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\begin{document}

\title{Fatigue and overstress indicators for ultra-light and light aircraft}



\author[1]{Tetiana Maslak}%
\author[1]{Mikhail Karuskevich}%
\author[1]{Sergey Ignatovich}%
\author[1]{Oleg Karuskevich}%
\author[2]{Łukasz Pejkowski}%
\author[3]{Pavol Kurdel}%
\affil[1]{National Aviation University}%
\affil[2]{Uniwersytet Technologiczno-Przyrodniczy im Jana i Jedrzeja Sniadeckich w Bydgoszczy}%
\affil[3]{Technical University of Košice Faculty of Aeronautics}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
The paper deals with the problem of ultra-light and light aircraft
structural health monitoring. The phenomenological basis and engineering
decisions for methods to monitor accumulated fatigue damage and to
register overstress of aircraft principal structural elements have been
shown. The proposed fatigue indicator is lightweight and autonomous; the
output information of the indicator reflects the inhering feature of the
fatigue damage -- appearance and growth of surface extrusions and
intrusions. The overstress indicator simplicity and correctness of the
information is provided by ``fuse'' principle of the design.%
\end{abstract}%



\sloppy


\textbf{Fatigue and overstress indicators for ultra-light and light
aircraft}

\selectlanguage{polish}\subsubsection*{\texorpdfstring{M. Karuskevich\textsuperscript{1},
S.Ignatovich\textsuperscript{1}, O.Karuskevich\textsuperscript{1},
T.Maslak\textsuperscript{1,*}, Ł.Pejkowski\textsuperscript{2}, P.
Kurdel\textsuperscript{3}}{M. Karuskevich1, S.Ignatovich1, O.Karuskevich1, T.Maslak1,*, Ł.Pejkowski2, P. Kurdel3}}\selectlanguage{english}

{\label{m.-karuskevich1-s.ignatovich1-o.karuskevich1-t.maslak1-ux142.pejkowski2-p.-kurdel3}}

\textsuperscript{1} National Aviation University, Liubomyra Huzara ave.
1, Kyiv 03058, Ukraine

\textsuperscript{2} University of Science and Technology, S. Kaliskiego
7, 85-796 Bydgoszcz, Poland

\textsuperscript{3}Technical University of Ko\selectlanguage{polish}š\selectlanguage{english}ice, Rampov\selectlanguage{ngerman}á 7, 041 21
Ko\selectlanguage{polish}š\selectlanguage{english}ice, Slovakia

\textbf{1. Introduction}

Certification specifications for Light Sport Aeroplanes (CS-LSA) define
the strength requirements for the Light Sport aircraft and confirm the
importance of the fatigue analysis {[}1{]}.

The trend currently exists to monitor metal fatigue by Structural Health
Monitoring Systems. This approach is on the way to be implemented into
contemporary large planes. There are many reasons to use fatigue
monitoring for small planes as well. Taking into account the limitation
of the weight for this category of aircraft, the described here
miniature autonomous fatigue indicator looks a prospective alternative
to the complex monitoring systems.

Another problem of light planes is an operational overstress of
principal structural elements. Sometimes these planes are not equipped
with an accelerometer. Overstress of the plane components due to the
incorrect flight regime can lead to the primary structure deformation,
and even to the aircraft crash.

One fatal accident {[}2{]} with Cessna 210L Centurion was investigated
but the final precise decision regarding the cause of the aircraft
fracture was not made. The presence of the overstress indicator would
clarify the situation and develop some recommendations for pilots and
engineers.

\textbf{2. Small aircraft fatigue}

Like any aircraft, the LSA are subjected to a wide spectrum of
operational loads. The level of allowed acceleration for the LSA is
higher than for the planes of transport category: the maximum positive
load factor prescribed, for example for the Viper SD-4 {[}3{]} is equal
to +4.0g, the minimum is -- 2.0g.

