A Review on Finite Element Analysis Approaches in Durability Assessment of Automotive Components
This research describes the majority of interesting findings in the use
of the Finite Element Analysis (FEA) based fatigue for automotive components
in a form of review write-up. Thus, the theoretical background related
to the fatigue life prediction using FEA is presented which is the main
subject of this research. The challenge for FEA-based software developers
is to deliver reliable fatigue-analysis tools because over designing components
is no longer a viable option. Combination between a fatigue model based
on the crack initiation, the crack growth and the crack closures are performed
with consideration of cycle sequence effect together with finite element
results, which lead to the prediction of fatigue life under spectrum or
In automotive design, durability evaluation of components based
on experimental assessments is time-consuming and expensive, so analytical
approaches that include limited number of component verification tests
have gained more attention. Structural components such as a lower suspension
arm might be strong enough to withstand a single applied load. But what
happens when the component operates over and over, day after day? To predict
component failure in such cases requires whats called fatigue or durability
analysis. A vehicle can be considered as a compound structure made with
many mechanical components subjected to complex cyclic loading as a consequence
of their normal use (Curiel et al., 2006). Active vehicle suspensions
have attracted a large number of researchers in the past few decades and
comprehensive surveys can be found in the papers produced by Karnopp (1995),
Hrovat (1997) and Hrishikesh and Nam (2004).
The start of a fatigue failure is a strictly local process and it is
also one that depends on the dynamics of the system. The time history
of stress or strain, at the exact location where a crack is going to start,
is the critical factor. This is precisely why finite element analysis
is important in this discipline. The term finite element was introduced
by Clough (1960). Using Finite Element Analysis (FEA) an analyst can choose
any location within a model and concentrate attention on it, using the
intrinsic ability of the technique to bring in dynamic effects. For that
reason, the Finite Element Method (FEM) has become a reliable tool for
the numerical solution of a wide range of engineering problems. Results
are important in calculating and verifying safe part lifetimes. In the
past, durability analysis was largely the province of research Fluctuating
loads can cause failure which takes place when cracks initiate. In classic
structural analyses, failure predictions are solely based on the material
strength or the yield strength.
Durability analysis goes beyond this, evaluating failure based on repeated
simple or complex loading. Hence, the objective of the stress analysis
was to obtain the complete three dimensional stress and strain distributions
at a potential failure site, facilitating fatigue life predictions. Fatigue
durability is influenced by a number of factors (Plaskitt and Musiol,
2002), such as stress or strain range, mean stress, surface finish and
quality, surface treatments and cycle sequence effects.
In this research, the authors focused on the different fatigue analysis
attitudes with FEA or without FEA, on to the automotive components. By
getting an idea regarding the other attitudes in this field, the authors
work may lead to a novel finding, which can give a good effect in the
field of fatigue related FEA for the scientists and engineers. It is important
for the further development of fatigue life assessment and FEA technology
The researchers which they used the fatigue related FEA packages to get
the fatigue life as a final target for there works. Currently, most of
researchers used the models contained in commercial packages, which they
are most useful to get life estimation under constant amplitude loadings,
instead of variable amplitude loadings. Thus, the main benefit of this
paper is to get reasonable results under service loadings for fatigue
life prediction by combine finite element analysis with one of the fatigue
models which take into consideration the sequence effect on components
ELEMENTS IN LIFE ESTIMATION
For many years the fatigue analysis process has been thought based on the logic
shown in Fig. 1. In this overview the three input parameters,
i.e., geometry, materials and loading, are regarded as having similar functions.
In practice, most of the durability analysis follows the model produced by Bishop
and Sherratt (2000) as shown in Fig. 2. The geometry and loading
are initially used together in order to produce a stress-time (σ-t) or
strain-time (ε-t) history at a point of which it is likely to be critical.
The material properties are then introduced in order to estimate the fatigue
lives. The only material properties which are needed in the first step are the
things like Youngs modulus and the elastic-plastic stress-strain curve, which
they are not true fatigue properties. Thus, the actual cyclic material properties
should be determined in order to implement the fatigue life calculations.
The step from overall geometry and generalized loading, to a detailed
map of local stress and strain in a component, has traditionally required
towared the use of a variety of techniques. If the loading is fluctuating
with time, as it always will be in the case of fatigue, a further set
of uncertainties enters. Using the meaningful FEA technique, it gives
tighter control over the move from general geometry and loading to local
parameters and allows dynamic factors to be dealt with more analytically.
