Uniaxial Fatigue Analysis, using S-N (stress-life) and E-N (strain-life) approaches for predicting the life (number
of loading cycles) of a structure under cyclical loading may be performed by using HyperLife.
Multiaxial Fatigue Analysis, using S-N (stress-life), E-N (strain-life), and Dang Van Criterion (Factor
of Safety) approaches for predicting the life (number of loading cycles) of a structure under cyclical
loading may be performed by using HyperLife.
Seam Weld Fatigue analysis is available to facilitate Fatigue analysis for seam welded structures. It allows you to
simulate the Fatigue failure at the seam weld joints to assess the corresponding fatigue failure characteristics like
Damage and Life.
Surface condition is an extremely important factor influencing fatigue strength, as
fatigue failures nucleate at the surface. Surface finish and treatment factors are
considered to correct the fatigue analysis results.
Surface finish correction factor is used to characterize the roughness of the
surface. It is presented on diagrams that categorize finish by means of qualitative
terms such as polished, machined or forged. 1
Surface treatment can improve the fatigue strength of components. NITRIDED,
SHOT-PEENED, and COLD-ROLLED are considered for surface treatment correction. It is
also possible to input a value to specify the surface treatment factor .
In general cases, the total correction factor is
If treatment type is NITRIDED, then the total correction is .
If treatment type is SHOT-PEENED or COLD-ROLLED, then the total correction is = 1.0. It means you will ignore the effect of
surface finish.
The fatigue endurance limit FL will be modified by as: . For two segment S-N curve, the stress at the
transition point is also modified by multiplying by .
Surface conditions can be defined in the Assign Material dialog, where you assign them to each
part.
Fatigue Strength Reduction Factor
In addition to the factors mentioned above, there are various other factors that could affect the
fatigue strength of a structure, that is, notch effect, size effect, loading type.
Fatigue strength reduction factor is introduced to account for the combined effect of
all such corrections. The fatigue endurance limit FL will be modified by as:
The fatigue strength reduction factor may be defined in the Assign Material dialog and is assigned to
parts or sets.
If both and are specified, the fatigue endurance limit FL will
be modified as:
and have similar influences on the E-N formula through
its elastic part as on the S-N formula. In the elastic part of the E-N formula, a
nominal fatigue endurance limit FL is calculated internally from the reversal limit
of endurance Nc. FL will be corrected if and are presented. The elastic part will be modified as
well with the updated nominal fatigue limit.
Temperature Influence
The fatigue strength of a material reduces with an increase in temperature.
Temperature influence can be accounted by applying the temperature factor
Ctemp to modify the fatigue endurance limit FL.
Ctemp can either by assigned directly, or isothermal temperature across
the part/element set can be defined to calculate Ctemp as referred by FKM
guidelines for elevated temperatures. The temperature defined must be in degree
Celsius.
Ctemp at normal temperature = 1
Ctemp at elevated temperature defined as per FKM guidelines for the
following materials is highlighted in the table below.
Ctemp user-defined accepts a value between 0 <
Ctemp <= 1
Ctemp set to NONE = 1
Type
Temp. Condition
Ctemp Factor
None**
this is for materials other than the ones below
-
= 1
Fine Grain Structural Steel
60℃ < T < 500℃
=1 - [10-3 x (T/℃)]
Other Steels (other than stainless steel)**
100℃ < T < 500℃
=1 - [1.4*10-3 x (T/℃-100)]
GS (Cast steel and heat treatable cast steel)
100℃ < T < 500℃
=1 - [1.2*10-3 x (T/℃-100)]
GJS (Nodular Cast
Iron)
GJM (Malleable Cast Iron)
GJL (Cast iron with lamellar graphite)
100℃ < T < 500℃
=1 - aT,D x (10-3 *
T/℃)2
Aluminum materials
50℃ < T < 200℃
=1 - [1.2*10-3 x (T/℃-50)]
Material Group
GJS
GJM
GJL
aT,D
1.6
1.3
1.0
If both Ctemp and Kf are specified, the fatigue endurance limit
FL will be modified as: FL' = FL ⋅ Ctemp / Kf
Scatter in Fatigue Material Data
The S-N and E-N curves (and other fatigue properties) of a material is obtained from
experiment; through fully reversed rotating bending tests. Due to the large amount
of scatter that usually accompanies test results, statistical characterization of
the data should also be provided (certainty of survival is used to modify the curves
according to the standard error of the curve and a higher reliability level requires
a larger certainty of survival).
