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1

A parametric study of higher-mode natural frequencies of composite stiffened cylindrical shell with cut-out

Chaudhuri Puja Basu, Sahoo Sarmila, Mitra Anirban

Engineering Transactions

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2023

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Vol. 71, iss. 1

81--109

EN

A finite element-based dynamic study of cut-out borne composite cylindrical shells reinforced with stiffeners is conducted. Isoparametric shell element with eight nodes and beam element with three nodes are used to study the mode-frequency behavior of shells with varied edge conditions. Anti-symmetric angle-ply laminates of two, four and ten layers with varying lamination angles are considered. Ten-layer laminates are investigated further as they exhibit better performance in fundamental frequency than two and four-layer laminates. The reduced integration method is adopted to find the shell element’s stiffness and mass matrices and the subspace iteration method is used for the eigenvalue solution of free vibration formulation. Natural frequencies for the first five modes are considered. The effects of fiber orientation angle (θ), degree of orthotropy (E11/E22), and width/thickness ratio (b/h) on the natural frequency are determined through numerical studies. It is revealed that vibration behavior strongly depends on both the number and arrangement of boundary constraints.

2

Efect of heat treatment parameters on microstructure evolution, tensile strength, wear resistance, and fracture behavior of Ni-Ti multilayered composites produced by cross‑accumulative roll bonding

Ye Qing, Li Xuejun, Tayyebi Moslem, Assari Amir Hossein, Polkowska Adelajda, Lech Sebastian, Polkowski Wojciech, Tayebi Morteza

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e27, 2023

EN

The last decades have seen a huge growth in the investigation of intermetallic compounds at the interfaces of laminated composites due to their useful features. In this research, efects of the formation of intermetallic compounds on tensile properties and wear resistance of Ni/Ti composites produced by cross-accumulative roll bonding (CARB) process have been examined at diferent annealing times and temperatures. Scanning electron microscopy (SEM) images demonstrated that the layers were well bonded together, but Ni layers experienced instabilities in light of plastic deformation. The EBSD results showed lamellar structure and crystallographic texture on Ti and Ni layers during plastic deformation. According to X-ray difractometer (XRD) and energy-dispersive spectrometer (EDS) analyses, NiTi2 and NiTi were present in all annealed samples. The thickness of intermetallic compounds grew with an increase in annealing temperature and time. However, this growth led to a decrease in tensile strength while the values of elongation fuctuated. Based on the results of the wear test, the composite became more resistant to wear when the thickness of intermetallic layers increased. The surfaces of these layers with less roughness and lower coefcients of friction facilitated the movement of steel pin on samples during the wear test. Furthermore, wear mechanisms of adhesion, abrasion, and delamination were observed, and they were more noticeable at higher loads and lower annealing temperatures and times.

3

Effect of trapezoidal shapes on the thermal buckling behaviour of perforated composite plates

Maharudra R., Rajanna T., Arya B.

Advances in Materials Science

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2021

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Vol. 21, nr 1(67)

10--26

EN

Thermal buckling study on the symmetric laminated composite trapezoidal plate with a circular cutout subjected to a uniform increase in temperature for various boundary conditions is explored in this paper. In a mathematical model, the first-order shear deformation principle is employed in accordance with the variational energy system. For acquiring the thermal buckling temperature, a nine-node heterosis plate relation has been used in the finite element formulation. By correlating the present findings with accessible literature, the effectiveness of the present formulation is verified. The impact of different parameters, such as trapezoidal shape, cutout size, ply-orientation, plate edge conditions and plate width to thickness ratio have been considered to study the effect of each parameters on the buckling characteristics of plate under various temperatures. It is observed from the study that each parametric investigation significantly affect the thermal buckling behaviour of trapezoidal plates.

4

Characteristics of vibrating composite stiffened hypars with cut-out at different modes

Sahoo Sarmila

Engineering Transactions

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2019

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Vol. 67, iss. 1

75--99

EN

Vibration characteristics of laminated composite stiffened hypar (hyperbolic paraboloid shell bounded by straight edges) with cut-out are analysed in terms of natural frequency and mode shapes. A finite element code is developed for the purpose by combining an eight noded curved shell element with a three noded curved beam element for stiffener. Finite element formulation is based on first order shear deformation theory and includes the effect of cross curvature. The isoparametric shell element used in the present model consists of eight nodes with five degrees of freedom per node while beam element has four degrees of freedom per node. The code is validated by solving benchmark problems available in the literature and comparing the results. The generalised Eigen value solution is chosen for the un-damped free vibration analysis. New results are presented for first five modes of natural frequency by varying boundary conditions, ply orientation and curvature of the shell. The results furnished here may be readily used by practicing engineers dealing with stiffened composite hypars with cut-outs.

