Acta Polytechnica CTU Proceedings


doi:10.14311/APP.2016.3.0039
Acta Polytechnica CTU Proceedings 3:39–42, 2016 © Czech Technical University in Prague, 2016

available online at http://ojs.cvut.cz/ojs/index.php/app

DATABASE FINLIV – FOCUS ON STAIRCASE METHOD

Maxim Lutovinov∗, Jan Papuga, Milan Růžička

Faculty of Mechanical Engineering of Czech Technical University in Prague, Technická 4, Prague, Czech
Republic

∗ corresponding author: maxim.lutovinov@fs.cvut.cz

Abstract. This paper introduces FinLiv database focused on gathering, manipulating and providing
experimental static and fatigue data. One of its new features is the ability to include also fatigue tests
realized by the staircase method.

Keywords: fatigue, database, staircase method, fatigue limit.

1. Introduction
FinLiv is a database intended to gather the infor-
mation about static and stress- and strain-controlled
fatigue experiments and also about parameters of
various static and fatigue material models derived
from such data. It was developed to resolve the prob-
lems of researchers in a lack of quality data, their
frequent second-hand use, and the way the data items
are selected for various benchmark tests. By now,
FinLiv has a large set of tools for entering and pro-
cessing data. One of the newest tools is the staircase
method [1] that automatically evaluates data from
stress-controlled experiments and provides the fatigue
limit as a result.

2. FinLiv
FinLiv is represented by two parts, which closely co-
operate, but which also can be used as standalone
applications. The first part serves for entering data,
while the second part serves for listing them. The
second part is implemented as a web database and
can be found at www.fadoff.cz/page/finliv. It al-
lows the user to have permanent access to the raw
experimental data or to the final regression curves
retrieved from them. In the web part there are no
tools to process the data, it simply retrieves and lists
them on a request in a raw or processed form.

The first part, FinLiv.VBA [2], was built as an MS
Excel application written in Visual Basic for Applica-
tions, and its main purpose is to enter experimental
data and to process them. Data processing is neces-
sary in order to e.g. perform regression analysis or
to prepare automated input for fatigue solvers, if a
particular experimental data set has to be used within
a benchmark of a particular calculation method. The
MS Excel platform was chosen because of its preva-
lence among engineers, and because it is substantially
cheaper than Matlab. The application can be accessed
from any computer which has MS Excel installed.
The main interface of FinLiv.VBA is represented

by "form" sheet (see the part of the input interface
in Figure 1). It consists of a group of tables, combo

boxes and buttons. Data input is realized by filling
in the salmon colored cells and by choosing options
from the combo boxes. In the first non-empty column
there are designations that correspond to the input
parameters. The same designations are used in the
datasheets (Figure 2), where the material data are
stored. The datasheets are placed in the same work-
book as the “form” sheet, and their structure is quite
simple: in the second column there are designations
that represent the entered parameters, while the other
columns contain information on individual curves of
the particular data set.
FinLiv works with data from static experiments

and stress- and strain-controlled fatigue experiments.
Since each type of experiments uses a different set of
parameters, the “form” sheet changes its structure to
accommodate the selected type.

In addition to entering data, FinLiv.VBA can also
process data. With the help of the application the user
can easily perform regression analyses of experimental
data and obtain corresponding regression parameters.
For strain-life data there are two types of a regression
analysis. The first one is carried out in a conventional
way, which is represented by linear regression using
the least square method. The second method performs
non-linear regression according to the 3-D method [3].
The 3-D method is based on the assumption that one
value of the total strain amplitude corresponds to only
one stress amplitude and to a single number of cycles.
If this assumption is valid a curve can be drawn in a
3-dimensional space which besides formulation of the
total characteristics depicts also plastic and elastic
strain. Unfortunately, implementing such a non-linear
3-D regression in Excel is problematic, therefore it
was decided to carry out the regression analyses in an
external Matlab application. To prepare an input file
for that application the user should click "Input for
Regression" button. To load the resulting parameters
of the regression analysis to FinLiv, the user should
click "Get regression data" button and choose the
output file created by the Matlab application.
For stress-life data, there are also two types of a

regression analysis, but unlike the case of strain-life

39

http://dx.doi.org/10.14311/APP.2016.3.0039
http://ojs.cvut.cz/ojs/index.php/app


M. Lutovinov, J. Papuga, M. Růžička Acta Polytechnica CTU Proceedings

Figure 1. "Form" sheet of FinLiv with sample data.

Figure 2. A datasheet of FinLiv with sample data.

data both types of the regression are carried out in
the Excel environment. Regression analyses of S-N
data as well as a visual display of obtained e-N curves
are available in another workbook that is generated
automatically from FinLiv. Individual sheets in that
workbook correspond to the data sets that were se-
lected for processing. At each page of such data there
are two plots of regression curves. In the case of
strain-life data, there are two Manson-Coffin curves,
constructed on the basis of parameters obtained from
conventional regression analyses and 3-D analyses. In
the case of stress-life data, the first regression curve is
represented by the Basquin relation and another one
by Kohout-Vechet relation. For S-N data, a new tool
is also available in the same workbook - the staircase
method, which is described below.

2.1. Staircase Method
The staircase method is a standardized method [1] for
carrying out and evaluating experiments in order to
determine the fatigue limit related to a given number
of cycles. The essence of the method is to increase or
decrease the load amplitude of a new test specimen by
a constant pre-selected value based on the response of
the previous specimen, i.e. whether a failure occurred
during the previous experiment.

