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Effect of a crack on the nonlinear behavior of a stiffened composite panel
Houda Beghdada, Nacer Rahalb, Abdelaziz Souicic,
Sara Zatird, Khaled Benmahdie, Halima Aouadf a Mustapha Stambouli University, Department of Civil Engineering, Mascara, People's Democratic Republic of Algeria, e-mail: [email protected], corresponding author, ORCID Ю: https://orcid.org/0009-0001-3548-5138
b Mustapha Stambouli University, Department of Civil Engineering, Mascara, People's Democratic Republic of Algeria;
University of Sciences and Technology, Laboratory of Mechanical Structure and Construction Stability, Oran,
People's Democratic Republic of Algeria, e-mail: [email protected],
ORCID Ю: https://orcid.org/0009-0002-0400-8360
c Mustapha Stambouli University, Department of Civil Engineering, Mascaral, People's Democratic Republic of Algeria;
University of Sciences and Technology, Laboratory of Mechanical Structure and Construction Stability, Oran,
People's Democratic Republic of Algeria, e-mail: [email protected],
ORCID Ю: https://orcid.org/0009-0004-3845-7409
d University Tahri Mohamed of Bechar, Architecture and Urban Department, Bechar, People's Democratic Republic of Algeria, e-mail: [email protected],
ORCID Ю: https://orcid.org/0000-0002-6187-3441
e Mustapha Stambouli University, Department of Civil Engineering, Mascara, People's Democratic Republic of Algeria, e-mail: [email protected],
ORCID Ю: https://orcid.org/0000-0002-8244-5817
f Mustapha Stambouli University, Department of Civil Engineering, Mascara, People's Democratic Republic of Algeria, e-mail: [email protected],
ORCID Ю: https://orcid.org/0009-0004-1999-1489
doi https://doi.Org/10.5937/vojtehg72-47123
FIELD: mechanics, materials ARTICLE TYPE: original scientific paper
Abstract:
Introduction/purpose: During their lifetime, ships and aircraft are subjected to severe service and aerodynamic loads that can cause structural damage and cracking. These cracks grow and propagate over time. Extending the life of a damaged structure is a very important area of research. In this
Beghdad, H. et al, Effect of a crack on the nonlinear behavior of a stiffened composite panel, pp. 1171-1187
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context, the repair of composite panels is recommended to restore the performance of cracked structures.
Methods: In order to minimize the concentration of stresses at the bottom of a crack, to stop and even to delay the propagation of this crack, this study seeks to propose a two-dimensional analysis by the software ANSYS to predict the effect of the propagation of a possible crack on the nonlinear behavior of cracked stiffened composite panels.
Results: The results from this analysis will be a very good reference for improving performance and repairing cracked composite panels using stiffeners.
Conclusion: It is recommended to provide patches for repairing cracked panels based on the modeling given in this study.
Key words: composite panels, damaged structure, crack propagation, ANSYS, concentration of stresses.
Introduction
Over the past two decades, composite materials have played an important role in the development of high-performance structures. Researchers have studied different topics in this field such as the control of cracks, vibrations, shape, buckling, and stresses in structures (Fesharaki et al, 2016).
Unfortunately, an important aspect of the behaviour of composites is their impact resistance as ships and aircraft are subjected to severe service and aerodynamic loads that can cause structural damage and cracking. During their service, cracks develop in the structures of ships and aircraft. In addition, other unexpected damaging loads or use beyond their service life exaggerate the growth of these cracks (Mall & Conley, 2009). The occurrence of cracks in the stiffened plates will reduce their ultimate compressive strength (Bayatfar et al, 2014; Shi et al, 2019; Xu et al, 2014; Xu et al, 2021), as the damage will induce earlier collapse (Shi et al, 2021). This situation constitutes a subject of great importance and a temptation to resolve it has become necessary. Therefore, repair techniques for cracked aerospace structures are needed (Mall & Conley, 2009).
To regain the initial structural capacity for which the device was designed, repairing or reinforcing the cracked or weakened part of the structure is an essential operation, thus requiring in-depth mastery. In recent years, a bonded composite patch is widely used as a very good alternative to repair cracked aerospace structures (Duong & Wang, 2007; Baker et al, 2003). In this context, to better understand the effect of crack propagation on the behavior of structures repaired by bonded patches,
many studies have been carried out (Baker, 1993; Sun et al, 1996; Young et al, 1993; Jones et al, 1982; Jones et al, 1988; Rose, 1982; Tarn & Shek, 1991; Naboulsi & Mall, 1998, 1999; Denney & Mall, 1997; Heller et al, 1989; Chue et al, 1994; Xu & Guedes Soares, 2012; Xu & Guedes Soares, 2013; Shi et al, 2017). The bonded patch repair reduces the stresses near the crack, it retards or completely stops the growth of this crack. Bonded composite patch repairs offer advantages such as the absence of additional stress concentration, a higher stiffness-to-weight ratio, the ability of the patch to be formed into complex shapes, and the ability to repair irregular components (Makwana et al, 2021).