As a proof of the necessity of the special attention to the metal
fatigue for small aircraft the fatigue damage case study of the Piper
aeroplane primary structure may be considered. During a routine
inspection of a Piper Model PA-46-350P aeroplane, 1.53-inch () fatigue
crack was discovered in the main spar lower cap (Fig.1). The crack
discovery was at 5,273-hour time-in-service (TIS) versus the type
certificated life limit of 15,580 hours TIS {[}4{]}.

The list of fatigue issues could be extended, but even these examples
prove the requirements for the special attention for the aircraft
primary structure fatigue.

\textbf{3. Fatigue monitoring}

The methods for fatigue monitoring for the Light Aircraft must differ
from the systems which can be developed for and used on large transport
planes. The indicator must be an autonomous, self-data-registering unit,
miniature and lightweight.

All these requirements meets the Surface Relief Fatigue Indicator
(SRFI).

Fatigue process for some metals is accompanied by formation and
evolution of the surface deformation relief -- the pattern of surface
extrusion, intrusion, persistent slip bands (Fig. 1) {[}5{]}. The
deformation relief is a three-dimensional structure.

The pure aluminium due to its plasticity react on deformation by the
exhibiting surface relief. Pure aluminium is not used as constructional
material, but it is often used for the protection of aluminium alloys
against corrosion being clad layer of so- called Al-Clad aluminium
alloy. The 2024-T3, 7075-T6 are well known examples of Al-Clad alloys
used in the aviation industry.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Fig. 1. Surface relief extrusion/intrusion pattern scheme {[}5{]}

The relief parameters were proposed and verified by the numerous
experiments {[}6-9{]}.

The primary damage parameter considers the intensity of the surface
relief:

,

where: \emph{S\textsubscript{deform. relief}} - surface area with
deformation relief; S\emph{\textsubscript{total}} - total investigated
area.

The additional damage parameter is a fractal dimension of the surface
pattern. It describes quantitatively the shape of surface relief
clusters. The fractal dimension Dp/s is based on the ratio of the
perimeter of the clusters to their area:

,

where: \selectlanguage{greek}\emph{Np(δ), Ns(δ)}\selectlanguage{english} - number of cells with the size \selectlanguage{greek}\emph{δ} \selectlanguage{english}in
pixels, which cover the perimeter and area of deformation relief
clusters.

It was proved, that the remaining life of the component, made of a metal
exhibiting surface relief could be calculated with an empirical
relationship between the number of cycles to failure and relief
parameters:

N\textsubscript{remaining} = f (D, Dp/s).

Some bearing components of the primary structure are not able to exhibit
surface relief after cyclical loading due to their physical properties,
that's why the attachable fatigue indicator has been proposed as an
alternative to the direct investigation of the surface of the
components.

Indicator (sensor) looks like a micro specimen for fatigue tests (Fig.
2) made of Al-clad alloy.

The strain of the indicator is not constant value along the indicator
axis; it depends on the stiffness, which varies due to the different
cross sections. The required level of strain and stress in the inspected
cross section of the indicator can be achieved by the proper selection
of the indicator's geometry. This procedure is provided by the
application of Finite Elements Analysis (FEA) using ANSYS software.

\textbf{Hosted file}

\verb`image4.emf`  available at \url{https://authorea.com/users/361817/articles/483133-fatigue-and-overstress-indicators-for-ultra-light-and-light-aircraft}

Fig. 2. Fatigue indicator dimensions

Whilst the task for sensitivity increase looks realistic by manipulation
with geometry, the problem of buckling prevention introduces limitations
on the indicator practical use.

The problem is that some aircraft components, for example, wing, work
under both the compression and tension. This situation causes
limitations on the indicator geometry. The buckling analysis has been
conducted by two methods: a) following the classic Euler's formula for
critical load; b) using eigenvalue buckling analysis in ANSYS software
(Fig.3).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Fig. 3. ANSYS buckling simulation

It was proved by the ANSYS buckling simulation that the danger of the
stability loss doesn't exist at the realistic spectrum of loads on
aircraft wing.

