanical fatigue life. The method is based on the observation
that the strain range of any stress–strain hysteresis loop associated with
thermo-mechanical fatigue can be partitioned into four basic strain-range
elements in order to account for their different impact on the fatigue life.
The partitioning depends on whether creep occurs and whether the strain is
in compression or tension. The four strain range components are:
1. plastic strain in tension and plastic in compression, De
pp
2. plastic in tension and creep in compression, De
pc
3. creep in tension and plastic in compression, De
cp
4. creep in tension and creep in compression, De
cc
.
The relationship between the strain range De and fatigue life N
f
is
introduced in Section 2.8.5. The fatigue lifetimes of the four components
are ranked from low to high as: N
f,cp
, N
f,cc
, N
f,pc
, and N
f,pp
(Fig. 2.4). The
total life N
f,fc
due to fatigue and creep is given by the single-cycle damage
model as:
1
=
1
+
1
+
1
+
1
,,
,,
NN
=
NN
=
NN
+
NN
+
N
ff
,,ff,,
NN
ff
NN
cf
,,cf,,
NN
cf
NN
ffcfff
,,ff,,cf,,ff,,
NN
ff
NN
cf
NN
ff
NN
pp
fp
,,fp,,
NN
fp
NN
cf
,,cf,,
NN
cf
NN
cp
fc
,fc,
c
2.3
Equation 2.3 can be further modi ed by including weighting factors or
proportional coef cients in order to make the life prediction more accurate.
The total damage is the superposition of these four types of mechanisms.
The history and details of the TS–SRP method were reviewed by Ogarevic
et al. (2001).
In the Sehitoglu method, the total damage of the thermo-mechanical fatigue
cycle is the sum of the damage due to fatigue, oxidation, and creep. The
De
pp
De
pc
De
cc
De
cp
Log (De)
Log (N
f
)
2.4 Total strain–strain range partitioning.
Diesel-Xin-02.indd 131 5/5/11 11:44:49 AM
132 Diesel engine system design
© Woodhead Publishing Limited, 2011
fatigue life is calculated by a strain-based approach. The Chaboche method
is a stress-based approach. In fact, it is generally believed that a strain-based
method is more suitable than a stress-based method for LCF problems because
LCF is controlled mainly by the plastic strain rather than the elastic stress as
encountered in the case of HCF. As an example, in the Chaboche’s model,
the number of cycles to failure for each decomposed simple fatigue cycle due
to pure fatigue, N
fi
, is calculated based on stresses as below (for example,
used by Morin et al. (2005) for a diesel cylinder head):
N
ss
ss
s
C
fi
ui
ss
ui
ss
l
i
=
ss
ui
ss – ss
ui
ss
,
,1
C
,1
C
l,1l
,1
ss
,1
ss
ss – ss
,1
ss – ss
–
ma
x
maxma
im
ss
im
ss
,1im,1
ss
,1
ss
im
ss
,1
ss
,1ax,1
ss
,1
ss
ax
ss
,1
ss
f
lfl
f
,1f,1
l,1lfl,1l
Ê
Ë
Á
Ê
Á
Ê
Ë
Á
Ë
ˆ
¯
,1
¯
,1
˜
ˆ
˜
ˆ
¯
˜
¯
,1
¯
,1
˜
,1
¯
,1
D
Ê
Ë
,1
Ë
,1
Á
Ê
Á
Ê
Ë
Á
Ë
,1
Ë
,1
Á
,1
Ë
,1
ˆ
¯
˜
ˆ
˜
ˆ
¯
˜
¯
CCC
2
2.4
where i indicates the ith decomposed simple fatigue cycle, s
u
is the ultimate
stress, s
i,max
is the maximum stress, s
fl
is the fatigue limit stress, Ds
i
is the
stress amplitude, and C
1
and C
2
are material constants.
These three prevailing models of life prediction, along with their
corresponding material testing procedures, were elaborated by Ogarevic et
al. (2001). It should be noted that the three methods are not interchangeable.
Therefore, once a method is chosen, it is not easy to change to another one
because the empirical database is usually built with one method.