5

Effect of Boundary Conditions on the Distribution of Mode I Fracture Toughness along Delamination Front in CFRP Laminates with General Fiber Orientation

Samborski S.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 2

121--127

EN

The paper deals with numerical analysis of the DCB test configuration together with the data reduction scheme described in the ASTM D 5528 Standard for determination of the mode I fracture toughness in case of the laminated composites with mechanical couplings. The numerical analysis based on the FEM approach was performed with the Abaqus software exploiting the VCCT technique. The results show, that the distribution of the Strain Energy Release Rate can be asymmetric and that mode mixity can occur. A need for mode separation procedures and appropriate data reduction schemes has been revealed.

6

Stiffness behavior of hybrid laminated composites with surface crack

Güneş A., Şahin Ö. A.

Archives of Materials Science and Engineering

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2016

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Vol. 80, nr 2

49--52

EN

Purpose: The purpose of this paper investigates to stiffness behavior of hybrid laminated composites with surface crack. Design/methodology/approach: Hybrid laminated composites has 18 layers and 90x25 mm size with two different layers line up. The low velocity impact test of hybrid laminated composites carried on 3 m/sec with a/t=0.4 and a/c=0.4 surface crack parameters. Findings: The results are presented as the change of force-time and force-displacement graphs. As a result of this study, effects of stacking sequence on hybrid composite plates were analysed. Research limitations/implications: The research of stiffness behavior or dynamic response of hybrid laminated composites can contribute to developing new composite materials. Practical implications: These hybrid laminated composites materials could be used for different aviation areas. Originality/value: This paper is based on studies from Selçuk University and all the experiments and results were conducted by me.

7

Effect of surface crack depth on hybrid laminated composites

Güneş A., Şahin Ö. S.

Archives of Materials Science and Engineering

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2016

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Vol. 82, nr 1

38--41

EN

Purpose: The purpose of this paper researches to effect of different surface crack depth on hibrid laminated composites under low velocity impact forces. Design/methodology/approach: Hybrid laminated composites have 90x25 mm size and 18 layers with two different stacking sequence. Low velocity impact test of hybrid laminated composites with surface crack have been investigated with different a/t surface crack parameters and 3 m/sec velocity. Findings: The results are presented force-time and energy-time graphs than effects of different crack parameters were observed. As a result of this study, effects of surface crack depth on hybrid composite plates were analysed. Research limitations/implications: The research of dynamic behavior of hybrid laminated composites with surface crack can contribute to literature searches. Practical implications: These hybrid laminated composites materials could be used for different aviation areas. Originality/value: This paper is based on studies from Selçuk University and all the experiments and results were conducted by me.

8

Tensile behaviour of laminated titanium-intermetallic composite synthesised using titanium and copper foils

Konieczny M.

Kompozyty

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2009

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R. 9, nr 2

117-121

EN

Ti-intermetallic laminated composites have been fabricated via reaction synthesis in vacuum using 0.15, 0.20 and 0.25 mm thick foils of titanium and 0.05 mm thick foil of copper with controlled temperature and pressure. Effects of treating time at 900°C were studied by interrupting the reaction progressing after 0.5 and 5 hours. Microstructural investigations by scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDX) showed that after 0.5 hour of heat treatment at 900°C intermetallic compounds: Ti2Cu, TiCu, Ti3Cu4, Ti2Cu3, TiCu4 were formed. The intermetallics layer consisted of thin layers of Ti2Cu, thick layers of TiCu and the reaction zone consisting of TiCu4 particles in Ti3Cu4+Ti2Cu3 matrix. Since titanium could diffuse through the Ti2Cu and TiCu layers to the reaction zone, it leaded to the growth of TiCu at the expense of other phases. As a result, after 5 hours of treating the intermetallic layer was transformed almost wholly into TiCu, but with a thick Ti2Cu interphase layer. The mechanical properties and fracture behaviour of the fabricated composites were examined through tensile test. The results showed that treating time at 900°C was a main factor determining properties because it led to an increase in volume fraction of the intermetallics. Unfortunately, long heat treatment caused a degradation of the intermetallic layers by oxidation because implemented vacuum was not high enough. After 0.5 hour of treating at 900°C the oxides on interlayer had no significant influence on the strength of the layers. EDX results showed that after long heat treatment the oxides were captured in the growing intermetallic layers to form inclusions or voids. This resulted in the formation of weak points in the intermetallic layers, from which cracks would have initiated easily, leading to premature failure of the layers during loading. Investigations indicated that the yield strength of all fabricated composites increased with increasing of the treating time. On the other hand, after 0.5 hours of treating the composites had higher ultimate tensile strength and higher strain at fracture. The results also showed that the composites exhibit a good cohesion between titanium layers and layers of intermetallic phases during tensile test.

