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VII International Conference “In-service Damage of Materials: Diagnostics and Prediction (DMDP 2023)

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Procedia Structural Integrity 59 (2024) 1–2

VII International Conference “In -service Damage of Materials: Diagnostics and Prediction ” (DMDP 2023) Preface – In-service Damage of Materials: Diagnostics and Prediction Oleg Yasniy a , Olha Zvirko b , Hryhoriy Nykyforchyn b, *, Volodymyr Iasnii a a Ternopil Ivan Puluj National Technical University, 56 Ruska St., Ternopil 46011, Ukraine b Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, 5 Naukova St., Lviv 79060, Ukraine

© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers

Keywords: preface, damage, fracture, modelling, prediction, diagnostics; non-destructive evaluation, environmental effects.

During operation, materials of structural elements are subjected to damages whose nature is dependent on the mode of loading and operating conditions (high and low temperatures, cyclic loading, corrosive environment, irradiation, etc.). Diagnostics of material damages and their description are highly important for the development of methods for improving the reliability, prediction of the residual life of structural elements and optimization of the physical and mechanical properties of materials. Investigations of the damage accumulation in metals involve both the development of the fundamentals for describing this phenomenon and methods for assessing the strength and life of structural and elements taking into account the whole set of the design and operational factors. VII International Conference “In - service Damage of Materials: Diagnostics and Prediction” , organized under the auspice of the European Structural Integrity Society (ESIS), has a long history. Previous conferences were held in Ternopil in 2009, 2011, 2013, 2015, 2017, 2019, and 2021. Ternopil Ivan Puluj National Technical University, Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Ukrainian Society on Fracture Mechanics (USFM) and G.S. Pisarenko Institute for Problems of Strength the National Academy of Sciences of Ukraine were the main organizers of these conferences.

* Corresponding author. Tel.: +380 322 294213. E-mail address: hnykyforchyn@gmail.com

Oleg Yasniy et al. / Procedia Structural Integrity 59 (2024) 1–2 Oleg Yasniy, Olha Zvirko, Hryhoriy Nykyforchyn, Volodymyr Iasnii / Structural Integrity Procedia 00 (2019) 000 – 000

The DMDP 2023 was held online between 18-20 October 2023. The USFM presents Ukraine in the ESIS via the Ukrainian National Group, which also participates actively in the ESIS Technical Committee TC10 “ Environmentally Assisted Cracking ” . The DMDP 2023 brought together leading scientists, researchers and research scholars to share their experience, research results and scientific ideas regarding key areas of fracture and damage mechanics, structural integrity assessment and maintenance. It has become an interactive platform for discussion of recent advances, trends and practical challenges in the field of fracture mechanics and structural integrity. The Conference hosted 114 oral presentations. Contributions from Italy, Spain, Germany, Poland, France, the Slovak Republic, Hungary, Indonesia, Vietnam, South Korea, Canada, and Ukraine presented at the DMDP 2023 Conference covered the following topics of the Conference: • Localized and Nonlocalized Damage of Materials; • Damage Prediction;

• Non-destructive Testing and Damage Detection; • Degradation Assessment and Failure Prevention; • Crack Initiation and Propagation; • Fractography and Advanced Metallography; • Damage Tolerance; • Environmental Effects; • Durability; • Structural Integrity; • Reliability and Life Extension of Components; • Failure Analysis and Case Studies.

Also, in the frame of the conference, there was organized the mini- symposium “Environmental Effects: Hydrogen and Corrosion” (chaired by Prof. J. Toribio, Prof. H. Nykyforchyn, Prof. I. Dmytrakh and Prof. O. Zvirko). The TC10 meeting took place during the conference. This special issue contains the full-text conference papers accepted for publishing after the peer review. We hope that this issue will be interesting for scientists and researchers in the field of fracture mechanics, materials science and structural integrity, as well as for the lecturers of high schools and post-graduate students of the corresponding specialities. We also hope that it will be useful for experts and engineers in the industrial sectors, such as energy generation, machinery, transport, chemical industry, civil engineering, etc. As the Guest Editors of this Conference Proceedings, we wish to thank all authors for their contributions. Guest Editors of the Procedia Structural Integrity DMDP 2023 Conference Proceedings:

Oleg Yasniy, Olha Zvirko, Hryhoriy Nykyforchyn, Volodymyr Iasnii

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Procedia Structural Integrity 59 (2024) 724–730

© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers Abstract A tunnel crack with finite electrical permeability between two piezoelectric rectangular parallelepipeds is investigated. Assuming at the beginning that the width of the crack is much smaller than the size of the body, we consider the crack in an infinite bimaterial space. Assuming also that the external loading does not change along the coordinate co-directed with the crack front, the plane strain problem for the middle section of the 3-D domain is considered. An analytical solution to this problem has been found, and the electric flux through the crack region has been defined. Using this flux as an initial approximation for the 3-D case and choosing certain characters of materials, geometry and loading, the finite element method (FEM) is applied. Refining the finite element mesh at the crack region, especially at its fronts, was used. An iterative algorithm for determining the electric flux through the crack region was applied, and the results were presented in table and graph forms. © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers Keywords: piezoelectric bimaterial; limited permeable interface crack; spatial deformation Abstract A tunnel crack with finite electrical permeability between two piezoelectric rectangular parallelepipeds is investigated. Assuming at the beginning that the width of the crack is much smaller than the size of the body, we consider the crack in an infinite bimaterial space. Assuming also that the external loading does not change along the coordinate co-directed with the crack front, the plane strain problem for the middle section of the 3-D domain is considered. An analytical solution to this problem has been found, and the electric flux through the crack region has been defined. Using this flux as an initial approximation for the 3-D case and choosing certain characters of materials, geometry and loading, the finite element method (FEM) is applied. Refining the finite element mesh at the crack region, especially at its fronts, was used. An iterative algorithm for determining the electric flux through the crack region was applied, and the results were presented in table and graph forms. © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers Keywords: piezoelectric bimaterial; limited permeable interface crack; spatial deformation VII International Conference “In -service Damage of Materials: Diagnostics and Prediction ” (DMDP 2023) 3-D analysis of a crack with finite electrical permeability between two piezoelectric materials M. Levchenko a , Y. Lapusta b , V. Loboda a * a Department of Theoretical and Computational Mechanics, Oles Honchar Dnipro National University, Gagarin Av., 72, Dnipro, 49010, Ukraine b Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut Pascal, F-63000 Clermont-Ferrand, France VII International Conference “In -service Damage of Materials: Diagnostics and Prediction ” (DMDP 2023) 3-D analysis of a crack with finite electrical permeability between two piezoelectric materials M. Levchenko a , Y. Lapusta b , V. Loboda a * a Department of Theoretical and Computational Mechanics, Oles Honchar Dnipro National University, Gagarin Av., 72, Dnipro, 49010, Ukraine b Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut Pascal, F-63000 Clermont-Ferrand, France

* Corresponding author. Tel.: +38 097 3647266; fax: +38 056 374 98 42 E-mail address: loboda@dnu.dp.ua * Corresponding author. Tel.: +38 097 3647266; fax: +38 056 374 98 42 E-mail address: loboda@dnu.dp.ua

2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers 2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers

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1. Introduction Piezoelectric materials are widely used in practice, but piezoelectric ceramics are very brittle and prone to destruction. In addition, delamination of the piezoelectric materials interfaces is possible. It can lead to the appearance of cracks at the interface, which can be the reason for the destruction of devices. Therefore, the investigation of a crack between two piezoelectric materials is important. When studying such cracks, their electrically permeable and insulated models (Suo et al., 1992) are most often used, which are extreme cases of real cracks. For real cracks in a homogeneous piezoelectric material and between two piezoelectric materials, the model of a crack with finite electrical permeability, proposed by Hao and Shen (1994), is the most adequate reality. Subsequently, this model was developed mainly concerning the cracks in a homogeneous piezoelectric material. Its application to an interface crack in a piezoelectric bimaterial has been carried out by Govorukha et al. (2006), Li and Chen (2007, 2008), Lapusta et al. (2011) and Loboda et al. (2023). However, the study of this model concerning the spatial case of an interface crack in a 3-D body is unknown to the authors of this paper. Such problem investigation is the main purpose of the present paper. 2. Formulation of the problem region 1 b x b    of the material interface 3 0 x  there is a tunnel crack that has finite electrical permeability and is free of stresses and electrical charges on its faces. Tensile stresses 33    and shear stress 23    act on the upper and lower faces of the parallelepiped and electric flux 3 D d  passes through the body. It is assumed that   m ijkl c ,   m lij e ,   m ij  ( 1,2 m  ) are the matrices of the modulus of elasticity, piezoelectric constants and dielectric constants for the top and bottom materials, respectively, and both materials have a symmetry class 6mm with the direction of polarization 3 x . We assume that the crack filler has dielectric permeability A bimaterial piezoelectric parallelepiped 1 1 1 l x l    , 2 2 2 l x l    , 3 3 3 l x l    (Fig. 1) is considered. In the

0 a r     ,

(1)

and the electric field inside the cracks can be found as

u u        

for 1 ( , ) x b b   ,

a E



where r  is the relative dielectric constant,

is the dielectric constant of vacuum.