The sensitivity of the deformation relief evolution to the stress level
can be illustrated by results of surface relief monitoring for three
sensors of different sensitivity (Fig.4). The structural elements with
sensors were loaded by cycle with =157 \selectlanguage{russian}МPа, \emph{R} =0.

\textbf{Hosted file}

\verb`image7.emf`  available at \url{https://authorea.com/users/361817/articles/483133-fatigue-and-overstress-indicators-for-ultra-light-and-light-aircraft}

N, thousands cycles

Fig. 4. Damage accumulation for three indicators of different
sensitivity: 1 -- indicator with local stress 280 МPа; 2 -- indicator
with local stress 260 МPа; 3 -- indicator with local stress 240 МPа

\textbf{4. Overstress Indicator for Ultra-Light and Light Airplanes}

The practice of the fuses and mechanical safeguards application in the
engineering structures and mechanisms for prevention of over regular
regimes. Different types of safeguard devices are successfully used in
the different fields of technics to prevent failure of the machines,
equipment, and systems.

Design of proposed Overstress Indicator resembles the described above
fatigue sensor. Whilst the fatigue indicator reacts to repeating loads
by the evolution of the sensor's surface state, the overstress indicator
reacts excessive strain by its complete failure. Similar to the fatigue
sensor, the sensitivity of the indicator depends on the geometry: necked
working section has higher strain than any others indicator's section.

Transmitting overstress indicator's signal into the cabin doesn't
require very much sophisticated arrangement. The onboard system of
relays can be used to supply information regarding the state of the
indicator.

\textbf{5. Conclusion}

Fatigue and overstress of the principal structural element are crucial
problems for all categories of aircraft. Light and Ultra-Light aircraft
have limited opportunities for the application of advanced Structural
Health Monitoring Systems. That is why the autonomous Surface Relief
Fatigue Indicator (SRFI) may be considered as a reliable tool for the
fatigue monitoring.

Light and Ultra-Light due to the action of the unallowable accelerations
in manoeuvers meet the overstress conditions for the components. The
excessive stresses can lead to the deformation of the structure, loss of
the aerodynamic characteristics and even to an aircraft crash. The
overstress can be revealed by the simple proposed device, called here
Overstress Indicator. It allows for prevention flight with damaged
structure, thus increases the safety of the operation.

\textbf{References}

\begin{enumerate}
\tightlist
\item
  Easy Access Rules for Light Sport Aeroplanes (CS-LSA) (Amendment 1),
  EASA Rules Nov. 2018. - P.24.
\item
  \emph{https://bst-tsb.gc.ca/eng/rapports-reports/aviation/2001/a01o0165/a01o0165.html}
\item
  \emph{http://tomarkaero.com/en/}
\item
  \emph{http://www.aero-news.net/index.cfm?do=main.textpost\&id=7ba6dcbb-aeb7-41b2-a8e1-3754e6ff94b9}
\item
  \emph{https://fcp.mechse.illinois.edu/files/2014/07/02\_fundamentals.pdf}
\item
  M. Karuskevich, O. Karuskevich, T. Maslak, S. Schepak, Int J Fatigue
  39, 116-121(2012).
\item
  M. Karuskevych, I. Zhuravel', T.~Maslak, Materials Science 47, 621-626
  (2012).
\item
  M. Karuskevich, S. Ignatovich, M. Petrasek, T. Maslak Advances in
  military technology 8, 83-91(2013).
\item
  \selectlanguage{polish}Ł. \selectlanguage{english}Pejkowski, M. Karuskevich, T. Maslak Extrusion/intrusion structure
  as a fatigue indicator for uniaxial and multiaxial loading. Fatigue
  Fract Eng Mater Struct. -- 2019. - Volume 42. Issue 10 -- P.2315-2324.
\end{enumerate}

\selectlanguage{english}
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