A diagrammatic model in Fig. 3 describes another life
estimation process, emphasizing the importance of FEA in a situation where
analysis at precise locations is essential.
The role of a fatigue calculation varies according to the component,
the loading and the situation in which the component are to be used. A
component with simple geometry and simple loading which is to be used
in a situation where failure would cause only minor inconvenience may
be manufactured and put into service purely on the basis of a calculation.
||Conventional view of the fatigue life assessment procedure
||An alternative schematic beyond fatigue
||A diagrammatic flow of life estimation scheme using
This is particularly so if only small numbers of the article are to be made. If the situation
is more complex and the penalties for wrong estimates are higher, verification
of the calculation by testing becomes necessary (Bishop and Sherratt,
A more typical situation is a component with complicated geometry and
multiple loads is to be produced in large numbers. For this case, it requires
the minimum weight and it also to be used in a safety-critical application.
Prototype components or full-scale assemblies should be tested under a
specific loading which is as close as possible to an expected loading
in service. However, it seems to be an expensive operation in the case
of durability assessment. In addition to this expense, a significant drawback
with this type of testing is that it cannot be undertaken until a prototype
exists. If a design problem is then occurred it is likely to be difficult
and expensive to rectify. The more accurate and reliable the life prediction
process becomes the less likely it is that late modifications will be
needed. The main contribution of FEA based fatigue tool is then to enable
reliable fatigue life calculations to be done at the design stage of a
development process, long before tests are possible.
Though many low-cycle fatigue data have been published with the application
of different components with or without FEA techniques, a few of low cycle
fatigue research for the automotive components, for example in the case
of a lower suspension arm, have been conducted with different attitudes
as illustrated in this literature review. In this research, they did mention
on the use of vehicle simulation which lead to the finite element results
for generating the fatigue life contours for the chassis components using
automotive providing ground load history results combined with the computational
techniques. It was concluded that the combination of the vehicle dynamics
modeling, FEA and fatigue analysis are seems to be the viable techniques
for the fatigue design of the automotive components.
In another study, Devlukia and Bargmann (1997) conducted the fatigue
assessment of a suspension arm using the deterministic and probabilistic
approaches. The strength reduction effect due to the surface roughness
was accounted for by representing the surface as a collection of notches
and making use of Neubers rule. It was concluded that the residual stress
demonstrated a more pronounced effect under constant amplitude loading
as compared to variable amplitude loading. The cumulative damage potential
under the variable amplitude loading sequences of the long duration on
a simple specimen data and strain-life method was conservative by a factor
of two. After that, Ringsberg and Lindback (2001) developed a strategy
for fatigue life prediction of Rolling Contact Fatigue (RCF) crack initiation.
It combines the elastic-plastic Finite Element (FE) analysis, the multiaxial
fatigue crack initiation models used together with the critical plan concept,
the fatigue damage summation calculations and the comparison of results
from numerical analysis and experiments. The strategy and evaluation methodology
can be used for fatigue life predictions of RCF crack initiation caused
by low-cycle fatigue and ratcheting failure.
Experimental investigation to rationalize and quantify the low cycle
bending fatigue strength of steel bars under variable amplitude loading
histories has also been performed by Liu (2001). By examining the microstructure
of the tested specimens, the random low cycle bending fatigue life is
highly dependent on the orientation angles of the material grain. Based
on this observation, a physical model was established in order to explain
the various failure patterns of the test specimens. A more accurate formula
for describing and quantifying the low cycle bending fatigues strength
of A36 steel bars under general loading histories was also established
and formulated from this study.
A work from Haiba et al. (2002) has been seen as another FEA application
in fatigue life estimation. They estimated the fatigue lives of metallic
material in both time and frequency domain methods under FEA. Comparison
between several approaches to fatigue life prediction using a real automotive
engineering case study has also been performed. In addition, the study
was taking into account the optimisation based on fatigue life which requires
accurate relative distribution rather than exact values. Haiba et al.