12 0 8.85 10 / C Vm    

Taking into account that

3 a a D E   , we arrive to the following electrical condition

u u        

for 1 ( , ) x b b  

(2)



a 

along the crack region which was previously used by Hao and Chen (1994)]. Thus, the boundary conditions at the material interface can be written as













1 , x b b   :

(3)

for

1 2 , ,0 0, x x 

1 2 ,,0 0 x x 





   13 1 m



   33 1 m



 

1 , x b b   :

, x x

2 ,0 0, 

, ,0 0

x x



 ,

0  ,

for

3 1 D x

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 D x

 







(4)

1 2 x x    ,

u x

3 1 2 3 1 2 where { } ,  function when crossing the plane 3 0 x  . a

 13 23 33 3 , , , T D     t and the angle brackets mean the jump of the corresponding

Fig. 1. Piezoelectric bimaterial plane with an interfacial crack having finite electrical permeability.

If the size of the parallelepiped in the direction of the axis 2 x is much larger than in other coordinate directions, then in the cross-section 2 0 x  and around it a stress-strain state close to plane strain will be realized. In this case, based on the results of Govorukha et al (2006) for the piezoelectric bimaterial plane, the following representations will be valid (in the following formulas, the coordinate 2 x is temporarily removed):             1 1 1 33 1 4 3 1 1 13 1 ,0 ,0 ,0 j j x m D x іm x        1 1 ( ) j j j F x F x      , (5)





  1 j j F x F x   

  1

  j j n u x i n u x n       1 1 1 j 3 3 1

  1

x  



(6)







, , jl j m n j l   jl

, 1,3,4

1 3 z x ix   ,

are defined by material constants and have real values for certain   j F z is analytical throughout the cross-section 2 0 x  .

where

classes of piezoceramics. In addition, the function,

3. Analytical solution of the plane problem for the central cross-section Suppose that in the section 2 0 x  the electric displacement is constant along the crack faces, i.e     3 1 3 1 ,0 ,0 D x D x D     for   1 , x b b   .  , b b  much smaller than the cross-sectional size 2 0 x  . Then this section can be considered infinitely large and the conditions on its sides can be interpreted as conditions at infinity. Equations (5) and (7) together with conditions on the interface (4) lead to the following Hilbert-Riemann problem of linear relationship (7) We will also assume that the size of the crack 

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  1

  1 F x m D    4 j j j

, 

 1,3,4 j  , where





1 , x b b   .

F x 



(8)

The solution of the problem (8) satisfying the required conditions at infinity is obtained by use of Muskhelishvili (1975) in     43 1 1 13 2 44 1 1 14 2 a n H x n H D n H x n H     for 1 ( , ) x b b   , (9)

where

1 1  



 4





0 1        , 1 ˆ ( cos ˆ sin )

4 ˆ 2   ,

( )

H x





1    ,

ˆ j r    

1 j j m r  /

m d

j 



1 1

1 



1 b x b x    1    

ln  

 



j 



For each value 1 x the relation (9) is a transcendental equation with respect to electric flux D . Its solution can be easily found numerically. It is important to note that for real piezoelectric materials the value 1  is very small, therefore cos( )  і sin( )  practically do not change for 1 ( , ) x b b   . This means that 1 1 ( ) H x almost does not change in this interval. Thus the magnitude of the electric displacement D is practically a constant for every a  . For example, Table 1 shows the values of the roots of equation (9) for different 1 ( , ) x b b   at 0 a    and 10 b  mm. The bimaterial PZT-4/ PZT-5 was used. Table 1. The value of the roots of equation (10) for different 1 (0, ) x b  at 0 a    and 10 b  mm. 1 x , mm 0 1 2 3 4 5 6 7 8 9 9.5 This table shows that in most part of the interval (0, ) b the value of D remains almost constant and only near the point b there is a slight deviation in magnitude 0.067%  . This confirms the validity of the assumption regarding the constant value of the electric displacement through the crack and allows of using, say, the middle of the crack 1 0 x  for its finding. 4. Numerical analysis for 3-D case Let us now consider the 3- dimensional case formulated above. We’ll assume 1 3 25 l l   mm, 2 40 l  mm, 5 b  mm. The solution was carried out by using the finite element method. There was little refining of the mesh when approaching the crack, especially to its left and right fronts. The structure of the mesh as well as the distribution of the electric potential in the whole region and at the crack tip are shown in Fig. 2. 3 2 10 , / D C m 5.0709 5.0709 5.0710 5.0710 5.0710 5.0711 5.0712 5.0713 5.0715 5.0710 5.0720