2.8.4 Thermo-mechanical failure modes
Mechanical failures in engines include mainly fracture (rupture and crack),
buckling, fatigue, creep, corrosion, oxidation, cavitation, wear, fouling,
boiling, and deposits. Fracture can be caused by mechanical overload
(e.g., an instant catastrophic failure due to rupture or breakage) or fatigue
(i.e., macroscopic large broken cracks resulting from the fatigue-initiated
microscopic small cracks which chronically propagate and grow). Fatigue
includes high cycle fatigue and low cycle fatigue. Buckling is a special
failure mode for long and slender components (e.g., the pushrod). Creep
is a chronic plastic deformation of the material under stress. The causes of
fracture, fatigue, and creep are stresses.
Thermal failures refer to any failures caused or aggravated by temperature
effects such as thermal stress, thermal expansion, and material degradation at
high temperatures. Thermo-mechanical failures refer to the combined effects of
mechanical and thermal failures. Only the components exposed to the normal
ambient temperature in the engine may experience pure mechanical failure
with negligible thermal effects (e.g., the compressor inlet pipe, the engine
mount). Most engine components experience both mechanical and thermal
effects and may be subject to thermo-mechanical failure. Most commonly
encountered failures are in the cylinder head, the exhaust manifold, or the
piston bowl. For example, the gas-side of the cylinder head may have high
Diesel-Xin-02.indd 132 5/5/11 11:44:49 AM
133Durability and reliability in diesel engine system design
© Woodhead Publishing Limited, 2011
temperature LCF failures, while the coolant-side of the cylinder head may
have high temperature HCF failures. Which failure occurs rst depends on
particular engine applications. There are interactions between the mechanical
and thermal failure modes, also between the various more detailed failure
modes such as fatigue, creep, and oxidation. Material strength decreases
due to the accelerated aging of the mechanical properties under elevated
temperatures. The interactions affect the lifetime of the component. For
a detailed introduction to engine thermal loading, the reader is referred to
Heywood (1988) and French (1999).
Thermal failures
Thermal failures are caused by the thermal load which is essentially the
metal temperatures, temperature gradients and thermal stresses in the
component. Thermal load in engine components is related to gas temperature,
heat ux, component design, and material properties. The components
exposed to excessively high temperatures may have failure due to ablation,
distortion, corrosion, creep, relaxation, and thermal fatigue. Material property
degradation at high temperatures reduces the material strength to resist
the failures. Excessive thermal deformation may induce the problems of
scufng and clearance interference, and aggravate the wear of tribological
components. Alternating thermal stresses and strains cause thermal fatigue,
especially under the effects of creep and relaxation. Thermal stresses may
also aggravate mechanical fracture failures when the total of mechanical
and thermal stresses exceeds the ultimate tensile strength of the material.
As engine power density increases, thermal failures have become more
difcult to control than mechanical failures. Thermal failures have become
the primary limiting factor for engine reliability.
In-cylinder gas temperature and exhaust manifold gas temperature are
two most important indicators of the thermal load for engine components.
In-cylinder gas temperature affects the metal temperatures of the cylinder
head, the injector tip, and the piston. Exhaust gas temperature affects the
metal temperatures of the exhaust valve, the valve seat, and the exhaust
manifold. It should be noted that the peak in-cylinder gas temperature and
the exhaust manifold gas temperature are not always coherent. At a xed
engine speed, a higher peak in-cylinder temperature resulting from higher
power or lower air–fuel ratio corresponds to a higher exhaust temperature.
However, a lower peak in-cylinder temperature resulting from retarded fuel
injection timing causes an increase in the exhaust temperature. The heat
transferred to the component at different engine speeds is dependent on the
timescale rather than the crank angle scale. Moreover, using the maximum
temperature in a thermo-mechanical cycle to predict isothermal fatigue life
may not be the safe or conservative method (Ogarevic et al., 2001).
Diesel-Xin-02.indd 133 5/5/11 11:44:49 AM
134 Diesel engine system design
© Woodhead Publishing Limited, 2011
Ablation and excessive thermal deformation
Examples of ablation include unusual burn-out due to over-fueling for
power cylinder components, backre, or uncontrolled burning of soot in
the DPF. Excessive thermal deformation usually occurs in the piston, the
cylinder head and the exhaust manifold, and is caused by high in-cylinder
gas temperatures or exhaust manifold gas temperatures. For instance, the
piston temperature at the top ring position should not become excessively
high, otherwise the lubrication of the ring may fail, resulting in ring scufng
or sticking in the ring groove.