(2002) used a multibody dynamics (MBD) solution. William (2002) also modeled
a vehicle on a computer with MBD simulation software package and combined
the related work with physical laboratory tests for the purpose of optimizing
durability testing. The intension of the research by William (2002) was
to mirror as close as possible the behavior of a physical vehicle on a
road test simulation in order to determine its durability characteristics
under varying road conditions. The results from this research bode well
for increasing connection between the virtual and real worlds of durability
testing. Another research by Haiba et al. (2003) introduced a new
structural optimization algorithm based on fatigue life. The paper investigates
the effects of different assessment strategies on the predicted fatigue
life of a lower suspension arm, the properties of which are modified to
generate different degrees of interaction between the arm natural frequencies
and the frequency range of the applied forcing functions. The results
of this investigation were used to derive a new form of structural optimization
algorithm which is more robust and efficient.
Rindnour (2003) predicted mechanical failures before they occur and determined
the useful life of M1101 High Mobility trailer (HMT) that is normally
towed behind a High mobility multi-purpose Wheeled Vehicle. For the analysis,
the experimental data was taken from a HMT traveling over several test
courses. The data was used to validate a computer simulation and also
to determine the feasibility of life consumption monitoring. Multivariate
regressions and principal component analysis were used to determine which
sensors most accurately reflect the loads on the drawbar at the failure
point. Regression and dynamic models were made after the proper decimation
and filtering of the data was determined. The models that have been developed
were used to predict the fatigue life of the trailer surge brake. The
fatigue life prediction is divided into two parts: initiation and propagation.
The fatigue crack initiation life prediction uses a multiaxial local strain
approach and failure is assumed to occur when the crack has reached 2
mm in length. The fatigue crack propagation life prediction uses the FLAGRO
software for which this software was developed by NASA. The results showed
that the simulation can be modified to represent of the tested vehicle
also. In addition, the fatigue life and durability of the vehicle can
also be predicted with a model and data obtained from some sensors which
have been placed on the vehicle components.
In different situation, Kim et al. (2003) analyzed the hydroforming
process of an automobile lower arm using finite element program of HydroFORM-3D
in order to accomplish its proper design and the process control. An optimum
process trial was then proposed through the numerical simulation to select
a suitable internal hydraulic pressure level and the axial feeding displacement
path. This work showed that the FEM program of HydroFORM-3D provided valuable
information regarding to the forming process and was also dramatically
improved the potential of the hydroforming process. Though the computer-aided
design approach was proposed in this study, the designer can improve the
design efficiency, as well as to avoid expensive and time-consuming trial-and-error
and extensive process design experience.
Williams et al. (2003) proposed a method that ensures the data
used in the derivation of the fatigue parameters is appropriate and indicative
of the material physical behavior. The use of this method allowed the
accurate derivation of the fatigue parameters and thus allowed the use
of fatigue simulation software in order to shorten the product development
cycle by reducing the number of iterations in the design and test cycle.
A study by Yoon et al. (2003) showed the development of an acceptable
testing method for steel pipe under axial Low Cycle Fatigue (LCF) testing.
The plastic buckling of thin wall pipe under monotonic and cyclic loading
was studied by theoretical, numerical and experimental means. In the case
of monotonic compression, the FEA showed good agreement with experimental
results and theoretical predictions were more conservative than other
means of assessing buckling criterion. Under cycling loadings, the buckling
strain was much less than that of monotonic compression. Using FEA, a
non-buckling region that permitted successful for LCF testing has been
Then, Fatemi and Zoroufi (2004) did an experimental and analytical work
using FEA, the durability assessment and also an optimization analysis.
They developed methodologies that can be applied to a wide range of automotive
and other components. Some of the findings are the FEA simulation for
cyclic loadings which is important for fatigue damage analysis. The life
prediction based on local approaches, i.e., the Morrows mean stress parameter
provided better predicted fatigue lives than the Smith-Watson-Toppers
(SWT) mean stress parameter.
Nadot and Denier (2004) has then studied the fatigue phenomena for automotive
suspension arms using high cycle fatigue conditions which it behavior
has been controlled mainly by surface defects. For this case, the effect
from LCF was governed by multiple cracks which was independently initiated
from casting defects. A methodology was then proposed in order to define
the maximum defect size allowed in a casting component. It was correlated
with the empirical method that proposed by Murakami (1993) and also to
determine the evaluation of the fatigue limit with the defect size and
a multiaxial endurance criterion based on the Dang Van model (1993). The
junction between these two approaches gave a concurrent tool for the fatigue
design of casting components.