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(a) (c) Fig. 2 Mesh structure and electric potential distribution for (a) a whole model, (b) vicinity of the crack, (c) scale. (b)

It is assumed that the upper part of the region is made of piezoelectric material PZT-4, the lower part is piezoelectric PZT-5. The properties of these materials in the system of SI units are given by known matrices of stiffness, piezoelectric and dielectric constants, namely

9 11 139 10 c   , 15 13,4 e  , 31 9 11 121 10 c   , 15 12.3 e  , 31

9 33 113 10 c   ,

PZT-4:

74,3 10

25,6 10

12 13 c c   

c  

6.98

, 33 13,8 e  ,

;

e 

6 10

5,47 10



 

PZT-5:

75.4 10

111 10

21.1 10

12 13 c c   

33 c  

c  

5.4

, 33 15.8 e  ,

e 

8.1 10

7.3 10



 

It was considered that: - a uniformly distributed normal tensile stress

10 , MPa   is applied to the upper and lower faces of the

bimaterial body; - an electric flux

2 2 10 / d C m   passes through the entire area, which is implemented by setting a uniformly

distributed charge of intensity (

2 2 10 / C m   ) on the upper face;

- zero electric potential is prescribed on the bottom face; We’ll assume further that the crack is filled with air. Then according to the table 1 the electric flux through the crack, in the plane case, is equal approximately 2 0.005 / C m . Let us assume that such electric flux of constant magnitude also occurs in the 3-dimensional case. That is, according to the rules of the FEM Abaqus package, in order to implement the specified electric flux through the crack on its upper face, it is necessary to set a uniformly distributed charge of 2 0.005 / C m , and on the lower one should be uniformly distributed charge 2 0.005 / C m  . For the indicated external factors, the calculation was carried out on the mesh shown in Fig. 2. The colored levels in this figure shows the resulting electric potential distribution. In addition, the following most interesting results can be noted: Crack opening and electric potential jump through the crack were obtained for different cross-sections in the direction of the axis 2 x and are shown in Fig. 3. Lines I and II correspond to 2 0 x  and 2 2 /2 x l  (their values are very near of each other and the correspondent lines almost coinsides). The line III is drawn for the cross-section 2 2 9 /10 x l  , which is situated very near to the face of the body. It follows from this figure that the crack opening increases for the cross-sections approaches to the face 2 2 x l  of the body whilst the jump of the electric potential decreases for these sections. The jumps of the electric potential through the crack are shown in Fig. 4 for the same cross-sections as in Fig.3.

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0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

0 -0,005

0,005

III

-500

I, II

-1000

ІІІ

І,ІІ

-1500

-2000

-0,005

0,005

Fig. 3. Crack opening (a) and electric potential (b) jump through the crack for different cross-sections of the body.

Fig. 4. Potentials jumps for different cross-sections of the body.

Crack opening at the middle point of the middle cross-section is equal to

6 3.07 10 m   , and the potential jump at

this point is equal to

3 1.74 10 В   . Calculations according to formula (2) give the value of

3 D equal to

2 0.005009 / . C m Table 2 shows the values 3 D in three cross-sections. As expected, for the middle cross-section the agreement of the obtained electric flux with the specified one is very good (the error is 0.18%), for the cross section distant from of the front end by ¼ the length of the parallelepiped 3 2 l , this error is 0.74%. For the cross sections located in close proximity to the end, this error grows and, for example, at a distance 3 /10 l from the end it is 11.8%.

Table 2. The value of the electric flux trough the crack for different cross-sections. Coordinate 2 x of the cross-section 0(center) 2 / 2 l 2 9 /10 l 3 D 0.005009 0.004963 0.004411

Since the results in Table 2 do not agree well enough with the specified values of the electric flux through the crack, the specified values were refined using the iteration method. For this, the faces of the crack were divided into strips of width 2 2 / l n , and different values of the electric flux were set on each of them. Further, the calculation was carried out according to the finite-element algorithm indicated above, and the obtained results were compared with the given ones. In case of their unsatisfactory agreement, the next iteration was carried out in a similar way, etc. Table 3 shows the result of calculations carried out at 8 n  .