PL

Używając folii tytanowych o grubościach: 0,15, 0,20 i 0,25 mm oraz folii miedzianej o grubości 0,05 mm, wytworzono na drodze reakcji syntezy kompozyt warstwowy tytan-fazy międzymetaliczne. Kontrolując temperaturę procesu oraz nacisk, doprowadzono do całkowitego przereagowania warstw miedzi, które z częścią tytanu utworzyły fazy międzymetaliczne. Zbadano wpływ czasu wygrzewania kompozytu w temperaturze 900°C na jego strukturę i własności. Reakcje syntezy faz przerywano po 0,5 i 5 godzinach. Badania z użyciem mikroskopu skaningowego i mikroanalizatora rentgenowskiego wykazały, że w kompozycie wygrzewanym przez 0,5 godziny występowały fazy: Ti2Cu, TiCu, Ti3Cu4, Ti2Cu3,TiCu4. Warstwy faz międzymetalicznych składały się z cienkich warstw fazy Ti2Cu, grubych warstw fazy TiCu i obszarów zawierających cząstki fazy TiCu4 w osnowie z mieszaniny faz Ti3Cu4+Ti2Cu3. Ponieważ tytan mógł dyfundować przez warstwy faz Ti2Cu oraz TiCu, powodowało to wzrost ilości fazy TiCu kosztem pozostałych faz. Po 5 godzinach wygrzewania warstwy faz międzymetalicznych składały się prawie wyłącznie z fazy TiCu i cienkich warstw fazy Ti2Cu. Przeprowadzono próby rozciągania uzyskanych kompozytów i stwierdzono, że głównym czynnikiem wpływającym na własności mechaniczne był czas ich wygrzewania w temperaturze 900°C. Wzrastał wówczas udział objętościowy faz międzymetalicznych oraz następowała degradacja warstw spowodowana ich utlenianiem. Badania z użyciem mikroanalizatora rentgenowskiego wykazały, że po 30 minutach wygrzewania tlenki występowały na granicy między tytanem i warstwami faz międzymetalicznych. Natomiast po 5 godzinach wygrzewania tlenki dostawały się do wnętrza warstw faz międzymetalicznych, powodując powstawanie inkluzji, które mogły być łatwymi zarodkami pęknięć. Dlatego kompozyty po 30 minutach wygrzewania charakteryzowały się większą wytrzymałością na rozciąganie oraz większym wydłużeniem. Z wyników prób rozciągania wynika także, że granica plastyczności wszystkich badanych kompozytów, niezależnie od grubości użytych do ich wytworzenia folii, wzrastała wraz ze wzrostem czasu wygrzewania w temperaturze 900°C. Badania wykazały również, że w trakcie próby rozciągania kompozyty wykazywały dobrą kohezję pomiędzy warstwami tytanu i faz międzymetalicznych.

9

Structural changes during formation of laminated titanium-intermetallic composite

Konieczny M.

Kompozyty

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2008

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R. 8, nr 2

168-171

EN

Well-bonded and almost fully dense laminated composites have been fabricated successfully by reactive sintering in vacuum using Ti and Cu foils. Since the copper layers were completely consumed by forming phases, the final microstructure consisted of alternating layers of intermetallic phases and unreacted titanium. Effects of treating time at 900 °C and the microstructural changes were studied by interrupting in steps the reaction progressing after 0.5, 1, 2, 3, 4 and 5 hours. With the liquid phase appearance a fast growing of the layers containing intermetallic phases was observed. Because the structure resulting from solidification of locally melted reaction zone contained phases rich in copper (especially TiCu4), melting consumed more copper than titanium. For this reason, the boundary between the intermetallic layers and copper migrated toward the copper side. Microstructural investigations by scanning electron microscopy (SEM) and energy dispersive spectro scopy (EDX) showed that after 0.5 hour of heat treatment at 900° C intermetallic compounds: Ti2Cu, TiCu, Ti3Cu4, Ti2Cu3, TiCu4 and solid solution Ti were formed. After the completely consumption of Cu, the intermetallics layer consisted of thin layers of Ti2Cu (adjacent to eutectioid layer and titanium), thick layers of TiCu and the reaction zone consisting of TiCu4 particles in Ti3Cu4+Ti2Cu3 matrix. The particles were probably produced by stresses resulting from the growth of the intermetallic layer. Since titanium could diffuse through the Ti2Cu and TiCu layers to the reaction zone, it leaded to the growth of TiCu at the expense of TiCu4, Ti3Cu4 and Ti2Cu3. As a result, the TiCu compound became dominant phase if the treating time was longer than 1 hour. After 5 hours of treating the intermetallic layer was transformed almost wholly into TiCu, but with a thick Ti2Cu interphase layer. The formation of the TiCu phase is thermodynamically favoured over the formation of the other phases and can be understood from the steps occurred through a series of solid-liquid and solid state reactions involving TiCu4 as one of the starting phases.