Abdullah (2005) worked on the novel approach of fatigue data editing
technique, called Wavelet Bump Extraction (WBE), to summarise the load
history. This algorithm was later used, to obtain fatigue lives under
VA loadings for the experimental and predicted method. For the predict
process, four strain-life fatigue damage models have been used, i.e.,
Coffin-Manson, Morro, SWT and Effective Strain Damage (ESD). The correlated
fatigue lives between the ESD model and experiments were distributed around
the 1:1 line and within the range of ± a factor of 2. However,
the correlation points produced from the data of the three other strain-life
models were located outside the range of ± a factor of 2.
In different work and scope by Sun et al. (2005), the displacement-controlled
low cycle fatigue testing has been performed using the Sn-8Zn-3Bi and
Sn-37Pb solder joints on lap shear samples. The test amplitude was varied
whilst the frequency was kept constant at 0.2 Hz and the failure was defined
as a 50% load reduction. The finite element modeling was used for the
analysis and the results were then compared to the experimental data.
The average lifetime for the Sn-8Zn-3Bi solder joints was 17% longer compared
to the Sn-37Pb solder joints. The locations of the maximum equivalent
stress from the FE simulation were found to be at the two opposite corners
of the solder joints, coinciding with the experimental observations of
In a case study by Xianjie (2005), he investigated the cyclic strain
low cycle fatigue and cyclic stress ratcheting failure of carbon steel
45 with quenched and tempered treatment. The tests for this cyclic strain
low cycle fatigue with or without mean strains were carried out in order
to investigate the effect of the mean strain on low cycle fatigue behavior.
The evaluation equation of fatigue damage was then proposed based on the
symmetric cyclic strain LCF testing results and the equation was used
to evaluate the effect of the fatigue damage on the ratcheting failure
under different cyclic stressing. Yi-Ming et al. (2006) analyzed
the experimental fatigue life of the sleeve-pin-shaft connection specimens
under cyclic axial and pure torsional loading. Crack initiation and crack
initiation life have been predicted using FEM. The FE code used is ANSYS.
Has been found from the results that among the four stress-based parameters
and three strain-based parameters, the corresponding critical plane parameter
(FS parameter) predicts the crack initiation life within reasonable deviation
bands. The FS parameter also effectively predicts the locations of crack
In a work by Zoroufi and Fatemi (2006), the fatigue behavior of vehicle
suspension components (forged steel and cast aluminium steering knuckles)
were investigated under constant-amplitude load-controlled fatigue tests.
Three of the finite element models of the knuckles were analysed using
linear and non-linear methods. The nominal stress, the local stress and
the local strain life prediction approaches were then employed and compared
to the experimental results in order to evaluate the accuracy and validity
of these approaches. It was observed that among the contemporary life
prediction procedures used in the automotive industry, the local strain
approach using linear elastic FEA results in conjunction with Neuber-corrected
stresses were reasonable. In addition, it has been found that the results
were close to those obtained on the basis of non-linear elastic-plastic
A recent research by Hasegawa et al. (2007) exposed the fatigue
properties on extruded AZ31 bar under uniaxial loading by both strain
and stress controlled conditions. The fatigue life evaluation method has
been discussed together with the analysis of cyclic stress-strain behavior.
The SWT model makes an excessive forecast for fully reversed stress controlled
test, especially fatigue life is smaller. A new model has been derived
by adding a correction term of -σm/2E to the Manson-Coffin type equation.
Then, Hurley et al. (2007) focused on the application of numerical
models for predicting LCF initiation lives. A series of FE simulations
of the strain control specimens were run using the Mroz user-subroutine
to demonstrate how the stabilized hysteresis loops may be modeled with
sufficient accuracy using this method. Then a number of fatigue initiation
criteria have been developed based on the strain control testing. For
comparison purposes, three different fatigue parameters were utilized
for predicting notch fatigue lives, i.e., Walker, SWT and the total strain
energy density. At the room temperature, these three models led to accurate
predictions of fatigue lives, but led to less accurate predictions at
lower stresses/longer lives. At higher temperature values, the accuracy
of the purely plasticity-based finite element and the Neuber models for
predicting the mechanical response in notched specimens was shown to be
questionable due to inaccurate results of predicting.
Recently Mrzyglod and Zielinski (2007) developed an optimization algorithm
which can be used for structures such as the suspension arm with the application
of high-cycle load conditions. This work has been concentrated on the
fatigue of material (multiaxial criteria of high-cycle fatigue), parametric
optimization of structures and application of finite element method by
using ANSYS®. The main process of fatigue optimization
was preceded by the testing of methods of structure optimization and the
preparing the tools for improving the efficiency of the optimization algorithm.