8 n  .

Table 3. The value of the electric flux for different cross-sections at

Coordinate 2 x of the cross-section

2 /10 l

2 3 /10 l

2 / 2 l 4.98

2 7 /10 l

2 9 /10 l

1000 3 D 1000 3 ˆ D

5.0

4.99

4.97

4.45

5.015

5.014

5.013

4.939

4.401

3 D specified in the corresponding section of the upper

Table 3 represents the value of the electric displacement

edge of the crack, and 3 ˆ D is the value of the electric displacement obtained as a result of the finite-element solution and the application of the formula (2). Since the difference between these values for all cross-sections does not exceed 1%, the values 3 ˆ D can be considered as the required values of the electric flux through the crack. The results in Table 3 are given for the midpoints of each cross-section. But, as was confirmed in the analysis of the plane problem (Table 1), the distribution along the crack for each section is almost constant. In the 3

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dimensional case such behavior was also confirmed and was shown that the electric flux in each cross-section demonstrates practically constant values for the main part of the crack region, and only in the immediate vicinity of the crack fronts slight deviations from the constant values are observed. 5. Conclusions Two bonded rectangular piezoelectric parallelepipeds with a limited permeable crack in their interface are considered. The plane strain problem for the middle section of 3-D domain is studied at the beginning, and an analytical solution to this problem is found. The electric flux through the crack region is determined from this solution and used as an initial approximation for the 3-D problem solution. The finite element method was used to analyse the last one. An iterative algorithm for the determination of the electric flux through the crack region was applied, according to which the mentioned flux at each step was determined by the use of FEM and the equation (2). Due to this approach, the values of the electric flux were found with high accuracy, and the conformation concerning its quasi-uniform distribution along the crack faces for any cross-section of the 3-D body was revealed. Acknowledgements A support from the French National Research Agency as part of the “Investissements d’Avenir” through the IMobS3 Laboratory of Excellence (ANR-10-LABX-0016) and the IDEX-ISITE initiative CAP 20-25 (ANR-16 IDEX0001), program WOW and International Research C enter “Innovation Transportation and Production Systems” (CIR ITPS) in the FACTOLAB common laboratory (CNRS, UCA, Michelin), and from the Humboldt Foundation, Germany is gratefully appreciated. References Govorukha, V. B., Loboda, V. V., Kamlah, M., 2006. On the influence of the electric permeability on an interface crack in a piezoelectric bimaterial compound. Int. J. Solids Struct. 43, 1979 – 1990. Hao, T. H., Shen, Z. Y., 1994. A new electric boundary condition of electric fracture mechanics and its applications. Eng. Fract. Mech 47, 793 – 802. Li, Q., Chen Y. H., 2007. Solution for a semi-permeable interface crack between two dissimilar piezoelectric materials. J. Appl. Mech. 74, 833 – 844. Li Q., Chen Y. H., 2008. Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric biomaterials. J. Appl. Mech. 75, 0110101. Lapusta, Y., Komarov A., Labesse-Jied F., Moutou Pitti R., Loboda V., Limited permeable crack moving along the interface of a piezoelectric bi material. European Journal of Mechanics A/Solids 30, 639-649. Loboda, V., Sheveleva, A., Chapelle, F., Lapusta, Y., Multiple electrically limited permeable cracks in the interface of piezoelectric materials. Mechanics of Advanced Materials and Structures, Published online: 22 Feb 2023. https://doi.org/10.1080/15376494.2023.2180695 Muskhelishvili, N.I., 1975. Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen. Suo, Z., Kuo, C.M., Barnett, D.M., Willis, J.R., 1992. Fracture mechanics for piezoelectric ceramics. Journal of Mechanics and Physics of Solids 40, 739 - 765.