Modeling
This present research consists of modeling, using the ANSYS software, the nonlinear behaviour of a composite panel with a crack. The considered panel is simply supported on its periphery and is subjected to a bidirectional tensile loading (Figure 1).
Figure 1 - Simply supported panel under a bi-axial tensil loading
The panel is made entirely of a graphite/epoxy composite with the mechanical characteristics given in Tables 1 and 2.
Table 1 - Mechanical characteristics of an epoxy graphite composite
E1 (GPa) E2 (GPa) E3 (GPa) G12 (GPa) G13 (GPa) G23 (GPa) V12 V13 V23
130 10 10 4.85 4.85 3.62 0.31 0.31 0.52
Beghdad, H. et al, Effect of a crack on the nonlinear behavior of a stiffened composite panel, pp.1171-1187
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Table 2 - Strengths of a graphite epoxy composite
Xt (MPa) Xc (MPa) Yt (MPa) Yc (MPa) S (MPa)
1933 1051 51 141 61
Ratio and the resistance index
In the ANSYS software, the resistance ratio R, also called the safety factor, is expressed by:
A =
R = 1.0/| -— + yj(B/2 A)2 +1.0/A l 2 A
((7x )2 , (0 )2 , (0 )2 , (0 f , (Qz f , (о„ )2
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Cxz oxoz
xz x z
О о* о* О ООоО 0* 0* 0* 0*
xt xc yt yc yt yc zt zc xt xc zt zc
B =
( _!
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V Уг Уг )
zt zc
1 J_
ко* о* ,
(1)
(2)
(3)
Cxy, Cyz, Cxz = x-y, y-z, x-z are respectively the coupling coefficients for the Tsai-Wu theory.
The rupture will take place if this resistance report satisfies the condition 0<R<1.
The resistance index 4 can also be expressed as:
4 = A + B (4)
If 4 < 1, the structure is completely safe. Otherwise, breakage is likely to occur.
Finding the critical zone
In order to find the critical values of the resistance index 4, three points likely to have the critical stresses have been chosen. The first point is at the tip of the crack, the second one is in the position of the transverse stiffener and the third point is at the end of the panel (Figure 2). Figure 2 represents the distribution of the resistance index under a loading P=50MPa.
In order to find the most critical zone, the authors analysed the evolution of this index as a function of time for the three points chosen on the screen. The modeling results (Figure 3) show that the most important
values are offered at point 1 (point of the crack). Therefore, point 1 represents more risk for the panel because of the presence of the crack which tends to propagate for resistance indices greater than the value 1. To this end, the analysis focuses on the point 1 strong constraint.
AN
S83E-03 .057ЭЭ4 .115406 .172817 .230229
_________.029288___________.0867_____________.144111___________.201523___________.258934
Figure 2 - Resistance index % of a stiffened panel for a load of 50 N/m
0,1
0,01
1E-3 •
or point of the crack 1
point of the crack 2 point of the crack 3
------1----1------1----1------1----1-----1-----1-----1-----1
0,0 0,2 0,4 0,6 0,8 1,0
Time (s)
Figure 3 - Evolution of the resistance index % as a function of time for three points
Beghdad, H. et al, Effect of a crack on the nonlinear behavior of a stiffened composite panel, pp. 1171-1187
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Results and the discussion
Effect of loading
In order to see the effect of the load variation on the evolution of the resistance ratio R and the resistance index 5, the cracked panel was subjected to several loadings.
The results obtained (Figure 4) clearly show that initially, at time t = 0.1 second, this ratio is very high and decreases as the simulation time increases. In parallel, this ratio R increases with increasing load. For example, at time t = 1s, this ratio goes from 40.225 for P=5 MPa to 0.47504 for P=400 MPa. This means that the load has a considerable effect on the evolution of the resistance ratio R.
Since the resistance index 5, is the inverse of the resistance ratio R, the curves of Figure 5 are therefore inverse of those of Figure 4. By way of example, at time t = 1s, the resistance index 5 reached = 0.02486 for a load of 5 MPa. Under the application of a load of 400 MPa, the latter is = 2.1051.