For evaluation, the staircase method uses a special
table (Figure 3) constructed according to the stan-
dard ISO 3800 [1]. The rows of the table represent
stress levels and the columns represent the order of
the experiments. A symbol “o” is entered into the
appropriate cell when a failure doesn’t occur, and a
symbol “x” in the opposite case. If the essence of the
method has been respected, then the symbols “x” and
“o” are arranged in the table into the sequence that

40



vol. 3/2016 Database FinLiv – Focus on Staircase Method

Figure 3. Process of generating the output table according to the staircase method in FinLiv.

looks like stairs. In case of a suitable choice of the first
stress level and a step size between individual levels,
the stress levels after several experiments (about 10
experiments) will oscillate around a certain value – the
fatigue limit. The fatigue limit and the corresponding
standard deviation can be then calculated with the
help of the equations given by the standard [1], which
uses values from the left part of the table (Figure 3,
columns 3 to 8). The fatigue limit labeled as Sig_50
in Figure 3 is calculated according to:

Sig_50 = σao + ∆σall(
A

C
+ x) (1)

Here, σao is the lowest load amplitude level at which
the first non-failed specimen appears, given that the
total sum of the non-failed specimens is less than the
total sum of the failed specimens. In the opposite case,
the load level corresponding to the first failed specimen
should be input. The standard doesn’t specify how to
proceed in the case when the total sums of the failed
and non-failed specimens are equal. The observations
show that in such case the result will be the same
regardless of whether failed or non-failed specimens
are selected as the reference type. The algorithm
implemented in FinLiv in cases like that calculates
the fatigue limit in two steps, with the failed and
non-failed specimens as the reference type and then

chooses the lowest fatigue limit.
The parameter ∆σall is the step size between indi-

vidual load levels. A and C are sums of the values
in the columns z*f and f. The parameter x is equal
to +0.5 when the number of the non-failed specimens
is lower than the number of the failed specimens, or
-0,5 in the opposite case. It is worth noting that the
method can be applied to the load levels represented
by stress as well as to the levels represented by forces.
The result is then the fatigue limit or the force corre-
sponding to the fatigue limit.

The parameter S(Sig) is a standard deviation of the
distribution and is calculated according to:

S(Sig) = 1.62∆σall(
CE − A2

C2
+ 0.029) (2)

where E is the sum of values in the column zˆ2*f.
The staircase method was extended in FinLiv, and

the application analyzes whether the data are suitable
for being processed by the staircase method at all.
Thanks to that, the method can also be used on data
that were obtained from experiments initially unin-
tended to be processed by the staircase method. If the
data are suitable for the method, FinLiv automatically
draws an output table (Figure 3).

The algorithm that analyzes data from the selected
load levels assembles various combinations that differ

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M. Lutovinov, J. Papuga, M. Růžička Acta Polytechnica CTU Proceedings

in the step size between levels and/or by the number
of levels. Then individual combinations are checked
according to the criteria that say whether individual
sets of load levels and corresponding sets of specimen
states (failure, non-failure) are suitable for evaluation
by the staircase method. These criteria are derived
from the essence of the method. For example, one of
the criteria says that if the number of the non-failed
specimens at the highest load level is more than one,
then such set of load levels and specimen states is
not suitable for the staircase method. According to
the method, the appearance of a non-failed specimen
leads to increasing the value of load amplitude. If the
experiment with such specimen is not the last one,
then the next experiment should be carried out at a
higher level of load amplitude, which means that the
level of load amplitude corresponding to the non-failed
specimen in question is not the highest level in the
particular set of experiments. In the other case, if the
experiment at the highest load level with non-failed
is the last one, then at the same level there cannot be
other non-failed specimens.

After selected data are checked by the criteria, Fin-
Liv provides the user the list of possible combinations
of load levels and corresponding steps to choose from
(Figure 3). The combinations are ordered by the num-
ber of included specimens. For each combination there
are also listed corresponding step sizes and calculated
fatigue limits. While selecting a combination it is im-
portant to check the ratio of the fatigue limit and the
step size. The smaller is the ratio, the more accurate
the estimate should be.

The drawback of the implemented check is that it
works only with load levels and can’t take into account
the possibility of individual specimens being removed
from evaluation in order to assemble a suitable com-
bination of the load levels and specimen states.

3. Summary
The paper refers to FinLiv database for storing, listing
and manipulating experimental static and fatigue data.
It describes its newest feature, which is the ability to
process data by the staircase method.

Acknowledgements
The authors thank for the support of their research by
SGS14/181/OHK2/3T/12 CTU grant.

References
[1] ISO 3800:1993(E). Threaded fasteners - Axial load
fatigue testing - Test methods and evaluation of results.
Switzerland: International Organization for
Standardization, 1993.

[2] J. Papuga, M. Lutovinov. Help for FinLiv.VBA Excel
database [ver. C], FME CTU in Prague & Evektor, spol.
s.r.o., Prague 2014.

[3] A. Nieslony, C. Dsoki, H. Kaufmann, P. Krug. New
method for evaluation of the Manson–Coffin–Basquin
and Ramberg–Osgood equations with respect to
compatibility. International Journal of Fatigue 30(10-
11):1967–1977, 2008. doi:10.1016/j.ijfatigue.2008.01.012.

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http://dx.doi.org/10.1016/j.ijfatigue.2008.01.012

	Acta Polytechnica CTU Proceedings 3:39–42, 2016
	1 Introduction
	2 FinLiv
	2.1 Staircase Method

	3 Summary
	Acknowledgements
	References