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* Corresponding author. Tel.: +380672327485. E-mail address: volodymyr.krasnopolskyi@npp.nau.edu.ua * Corresponding author. Tel.: +380672327485. E-mail address: volodymyr.krasnopolskyi@npp.nau.edu.ua

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Water Displacing Hard Film, Non Water Displacing Soft Film, Non Water Displacing Hard Film as shown at corrosion-doctors.org. Excellent protective properties of CPCs have been proved by numerous standard and special tests. No doubts exist regarding their possibility to protect metal structures against aggressive surrounding. At the same time results of some experiments with aircraft components covered by the CPCs reveal possibility of negative side effects, these are both reduction of the riveted joints fatigue life (O'Neill and Smith, 1975, Schijve et al., 1977, Kolkman, 1982, Jaya et al. 2010a,b), and increase of the fatigue cracks propagation rate (Purry et al., 2003, Kuhlman et al., 2003). Some conceptual explanations for these phenomena have been proposed, but high level of the requirements to the aircraft reliability defines the demand for more experimental data accumulation. The described below experiments prove actuality of the problem for the aviation industry, throw light on the fatigue behavior of the typical aircraft structure in the presence of CPC, target the future research activity aimed on the development of the methodology for grounded selection CPCs for aircraft structures. 2. Aircraft parts protected by CPCs It is known that certain zones of aircraft structures are prone to corrosion in the biggest extend. These are: the battery compartments, bilge areas, bulkheads, wheel wells and landing gear, water entrapment areas, wing flap and spoiler recesses, areas hit by exhaust stream, and cooling air vents (aviation-safety-bureau.com). Parts of the aircraft structure where additional treatment by the water displacing CPCs is possible and currently used are described by well-known CPCs manufacture ARDROX (chemetall.com). Bilge area of the fuselage is one of the most vulnerable for the action of the aggressive environment, essentially liquid accumulated at the bottom of the structure. Structural joints of skin and first of all riveted elements are of the special interest because crevice corrosion of these elements combined with cyclical loading is able to lead to the fatigue crack nucleation, then propagation and finally lost of structural integrity (Aircraft Accident Report, 1988). Pure aluminum cladding layer doesn’t solv e the problem completely due to the destruction of this layer at holes for rivets. The same can be said regarding the protection by oxidizing, primer and paints which are vulnerable to the mechanical damage and environment influence. Analysis of the Aloha flight 243 accident, as well as analysis of the aircraft zones prone to corrosion, draws attention to critical zones of the aircraft. It was found (Aircraft Accident Report, 1988), that the fuselage failure initiated in the lap joint; the failure mechanism was a result of multiple site fatigue cracking of the skin adjacent to rivet holes along the lap joint upper rivet row and tear strap disbond which negated the fail-safe characteristics of the fuselage. The fatigue cracking initiated from the knife edge associated with the countersunk lap joint rivet holes; the knife edge concentrated stresses that were transferred through the rivets because of lap joint disbonding (Fig. 1) (Aircraft Accident Report, 1988).

Fig. 1. Fatigue crack location in lap joint (Aircraft Accident Report, 1988).

This analysis as well as analysis of contemporary aircraft fuselage structures have allowed correct selection of the specimens design for fatigue tests.

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3. Specimens for the negative effect investigation. Test procedure Specimen for fatigue test (Fig. 2) has been developed so that it reflects typical design of longitudinal riveted lap joint widely used in aircraft fuselage structures.

Fig. 2. Specimen for fatigue tests.

Material for specimens – is aluminium alloy 1163 ATВ in the as received condition. This is a high-strength alloy similar to Al 2024-T351. Mechanical properties of 1163 АТВ and its chemical composition, given by the manufacture are shown in Tables 1and 2.

Table 1. Mechanical properties of the 1163 АТВ alloy. Temper

Yield Strength, MPa Ultimate Strength , М P а

Max Elongation, %

302 – 311

419 – 430

17.5 – 20.5

АТВ

Table 2. Chemical composition of the 1163 АТВ alloy. Fe Si Mn Ni Ti Al

0.04 %

0.03 %

0.6 % 0.01 %

0.03 %

Basic component

4.28 %

1.24 %

0.02 %

Rivets made of aluminum alloy В65 ( Tables 3, 4) (Aviation materials. Handbook, 1982). Table 3. Mechainical properties of the B65 alloy ( Aviation materials. Handbook, 1982). Temper Yield Strength, MPa Yield Strength, MPa Max Elongation, % Т 40 23 23

Table 4. Chemical composition of the В65 alloy (splav-kharkov.com). Fe Si Mn Ti Al

Impurities

Below 0.2% Below 0.25%

0.3 – 0.5%

Below 0.1%

93.65 – 95.65% 3.9 – 4.5%

0.15 – 0.3% Below 0.1% Total 0.1%

CPCs selected for the investigation are those used currently in aviation industry and commercially available. Taken into account the preliminary character of the presented research results and need for more complex approach for the future experiments CPC used in this paper are noted as: CPC1, CPC2, and Reference Compound (RC). CPC 1 is a material with lowest viscosity and highest penetration. CPC 2 has greater viscosity and less penetration. Reference Compound is a mixture of kerosene and widely used grease Ciatim-201. Both components of the Reference Compound have lubricating properties, thus are considered as materials able to influence friction between the mating surfaces of the lap riveted joint.