Figure 4 - Evolution of the resistance ratio R at point 1 as a function of time and the
applied loading
о
13
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Pi
0,1 -
0,01 -
0,0
0,2
0,4
—I—
0,6
—I—
0,8
1,0
Time (s)
Figure 5 - Evolution of the resistance index £ at point 1 as a function of time and the
applied loading
Effect of the position of the transverse stiffeners
In order to analyse the influence of the spacing of the stiffeners on the evolution of the index and the resistance ratio, the position of the stiffeners was varied.
The stiffeners were located 40mm (Figure 6), 80mm (Figure 7) and 120mm (Figure 8) from the end of the panel.
Under a loading P= 50 MPa, it is obvious that the safety index is very high at the crack tip (Figures 6, 7, and 8). Moving away from the tip of the crack, the safety index values show that the panel is completely safe.
Beghdad, H. et al, Effect of a crack on the nonlinear behavior of a stiffened composite panel, pp.1171-1187
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Figure 6 - Strength index for the non-linear behavior of a stiffened panel with 40mm end spacing
Figure 7 - Strength index for the non-linear behavior of a stiffened panel with 80mm end spacing
Figure 8 - Strength index for the non-linear behavior of a stiffened panel with 120mm end spacing
The results (Figure 9) provided by this modeling indicate that the position of the stiffeners considerably affects the evolution of the resistance index The latter becomes smaller with the approximation of the stiffeners to the crack tip (for t=1s, =0.00446).
So there is more security. In addition, the evolution of the resistance ratio as a function of time, for the three positions of the stiffeners, is presented in Figure 10. In this figure, the resistance ratio tends towards zero when the position of the stiffeners moves away from the crack tip.
It can therefore be concluded that bringing the stiffeners closer to the tip of the crack prevents the propagation of the cracks and ensures fairly high resistance ratios.
Beghdad, H. et al, Effect of a crack on the nonlinear behavior of a stiffened composite panel, pp.1171-1187
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Time (s)
Figure 9 - Evolution of the resistance index ^ as a function of time of the cracked panel for different spacings of the transverse stiffeners
Time (s)
Figure 10 - Evolution of the resistance ratio R as a function of time for different spacings of the transverse stiffeners
Resistance index E,
Effect of the variation of the thickness of the stiffeners
To analyse this parameter, the stiffener thickness was changed while keeping the initial thickness of the panel constant.
From the results obtained (Figures 11 and 12), it is evident that the progressive increase in the thickness of the stiffener leads to a significant reduction in the resistance index 5, and an increase in the resistance ratio R.
Figure 11 - Evolution of the resistance index £, depending on the thickness of the
stiffener
In Figure 11, the resistance index at t=1s goes from 0.26 for a thickness of 1 mm to 0.06 for a thickness of 3.75 mm.
On the other hand, in Figure 12, the resistance ratio at t=1s is 3.86 for a thickness of 1 mm. On the other hand, for a thickness of 3.75 mm, it increases to 14.48.
Beghdad, H. et al, Effect of a crack on the nonlinear behavior of a stiffened composite panel, pp.1171-1187
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Figure 12 - Evolution of the resistance ratio R depending on the thickness of the stiffener
Conclusion
In order to follow the behaviour of a composite panel with a crack in its center in the case of large displacements, it seemed logical to carry out an analysis in the nonlinear domain.
In order to find the critical values of the index and the resistance ratio, along the panel, three points likely to have the critical stresses were chosen. The first point is at the bottom of the crack, the second one is at the level of the transverse stiffener while the third point is at the end of the panel.
From all the results provided by this modelling, it was noticed that the safety ratio increases remarkably, as a function of time, for the three chosen points. But the first point represents the most critical case because it is at the tip of the crack.
Regarding the effect of the variation of the load on the evolution of the safety ratio at the bottom of the crack, it was found that the initial state presents more risk for the panel because the resistance ratio registers to these lower values. On the other hand, the resistance index is quite important.
Following the results of this analysis, it is recommended to provide patches for the repair of cracked panels based on the presented modelling. In order to ensure structural stability, the authors intend to address panel buckling and associated stiffener-sheet separation in future research.
References
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Jones, R., Molent, L, Baker, A.A. & Davis, M.J. 1988. Bonded repair of metallic components: Thick sections. Theoretical and Applied Fracture Mechanics, 9(1), pp.61-70. Available at: https://doi.org/10.1016/0167-
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Makwana, A.H., Vyas, N. & Barot. R.S. 2021. Numerical investigation of composite patch repair of inclined cracked panel using XFEM. Materials Today: Proceedings, 45(6), pp.5128-5133. Available at:
https://doi.org/10.1016/j.matpr.2021.01.643.
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Naboulsi, S. & Mall, S. 1999. Methodology to analyze aerospace structures repaired with a bonded composite patch. Journal of Strain Analysis, 34(6), pp.395412. Available at: https://doi.org/10.1243/0309324991513849.