The fatigue optimization methodology can then be applied to any case of
structure subjected to high-cycle loads.
Rahman (2007) developed general procedures for durability assessment
and optimization of safety-critical free piston engine components. The
durability assessment process was performed using the condition of FEA
and the fatigue life analysis. The FEA technique has been used to predict
the fatigue life and the identification of the critical locations the
specific components by using MSC Software. The durability assessment results
were significant to be used for improving the specific component design
at the early developing stage. The results showed that the predicted fatigue
life appears to be more conservative for the tensile mean stress than
the compressive mean stress. It has been shown that the crack-initiation
approach of the Morrows mean stress correction method gave the most conservative
results for all loading conditions and various materials.
FATIGUE LIFE ASSESSMENT METHOD
The FE analysis results define the stress-state for a component
given the specific loading condition. The most common FE analysis method
used in conjunction with the fatigue analysis is to apply each load independently
as a unit load case. The inputs for the FE analysis are the component
geometry with FE model, the boundary conditions and the loading information.
The location and direction of each load input define the loading information.
The FE method assumes that the component behavior and material properties
are linearly elastic. The FE based durability analysis can be considered
as a complete engineering analysis for the components. The fatigue life
can be estimated for every element in the FE model and the contour plot
of life or damage. A more comprehensive treatment of fatigue mechanisms
and cyclic behavior can be found in Suresh (1998), Socie and Marquis (2000),
Skallerud and As (2002) and Kulkarni et al. (2003). The FEA- based
durability analysis helps to eliminate unnecessary tests by allowing the
engineer to check out the fatigue performance analytically and to optimize
the selection of the material, manufacturing process and geometry, within
the constraints of total cost and loading environment.
The strain-based approach to fatigue problems is widely used at present
for correlating with low-cycle fatigue as in Chen et al. (2006).
The most common application of this approach is in fatigue of notched
members. When the load history contains large overloads, significant plastic
deformation can exist, particularly at stress concentrations and load
sequence effects can be significant. In these cases, the strain life-approach
is generally superior to the stress-life approach for cumulative fatigue
damage analysis (Ralph et al., 2000). The most common application
of the strain-based approach, however, is in fatigue of notched members.
In a notched component subjected to cyclic loads, the behavior of the
material at the root of the notch is best considered in terms of strain.
Since the fatigue damage is assessed directly in terms of local strain,
this approach is called the local strain approach. Thus, it is common
that the service loadings caused by machines and vehicles is evaluated
using a strain-life fatigue damage approach (Tucker and Bussa, 1977; Downing
and Socie, 1982; Conle and Chu, 1997; Chu, 1998; Dowling, 1999). The strain-life
method has achieved the status of industry standard in the North American
automotive industry (Conle and Chu, 1997). In Europe, the automotive industry
shows a preference for stress-life methods (Berger et al., 2002).
Strain-life fatigue curves plotted on log-log scale are shown schematically
in Fig. 4, where Nf or 2Nf is
the number of cycles or reversals to failure, respectively. The strain-life
curve which shown in Fig. 4 has been resolved into the
elastic and the plastic strain components from the steady-state hysteresis loops.
||Strain-life curves showing total, elastic and plastic
At a given life, Nf, the total
strain is the sum of the elastic and plastic strains. Both the elastic
and plastic curves can be approximated as straight lines. At large strains
or short lives, the plastic strain component is predominant and at small
strains or longer lives the elastic strain component is predominant. It
is indicated by the straight-line curves and the size of the hysteresis
loop in Fig. 4. The intercepts of the two straight lines
at 2Nf = 1 are σf′/E for the elastic component
and εf′ for the plastic component. The slopes of the elastic
and plastic lines are b and c respectively. This provides the following
equation for strain-life data (Graham, 1968):
||Total strain amplitude = εa
||Elastic strain amplitude = Δσ/2E
||Plastic strain amplitude = Δε/2
||Fatigue ductility coefficient
||Fatigue ductility exponent
||Fatigue strength coefficient
||Fatigue strength exponent
||Modulus of elasticity
One method, often referred as the (Morrows mean-stress correction relations)
replaces σf′ with σf′ ε σm
in Eq. 2, where σm is the mean stress,
In Eq. 3, σm is taken to be positive
for tensile values and negative for compressive values. This equation
predicts the tensile mean stress is detrimental and the compressive mean
stress is beneficial. Equation 3 predicts more effect
of the mean stress relationship which can be derived at long lives. An
alternative version of the Morrows mean-stress where both the elastic
and plastic terms are affected by the equivalent mean stress, which is
mathematically given by Manson and Halford (1981)
Another the strain-life mean stress correction model was suggested by
Smith et al. (1970), or often called the SWT parameter. This relationship
was based on strain-life test data which was obtained at various mean
stresses. Thus, the SWT expression is mathematically defined as:
where, (σmax = σm + σa
and εa is the alternating strain). This equation is based
on the assumption that for different combinations of strain amplitude,
εa and mean stress, σm, the product σmax
εa remains constant for a given life.