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Two different procedures of specimens treatment by CPCs were used: First procedure presumes more intensive penetration of the CPC into the gap of the lap joint by the way of triple treatment by the CPC, this procedure is called here as "Excessive"; second procedure is single covering, it limits the volume of the CPC in the area of the joint, this procedure is called "Limited". The treatment by the Reference Compound was carried out according to the "Excessive" procedure. Fatigue tests have been carried out with test machine UTM-25 equipped by digital controller MTS FlexTest GT with loading frequency f = 2 Hz, maximum stress of cycle 120.0 MPa and stress ratio R = 0.1. 4. Experimental results and discussion Experimental results prove the actuality of the presented research and encourage further activity in the optimization of CPCs application technology. Figures 3 and 4 compare average fatigue life for the groups of the specimens treated by the CPC1, CPC2 and Reference Compound with life of the specimens without CPC. The number of specimens in group was from 5 to 8.

Fig. 3. Comparison of the average number of cycles to failure for groups of specimens: without CPC, and treated by the "Excessive" procedure: by the Reference Compound (RC); by CPC1; by CPC2.

As it is seen clearly from Fig. 3 "Excessive" application of the CPC1 reduces average number of cycles to failure up to 57%; "Excessive" application of the CPC2 reduces average number of cycles to failure up to 65%; "Excessive" application of the Reference Compound reduces average number of cycles to failure up to 32%. As following experiment shows, the situation can be improved by the optimization of the treatment procedure. Factor of friction is suggested as to be a dominant in the explanation of the revealed effect. General tribology considers the following basic types of friction: dry friction, as an interaction of mating surfaces without lubricants; fluid friction, as friction in the presence of a lubricant between rubbing bodies; mixed friction, where dry and fluid friction regions exist in the contact zone; and boundary friction, when the lubricant thickness is smaller than 10 atomic layers or two rubbing surfaces separated by a lubricant layer interact with each other due to asperities, roughness, and so on (Lyashenko, 2011). The friction coefficient obviously depends on the type of friction. The gap thickness between the elements of the riveted joint can vary. This can explain the reduction of the riveted joints fatigue life at the excessive volume of the lubricant and increase of the fatigue life at the limited volume of CPC. The search of the way to prevent negative side effects of the CPC application has led to the modification of the treatment procedure. As the negative effect is considered to be result of the friction, the reduction of the lubricant in the gap of the lap riveted joint is expected to reduce the CPC negative effect.

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The results presented on the diagrams below (Fig. 4) shows the possibility to avoid negative effect, probably by the change of the friction mode. From practical procedure point of view it means decrease of the CPC volume penetrating the gap of the riveted joints. Tests of specimens covered by the Reference Compound were not carried out because the fatigue life of this category with "Excessive" treatment has not demonstrated the lowest values, thus it could not be the reference point.

Fig. 4. Comparison of the average number of cycles to failure for groups of specimens: without CPC, and treated by the "Limited" procedure: by CPC1; by CPC2.

Numerical parameters that could be used for evaluation of CPC’s influence on riveted joints durability may be obtained from statistical processing of experimental data. In the test there were determined fatigue lives of specimens with no CPC in the joint, covered by Reference CPC, samples were treated by CPC1 and CPC2. On the basis of this data there were calculated average (expected) values of fatigue lives, variances, standard deviations, variation coefficients and made a try to describe the results by some known probability distributions (Table 5). Due to limited amount of specimens and experimental data the probability distribution approximation was possible only for no CPC case. The results show that the best correspondence can be seen in case of log-normal and Weibull distributions (Fig. 5 and 6).