PL

Używając folii tytanowej i miedzianej, wytworzono kompozyt tytan-fazy międzymetaliczne, charakteryzujący się dobrym połączeniem warstw i bardzo nieznaczną porowatością. W wyniku reakcji syntezy warstwy miedzi kompletnie przereagowały z częścią tytanu i utworzyły fazy międzymetaliczne. Badano wpływ czasu wygrzewania kompozytu w temperaturze 900° C na jego strukturę. Reakcje syntezy faz przerywano po 0,5, 1, 2, 3, 4 i 5 godzinach. Wraz z pojawieniem się fazy ciekłej zaobserwowano szybki wzrost grubości warstw faz międzymetalicznych. Ponieważ powstałe fazy były bogate w miedź (zwłaszcza faza TiCu4), reakcja pochłaniała więcej miedzi niż tytanu. Z tej przyczyny granice pomiędzy warstwami faz międzymetalicznych i miedzią migrowały w głąb warstw miedzi. Badania z użyciem mikroskopu skaningowego i mikroanalizatora rentgenowskiego wykazały, że w kompozycie wygrzewanym przez 30 minut i następnie chłodzonym razem z piecem (prędkość chłodzenia 0,16° C/s) występowały fazy: Ti2Cu, TiCu, Ti3Cu4, Ti2Cu3,TiCu4 oraz roztwór stały miedzi w tytanie [alfa]. Po całkowitym przereagowaniu miedzi warstwy faz międzymetalicznych składały się z cienkich warstw fazy Ti2Cu (przyległych do warstw eutektoidu (Ti2Cu+ ) i nieprzereagowanego tytanu), grubych warstw fazy TiCu i obszarów zawierających cząstki fazy TiCu4 w osnowie z mieszaniny faz Ti3Cu4+Ti2Cu3. Cząstki fazy TiCu4 powstały prawdopodobnie na skutek naprężeń występujących podczas wzrostu warstwy faz międzymetalicznych. Ponieważ tytan mógł dyfundować przez warstwy faz Ti2Cu oraz TiCu, powodowało to wzrost ilości fazy TiCu kosztem faz TiCu4, Ti3Cu4 oraz Ti2Cu3. W rezultacie tego TiCu stała się dominującą fazą, gdy czas wygrzewania kompozytu w temperaturze 900° C był dłuższy niż 1 godzina. Po pięciu godzinach wygrzewania warstwy faz międzymetalicznych składały się prawie wyłącznie z fazy TiCu i cienkich warstw fazy Ti2Cu (przyległych do warstw eutektoidu). Formowanie fazy TiCu jako dominującego produktu podczas reakcji pomiędzy tytanem i miedzią jest uzasadnione termodynamicznie i przebiega na drodze kolejnych etapów przemian z udziałem fazy ciekłej i w stanie stałym, a jedną z pierwszych powstających faz jest TiCu4.

10

Processing and structure of laminated iron-intermetallics composites

Konieczny M.

Archives of Foundry Engineering

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2008

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Vol. 8, iss. 4

71-76

EN

Using Fe sheets and Cu and Ti foils, Fe-intermetallic phases laminated composites have been fabricated through reactive sintering at 900°C for 15, 30 and 120 minutes in vacuum. After 15 minutes at 900°C all titanium layers were fully consumed but there were thin (about 40 žm) unreacted layers of copper. What was important, the copper layers could still block the diffusion of Ti to Fe. With increasing annealing time up to 30 minutes at 900°C the layers of Cu disappeared completely forming intermetallic phases. Thus, the final microstructure consisted of alternating layers of intermetallic phases and unreacted Fe metal. The microstructure was revealed in optical and scanning electron microscopy (SEM). The study exhibited the presence of different reaction products in the diffusion zone and their chemical compositions were determined by energy dispersive spectroscopy (EDS) [...]

11

On tolerance averaged model of the propagation of boundary displacement fluctuations in FGM-type laminated composite

Łacińska L., Wierzbicki E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2007

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Vol. 6, nr 1

133-140

EN

The object of the contribution is the analysis of a certain initial-boundary problems in elastodynamics of FGM-type multiphased laminated composites. The aim of the paper is to formulate an answer to the question what kind of assumptions are enough to be taken into account in the framework of the simplified tolerance model for the elastodynamics of the considered laminates the boundary effect will be observed.