To understand these parameters, let us consider the S-N curve as an example. When S-N
testing data is presented in a log-log plot of alternating nominal stress amplitude
Sa or range SR versus cycles to failure N, the relationship between S and N can be
described by straight line segments. Normally, a one or two segment idealization is
used.
Consider the situation where S-N scatter leads to variations in the possible S-N
curves for the same material and same sample specimen. Due to natural variations,
the results for full reversed rotating bending tests typically lead to variations in
data points for both Stress Range (S) and Life (N). Looking at the Log scale, there
will be variations in Log(S) and Log(N). Specifically, looking at the variation in
life for the same Stress Range applied, you may see a set of data points which look
like this.
S
2000.0
2000.0
2000.0
2000.0
2000.0
2000.0
Log (S)
3.3
3.3
3.3
3.3
3.3
3.3
Log (N)
3.9
3.7
3.75
3.79
3.87
3.9
As with many processes, the distribution of Log(N) is assumed to be a Normal
Distribution. The material data input in the
Material DB and My Material tabs is based on the mean of the scatter.
The experimental scatter exists in both Stress Range and Life data. In the
Assign Material dialog, the Standard Deviation (or Standard Error) of the
scatter of log(N) is required as input (SE field for S-N curve).
Any normal distribution is fully defined by specifying the mean and its standard
deviation, in the case of S-N fatigue analysis in HyperLife, the
mean is provided by the S-N curve as , whereas, the standard deviation is input via the
SE field in the
Assign Material dialog.
If the specified S-N curve is directly utilized, without any perturbation, then the
mean values of the normal distributions at each data point is assumed to be used,
leading to a certainty of survival of 50%, by default. This is a consequence of S-N
material data that is available for the mean values of log(N). Since a value of 50%
survival certainty may not be sufficient for all applications, HyperLife can internally perturb the S-N material data to the required
certainty of survival defined by you. To accomplish this, the following data is
required.
Standard Deviation (Standard Error) of log(N) normal distribution
(SEin
Assign Material).
Certainty of Survival required for this analysis (Certainty of Survival in the Fatigue Module context).
A normal distribution or gaussian distribution is a probability density function
which implies that the total area under the curve is always equal to 1.0. log(N)
values which are higher than the mean are always more conservative. Therefore, for
certainty of survival calculations, any value greater than 50% implies that the
log(N) values lower than the mean are being considered. The total area of the curve
starting from the right end of the Normal curve (which is typically positive
infinity for a PDF) is directly equal to the certainty of survival (or probability
of survival).
A typical normal distribution is characterized by the following Probability Density
Function:(1)
Where,
The sample value () for which the probability of occurrence
is calculated in a particular range (based on the specified certainty of
survival).
The mean
The standard deviation (or standard error, given by
SE field ).
The area of the curve from the right end can be understood to be equal to the
certainty of survival specified in the
Certainty of Survival field. This integral equation can be solved directly
to generate the value of (or ) which will allow a perturbation of the S-N curve.
However, the general practice is to convert the normal distribution function into a
standard normal distribution curve (which is a normal distribution with mean=0.0 and
standard error=1.0). This allows us to directly convert the certainty of survival
values into corresponding values (via Z-tables).
Note: The certainty of survival
is equal to the area of the curve under a probability density function between
the required sample points of interest. It is possible to calculate the area of
the normal distribution curve directly (without transformation to standard
normal curve), however, this is computationally intensive compared to a standard
lookup Z-table. Therefore, the generally utilized procedure is to first convert
the current normal distribution to a standard normal distribution and then use
Z-tables to parameterize the input survival certainty.
The equation used to convert the normal distribution to a standard normal
distribution is:(2)
This transformation leads to a corresponding standard normal distribution with a mean
of 0.0 and standard error of 1.0. Replacing the values with fatigue data, and
rewriting the equation.(3)
The value of is procured from the standard normal distribution
Z-tables based on the input value of the certainty of survival (which is the area
under the curve from the right end of the curve up to the corresponding negative
Z-value). Some typical values of Z for the corresponding certainty of survival
values are:
Z-Values (Calculated)
Certainty of Survival (Input)
0.0
50.0
-0.5
69.0
-1.0
84.0
-1.5
93.0
-2.0
97.7
-3.0
99.9
Based on the above example (S-N), you can see how the S-N curve is modified to the
required certainty of survival and standard error input. This technique allows you
to handle Fatigue material data scatter using statistical methods and predict data
for the required survival probability values.
References
1 Yung-Li Lee, Jwo. Pan, Richard B. Hathaway and Mark E.
Barekey. Fatigue testing and analysis: Theory and practice, Elsevier,
2005