Table 5. Parameters of probability distributions for specimens with different cover. Cover No CPC

Reference CPC

CPC1 Limited treatment

CPC1 Excessive treatment

CPC2 Limited treatment

CPC2 Excessive treatment

Parameter

Average number of cycles 162382

109950 16962 0.1542

208698 28096 0.1346

70277 31745 0.4517

169214 36605 0.2163

34071 10668 0.3131

Standard deviation

58233 0.3586

Coefficient of variation

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CDF

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

F( N )

50000 100000 150000 200000 250000 300000 Cycles

Fig. 5. Cumulative distribution function for groups of specimens: 1 – no CPC; 2 – approximation by log-normal distribution; 3 – approximation by Weibull distribution.

PDF

0,0E+00 1,0E-06 2,0E-06 3,0E-06 4,0E-06 5,0E-06 6,0E-06 7,0E-06 8,0E-06 9,0E-06

f( N )

0 50000 100000 150000 200000 250000 300000 Cycles

Fig. 6. Probability density function for groups of specimens: 1 – no CPC; 2 – approximation by log-normal distribution; 3 – approximation by Weibull distribution.

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To reveal the penetration of the CPCs into the gap between sheets of riveted joints the following procedure has been conducted: a) joints were disassembled; b) mating surfaces were covered by graphite powder; c) graphite power was blown out from the surface; d) black spots with remaining powder revealed the penetration of the CPCs. Fig. 7 shows the areas of the CPCs on the mating surfaces of the riveted joint after preparation.

Fig. 7. CPC on the insight surface of the riveted joint (black zones).

5. Conclusions Despite the high efficiency of the Corrosion Preventive Compounds against corrosion, the selection of the compound for aircraft structures requires test of the probable negative side effects on the fatigue life. Proposed test is based on the assumption of the CPC influence on the friction between the mating surfaces of the riveted joints and expected redistribution of the forces carried by the riveted joint components. It is proved by the tests that the method of the treatment, namely the volume of the compound use for the structure unit covering unit influences the results of the fatigue loading. Limitation of the CPCs volume leads to the eliminating of the negative effect. The effect is explained by the different characters of the friction between the mating surfaces depending on the thickness of the lubricating substances. Thus, the treatment procedure is a critical point of the CPC application. To get the real advantage of the CPC application, the technology must be optimized and mandatory followed. References Aircraft Accident Report. Aloha Airlines, Flight 243, Boeing 737-200, N73711, 1988. Report Number NTSB/AAR-89/03, pp.262. http://www.aviation-safety-bureau.com/aircraft-corrosion.html http://www.splav-kharkov.com/simil2_mat.php?type_id=11&name_id_113=2542&name_id_165=1452&count_mat=286 https://corrosion-doctors.org/Inhibitors/CPCs.htm https://www.chemetall.com/Documents/Media-Library-Documents/Literature/Brochures/2016/catalogue_Ardrox-AV-CIC_216_en_LR_final.pdf Jaya, A., Tiong, U. H., Clark, G. et al., 2010b. Corrosion treatments and the fatigue of aerospace structural joints. Procedia Engineering 2(1), 1523-1529. Jaya, A., Tiong, U. H., Clark, G., 2010a. Surface damage in riveted aircraft aluminium lap joints, in the presence of lubricants. Materials Science Forum 654-656, 2434-2437. Kolkman, H. J., 1982. Effect of penetrant on fatigue of aluminium alloy lap joints [Electronic resource]. Aerospace engineering reports of NAL. National Aerospace Laboratory, 1-18. Kuhlman, S. J. H., Abfalter, G. H., Leard, R., Dante, J., 2003. Environmentally assisted fatigue crack growth rate testing with corrosion prevention compounds. Heat treating and surface engineering. Proc. of the 22nd Heat Treating Society Conf. and the 2nd International Surface Engineering Congress « Heat Treating 2003 » . Indiana, USA, September 15-17, 2003, 347-354. Lyashenko, I. A., 2011. Tribological Properties of Dry, Fluid, and Boundary Friction. Technical Physics, Vol. 56, No. 5, 701-707. O'Neill, P. H., Smith, R. J., 1975. A short study of the effect of a penetrant oil on the fatigue life of a riveted joint. Aeronautical Research Council, C.P. No. 1305. 11-13. Purry, C., Fien, A., Shankar, K., 2003. The effect of corrosion preventative compound on fatigue crack growth properties of 2024-T351 aluminium alloys. International Journal of Fatigue, 25, 1175-1180. Schijve, J., Jacobs F. A., Tromp, P. J., 1977. Effect of an anti-corrosion penetrant on the fatigue life in flight-simulation tests on various riveted joints [Electronic resource]. Aerospace engineering reports of NAL. National Aerospace Laboratory, 1-34.

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