Fracture and rupture
Fracture refers to the separation of a material into two or more pieces
under the loading of stress. Fracture can be an instant or acute rupture of a
component caused by mechanical overload in a single event, or as a nal
result of the chronic crack initiated and propagated due to long-term fatigue.
Mechanical overload occurs when the applied load is greater than the ultimate
strength (tensile, compressive, or shear) of the component. It can result in a
tension failure, compression failure, shear failure, or bending failure (with
both tensile and compressive forces). Ductile rupture is the ultimate failure
of ductile materials as a consequence of extensive plastic deformation due
to tension. In brittle rupture, no plastic deformation occurs before rupture.
Rupture under tension occurs after the following steps: plastic deformation,
necking, void nucleation, crack formation, crack propagation, and surface
separation. The mechanism of cracking due to fatigue is different. At high
temperatures the ultimate strength of the metal material decreases so that
fracture occurs more easily. Fracture is a common structural durability
problem in engine components.
Fatigue
According to the source of stress, fatigue can be classied into mechanical
fatigue and thermal fatigue. For engine components the effects are usually
combined as thermo-mechanical fatigue. According to the number of cycles
to failure, fatigue includes high cycle fatigue and low cycle fatigue. HCF
produces failures after a high number of cycles (e.g., greater than 10
4
cycles)
with low stresses and elastic deformation. LCF produces failures after only
a low number of cycles (e.g., smaller than 10
4
cycles) with high stresses and
plastic deformation. Note that both mechanical and thermal fatigue can be
either HCF or LCF. The timescale of one cycle can vary greatly from one
engine cycle (e.g., for the loading cycle in HCF due to cylinder pressures)
to several hours (e.g., for the loading cycle in LCF such as slow thermal
Diesel-Xin-02.indd 134 5/5/11 11:44:50 AM
135Durability and reliability in diesel engine system design
© Woodhead Publishing Limited, 2011
cycles). Although the damage per cycle of LCF is greater than that of HCF,
if the occurrence frequency of LCF is much lower than that of HCF, the
component may reach a HCF failure earlier than a LCF failure. Different
failure modes (e.g., different crack locations) may have different fatigue
mechanisms (i.e., LCF or HCF, thermal stress induced or mechanical stress
induced). The discussions on the mechanism and modeling of fatigue are
detailed later.
Creep
Creep is a slow time-dependent irreversible process of plastic deformation for
a metal material under the inuence of stresses which are lower than the yield
strength of the material. Creep results from long-term stresses and generates
chronic strain accumulation or stress relaxation. Creep is generally damaging
and related to inter-granular cracking and void growth over time.
The strain increase in creep is usually nonlinear with time. Both temperature
and mechanical stress can generate creep, with temperature as the primary
factor. Creep is especially signicant at in-phase-loading conditions and
less signicant in the situation of out-of-phase loading. The creep under
alternating mechanical or thermal stress is larger than the static creep.
Creep increases with temperature. The rate of creep in terms of strain rate
increases exponentially with metal temperature at high temperatures. The
effect of creep becomes noticeable at approximately 30% of the melting
temperature of metals. Large creep strain may cause cracks and fracture.
When the temperature is sufciently high, even if the stress is designed much
lower than the yield strength, creep may occur as a plastic deformation to
cause failure. Creep and plastic deformation occur at elevated temperatures
in thermal cycles. This produces tensile stresses after the thermal load is
removed.
Creep needs to be considered in the thermal failures encountered in
high temperature operations of the engine. The plastic strain due to creep
can be modeled as a function of time, temperature, and stress. The rate-
dependent visco-plasticity theory needs to be included in the stress analysis
for creep.
Corrosion
Chemical corrosion in the engine occurs due to the corrosive combustion
products (e.g., sulfur in the fuel) in the exhaust gas in the combustion chamber,
the exhaust and intake systems, the EGR system, and in the lubricant oil.
Corrosion aggravates fatigue and wear of the component.
Diesel-Xin-02.indd 135 5/5/11 11:44:50 AM