The main task performed during durability analysis is the fatigue life
assessment of components such as engine parts, suspension parts and body
structures (Bignonnet, 1999). The life of the lower suspension arm can
be calculated by using the Morrow approach due to widely accepted by the
automotive industry (Tucker and Bussa, 1977). The SWT approach is also
widely used because it is difficult to categorically select one procedure
in preference to the other (Fatigue, 2001). Suspension system arms can
be fabricated using cast steel (Mahishi, 2005). In the last decade, aluminium
has also found use in structural applications in mass market cars, such
as brake components, steering components and suspension control arms (As,
2006). The prediction of fatigue life under variable amplitudes-despite
innumerable claims to the contrary in literature (Schütz and Heuler,
1994; Schütz, 1996). Neither the Miner calculation in its many variations
nor the local-strain approaches attain a sufficient accuracy, as shown
in Fatemi and Yang (1998).
Several investigators have proposed methods for improving the fatigue
life prediction for components subjected to variable amplitude VA loadings.
Models have been derived using random vibration theory (Liou et al.,
1999), non-linear damage summation (Plumtree and Shen, 1990; Shang and
Yao, 1999) and the adaptation of a fracture mechanics approach (Veers
et al., 1989; Taheri et al., 2003). Methods of modifying
the stress-life and strain-life approaches have also been suggested in
order to predict the fatigue life of the metal structures and automobile
components which are exposed to VA loadings (Conle and Topper, 1980; Yan
et al., 1992). A fatigue damage model for use with VA strain loadings
was developed by DuQuesnay et al. (1993). The idea of developing
this model was based on the crack growth and the crack closure mechanisms
of metallic materials, particularly for steel and aluminium. It has been
shown to work well for a wide range of materials, load spectra, component
geometries, strain magnitudes and mean-strain effects (DuQuesnay et
al., 1992a, b, 1993; Topper and Lam, 1997; DuQuesnay, 2002).
The DuQuesnays strain-life model was developed for the purpose of life
to crack detection, which is based on the use of the effective strain
range as the damage parameter. Using this model, the fatigue damage can
be analysed based on the assumption of the short crack growth and it is
because of the the crack length at failure is usually less than a few
millimeters. This model strain-life model is mathematically defined as:
where, E is the elastic modulus of the material, Δε* is the
net effective strain range for a closed hysteresis loop which is related
to the fatigue crack growth, A and B are material constants and Nf
is the number of cycles to failure.
Accurate calculating fatigue life requires considering every significant
load in the service life. Loading complexity and resulting stress states
mean fatigue analysis is more challenging than simply designing a component
to withstand maximum loads. In addition, it is too computationally intensive
to use finite element method in order to get the fatigue life prediction
for the components which subjected to service loadings.
Several recent finite element software for fatigue life prediction purposes,
using models which they are more suitable for constant amplitude loading
than variable like the Morrow and the Smith-Watson-Topper (SWT) models.
Thus, this study presents a review on the FEA approaches in order to solve
the low cycle fatigue problem. The results of applying the Morrow and
the SWT strain-life equations are still not give the perfect results.
These approaches are not suitable for VA loadings because cycle sequence
effects are not taking into consideration.
In a nutshell, there are many models can give more reasonable results
for the fatigue life prediction by taking into consideration the sequence
effect on life components. For instance, the use of the DuQuesnay model
with the combination of the FEA approach in order to predict fatigue life
under service loading will also be done as an effective algorithm, which
leads to an alternative solution in the durability research.
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