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Efecto de una grieta en el comportamiento no lineal de un panel compuesto rigidizado
Houda Beghdada, autor de correspondencia, Nacer Rahalab,
Abdelaziz Souiciab, Sara Zatirc, Khaled Benmahdia, Halima Aouada a Universidad Mustapha Stambouli, Departamento de Ingenierla Civil,
Mascara, Republica Argelina Democratica y Popular b Universidad de Ciencias y Tecnologla,
Laboratorio de Estructura Mecanica y Estabilidad de la Construccion,
Oran, Republica Argelina Democratica y Popular
c Universidad Tahri Mohamed de Bechar, Departamento de Arquitectura y Urbanismo, Bechar, Republica Argelina Democratica y Popular
CAMPO: mecanica, materiales
TIPO DE ARTICULO: articulo cientifico original
Resumen:
Introduccion/objetivo: Durante su vida util, los barcos y aeronaves estan sometidos a cargas aerodinamicas y de servicio severas que pueden causar danos estructurales y grietas. Estas grietas crecen y se propagan con el tiempo. Extender la vida util de una estructura danada es un area de investigacion muy importante. En este contexto, se recomienda la reparacion de paneles compuestos para restaurar el rendimiento de las estructuras agrietadas.
Metodos: Con el fin de minimizar la concentracion de tensiones en el fondo de una grieta, detener e incluso retrasar la propagacion de esta grieta, este estudio busca proponer un analisis bidimensional mediante el software ANSYS para predecir el efecto de la propagacion de una posible grieta en el comportamiento no lineal de paneles compuestos rigidos agrietados. Resultados: Los resultados de este analisis seran una muy buena referencia para mejorar el rendimiento y reparar paneles compuestos agrietados utilizando rigidizadores.
Conclusion: Se recomienda proporcionar parches para reparar paneles agrietados en funcion del modelado proporcionado en este estudio.
Palabras claves: paneles compuestos, estructura danada, propagacion de grietas, ANS YS, concentracion de tensiones.
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Влияние трещин на нелинейное поведение упрочненной композитной панели
Хауда Бегдада, корреспондент, Насер Рахалаб, Абдулазиз Соициаб,
Сара Затарв, Халед Бенмахдиа, Халима Аведа
а Университет Туши Мустафы Стамбули, строительный факультет, г. Маскара, Алжирская Народная Демократическая Республика
б Университет естественных наук и технологий,
Лаборатория машиностроения и прочности конструкций, г. Оран, Алжирская Народная Демократическая Республика в Университет Тахри Мохаммед Бешар, департамент архитектуры и урбанизма, г. Бешар, Алжирская Народная Демократическая Республика
РУБРИКА ГРНТИ: 67.09.33 Бетоны. Железобетон. Строительные растворы, смеси, составы ВИД СТАТЬИ: оригинальная научная статья
Резюме:
Введение/цель: В течение срока службы суда и самолеты подвергаются серьезным эксплуатационным и аэродинамическим нагрузкам, которые могут привести к повреждению конструкции и образованию трещин. Эти трещины со временем увеличиваются и распространяются. Продление срока службы поврежденной конструкции является весьма важной областью исследований. В связи с этим рекомендуется ремонт композитных панелей для восстановления эксплуатационных характеристик конструкций с трещинами. Методы: Для того, чтобы свести к минимуму концентрацию нагрузки на дно трещины и для того, чтобы остановить или задержать распространение этой трещины в данном исследовании предлагается двухмерный анализ с помощью программного обеспечения ANSYS в прогнозировании влияния распространения трещины на нелинейное поведение
порежденных упрочненных композитных панелей.
Результаты: Результаты данного исследования будут хорошим руководством для улучшения эксплуатационных характеристик и ремонта треснувших композитных панелей с использованием ребер жесткости.
Выводы: Рекомендуется использование заплаты в ремонте треснувших панелей на основе моделирования, приведенного в этом исследовании.
Ключевые слова: композитные панели, поврежденная
конструкция, распространение трещин, ANSYS, концентрация нагрузки.
(www.vtg.mod.gov.rs, втг.мо.упр.срб). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.Org/licenses/by/3.0/rs/).
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Beghdad, Н. et al, Effect of a crack on the nonlinear behavior of a stiffened composite panel, pp. 1171-1187
Утица] прелине на нелинеарно понашаьье ojanaHor композитног панела
Хауда Бегдад3, аутор за преписку, Насер Рахалаб, Абделазиз Соициаб, Сара Затарв, Калед Бенмахди3, Халима Аведа
